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Umbilical cord blood-derived CD11c+ dendritic cells could serve as an alternative allogeneic source of dendritic cells for cancer immunotherapy Jeetendra Kumar1, Vaijayanti Kale1 & Lalita Limaye1 Allogenic dendritic cells (DCs) generated from healthy donors, who are complete or partially HLA-matched, have been used for clinical trials. One of the sources for allogenic DCs is umbilical cord blood (UCB) cells. However, as far as cord blood cells are concerned, looking at their naïve nature, there is a concern as to whether the DCs generated from them will have enough potential to elicit a proper T cell response. For this, we compared CD11c+ UCB-DCs/ Cytotoxic T lymphocytes (CTLs) with the conventional source, i.e. peripheral blood (PBL) monocyte DCs/CTLs, using various parameters. CD11c+ DCs generated from the two sources were compared morphologically, phenotypically and functionally. Functional assays included antigen uptake, chemotactic migration and MLR (mixed lymphocyte reaction). The CTLs generated were examined for the activation markers, granzyme A & granzyme B, and IFN-γ secretion. MUC1 (STAPPVHNV) peptide-specific CTLs were quantified by Streptamer staining. In vitro CTL activity was assessed by their efficiency in killing MCF-7 cells. For in vivo CTL assay, a xenograft of MCF-7-luc-F5 cells in female NOD/SCID mice was employed. Regression of tumors in mice was monitored using an in vivo imaging system before and after ten days of CTL infusion. Statistical analysis of all the experiments between the two groups was evaluated by one-way ANOVA. The CD11c+ DCs from the two sources were morphologically and phenotypically similar. Their capacity to uptake antigen, migration towards CCL-19 and MLR activity were equivalent. UCB-CTLs had significantly higher levels of activation markers, number of MUC1 specific CTLs, IFN-γ secretion and IL-12p70/IL-10 ratio than that of PBL-CTLs. Hematoxylin and Eosin-stained tumor sections showed T cell infiltration, which was further confirmed by immunofluorescence staining. In vivo CTL activity was found to be similar with the two sources. Our data demonstrate that CD11c+ UCB-DCs/CTLs are as potent as standard CD11c+ PBL-DC/CTLs and could therefore be used as an allogenic source for therapeutic purposes. The findings of this study could help in taking us one step closer towards the personalized therapy using DC based cancer vaccines. Dendritic cells (DCs) are crucial for the induction of both primary and secondary immune responses, as well as for eliciting immunological tolerance. Their capacity to effectively cross-present exogenous antigens to T lymphocytes makes DCs essential for the induction of adaptive immune responses against malignant cells. This unique attribute of DCs has offered the possibility of developing clinical protocols involving DCs for use in cancer immunotherapy. DCs were introduced as adjuvants in vaccination strategies that aimed to induce antigen-specific effector and memory cells. DC therapy represents a new and promising immunotherapeutic approach for the treatment of advanced cancers. In the last two decades, large numbers of clinical trials have been conducted using DC vaccines targeting different kinds of tumors, and it was found that they were able to initiate promising clinical responses against a number of diseases, like renal cell carcinoma, melanoma, HIV, multiple myeloma, acute myeloid leukemia, breast cancer etc. [1–13]. Immunotherapies with allogeneic DCs pulsed with tumor antigens to generate specific T cell responses have been tested in clinical trials with patients having solid tumors as well as in different hematological malignancies [14, 15]. Allogeneic DCs can be generated from CD34+ cells derived from umbilical cord blood (UCB) [16–28]. Thus, UCB could be exploited as an additional source for the generation of allogeneic DCs. UCB-derived DCs have been used in the pilot phase of clinical trials as well, in hematological disorders like AML, as a therapeutic agent to increase the survival of patients [29, 30]. We have earlier standardized methods for the large scale generation of DCs from UCB-derived CD34+ cells and mononuclear cells (MNCs), [25, 26] and DCs with enhanced functionality [31]. These DCs were characterized by immunophenotyping and functional assays like mixed lymphocyte reaction (MLR), antigen uptake and chemotactic migration. However, for efficacious DC vaccines, the basic requirement is that the DCs should generate effector and memory cytotoxic T lymphocytes (CTLs), to elicit a comprehensive immune response. The standard treatment procedures utilize peripheral blood (PBL) monocyte-derived DCs. There are very few reports where the potency of UCB-derived DCs has been compared with PBL monocyte-derived DCs [32, 33]. Therefore, here we report a systematic study of a comparison between UCB-DCs/CTLs and PBL-DCs/CTLs, using various parameters. As the basis of CTL assay is HLA-A0201-restricted, which is a major histocompatibility complex (MHC) class I polymorphism, we generated DCs from HLA-A0201positive PBL/UCB samples. We then carried out in-depth characterization and functionality tests with these DCs/CTLs. Data generated from this study clearly demonstrate that UCB-DCs are as potent as their standard vaccine counterparts i.e., PBL monocyte DCs, and could therefore be used as an allogenic source for therapeutic applications. The recombinant human cytokines used for the study were fms-like tyrosine kinase-3 ligand (Flt-3L), thrombopoietin (TPO), stem cell factor (SCF), IL-4, IL-2, IL-7, granulocyte-macrophage colony stimulating factor (GM-CSF), TNF-α, CD40L (CD40 ligand) and macrophage inflammatory protein 3β (CCL-19). All recombinant human cytokines were purchased from Peprotech Asia, Rehovot Israel. The antibodies used for flow cytometry were mouse anti-human mAbs: CD1a, CD25, CD11c, CD40, CD8 - antigen presenting cell (APC)-tagged; CD58, CD54, CD80, CD83, CD86, HLA-A2, CD45RA, granzyme A - phycoerythrin (PE)-tagged; CD3, HLA-DR, HLA-ABC, granzyme B - fluorescein isothiocyanate (FITC)-tagged and CD 69 PECy7-tagged. For immunofluorescence staining primary antibody was mouse anti-human purified CD3 and secondary antibody was goat anti-mouse tagged with Alexa Fluor® 488 (Life technologies, MA, USA). All monoclonal antibodies and respective isotype controls used for the study were purchased from BD pharmingen (San Diego, CA, USA). MCF-7 was used in the cell lysate preparation, in vitro and in vivo CTL assay. MCF-7-luc-F5 (Caliper Life Sciences, Hopkinton, MA, USA) was used for in vivo CTL assay using in vivo imaging system (IVIS). H1229 and SH-SY5Y were used as nonspecific targets for the CTLs generated from the MCF-7 lysate-pulsed DCs. Culture medium and other reagents used Iscove's modified Dulbecco's medium (IMDM), Roswell Park Memorial Institute-1640 (RPMI-1640), (DMEM), Dulbecco's modified Eagle's medium/nutrient F-12 Ham 1:1 nutrient mixture (DMEM/F-12 media) and IMDM without phenol red were procured from Sigma Aldrich, St. Louis, MO, USA. Histopaque (ρ-1.007g/ml), FITC-labeled dextran (40 kDa), Wright Stain, Giemsa Stain, Hematoxylin Solution-Mayer's, Eosin Y solution, DPX mountant, lipopolysaccharide (LPS), keyhole limpet hemocyanin (KLH), dimethyl sulfoxide (DMSO), PPO, POPOP were all from Sigma Aldrich, St. Louis, MO, USA; ELISA kit (BD OptEIA); heparin (SRL Pvt. Limited Mumbai, India); Rosette Sep for T cell isolation (Stem Cell Technologies, Vancouver, Canada); [3H] thymidine (240 GBq/ milli mole, BRIT, Navi Mumbai, India); Intracellular fixation & permeabilization buffer set (ebiosciences San Diego, CA, USA) Steptramers (Iba-lifesciences, Goettingen, Germany), Luciferin D Potassium Salt (Perkinelmer, Waltham, MA, USA), reduced growth factor Matrigel (Becton-Dickinson), HBSS buffer (Life technologies, MA, USA) and CRYO-OCT compound (Thermo Fisher Scientific Inc. MA, USA). Ethical statements for use of human samples Protocols for collection and processing of all human samples used in this study were approved by the Institutional Ethics Committee (IEC of NCCS) and Institutional Committee for Stem Cell Research (IC-SCR of NCCS). The guidelines followed by these committees are in accordance with the Declaration of Helsinki. Prior informed written consent was obtained from the donors. The human samples used in this study were as follows: Umbilical cord blood: these were used for generating DCs and for isolating autologous T cells for CTL assay Peripheral blood: these samples were used to isolate MNCs and T cells for use in MLR assays Buffy coat: these were used for generating DCs and for isolating autologous T cells for CTL assay Collection of blood samples Collection of blood samples was as follows: Umbilical cord blood (UCB): the samples were collected in preservative-free heparin (40 IU of heparin/ ml of blood) with plain IMDM in sterile containers. Then samples were brought to the laboratory on ice packs and were processed to isolate MNCs Peripheral blood (PBL): buffy coat bags were brought to the laboratory on ice packs and were subsequently processed to isolate MNCs Processing of blood samples Processing of blood samples was as follows: Isolation of MNC from UCB and PBL: UCB MNCs and PBL MNCs were separated by Histopaque® density gradient centrifugation. Turk's solution was used to take nucleated cell counts, using a hemocytometer. MNCs thus obtained were used for DC generation Isolation of T-cells from peripheral blood: T cells were isolated from blood for MLR assay, using the RosetteSep™ (negative selection kit), according to the manufacturer's instructions In vitro generation and culture of DCs from UCB DCs were generated from umbilical cord blood samples by our method as described earlier [25, 26, 31]. Briefly, MNCs from peripheral blood samples were seeded at a density of 107 cells/2 ml/well in six-well plates. Monocytes were enriched by plastic adherence and were used for DC generation. The terminal differentiation of precursor cell populations to DCs were induced by subsequently culturing them with GM-CSF (50 ng/ml) and IL-4 (30 ng/ml) for 3 days and GM-CSF (50 ng/ml) + TNF-α (50 ng/ml) for 4 days in IMDM supplemented with 5 % autologous/AB+ plasma. Immature DCs were harvested on day 5 and were used for antigen uptake assay. On day 7, the cells were subjected to maturation with a combination of pro-inflammatory signal, a combination of TNF-α, LPS and CD40L, at the concentration of 100 ng /ml each, for 48 h. Mature DCs were used for all other assays. Experimental design for generation of DCs is given in a flow chart in Additional file 1: Figure S1. In vitro generation and culture of DCs from PBL Mononuclear cells were obtained by histopaque density gradient centrifugation of buffy coat samples. MNCs were seeded at the density of 107 cells/well in six-well plates containing 2 ml of IMDM supplemented with 1 % human AB+ plasma. The cells were kept for 1.5 h at 37 °C in a 5 % CO2 incubator and the non-adherent and the loosely adherent cells were removed by washing with IMDM. The adherent cells were used for DC generation in a similar way as described for the UCB samples. The experimental design for generation of DCs is given in a flow chart in Additional file 1: Figure S1. Morphological and phenotypic analysis Morphological characterization of DCs was done by staining with Wright and Giemsa stains and observing under a microscope. For phenotypic analysis, the cells were stained with a panel of ten antibodies namely CD1a, CD11c, CD40, CD58, CD54, CD80, CD83, CD86, HLA-DR and HLA-ABC along with appropriate isotype controls and acquired using the FACS Canto II (BD San Jose, CA, USA) [25, 26, 31]. For all flow cytometry analysis, the cells were suspended in 100 μL of cold PBS containing 1% BSA. Specific labeled mAbs and appropriate isotype controls were added and the cells were incubated on ice for 30 minutes. Cells were washed thrice with ice cold PBS and re-suspended in 1 % paraformaldehyde. Cells were acquired using the FACS Canto II. Data were analyzed by FACS Diva (BD) and histogram overlays were prepared using FlowJo (LLC, Ashland OR, USA). Functional characterization of DCs The assays used to access the functionality of in vitro generated UCB-DCs and PBL-DCs were as follows: Endocytosis assay with FITC-tagged dextran: we tested the receptor-mediated endocytosis in the generated DCs using FITC-tagged dextran. Immature DCs were harvested on day 5 and incubated with FITC-dextran (20 μg/ml), either at +4 °C (internalization control) or at +37 °C, for 30 and 60 minutes. The cells were then acquired using the FACS Canto II [25, 26, 31] Chemotaxis: the chemotaxis of the in vitro generated UCB and PBL-DCs toward CCL-19 was assessed in a 24-well cell culture plate with BD Falcon ™ Cell culture inserts (pore size 8.0 μm) as described earlier [25, 26, 31] Mixed lymphocyte reaction (MLR): the immunostimulatory capacity of in vitro generated UCB and PBL-DCs was assessed by MLR. Allogenic T cells were obtained from peripheral blood of healthy donors and were distributed at 105 cells per well into round-bottomed 96-well micro plates (NUNC). Cells were co-cultured in the presence of graded numbers of irradiated DCs (2,500 rad, Co 60 source, BRIT, Navi Mumbai, India) in 200 μL of medium containing 10 % pooled AB+ plasma. Thymidine incorporation was measured on day 3 followingan 18-h pulse with [3H] thymidine (1 μCi/well) (BRIT, India) using standard procedures [25, 26, 31]. Generation of CTLs CTLs were generated from UCB and PBL samples by our method as described earlier [30]. Briefly HLA-A0201-positive UCB MNCs and PBL MNCs were used to generate DCs. Immature DCs were pulsed with MCF-7 lysate to a final concentration of 100 μg/ml of protein along with KLH (50 μg/ml) for 48 h as maturation stimuli in the culture medium for cross presentation of tumor antigen to autologous/allogenic sorted naïve T cells. For the negative control set of DCs, the maturation stimuli comprise 100 ng/ml each of LPS, CD40L and TNF-α, respectively. The autologous/allogenic naïve T cells were obtained by sorting of CD3-, CD8-, and CD45RA-positive cells using the FACS ARIA III (BD). The naïve T cells were co-cultured with MCF-7 lysate-pulsed DCs that were generated from the autologous/allogenic UCB or PBL sample. DC-T cell co-culture was maintained for 3 weeks with the addition of cytokines IL-2 (0.1 μg/ml) and IL-7 (5 μg/ml) and weekly re-stimulation with fresh antigen-pulsed DCs to generate effector cytotoxic killer T cells. Though obtaining HLA-A0201-positive cord blood samples was relatively easier for CTL assay this was not true for peripheral blood samples. PBL were obtained as buffy coat samples from blood banks after getting institutional ethical clearance. Subsequently they were screened for HLA-A0201 positivity, and only HLA A2-positive samples could be used for CTL assay. The frequency of obtaining HLA-A0201 positivity was 1 in 10 samples screened. Procuring large volumes of HLA-A0201-positive PBL samples (to isolate naïve T cells) also had ethical constraints. Moreover, literature suggests that a lower titration of target to killers have been used by many investigators [34, 35]. So we had taken into consideration the intermediate titration ratio of target to killers in this study (i.e., 1:0, 1:3……1:18). The experimental design for generation of CTLs is given in a flow chart in Additional file 2: Figure S2. Functional characterization of CTLs CTLs were characterized as follows: Assessment of activation by surface markers expression: on day 5 or day 7 of UCB/PBL, DC-T cell (DC-TC) co-culture cells were harvested and screened for the expression of early activation marker like CD69 along with CD25. After staining with CD69 and CD25 mAbs or with appropriate isotype controls, cells were acquired using the FACS Canto II from BD. Intra cytoplasmic staining for granzyme A and B: CTLs generated in vitro were tested for the presence of these serine proteases enzymes within the intracellular compartments. Cells were harvested on day 21 of UCB/PBL DC-TC co-cultures and were stimulated by phorbol 12-myristate 13-acetate (PMA) (40 ng/ml) and ionomycin (100 ng/ml), along with Golgi stop Brefeldin A (1:1,000 diluted) for 4 h. After harvesting, the cells were subjected to surface staining with CD8 for 30 minutes. After fixation and permeabilization, granzyme A and B mAbs and appropriate isotype controls were added and the cells were incubated on ice for 60 minutes. Cells were acquired using the FACS Canto II from BD. Streptamer staining for Mucin1 (MUC1)-STAPPVHNV-specific T cells: different specificities of CTLs arise when naïve T cells are cultured with pulsed DCs, depending on the antigen presentation capacity of the DCs. The cells were harvested on day 21 of UCB/PBL DC-TC co-culture. MUC1-STAPPVHNV [36] tagged with R-PE was used to estimate the presence of MUC1-specific CTLs as per the manufacturers' instructions. After staining, cells were acquired using the FACS Canto II from BD. The schematic of the staining procedure is given in Additional file 3: Figure S3. Cytokine profiling of DC-TC co-cultures by ELISA: supernatant from the in vitro-generated pulsed UCB-DCs or PBL-DCs and sorted naïve T cell co-cultures was collected on day 21 and stored at −20 °C. IL-12p70 and IL-10 or interferon gama (IFN-γ) content in the supernatants were assayed by ELISA using BD OptEIA™ ELISA kit (BD, Pharmingen) as previously reported [31]. The amount of secreted interleukins present in the samples was calculated by the standard curve method. In vitro CTL assay CTL assays were performed as described previously [31]. Briefly CTLs generated from unpulsed and pulsed sets of DCs were co-cultured with the target cells MCF-7 for 18 h in a flat bottom 96-well plate. Cells were then washed with plain media and then pulsed with [3H] thymidine for 8 h. Percent killing of MCF-7 was calculated by P-JAM assay using the formula: $$ \%\ \mathrm{Killing} = \mathrm{CPMA}\ \left[\mathrm{Target}\ \mathrm{alone}\ \hbox{--}\ \mathrm{Target} + \mathrm{Killer}\right] \times 100/\mathrm{CPMA}\ \mathrm{Target}\ \mathrm{alone} $$ In vivo CTL assay (xenograft model) The NOD/LtSZ-scid/scid mice were purchased from Jackson Laboratories and were bred in the animal facility of our institute. The study was conducted adhering to the institution guidelines for animal husbandry and has been approved by the Institutional animal ethical committee-NCCS /Committee for the Purpose of Control and Supervision of Experiments on Animals (IAEC-NCCS/CPCSEA). Animal procedures involving intravenous (IV) infusion were carried out under anesthesia. The right flanks of age-matched female NOD/SCID mice, 4–6 weeks old, were subcutaneously injected with 4 × 106 of MCF-7-luc-F5 cells in a total volume of 200 μL, which included 100 μL cell suspension in HBSS buffer plus 100 μL reduced growth factor Matrigel (Becton-Dickinson). Estradiol valerate USP (Cadila Healthcare Ltd.) (200 μg) was injected intraperitoneally (i.p.) per day from day zero until the tumor size reached a minimum of around 5 mm in lengthand in width, i.e., 62.5 mm3 in volume. One week after stopping estradiol injections, the mice were divided into three groups namely the control, the UCB-CTL and the PBL-CTL groups. The first day of imaging was considered as day zero. Before imaging the mice, tumor volume measurements were done for each mouse in all groups using digital Vernier calipers and the volume was calculated using the formula (length × width × width)/2. Mice were anesthetized by ketamine and xylazine (4:1 ratio) 0.05 ml per 20 grams of body weight. Then Luciferin D potassium salt (15 mg/ml) 0.2 ml was administered i.p. per mouse, followed by imaging using the IVIS 200 (Xenogen, PerkinElmer, MA, USA) and analysis by Living Image® (version 4.4). On the following day, each mouse in the UCB and PBL test group was infused via the tail vein with 107 CTLs, generated from pulsed UCB and PBL-DCs, respectively. No CTLs were infused in the control sets. On the tenth day post CTL infusion, tumor volume measurements were taken and documented, followed by IVIS imaging as described above. On the same day, mice were sacrificed and the tumors were harvested and divided in two equal halves. One half was fixed in 10 % formalin for paraffin sectioning, followed by H&E staining. Images were taken using the Leica DMI6000 inverted microscope. The other half of the tissue was embedded in CRYO-OCT compound and kept frozen at −80 °C till further use. Shandon Cryotome was used to obtain 10-μ cryosections of frozen tissues. Mouse anti-human CD3 primary antibody and goat anti-mouse secondary antibody conjugated with Alexa Fluor® 488 was used in immunofluorescence staining to confirm the presence of infiltrating T cells in the xenograft tissue. Nuclei were stained with 4',6-diamidino-2-phenylindole (DAPI) to demarcate cellular structures and images were taken using the Zeiss LSM 510 Meta confocal microscope. Different variables of UCB-DCs/CTLs and PBL-DCs/ CTLs were compared. All results were expressed as means ± SD. Statistical analysis and graphs were prepared using SigmaPlot software (Version 11) (Jandel Scientific, CA, USA) and GraphPad Prism 6 Software (San Diego, CA, USA). All the statistical analysis of experiments comparing the two groups was evaluated by one-way analysis of variance (ANOVA). Probability values ≤0.05(), ≤0.01() and ≤0.001() were considered statistically significant. UCB and PBL-derived DCs have similar morphology and phenotype DCs were generated from PBL monocytes and UCB MNCs as described earlier (a flow chart illustration is depicted in Additional file 1: Figure S1). The morphology of CD11c+ DCs from the two sources was studied by observing the culture plates under a phase contrast microscope (Fig. 1a, b, e, f) and by observing Wright-Giemsa stained culture plates (Fig. 1c, d, g, h). They showed stellate processes with a typical veiled appearance, dense cytoplasm, irregular nuclei and some cells in clumps, forming clusters. Wright-Giemsa stained cells showed long cytoplasmic projections i.e., dendrites, the hallmark of these cells. The DCs were further identified phenotypically by staining them with a panel of ten antibodies and acquiring on a flow cytometer. Representative FACS histogram profiles for UCB and PBL are depicted in Fig. 1i and j, respectively. Cumulative data for three samples (mean ± SD, n = 3) for percent CD expression is shown in Fig. 1k and MFI values in Fig. 1l. DCs generated from both sources had higher expression of DC-specific markers such as CD 1a, 11c, 80, 83, 86, etc. Typical DC-specific markers along with the co-stimulatory molecules, associated integrins and adhesion molecules were also expressed on the cells from both sources and were comparable. There was no significant difference in the percent expression of markers on DCs from the two sources, except for CD40 (Fig.1k), which was higher in UCB-DCs. There was also a significant difference in the MFI of CD58 (Fig. 1l), which was higher in UCB-DCs, and CD54 (Fig. 1l), which was higher in in PBL-DCs (p ≤0.05). These data underscore the fact that UCB-DCs are equivalent in nature to PBL DCs with respect to morphology and phenotype. Morphology and phenotype of dendritic cells (DCs) generated from the two sources: Phase contrast images of umbilical cord blood DCs (UCB-DCs) (a, b) and peripheral blood PBL DCs (PBL-DCs) (e, f) at lower and higher magnification, respectively. Both sources generated the typical clusters of mature DCs. Wright-Giemsa-stained adherent cell clusters of UCB-DCs (c) and PBL-DCs (g) at lower magnification and morphology of single cells at higher magnification (d, h). FACS histogram overlay profile of a representative experiment from UCB-DCs (i) and PBL-DCs (j). Black line isotype control and colored lines specific CD molecules. Percent expression and mean fluorescence intensity (MFI), respectively, from three samples are shown in (k, l). It is evident that fully mature DCs were generated and there was no significant difference in the expression level of different surface markers, except for CD40, which was higher in UCB-DCs (k). In terms of MFI, CD58 was found significantly higher in UCB-DCs and CD54 in PBL-DCs (l). The data shown are mean ± SD, n = 3 (p <0.05). PE phycoerythrin, FITC fluorescein isothiocyanate UCB-DCs and PBL-DCs are functionally equivalent DCs have the characteristic property of activating naïve T cells, and this functionality depends upon the efficacy of their antigen uptake, chemotactic migration, antigen processing and presentation. We tested these functional attributes by performing in vitro assays, such as uptake of FITC-tagged dextran, chemotactic migration towards CCL-19, and MLR. We observed that both immature DC sets performed uptake of dextran-FITC within 30 and 60 minutes of the incubations tested. After 60 minutes of incubation time, there was 51 % uptake in UCB-DCs, whereas there was 49 % uptake in PBL-DCs. Figure 2a shows a histogram overlay profile of a representative sample with MFI values in brackets. Figure 2b shows cumulative data from three samples for percentage uptake of FITC-tagged dextran and Fig. 2c bar graph shows the cumulative MFI values from three samples (mean ± SD, n = 3). Migratory ability of the DCs towards CCL-19 was studied by in vitro assay using cell culture inserts as described earlier. As is evident from Fig. 2d (mean ± SD, n=3), migration ability was also similar between DCs from both sources. The MLR assay was performed by co-culturing DCs and T cells in different ratios and then checking the stimulatory capacity of DCs on T cells in terms of thymidine uptake. Figure 2e (mean ± SD, n = 3), clearly shows that both types of DCs elicited similar responses. Out of the six ratios tested, only at one ratio i.e., 1:100, did PBL-DCs appear to be significantly superior (P = 0.007); P values for the other ratios tested were 0.752, 0.107, 0.218, 0.775 and 0.258, respectively, which were not significant. This finding is important because MLR measures early events in the sensitization phase of antigen-specific cell-mediated immune response. With respect to these three attributes, we can conclude that UCB-DCs are as robust in functionality as PBL monocyte-derived DCs. Functional characterization of dendritic cells (DCs). a FACS histogram overlays of dextran-fluorescein isothiocyanate (FITC) uptake profile of a representative experiment from umbilical cord blood DCs (UCB-DCs) and peripheral blood DCs (PBL-DCs) with mean fluorescence intensity (MFI) values in brackets, and b data from three experiments for percentage antigen uptake. c Cumulative MFI values from three samples. d Chemotaxis of DCs towards CCL-19. Low spontaneous migration was observed in the wells, without CCL-19, whereas both UCB-DCs and PBL-DCs efficiently migrated towards CCL-19 gradient. e Mixed lymphocyte reaction (MLR) from three independent experiments reveals that DCs generated from both sources exhibited similar MLR at a different effector-to-target ratio. The data shown are mean ± SD, n = 3 (*p <0.01). CPMA count per minute for beta Characterization of CTLs obtained from UCB and PBL-DCs CTLs were generated by co-culturing sorted naïve HLA-A0201-positive CD8+ T cells with HLA-A0201-positive DCs, pulsed with MCF-7 lysate (a flow chart illustration is depicted in Additional file 3: Figure S3). CTLs thus generated by pulsed DCs from both sources were characterized for activation of surface markers such as CD69 and CD25, and intracellular levels of granzyme A and granzyme B. MUC1-specific CTLs were quantified by staining with MUC1-specific streptamer. Levels of secreted IFN-γ, IL-12p70 and IL-10 in the DCs and T cells co-cultured supernatant were assessed by ELISA. The expression of activation markers is significantly higher in UCB-derived CTLs Activation of T lymphocytes, both in vivo and in vitro, induces the expression of CD69. Induction of CD25 (the high affinity IL-2 receptor) and CD69 (the early activation antigen) is a characteristic feature of activated CTLs. Activation markers were detected on the cell surface using flow cytometry. Our data clearly show that CTLs generated from both sources express these two molecules. The FACS profile of one representative sample is shown in Fig. 3a. Figure 3b shows cumulative data from five samples (mean ± SD, n = 5). The data show that the CTLs from UCB-DCs appeared significantly more potent (P = 0.008) than their PBL counterparts in expression of these activation-associated markers. Functional characterization of CTLs: (a) Dot plot depicting the gating strategy and expression of activation markers CD69 & CD25 for a representative experiment from UCB/PBL. The dual positive cells from pulsed UCB/PBL-DCs are seen in upper right quadrant of lower panel. (b) Showing significantly higher CD69 & CD25 dual positive cells in UCB-derived CTLs than that of PBL-derived CTLs. (c) The gating strategy for intracellular staining of granzyme A & B in CTLs. Upper right quadrant in lower panel shows dual positive cells. (d) Showing presence of dual positive cells for granzyme A & B in pulsed UCB/PBL derived CTLs. (e) Dot plot and histogram showing the presence of MUC1 STAPPVHNV-specific T cells (lower panel) in total pool of CTLs from both the sources. (f) Showing significantly higher percentage of MUC1 specific TCRs in pulsed PBL/UCB-CTLs set as compared to unpulsed set. MUC1 specific TCRs in pulsed UCB-CTLs set was significantly higher than the PBL counterpart. (g) UCB-CTLs were capable of secreting significantly higher levels of IFN-γ than that of PBL-CTLs (n=5) in the co-culture derived from pulsed UCB/PBL-DCs. (h) Represents the levels of IL-10 and IL-12p70 in the co-culture. The UCB-DCs secreted significantly higher level of IL-12p70 and a significantly lower level of IL-10 than PBL-DCs. (I) IL-12 p70/IL-10 ratio in the co-culture. Ratio was significantly higher in cultures with UCB-DCs as compared to PBL DCs. The data shown are mean ± SD, n = 3/5 (p < 0.05, p < 0.01, p < 0.001) Percentage of granzyme-positive cells is also higher in UCB-CTLs A major pathway by which the CTLs induce their killing activity is via targeted exocytosis of cytoplasmic granules containing serine proteases, such as granzymes. Other locations where the granzymes can be detected are rough endoplasmic reticulum, golgi complex, and the trans-golgi reticulum, hence intracytoplasmic staining is needed to detect the presence of these proteases in the cells along with the use of Golgi stop (Brefeldin A). We found that the MCF-7 lysate-pulsed PBL-DC-CTLs/UCB-DC-CTLs produced granzyme A and B. The FACS profile is depicted in Fig. 3c. Cumulative data from three samples (mean ± SD, n = 3), showed a higher amount of these proteases in pulsed UCB-CTLs than in pulsed PBL-CTLs (Fig. 3d). UCB-CTLs contain higher number of MUC1-specific CTLs Out of all of the T cells in a given population, only a few may be specific for a given peptide against which its TCR match and are expanded on antigen presentation along with co-stimulation by APCs. To test the capability of MCF-7 lysate-pulsed UCB- and PBL-derived DCs to generate antigen-specific T cells after a secondary stimulation, sorted naïve HLA-A0201-positive CD8+ T cells were weekly re-stimulated with freshly MCF-7 lysate pulsed HLA-A0201-positive DCs. MUC1 is overexpressed in MCF-7 cells and it is also HLA-A0201-restricted. The presence of MUC1-specific CD8+ T cells were quantitated by peptide-specific streptamer. Percentage of MUC1 peptide-STAPPVHNV-specific TCR present in the proliferating clones of T cells is represented in Fig. 3e and f, and in schematics in Additional file 3: Figure S3. We found a significantly higher percentage of streptamer-positive UCB-CTLs compared to PBL-CTLs. Figure 3e shows the FACS profile of one representative sample and Fig. 3f depicts cumulative data from three samples (mean ± SD, n = 3). These findings suggest that pulsed UCB-DCs and PBL-DCs were efficient in generating MUC1-specific CTLs. UCB-CTLs secrete higher levels of IFN-γ IFN-γ regulates multiple aspects of CD8+ T cell homeostasis as it promotes CD8+ T cell expansion and memory cells formation. CTLs are characterized by the secretion of IFN-γ. DCs from both sources were able to generate CTLs, which were capable of secreting a substantial amount of IFN-γ. However, pulsed UCB-CTLs were capable of secreting significantly larger amounts of IFN-γ, as compared to pulsed PBL-CTLs. Figure 3g represents cumulative data from five samples (mean ± SD, n = 5). It is evident from these data that UCB-CTLs are better than the PBL-CTLs in this respect. Ratio of IL-12p70 to IL-10 was higher in supernatants of UCB-derived DC-T cell co-cultures IL-12 is essential for ontogenesis of effector functions in T cells and in the establishment of functional memory. In vitro generated pulsed DCs were able to secrete higher levels of IL-12p70, as compared to IL-10. The UCB-DCs showed a better IL-12p70 secretion profile than PBL-DCs. Figure 3h represents the levels of IL-10 and IL-12p70 in the co-culture. The levels of IL-12p70 (pg/ml) were 64.41 ±4.31 and 41.84 ±1.73 for UCB and PBL-DCs, respectively. On the other hand, the level of IL-10 secretion by PBL-DCs was higher than for UCB-DCs. The levels of IL-10 (pg/ml) were 49.86 ± 9.72 and 83.53 ± 8.72 for UCB and PBL-DCs, respectively. Figure 3i represents the ratio of IL-12p70/IL-10. This ratio was significantly higher in UCB-DCs (mean ± SD, n = 5). It is evident from these data that the UCB-DCs have a more favorable T helper (Th)1 cytokine profile, as compared to PBL-DCs. The activated CD8+ T cells from both the DCs sources show comparable CTL activity Figure 4a represents the cumulative data from three different biological replicates at different target-to-T-cell ratios. All the intermediate titration ratios of target-to-killers used in this study have shown that the DCs from the two sources have a similar killing effect. There was no spontaneous death as is evident for the 1:0 ratio where we saw zero percent killing as calculated by the formula in the P-JAM assay. This is depicted in Fig. 4a (x-axis 1:0 ratio). No significant difference was observed in the killing efficiency of CTLs derived from the two sources. As a negative control, CTLs were raised with un-pulsed UCB and PBL-DC sets. The CTLs thus generated were not effective in killing the target cells. To check the target specificity, CTLs obtained from MCF-7 lysate-pulsed UCB DCs were used in the CTL assay against H1299 and SH-SY5Y cell lines; a negligible killing effect was seen in these sets. Figure 4b shows the percent killing of the irrelevant target cell line H1229. The CPMA value in the SH-SY5Y control was 1,710 (SD ± 30), and in the pulsed and un-pulsed group at highest target-to-T-cell ratios were 1680 (SD ± 47) and 1,650 (SD ± 36), respectively. Additional file 4: Figure S4A and B depict the propinquity interaction of pulsed DCs and naïve T cells in the co-culture system. It is clearly seen (Additional file 4: Figure S4C) that CTLs from un-pulsed DCs do not cling to the target MCF-7 cells in the CTL assay. Additional file 4: Figure S4D and Additional file 4: Figure S4E illustrate the assailing nature of CTLs from pulsed DCs towards the target cells. In vitro cytotoxic T lymphocyte (CTL) assay. a CTL assay data from three experiments depicting the killing efficacy of the target MCF-7 cells by CTLs generated by pulsed umbilical cord blood (UCB)/periperal blood (PBL)-dendritic cells (DCs). b Percent killing in the irrelevant target cell line H1229. Negligible killing effect was seen in these sets by pulsed UCB/PBL-DCs. Data shown are mean ± SD, n = 3 In vivo CTL assay-xenograft model To assess the in vivo potency of the CTLs generated from both the sources, a xenograft model was used. Representative IVIS images of one experiment including control (not infused with CTLs), UCB and PBL groups on day 0 and day 10 are depicted in Fig. 5a and b, c and d, and e and f, respectively. There was marginal change in tumors in the control group, whereas in both the treated groups there was a significant decrease in the radiance. Three independent experiments having two or three mice in the control group and five mice in each test group were performed using 37 female NOD/SCID mice, 7 in the control set and 15 mice each in the UCB and PBL sets. Figure 5g represents cumulative data for average radiance (p/sec/cm2/sr) of three experiments. There was a significant regression in the tumor mass in the UCB group and PBL group on day 10 as compared to day 0, after CTL infusion. Figure 5h depicts the cumulative data for tumor volume (mm3) from three experiments, which shows that there was a significant decrease in tumor volume in the UCB group and the PBL group in the experimental time window, as compared to the control group. H&E staining for the MCF-7-luc-F5 xenograft tumor section for the control set is depicted in Fig. 5i and j. Figure 5k and l, and Fig. 5m and n represent UCB and PBL-CTLs infused test samples, respectively. CTL infiltrations were clearly evident (indicated by arrows). Figure 5o-q shows the immunofluorescence staining data for one slice of the section, which further confirms the T cell infiltration inside the tumor. Figure 5r bar graph shows the quantification of tumor-infiltrating T cells, which was enumerated by Z stack using the Zeiss LSM 510 Meta confocal microscope. In vivo cytotoxic T lymphocyte (CTL) assay xenograft model. Representative image from one of the experiments showing average radiance (measured on the in vivo imaging system (IVIS)) from female NOD/SCID mice bearing tumor consisting of MCF-7-luc-F5 cells. a, b Average radiance from a control mouse on day 0 and day 10. c and d, e and f Average radiance from the umbilical cord blood (UCB)/peripheral blood (PBL)-CTLs group of mice on day 0 and day 10 post CTLs infusion. g Average radiance data of three experiments on day 0 and day 10 post CTLs infusion. There was significant regression in the tumor in both treatment groups infused with pulsed UCB/PBL-CTLs. Horizontal lines mean values ± SD. h Tumor volume on day 0 and day 10 post CTLs infusion. Similar significant reduction in the tumor mass was observed in both treatment groups infused with pulsed UCB/PBL-CTLs. i, j H&E-stained section of MCF-7-luc-F5 cell xenograft tumor from a control mouse showing no infiltrating T cells. k and l, m and n H&E-stained sections from a mouse infused with pulsed UCB/PBL-CTLs. Infiltrating CTLs in both treatment groups are observed (arrows). o-q Immunofluorescence images of sections stained with anti-human CD3 Ab, which further confirms the absence and presence of CTLs in the control and treatment group infused with pulsed UCB/PBL-CTLs, respectively. r Quantification of tumor-infiltrating T cells, which was enumerated by Z stack using the Zeiss confocal microscope. Data shown are mean ± SD, n = 3 (P <0.05, * P <0.01, *** P <0.001) DC-based vaccination is an attractive immunotherapeutic strategy, because of its ability to induce tumor-specific T cell responses, which offers the desired anti-tumor effects with minimal toxicity. Allogenic DCs generated from healthy donors (HLA matching or partially matching) have been used in clinical trials as DC vaccines. These DCs initiated a CTL response and induced regression of the tumor [1]. Allogeneic DCs can also be generated from CD34+ cells derived from UCB. Our earlier studies had shown that UCB can serve as an alternative source for generating a homogenous DC population with high cell numbers [25, 26, 31]. However, as UCB are naïve cells, there is concern as to whether the DCs generated from them would elicit a CTL response as potent as that generated by PBL-derived DCs, and whether they could serve as good candidates for vaccines. To gain a better insight into this, we performed a systematic comparative study of standard PBL monocyte-derived DCs and UCB-generated DCs, with emphasis on CTL characterization and in vitro and in vivo CTL assays. DCs generated from the two sources were similar in morphology and phenotype. Starting with 107 MNCs per sample, 3.11 ± 1.495 × 107 DCs were generated from three UCB samples and 0.53 ± 2.771 × 107 DCs were generated from three PBL samples. Their functional attributes, such as antigen uptake capacity and ability to migrate towards a chemokine gradient of CCL-19 and MLR activity, i.e., potent immunostimulatory capacity, were equivalent. The CTLs generated were examined for activation markers (CD69 and CD25), granzyme A and B and quantitation of MUC1 peptide (STAPPVHNV)-specific CTLs by streptamer. Expression of granzyme A and B in human cytotoxic lymphocyte subsets as analyzed by flow cytometry have been reported by Grossman et al. [37]. The cytokines secreted by UCB-DCs and PBL-DCs in the co-culture system were favorable for a Th1 response. A low level of interleukins in the long term cultures is in accordance with the findings of Wong KL et al. [38]. Our data indicate that CTLs from UCB-DCs are superior to CTLs from PBL-DCs. Cytotoxic T lymphocytes are important constituents of an adaptive immune system. We tested the level of the known HLA-A0201-restricted MCF-7-associated antigen, MUC1- STAPPVHNV peptide, by the streptamer assay and found that the pool of CTLs had a high percentage of MUC1-specific CTLs. As UCB T cells have different activation thresholds as compared to T cells in adults, it appears that the combination of UCB-DCs with UCB T cells generated superior levels of MUC1-specific CTL than that of PBL-DCs. However cross-stimulation of UCB-DCs with adult T cells, and vice-versa, would be required to ascertain if the increased potency was due to the presenting and/or responding cell type. Thus, a pure antigen-specific CD8+ T cell population could be generated, which could eventually be sorted out to give a single antigen-specific response in CTL assays. Our data are in agreement with those of Fernandez et al. [39] who described an in vitro system for the generation of functional, antigen-specific T cells from human stem cells, which could eventually provide a readily available cell source for adoptive transfer immunotherapies, and also enable better understanding of human T cell development. Defense against virally-infected and malignant cells depends on the action of cytotoxic T lymphocytes and natural killer cells. Although these use several mechanisms to eliminate target cells, the principal event is secretion of cytotoxic granules. These granules contain the pore-forming protein perforin, together with a variety of granule-associated proteases, which include the granzymes. Target cell recognition by cytotoxic lymphocytes induces secretion of the cytotoxic granular content towards the target and the induction of death [40]. We saw high levels of granzyme A and B in UCB-DC CTLs, further highlighting their potential killing ability. The in vitro CTL activity was assessed by determining CTL killing efficiency with MCF-7 as target cells, and we found that CTLs from both sources exhibited equivalent killing efficiency. All the intermediate titration ratios of target-to-killers used in this study have shown that the DCs from the two sources have a similar killing effect. It appears that a higher titration ratio may also lead us to the same conclusions; however, we need to examine this aspect. Nevertheless, we feel that using a higher effector-target ratio may not change the scenario further in terms of interpretation of the current data. We also found evidence of cytotoxic activity specific to tumor antigens in the in vitro CTL assay, and not against nonspecific targets like H1229 and SH-SY5Y. These data clearly suggest that UCB-DCs/CTLs are as potent as PBL-DCs/CTLs. In contrast, they showed ameliorating features. Chang et al. [32] have also compared PBL-DCs with UCB-DCs using in vitro assays and they report similar findings. Signaling pathways play a decisive role in the differentiation, survival, expression of co-stimulatory molecules and antigen presentation capacity of DCs. They have shown that CBSC-derived DCs have quicker and greater extracellular signal-regulated kinase (ERK) and Akt phosphorylation, and weaker p38 phosphorylation, than peripheral blood mononuclear cell (PBMC)-derived DCs, when stimulated with LPS. In our study we have placed emphasis on the characterization of CTLs obtained from DCs of UCB /PBL and also focused on in vivo CTL assays using a xenograft in NOD/SCID mice. Cord blood has many advantages over other sources, such as ready availability, low risk of severe Graft-versus-host disease and presence of stem cells with high proliferative potential. Thus, although UCB-DCs had greater capability in terms of vaccination and activation, there is a possibility of adverse effects associated with this line of therapy. These will have to be evaluated in pilot phases of clinical trials, thereby providing a better assessment and insight before moving forward with the other phases of clinical trials. Importantly, to compare the cancer vaccination or the stability of the two DCs from different resources, one must establish a competitive assay including UCB-DCs and PBL-DCs, employing immunosufficient mice. This experiment may yield valuable insight for our current understanding of effector functions in in vivo settings, which may help to verify the vaccination efficacy for the two DC sources. In other words, the future of UCB-derived DC vaccination depends largely on its in vivo behavior in patients, for which more stringent experiments on appropriate animal models need to be executed. Cord blood stem cells have longer telomeres and have longer survival. Monocytes from PBL are terminally differentiated cells, and therefore cannot proliferate. The major disadvantage of cord blood is the low number of stem cells but this is taken care of by the expansion step in our method. Cord blood banks from all over the world can be utilized for this purpose. When a stored sample is revived for transplantation, a small aliquot can be removed to generate DCs, which could then be transplanted into the patient, where they would migrate to lymph nodes and could elicit a strong T cell response against any residual tumor cells. de Haar et al. have already started such pre-clinical trials in the therapy of pediatric Acute myeloid leukemia using UCB-DCs [29]. Hutten et al. describe the first pre-clinical evidence for the suitability of UCB-DC either for the induction or for the reactivation of minor histocompatibility antigen (MiHA) HA-1-specific cytotoxic T cells. Their findings are of clinical significance in transplanted patients suffering from hematological malignancies [30]. To the best of our knowledge, we provide here for the first time, direct evidence in a xenograft model of a solid tumor, an adoptive T cell therapy by using ex vivo expanded CTLs having the antitumor activity derived from HLA-A0201-positive UCB and PBL samples. We found that UCB/CTLs and PBL/CTLs had immunotherapeutic effects against MCF-7-luc-F5 solid tumors in female NOD/SCID mice. It is evident from the IVIS data that there is a significant remission in tumors 10 days after CTL infusion. The H&E and immunofluorescence staining of tumor sections revealed substantial homing and infiltration of CD8+ T cells. It needs to be determined whether frequent booster doses of CTLs over longer period could achieve complete regression. It is also important to generate DCs by our method from other sources such as CD34+ from mobilized PBL or enriched apheresis samples and test their killing efficacy, using a different cell line in in vivo xenograft experimental models. We have come a long way since the first clinical trial with autologous pulsed DCs to stimulate anti-tumor immunity in humans. We are still in the quest to find the answer to the main problem i.e., what is required to evoke a therapeutic immunity against cancer, which emerges by evading the defense system of the host. With the advancement in technology our perspective on the role of DCs as adjuvant in cancer immunotherapy has broadened remarkably. We are at the point of entering a new era, in which immunotherapy is going to revolutionize the treatment of almost every kind of cancer. Our data conclusively show that UCB-derived DCs are equally potent as the standard source of DC vaccines, i.e., PBL monocyte-derived DCs. In other words, UCB-DCs or the CTLs derived from them could be used effectively in allogeneic anti-tumor vaccines for immunotherapy, as an alternative to peripheral blood or bone marrow-derived DCs/CTLs. 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Identification of HLA-A2-restricted T-cell epitopes derived from the MUC1 tumor antigen for broadly applicable vaccine therapies. Blood. 1999;93:4309–17. Grossman WJ, Verbsky JW, Tollefsen BL, Kemper C, Atkinson JP, Ley TJ. Differential expression of granzymes A and B in human cytotoxic lymphocyte subsets and T regulatory cells. Blood. 2004;104:2840–8. Wong KL, Lew FC, MacAry PA, Kemeny DM. CD40L-expressing CD8 T cells prime CD8alpha(+) DC for IL-12p70 production. Eur J Immunol. 2008;38:2251–62. Fernandez I, Ooi TP, Roy K. Generation of functional, antigen-specific CD8+ human T cells from cord blood stem cells using exogenous Notch and tetramer-TCR signaling. Stem Cells. 2014;32:93–104. Bots M, Medema JP. Granzymes at a glance. J Cell Sci. 2006;15:119:5011–4. We acknowledge DBT, Govt. of India for funding the project. CSIR and DBT provided a fellowship for JK. We thank the Director, NCCS for supporting the project, and Dr. GC Kundu for the kind gift of MCF-7-luc-F5 cells. The authors thank Drs Prakash Daithankar, Arvind Sangamnerkar, Girish Godbole and Ranjeet Bhosale for providing UCB samples and Col. T Chatterjee (AFMC) for providing buffy coat samples. Special thanks to Dr. Jyoti Rao for English editing of the manuscript. We thank Mrs. Nikhat Firdaus Q. Khan for technical help and the NCCS core facilities such as the flow cytometry and animal experimentation facility. Stem Cell Laboratory, National Centre for Cell Science, Ganeshkhind, Pune, 411007, India Jeetendra Kumar , Vaijayanti Kale & Lalita Limaye Search for Jeetendra Kumar in: Search for Vaijayanti Kale in: Search for Lalita Limaye in: Correspondence to Lalita Limaye. LL conceived and designed the experiments. JK performed the experiments. JK, VK, and LL analyzed the data. LL and VK contributed reagents/materials/analysis tools. LL, VK, and JK wrote the paper. LL was the principal investigator in the project and VK was the co-principal investigator. All authors read and approved the manuscript. Additional file 1: Figure S1. Flow chart depicting experiment design for generation of dendritic cells (DCs). UCB umbilical cord blood, MNC mononuclear cells, GM-CSF granulocyte-macrophage colony stimulating factor, PBL peripheral blood, LPS lipopolysaccharide. (TIFF 2506 kb) Flow chart depicting experiment design for generation of cytotoxic T lymphocytes (CTL). UCB umbilical cord blood, PBL peripheral blood, LPS lipopolysaccharide, DC dendritic cells. (TIFF 3354 kb) Schematics for Streptamer staining. CTLs cytotoxic T lymphocytes. (TIFF 2289 kb) Depicts the interaction of pulsed dendritic cells (DCs) and naïve T cells. A Clonal expansion of naïve T cells during co-culture with pulsed DCs. B Larger magnification to show the tethering of many naïve T cells with a mature DC. C Negligible interaction of unpulsed cytotoxic T lymphocytes (CTLs) with the target MCF-7 cells. D, E Flocking of CTLs derived from pulsed peripheral blood (PBL)/umbilical cord blood (UCB) DCs to the target MCF-7 cells. (TIFF 2950 kb) Kumar, J., Kale, V. & Limaye, L. Umbilical cord blood-derived CD11c+ dendritic cells could serve as an alternative allogeneic source of dendritic cells for cancer immunotherapy. Stem Cell Res Ther 6, 184 (2015) doi:10.1186/s13287-015-0160-8 Revised: 17 August 2015 Cumulative Data Buffy Coat Sample Mixed Lymphocyte Reaction Assay	CommonCrawl
SEP performance of triangular QAM with MRC spatial diversity over fading channels Furqan Haider Qureshi1, Shahzad Amin Sheikh1, Qasim Umar Khan1 & Fahad Mumtaz Malik1 EURASIP Journal on Wireless Communications and Networking volume 2016, Article number: 5 (2016) Cite this article This paper presents the mathematical model for symbol error probability of triangular quadrature amplitude modulation in a single-input multi-output environment. The symbol error probability performance is evaluated over fading channels namely Rayleigh, Nakagami-m, Nakagami-n, and Nakagami-q. The maximal-ratio combining technique is considered as spatial diversity algorithm and unified moment-generating-function-based approach is applied to derive the results. The multiple channels considered are independent but not necessarily identically distributed. The results presented are valid for slow and frequency non-selective fading channels only. The symbol error probability expressions obtained contain single integrals with finite limits and integrand composed of elementary functions which help us evaluate our analytical expressions numerically. We also compare these expressions with the error performances obtained through computer simulation, which show excellent agreement. In addition, an example has been simulated to validate our derived mathematical expressions. An efficient signal constellation has always been an active research area since 1960s for the purpose of wired and wireless communication. Quadrature amplitude modulation (QAM) has become the dominant modulation scheme in terms of power and bandwidth efficiency. It was first suggested by C. R. Cahn in 1960 [1]. Since then, many developments have been made in the geometry of QAM. The constellation was named QAM. Hancock and Lucky [2] expanded the work of Cahn. They suggested constellations with signal points taken on concentric circles, with outer ring having more points than on the inner ring. Idea behind this was to remove errors due to phase shift. Later in 1962, Campopiano and Glazer [3] introduced a well-organized structure of even-bit signal constellation, which is presently known as square QAM (SQAM). In 1960s and 1970s, progressive research on the structure of a potent 16-ary constellation had been carried out. Since Square QAM retains a high minimum distance between constellation points and has simple detection technique, plenty of the digital communication systems using high modulation orders with 16 or greater number of constellation points have been utilizing the SQAM. Little literature on constellation designs defeating the SQAM in terms of good transmission capability is available since its birth. In [4], a honeycomb-like architecture of constellation whose signal points are taken at the origin and on the first and the second concentric hexagon has been advised. The authors named this constellation as Honeycomb Signal Set. In 1989, Shinjiro Oshita et al. [5] proposed another structure which had hexagonal packing; it was analyzed and named as triangular-shaped signal set (TSSS). In spite of the structures of constellations suggested in [4, 5] which give improved performance over the SQAM, they are not practicable because of the increase in detection complexity at the receiver end. Recently, in 2007, Sung-Joon Park [6] presented a novel symmetrical structure named as triangular quadrature amplitude modulation (TQAM) in which vertices of the equilateral triangles were taken as constellation signal points. TQAM has a proven efficiency against SQAM in terms of error probability performance and detection complexity in [6, 7]. TQAM uses even number of bits to represent a signal point in the constellation. The key reason behind the efficiency of TQAM constellation is its compact geometry. In 2010, symbol error probability (SEP) of TQAM was evaluated by K. Cho, J. Lee, and D. Yoon for additive white Gaussian noise (AWGN) channel [8] and also, an approximation of SEP expression for TQAM was derived for AWGN and fading channels by T. T. DUY and H. Y. KONG [9], in which maximal-ratio combining (MRC) was used to analyze TQAM over Rayleigh fading channel with multipath reception. In [10], θ-QAM was introduced to incorporate SEP of SQAM and TQAM in a single analytical expression over AWGN and Nakagami-m channels; however, J. Lee et al. [11] proved their work incorrect for higher modulation order and presented their own equations for exact SEP and bit error probability (BEP) over AWGN channel and also paved way for exact BEP over Rayleigh, Rician, and Nakagami-m channels. However, the SEP expressions provided in [10] are valid only for modulation order 16. In 2012, Sung-Joon Park analyzed the SEP performance of TQAM in AWGN channel using an approximate expression for the SEP [7]. Though an exact generalized mathematical SEP expression in the presence of AWGN channel is provided in [11], the mathematical model we provide in this article can be implemented easily when dealing with TQAM not only in AWGN, but also this model is extended to Rayleigh, Nakagami-m, Nakagami-n, and Nakagami-q channels. To the best of author's knowledge, generalized SEP expressions for fading channels incorporating diversity reception have not been presented before in [7–11]. In this paper, TQAM has been analyzed in single-input multi-output (SIMO) environment with spatial diversity. We use spatial diversity to mitigate fading. Diversity combining is the most powerful way to cater the aftermaths of multipath fading. These combining techniques were introduced by Brennan [12]. Diversity is available whenever multiple, independently fading channels link the transmitter and receiver. Such multiple channels naturally occur in multi-input multi-output (MIMO) applications for which the transmitter or receiver use an antenna array. These diversity combining techniques are actually the operations performed on an antenna array. The idea behind using diversity reception scheme is that, as the signal paths are independent, all of them have very low probability to experience deep fades simultaneously. Thus, we transmit same signal over independently fading paths in diversity reception scheme. In this article, at receiving end these paths are then combined using MRC algorithm that the fading amount of the combined received signal decreases and consequently its signal-to-noise ratio (SNR) improves. MRC was first proposed by Kahn [13]. In MRC, if there are total L antennas at the receiving end, the received signals from all of the L branches are weighted according to their individual SNR and then summed together to provide single output. The performance of M-ary QAM with space diversity in various fading channels has been analyzed in [9, 14–24], on which light, is shredded in terms of comparison in Section 5. Recently in 2010, Xi-chun Zhang et al. [25] utilized the MGF-based approach to evaluate the performance of cross QAM over fading channels, and later in 2013, their work was extended by Hua Yu et al. [26] to SIMO systems with MRC reception. Here, based on the moment-generating function (MGF) method, average SEP of M-ary TQAM is analyzed, whereas, MRC is used as the spatial diversity technique at the receiving end. The fading channels considered in this article are Rayleigh, Nakagami-m, Nakagami-n (Rice), and Nakagami-q (Hoyt). The results presented are valid for slow flat fading channels only. Moreover, we consider a coherent general order TQAM signal assuming perfect channel estimation. We are using finite integral form of Gaussian Q-function and the unified MGF-based approach to reach the final expressions. SEP closed-form expression provided here consists of single finite range integrals, and the integrand is composed of elementary functions which provide easy numerical evaluation. Moreover, the mathematical expressions are valid for general modulation order TQAM and are accurate and elementary enough that it becomes conducive and fast to quantify the SEP performance of TQAM with MRC. The remaining article is organized in six sections. In Section 2, we show the SEP expression for AWGN channel. In Section 3, we present the channel model for MRC spatial diversity. In Section 4, we pursue the derivation of SEP expression for M-ary TQAM with MRC. Section 5 presents numerical results with brief discussion. An example has been simulated in Section 6, which validates our results derived in Section 4, whereas, conclusion is given in Section 7. SEP of TQAM over AWGN channel From Fig. 1, it is observed that unlike SQAM, in TQAM, all the nearest neighbors to any signal point in constellation are equidistant. This is the key reason that SEP expressions provided here give exact fit over the simulation curves. Point P is taken at Euclidean distance d/2 from the origin at an angle of 60°, where d is the length of one side of the triangle, or we can say distance between any two adjacent signal points is d. M-ary TQAM is an even-bit representation of constellation points, i.e., M = 22m where m = 2, 3, 4, …, and M is the modulation order of the constellation. Signal constellation for 16-TQAM In Fig. 2, dots p j represents jth signal point, where j = 1, 2, 3, …, M and the lines show decision boundaries for 16-TQAM. Now here, four of the innermost signal points have hexagonal decision regions which resemble like honeycomb. The decision boundary lines for all the signal points are drawn based on the Campopiano-Glazer construction rule ([27]: Article 9.9.2). For 64-TQAM, [7: Fig. 1b] is referred. We assume here that all the signal points are equally probable and Re(p j ) and Im(p j ) are the real and imaginary values of signal point p j , respectively. Average energy per symbol E s for M-ary TQAM can be evaluated as: Decision boundaries for 16-TQAM $$ {E}_s=\frac{1}{M}\left[{\displaystyle \sum_{j=1}^M{\left\{\mathrm{R}\mathrm{e}\left({p}_j\right)\right\}}^2+{\displaystyle \sum_{j=1}^M{\left\{\mathrm{I}\mathrm{m}\left({p}_j\right)\right\}}^2}}\right] $$ $$ {E}_s=\frac{4}{M}\left[\frac{\sqrt{M}}{4}{\displaystyle \sum_{i=1}^{\sqrt{M}}{\left\{\left(2i-1\right)\frac{d}{2} cos{60}^o\right\}}^2+\frac{\sqrt{M}}{2}{\displaystyle \sum_{i=1}^{\raisebox{1ex}{$\sqrt{M}$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}{\left\{\left(2i-1\right)\frac{d}{2} sin{60}^o\right\}}^2}}\right] $$ In (2), upper limit of the summation is always a positive integer. Solving summation of polynomial expressions using Faulhaber's formula ([28]: p. 106): $$ {E}_s=\frac{\left(7M-4\right){d}^2}{48} $$ This leads us to minimum Euclidean distance d expression, $$ d=\sqrt{\frac{48{E}_s}{7M-4}} $$ since symbol's signal-to-noise ratio γ can be written as: $$ \gamma =\frac{E_s}{N_o}=\frac{\left(7M-4\right)}{24}{\left(\frac{d}{2\sigma}\right)}^2=\frac{\left(7M-4\right){\beta}^2}{24} $$ where σ 2 = N O /2 is the variance of Gaussian probability distribution function and β is the normalized least distance between adjacent symbols. Thus: $$ \beta =\sqrt{\frac{24\gamma }{\left(7M-4\right)}}=\sqrt{2D\gamma } $$ $$ D=\frac{12}{7M-4} $$ The SEP expressions in this section and Section 4 are derived in terms of β. The main reason for using the MGF-based approach is to utilize the technique of writing Gaussian Q-function with finite integration limits. Now in this constellation, there are five types of signal points based on the number of neighbors each point has, and unlike SQAM, for this particular constellation, each symbol has all the neighbors as the nearest neighbors. Table 1 tells us about the number of nearest neighbors for M-ary TQAM, where S N means number of signal points having N nearest neighbors. Table 1 Signal points S N having N nearest neighbors Probability of correct symbol reception P C, N for a symbol having N nearest neighbors is written as: $$ {P}_{C,2}={\left(1-Q\left(\beta \right)\right)}^2=1-2Q\left(\beta \right)+{Q}^2\left(\beta \right) $$ $$ {P}_{C,3}={\left(1-Q\left(\beta \right)\right)}^3=1-3Q\left(\beta \right)+3{Q}^2\left(\beta \right)-{Q}^3\left(\beta \right) $$ $$ {P}_{C,4}={\left(1-Q\left(\beta \right)\right)}^4=1-4Q\left(\beta \right)+6{Q}^2\left(\beta \right)-4{Q}^3\left(\beta \right)+{Q}^4\left(\beta \right) $$ $$ {P}_{C,5}={\left(1-Q\left(\beta \right)\right)}^5=1-5Q\left(\beta \right)+10{Q}^2\left(\beta \right)-10{Q}^3\left(\beta \right)+5{Q}^4\left(\beta \right)-{Q}^5\left(\beta \right) $$ $$ {P}_{C,6}={\left(1-Q\left(\beta \right)\right)}^6=1-6Q\left(\beta \right)+15{Q}^2\left(\beta \right)-20{Q}^3\left(\beta \right)+15{Q}^4\left(\beta \right)-6{Q}^5\left(\beta \right)+{Q}^6\left(\beta \right) $$ where Q(β) is the Gaussian Q-function and to evaluate it numerically, [29]: equation (9)] is used, which is its finite limit integral form. The exact probability of correct receiving symbol for M-ary TQAM is given as: $$ {P}_C\left(\beta \right)=\frac{1}{M}\left[{S}_2{P}_{C,2}+{S}_3{P}_{C,3}+{S}_4{P}_{C,4}+{S}_5{P}_{C,5}+{S}_6{P}_{C,6}\right] $$ $$ \begin{array}{l}{P}_C\left(\beta \right)=1-\left(\frac{2}{M}-\frac{8}{\sqrt{M}}+6\right)Q\left(\beta \right)+\left(\frac{18}{M}-\frac{35}{\sqrt{M}}+15\right){Q}^2\left(\beta \right)\\ {}-\left(\frac{44}{M}-\frac{61}{\sqrt{M}}+20\right){Q}^3\left(\beta \right)+\left(\frac{46}{M}-\frac{53}{\sqrt{M}}+15\right){Q}^4\left(\beta \right)\\ {}-\left(\frac{22}{M}-\frac{23}{\sqrt{M}}+6\right){Q}^5\left(\beta \right)+\left(\frac{4}{M}-\frac{4}{\sqrt{M}}+1\right){Q}^6\left(\beta \right)\end{array} $$ since P e (β) = 1 − P C (β): $$ \begin{array}{l}{P}_e\left(\beta \right)=6\left(1+\frac{1}{3M}-\frac{4}{3\sqrt{M}}\right)Q\left(\beta \right)-15\left(1+\frac{6}{5M}-\frac{7}{3\sqrt{M}}\right){Q}^2\left(\beta \right)\\ {}+20\left(1+\frac{11}{5M}-\frac{61}{20\sqrt{M}}\right){Q}^3\left(\beta \right)-15\left(1+\frac{46}{15M}-\frac{53}{15\sqrt{M}}\right){Q}^4\left(\beta \right)\\ {}+6\left(1+\frac{11}{3M}-\frac{23}{6\sqrt{M}}\right){Q}^5\left(\beta \right)-\left(1+\frac{4}{M}-\frac{4}{\sqrt{M}}\right){Q}^6\left(\beta \right)\end{array} $$ Equation (15) gives us the exact SEP of M-ary TQAM in the presence of AWGN channel. In Section 4, using (15), we evaluate the SEP over various fading channels with MRC reception after presenting channel model in Section 3. MRC spatial diversity channel models In SIMO system, the signal is transmitted over L diversity paths where each copy of the signal struggles through individual fading amplitude. The multipath receiver uses the algorithm of MRC diversity reception scheme to increase the SNR of the combined received signal by decreasing the SEP. For MRC, SNR of the combined output signal γ ∑ at the receiver is expressed as ([30]: equation (5.98)): $$ {\gamma}_{\sum }=\frac{E_s}{N_o}{\displaystyle \sum_{i=1}^L{\alpha_i}^2}={\displaystyle \sum_{i=1}^L{\gamma}_i}\kern0.6em \mathrm{where}\ i = 1,\ 2,\ 3, \dots,\ L $$ $$ {\gamma}_i=\frac{E_s}{N_0}{\alpha_i}^2 $$ where γ i is the instantaneous received SNR per symbol and α i is the instantaneous fading amplitude at the ith diversity path. SEP evaluation of TQAM over fading channels while using MRC diversity receiver demands knowledge of probability density function (pdf) of SNR γ ∑ of the combined signal at output. Before that, we take a look at the pdf of the instantaneous received SNR per symbol γ i of the ith diversity path over Rayleigh, Nakagami-m, Nakagami-n and Nakagami-q channels respectively, provided from [31] as: $$ {p}_{\gamma_i,\mathrm{Rayleigh}}\left(\gamma \right)=\frac{1}{\overline{\gamma_i}} exp\left(-\frac{\gamma }{\overline{\gamma_i}}\right),{\gamma}_i\ge 0 $$ $$ {p}_{\gamma_i,{m}_i}\left(\gamma \right)=\frac{{m_i}^{m_i}{\gamma}^{m_i-1}}{{\overline{\gamma_i}}^{m_i}\varGamma (m)} exp\left(-\frac{m_i\gamma }{\overline{\gamma_i}}\right),{\gamma}_i\ge 0,{m}_i\ge 0.5 $$ $$ {p}_{\gamma_i,{n}_i}\left(\gamma \right)=\frac{\left(1+{n_i}^2\right){e}^{-{n_i}^2}}{\overline{\gamma_i}} exp\left(-\frac{\left(1+{n_i}^2\right)\gamma }{\overline{\gamma_i}}\right){I}_0\left(2{n}_i\sqrt{\frac{\left(1+{n}_2\right)\gamma }{\overline{\gamma_i}}}\right),{\gamma}_i\ge 0,{n}_i\ge 0 $$ $$ {p}_{\gamma_i,{q}_i}\left(\gamma \right)=\frac{\left(1+{q_i}^2\right)}{2{q}_i\overline{\gamma_i}} exp\left(-\frac{{\left(1+{q_i}^2\right)}^2\gamma }{4{q_i}^2\overline{\gamma_i}}\right){I}_0\left(\frac{\left(1-{q_i}^4\right)\gamma }{4{q_i}^2\overline{\gamma_i}}\right),{\gamma}_i\ge 0,{q}_i\in \left[0,1\right] $$ where $ \overline{\gamma_i}=E\left[{\gamma_i}^2\right] $ is the average received SNR per symbol. E[.] is the expectation operator and I 0 (.) is the modified Bessel function of the first kind and zero order. Using (18)–(21) along with (22), the MGFs of Rayleigh, Nakagami-m, Nakagami-n, and Nakagami-q fading channels are respectively given in [31] as: $$ {M}_{\gamma_i}(s)={\displaystyle {\int}_0^{\infty }{e}^{s\gamma }{p}_{\gamma_i}\left(\gamma \right)}d\gamma $$ $$ {M}_{\gamma_i,\mathrm{Rayleigh}}(s)={\left(1+\overline{\gamma_i}s\right)}^{-1} $$ $$ {M}_{\gamma_i,{m}_i}(s)={\left(1+\frac{\overline{\gamma_i}}{m_i}s\right)}^{-{m}_i},{m}_i\ge 0.5 $$ $$ {M}_{\gamma_i,{n}_i}(s)=\frac{\left(1+{n_i}^2\right)}{1+{n_i}^2+s\overline{\gamma_i}} exp\left(\frac{{n_i}^2s\overline{\gamma_i}}{1+{n_i}^2+s\overline{\gamma_i}}\right),{n}_i\ge 0 $$ $$ {M}_{\gamma_i,{q}_i}(s)={\left(1+2s\overline{\gamma_i}+\frac{{\left(2s\overline{\gamma_i}\right)}^2{q_i}^2}{{\left(1+{q_i}^2\right)}^2}\right)}^{-1/2},{q}_i\in \left[0,1\right] $$ From (23) to (26), we can observe that these are MGFs of the individual ith diversity path. As we are considering multiple channels which are independent but not necessarily identical, then the MGF of the γ ∑ is written as the product of the individual MGFs of γ i : $$ {M}_{\gamma_{\sum }}(s)={\displaystyle \prod_{i=1}^L{M}_{\gamma_i}(s)} $$ Equation (27) gives us the MGF of the SNR of the combined signal at the output of the receiver. SEP of TQAM with MRC spatial diversity Now we attend our main objective, i.e., to find the SEP expression for M-ary TQAM in MRC diversity scheme. This is achieved by averaging the SEP formula (15) over the pdf of the SNR $ {p}_{\gamma_{\sum }}\left(\gamma \right) $ of the combined signal at the output. $$ {P}_{\mathrm{diversity}}={\displaystyle \underset{0}{\overset{\infty }{\int }}{P}_e\left(\gamma \right)}{p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma $$ P e (γ) is the exact SEP for M-ary TQAM in AWGN channel as provided in (15), whereas, from (6) we know that β is a function of γ. $$ \begin{array}{l}{P}_{\mathrm{diversity}}=6\left(1+\frac{1}{3M}-\frac{4}{3\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}Q\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma }-15\left(1+\frac{6}{5M}-\frac{7}{3\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^2\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma}\\ {}+20\left(1+\frac{11}{5M}-\frac{61}{20\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^3\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma }-15\left(1+\frac{46}{15M}-\frac{53}{15\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^4\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma}\\ {}+6\left(1+\frac{11}{3M}-\frac{23}{6\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^5\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma }-\left(1+\frac{4}{M}-\frac{4}{\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^6\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma}\end{array} $$ Ignoring the higher order terms Q i, i > 4, the average symbol error probability is approximately given as: $$ \begin{array}{l}{P}_{\mathrm{diversity}}\approx 6\left(1+\frac{1}{3M}-\frac{4}{3\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}Q\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma }-15\left(1+\frac{6}{5M}-\frac{7}{3\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^2\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma}\\ {}+20\left(1+\frac{11}{5M}-\frac{61}{20\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^3\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma }-15\left(1+\frac{46}{15M}-\frac{53}{15\sqrt{M}}\right){\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^4\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma}\end{array} $$ In (30), we remove the infinite upper limit in the integrals by using a few mathematical tools. From [32: equation (2)], we can write $ Q\left(\beta \right)=2{Q}_a\left(\beta, \raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$2$}\right.\right) $ and from [33: equation (12)], we can write $ {Q}^2\left(\beta \right)=2{Q}_a\left(\beta, \raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$4$}\right.\right) $, both for β ≥ 0. Where, $$ {Q}_a\left(\beta, \varphi \right)=\frac{1}{2\pi }{\displaystyle {\int}_0^{\varphi } exp\left[-\frac{\beta^2}{2{sin}^2\theta}\right]}d\theta $$ The form in (31) simplifies the evaluation of SEP performance over fading channels. For higher powers of the Gaussian Q-function, we refer to [31: Article 4.1.4]. The following relationships are applied: $$ Q\left(\beta \right)=2{Q}_a\left(\beta, \frac{\pi }{2}\right) $$ $$ {Q}^2\left(\beta \right)=2{Q}_a\left(\beta, \frac{\pi }{4}\right) $$ $$ \begin{array}{l}{Q}^3\left(\beta \right)=Q\left(\beta \right){Q}^2\left(\beta \right)\\ {}{Q}^3\left(\beta \right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]} exp\left(-\frac{\beta^2}{2{sin}^2\theta}\right)d\theta \\ {}+\frac{1}{2{\pi}^2}{\displaystyle \underset{0}{\overset{sin^{-1}\left(1/\sqrt{3}\right)}{\int }}\left\{\pi -{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]\right\}} exp\left(-\frac{\beta^2}{2{sin}^2\theta}\right)d\theta \end{array} $$ $$ \begin{array}{l}{Q}^4\left(\beta \right)={Q}^2\left(\beta \right){Q}^2\left(\beta \right)\\ {}{Q}^4\left(\beta \right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]} exp\left(-\frac{\beta^2}{2{sin}^2\theta}\right)d\theta \end{array} $$ Still we have not eliminated the infinite upper limit in the integrals of (30). We have only simplified the evaluation of higher powers of the Gaussian Q-function yet. Now, if $$ I\left(\beta, \varphi \right)={\displaystyle \underset{0}{\overset{\infty }{\int }}Q\left(\beta \right)}{p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma $$ then from relationships provided in (6) and (32), we can write $$ I\left(D,\varphi \right)=2{\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}_a\left(\sqrt{2D\gamma },\varphi \right)}{p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma $$ This integral can be expressed in terms of MGF of γ (22). Using (31), we get $$ I\left(D,\varphi \right)={\displaystyle \underset{0}{\overset{\infty }{\int }}\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\varphi }{\int }} exp\left[-\frac{D\gamma }{sin^2\theta}\right]d\theta }}{p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma $$ $$ I\left(D,\varphi \right)={\displaystyle \underset{0}{\overset{\varphi }{\int }}\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\infty }{\int }} exp\left[-\frac{D\gamma }{sin^2\theta}\right]}}{p}_{\gamma_{\sum }}\left(\gamma \right) d\gamma d\theta $$ $$ I\left(D,\varphi \right)=\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\varphi }{\int }}{M}_{\gamma}\left(\frac{D}{sin^2\theta}\right)}d\theta $$ Now (40) is applicable to 1st and 2nd power of the Gaussian Q-function. For 3rd and 4th power of the Gaussian Q-function, we define I Q3 (D, φ) and I Q4(D, φ) as: $$ \begin{array}{l}{I}_{Q3}\left(D,\frac{\pi }{6}\right)={\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^3\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma}\\ {}{I}_{Q3}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{M}_{\gamma}\left(\frac{D}{sin^2\theta}\right)d\theta \\ {}+\frac{1}{2{\pi}^2}{\displaystyle \underset{0}{\overset{sin^{-1}\left(1/\sqrt{3}\right)}{\int }}\left\{\pi -{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]\right\}}{M}_{\gamma}\left(\frac{D}{sin^2\theta}\right)d\theta \end{array} $$ $$ \begin{array}{l}{I}_{Q4}\left(D,\frac{\pi }{6}\right)={\displaystyle \underset{0}{\overset{\infty }{\int }}{Q}^4\left(\beta \right){p}_{\gamma_{\sum }}\left(\gamma \right)d\gamma}\\ {}{I}_{Q4}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{M}_{\gamma}\left(\frac{D}{sin^2\theta}\right)d\theta \end{array} $$ Now (30) can be expressed as: $$ \begin{array}{l}{P}_{\mathrm{diversity}}\approx 6\left(1+\frac{1}{3M}-\frac{4}{3\sqrt{M}}\right)I\left(D,\frac{\pi }{2}\right)-15\left(1+\frac{6}{5M}-\frac{7}{3\sqrt{M}}\right)I\left(D,\frac{\pi }{4}\right)\\ {}+20\left(1+\frac{11}{5M}-\frac{61}{20\sqrt{M}}\right){I}_{Q3}\left(D,\frac{\pi }{6}\right)-15\left(1+\frac{46}{15M}-\frac{53}{15\sqrt{M}}\right){I}_{Q4}\left(D,\frac{\pi }{6}\right)\\ {}\end{array} $$ The difference in (30) and (43) is that we have overcome the infinite limits of integration. The SEP expression (43) is used to measure performance of M-ary TQAM in diversity systems using MRC technique. On substituting MGF from (27) in (40), we get following four integrals with finite limits for Rayleigh, Nakagami-m, Nakagami-n, and Nakagami-q fading mediums, respectively as: $$ {I}_{\mathrm{Rayleigh}}\left(D,\varphi \right)=\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\varphi }{\int }}{\displaystyle \prod_{i=1}^L\left[\frac{sin^2\theta }{sin^2\theta +D\overline{\gamma_i}}\right]}}d\theta $$ $$ {I}_m\left(D,\varphi \right)=\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\varphi }{\int }}{\displaystyle \prod_{i=1}^L{\left(1+\frac{\overline{\gamma_i}}{m_i}\frac{D}{sin^2\theta}\right)}^{-{m}_i}}}d\theta $$ $$ {I}_n\left(D,\varphi \right)=\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\varphi }{\int }}{\displaystyle \prod_{i=1}^L\left(\frac{\left(1+{n_i}^2\right)}{1+{n_i}^2+D\overline{\gamma_i}{ \csc}^2\theta } exp\left(\frac{{n_i}^2D\overline{\gamma_i}}{sin^2\theta +{n_i}^2{sin}^2\theta +D\overline{\gamma_i}}\right)\right)}}d\theta $$ $$ {I}_q\left(D,\varphi \right)=\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\varphi }{\int }}{\displaystyle \prod_{i=1}^L{\left(1+\frac{2\overline{\gamma_i}D}{sin^2\theta }+{\left(\frac{2{q}_i\overline{\gamma_i}}{1+{q_i}^2}\right)}^2\frac{D^2}{sin^4\theta}\right)}^{-\frac{1}{2}}}}d\theta $$ Similarly, on substituting MGF from (27) in (41), we get following four integrals with finite limits for Rayleigh, Nakagami-m, Nakagami-n, and Nakagami-q fading mediums, respectively as: $$ \begin{array}{l}{I}_{Q3,\mathrm{Rayleigh}}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{\displaystyle \prod_{i=1}^L\left[\frac{{ \sin}^2\theta }{{ \sin}^2\theta +D\overline{\gamma_i}}\right]}d\theta \\ {}+\frac{1}{2{\pi}^2}{\displaystyle \underset{0}{\overset{{ \sin}^{-1}\left(1/\sqrt{3}\right)}{\int }}\left\{\pi -{cos}^{-1}\left[\frac{3 \cos 2\theta -1}{2{cos}^32\theta }-1\right]\right\}}{\displaystyle \prod_{i=1}^L\left[\frac{{ \sin}^2\theta }{{ \sin}^2\theta +D\overline{\gamma_i}}\right]}d\theta \end{array} $$ $$ \begin{array}{l}{I}_{Q3,m}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{\displaystyle \prod_{i=1}^L{\left(1+\frac{\overline{\gamma_i}}{m_i}\frac{D}{sin^2\theta}\right)}^{-{m}_i}}d\theta \\ {}+\frac{1}{2{\pi}^2}{\displaystyle \underset{0}{\overset{sin^{-1}\left(1/\sqrt{3}\right)}{\int }}\left\{\pi -{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]\right\}}{\displaystyle \prod_{i=1}^L{\left(1+\frac{\overline{\gamma_i}}{m_i}\frac{D}{sin^2\theta}\right)}^{-{m}_i}}d\theta \end{array} $$ $$ \begin{array}{l}{I}_{Q3,n}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{\displaystyle \prod_{i=1}^L\left(\frac{\left(1+{n_i}^2\right)}{1+{n_i}^2+D\overline{\gamma_i}{csc}^2\theta } exp\left(\frac{{n_i}^2D\overline{\gamma_i}}{sin^2\theta +{n_i}^2{sin}^2\theta +D\overline{\gamma_i}}\right)\right)}d\theta \\ {}+\frac{1}{2{\pi}^2}{\displaystyle \underset{0}{\overset{sin^{-1}\left(1/\sqrt{3}\right)}{\int }}\left\{\pi -{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]\right\}}{\displaystyle \prod_{i=1}^L\left(\frac{\left(1+{n_i}^2\right)}{1+{n_i}^2+D\overline{\gamma_i}{csc}^2\theta } exp\left(\frac{{n_i}^2D\overline{\gamma_i}}{sin^2\theta +{n_i}^2{sin}^2\theta +D\overline{\gamma_i}}\right)\right)}d\theta \end{array} $$ $$ \begin{array}{l}{I}_{Q3,q}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{\displaystyle \prod_{i=1}^L{\left(1+\frac{2\overline{\gamma_i}D}{sin^2\theta }+{\left(\frac{2{q}_i\overline{\gamma_i}}{1+{q_i}^2}\right)}^2\frac{D^2}{sin^4\theta}\right)}^{-\frac{1}{2}}}d\theta \\ {}+\frac{1}{2{\pi}^2}{\displaystyle \underset{0}{\overset{sin^{-1}\left(1/\sqrt{3}\right)}{\int }}\left\{\pi -{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]\right\}}{\displaystyle \prod_{i=1}^L{\left(1+\frac{2\overline{\gamma_i}D}{sin^2\theta }+{\left(\frac{2{q}_i\overline{\gamma_i}}{1+{q_i}^2}\right)}^2\frac{D^2}{sin^4\theta}\right)}^{-\frac{1}{2}}}d\theta \end{array} $$ Treating (42) in similar fashion with (27), we get I Q4(D, φ) for the stated fading mediums. $$ {I}_{Q4,\mathrm{Rayleigh}}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{\displaystyle \prod_{i=1}^L\left[\frac{sin^2\theta }{sin^2\theta +D\overline{\gamma_i}}\right]}d\theta $$ $$ {I}_{Q4,m}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{\displaystyle \prod_{i=1}^L{\left(1+\frac{\overline{\gamma_i}}{m_i}\frac{D}{sin^2\theta}\right)}^{-{m}_i}}d\theta $$ $$ {I}_{Q4,n}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{\displaystyle \prod_{i=1}^L\left(\frac{\left(1+{n_i}^2\right)}{1+{n_i}^2+D\overline{\gamma_i}{csc}^2\theta } exp\left(\frac{{n_i}^2D\overline{\gamma_i}}{sin^2\theta +{n_i}^2{sin}^2\theta +D\overline{\gamma_i}}\right)\right)}d\theta $$ $$ {I}_{Q4,q}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}{\displaystyle \prod_{i=1}^L{\left(1+\frac{2\overline{\gamma_i}D}{sin^2\theta }+{\left(\frac{2{q}_i\overline{\gamma_i}}{1+{q_i}^2}\right)}^2\frac{D^2}{sin^4\theta}\right)}^{-\frac{1}{2}}}d\theta $$ Since the four integrals from (44) to (55) are finite range, single integrals and integrand composed of elementary functions only; using (43), the average SEP of general modulation order TQAM with MRC spatial diversity over fading channels can be conveniently assessed through numerical integration methods. Numerical results and discussion Here, we verify our analytical formulas using computer simulations. In Fig. 3, (15) is compared with the SEP approximation provided in ([7]: equation (5)). Figure 3 shows the SEP of 16-TQAM and 64-TQAM against SNR in AWGN channel, and it is observed that our expression for exact SEP (15) completely agrees with the simulation curve. Figures 4 and 5 show symbol error rate performance of 16-TQAM and 64-TQAM over Rayleigh fading channel using MRC diversity scheme, respectively. In Fig. 4, comparison has been made with the SQAM results provided in [15]. We investigate the effect of m, the Nakagami-m fading parameter (m ≥ 0.5), in Figs. 6 and 7, which displays the SEP performance of M = 16 and M = 64 for Nakagami-m channel against SNR with MRC reception, where m = 2, 4. Figure 6 shows comparison with SQAM [16]. Figures 8 and 9 explain the SEP performance in Nakagami-n channel, where K = n 2 and various values of K considered are K = 1 dB, 7 dB. Here, n is the Nakagami-n fading parameter, which ranges from 0 to ∞. For comparison with SQAM, we apply the results of [17] in Fig. 8. Similarly from Figs. 10 and 11, we confirm analytical expression for Nakagami-q fading channel derived in (43) along with (47), (51), and (55) for q = 0, 0.3, where q is the Nakagami-q fading parameter (0 ≤ q ≤ 1). Comparison with SQAM [22] is shown in Fig. 10 for Nakagami-q medium. SEP performance of M-TQAM in AWGN channel SEP performance of 16-TQAM in Rayleigh channel SEP Performance of 16-TQAM in Nakagami-m Channel SEP performance of 16-TQAM in Nakagami-n channel SEP performance of 16-TQAM in Nakagami-q channel Table 2 provides power gains achieved because of using antenna array instead of single antenna in MRC scenario. We observe quite significant power gain, as L increases. The highest gain is obtained by going from single antenna to two-branch diversity. Now, as the diversity paths are increased from two to three, the power gain lessens as it was for going from one to two, generally as we keep on increasing L, the power gain diminishes. The gains for Nakagami-m, m = 1, and Nakagami-q, q = 1, are same as for the Rayleigh fading channel. It is clearly observed that the system performance improves as the diversity order increases. The results illustrate the advantage of diversity as a means for combating the fading phenomena. Table 2 Power gains for TQAM with MRC diversity scheme at P e = 10−2 To further validate the analytical SEP expressions (43) to (55) for M-ary TQAM in MRC, we simulate an example. We take five diversity branches, each with different type of channel fading. The experiment is performed over both 16-TQAM and 64-TQAM, respectively. Following are the channel fadings being considered over different diversity branches: First branch: Rayleigh fading Second branch: Nakagami-m fading (m = 2) Third branch: Nakagami-m fading (m = 4) Fourth branch: Nakagami-q fading (q = 0) Fifth branch: Nakagami-q fading (q = 0.3) Now to evaluate the analytical expression for this experiment, we use (43); however, the integrals are evaluated using (56), (57), and (58) as below: $$ \begin{array}{l}I\left(D,\varphi \right)=\frac{1}{\pi }{\displaystyle \underset{0}{\overset{\varphi }{\int }}\left[\frac{sin^2\theta }{sin^2\theta +D\overline{\gamma}}\right]\left[{\left(1+\frac{\overline{\gamma}}{2}\frac{D}{sin^2\theta}\right)}^{-2}\right]\left[{\left(1+\frac{\overline{\gamma}}{4}\frac{D}{sin^2\theta}\right)}^{-4}\right]}\\ {}\left[{\left(1+\frac{2\overline{\gamma}D}{sin^2\theta}\right)}^{-\frac{1}{2}}\right]\left[{\left(1+\frac{2\overline{\gamma}D}{sin^2\theta }+{\left(\frac{2(0.3)\overline{\gamma}}{1+{0.3}^2}\right)}^2\frac{D^2}{sin^4\theta}\right)}^{-\frac{1}{2}}\right]d\theta \end{array} $$ $$ \begin{array}{l}{I}_{Q3}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}\left[\frac{sin^2\theta }{sin^2\theta +D\overline{\gamma}}\right]\left[{\left(1+\frac{\overline{\gamma}}{2}\frac{D}{sin^2\theta}\right)}^{-2}\right]\\ {}\left[{\left(1+\frac{\overline{\gamma}}{4}\frac{D}{sin^2\theta}\right)}^{-4}\right]\left[{\left(1+\frac{2\overline{\gamma}D}{sin^2\theta}\right)}^{-\frac{1}{2}}\right]\left[{\left(1+\frac{2\overline{\gamma}D}{sin^2\theta }+{\left(\frac{2(0.3)\overline{\gamma}}{1+{0.3}^2}\right)}^2\frac{D^2}{sin^4\theta}\right)}^{-\frac{1}{2}}\right]d\theta \\ {}+\frac{1}{2{\pi}^2}{\displaystyle \underset{0}{\overset{sin^{-1}\left(1/\sqrt{3}\right)}{\int }}\left\{\pi -{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]\right\}}\left[\frac{sin^2\theta }{sin^2\theta +D\overline{\gamma}}\right]\left[{\left(1+\frac{\overline{\gamma}}{2}\frac{D}{sin^2\theta}\right)}^{-2}\right]\\ {}\left[{\left(1+\frac{\overline{\gamma}}{4}\frac{D}{sin^2\theta}\right)}^{-4}\right]\left[{\left(1+\frac{2\overline{\gamma}D}{sin^2\theta}\right)}^{-\frac{1}{2}}\right]\left[{\left(1+\frac{2\overline{\gamma}D}{sin^2\theta }+{\left(\frac{2(0.3)\overline{\gamma}}{1+{0.3}^2}\right)}^2\frac{D^2}{sin^4\theta}\right)}^{-\frac{1}{2}}\right]d\theta \end{array} $$ $$ \begin{array}{l}{I}_{Q4}\left(D,\frac{\pi }{6}\right)=\frac{1}{\pi^2}{\displaystyle \underset{0}{\overset{\raisebox{1ex}{$\pi $}\!\left/ \!\raisebox{-1ex}{$6$}\right.}{\int }}{cos}^{-1}\left[\frac{3 cos2\theta -1}{2{cos}^32\theta }-1\right]}\left[\frac{sin^2\theta }{sin^2\theta +D\overline{\gamma}}\right]\left[{\left(1+\frac{\overline{\gamma}}{2}\frac{D}{sin^2\theta}\right)}^{-2}\right]\\ {}\left[{\left(1+\frac{\overline{\gamma}}{4}\frac{D}{sin^2\theta}\right)}^{-4}\right]\left[{\left(1+\frac{2\overline{\gamma}D}{sin^2\theta}\right)}^{-\frac{1}{2}}\right]\left[{\left(1+\frac{2\overline{\gamma}D}{sin^2\theta }+{\left(\frac{2(0.3)\overline{\gamma}}{1+{0.3}^2}\right)}^2\frac{D^2}{sin^4\theta}\right)}^{-\frac{1}{2}}\right]d\theta \\ {}\end{array} $$ The simulation result for this example is shown in Fig. 12. A good fit of SEP simulation curve over the theoretical curve adds to the validity of our analytical expressions derived in Section 4. SEP performance of M-ary TQAM in various fading channels, L = 5 In this article, the SEP performance of TQAM with MRC spatial diversity over independent but not necessarily identical multi-branch fading channels, including Rayleigh, Nakagami-m, Nakagami-n, and Nakagami-q channels, have been evaluated based on the unified MGF-based approach. The SEP expressions are simple and accurate and can be applied to any even-bit general modulation order TQAM. These SEP expressions consist of single integrals with finite limits and integrand composed of elementary functions only, which can be accurately evaluated numerically. The simulation results, along with the example, also confirm the efficacy of numerical expressions obtained for the abovementioned channels. So, by choosing only the modulation order of the constellation and the diversity order of MRC, we can study the impact of diversity reception, which removes the need for Monte Carlo simulations to optimize any wireless system parameters using TQAM. MGF: moment-generating function MIMO: multi-input multi-output MRC: maximal-ratio combining QAM: quadrature amplitude modulation SEP: symbol error probability SIMO: single-input multi-output SNR: SQAM: square quadrature amplitude modulation TQAM: triangular quadrature amplitude modulation CR Cahn, Combined digital phase and amplitude modulation communication system. IRE Trans. Commun. Syst. 8(3), 150–155 (1960) JC Hancock, RW Lucky, Performance of combined amplitude and phase modulated communications system. IRE Trans. Commun. Syst. 8(4), 232–237 (1960) CN Campopiano, BG Glazer, A coherent digital amplitude and phase modulation scheme. IRE Trans. Commun. 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Department of Electrical Engineering, College of Electrical and Mechanical Engineering, National University of Sciences and Technology, Islamabad, Pakistan Furqan Haider Qureshi , Shahzad Amin Sheikh , Qasim Umar Khan & Fahad Mumtaz Malik Search for Furqan Haider Qureshi in: Search for Shahzad Amin Sheikh in: Search for Qasim Umar Khan in: Search for Fahad Mumtaz Malik in: Correspondence to Furqan Haider Qureshi. Qureshi, F.H., Sheikh, S.A., Khan, Q.U. et al. SEP performance of triangular QAM with MRC spatial diversity over fading channels. J Wireless Com Network 2016, 5 (2016). https://doi.org/10.1186/s13638-015-0511-2 AWGN Fading channel Nakagami-m Nakagami-q	CommonCrawl
Genome-wide expression profiling in muscle and subcutaneous fat of lambs in response to the intake of concentrate supplemented with vitamin E Laura González-Calvo1, Elda Dervishi2, Margalida Joy1, Pilar Sarto1, Roberto Martin-Hernandez3, Magdalena Serrano4, Jose M. Ordovás5 & Jorge H. Calvo1,6 BMC Genomics volume 18, Article number: 92 (2017) Cite this article The objective of this study was to acquire a broader, more comprehensive picture of the transcriptional changes in the L. Thoracis muscle (LT) and subcutaneous fat (SF) of lambs supplemented with vitamin E. Furthermore, we aimed to identify novel genes involved in the metabolism of vitamin E that might also be involved in meat quality. In the first treatment, seven lambs were fed a basal concentrate from weaning to slaughter (CON). In the second treatment, seven lambs received basal concentrate from weaning to 4.71 ± 2.62 days and thereafter concentrate supplemented with 500 mg dl-α-tocopheryl acetate/kg (VE) during the last 33.28 ± 1.07 days before slaughter. The addition of vitamin E to the diet increased the α-tocopherol muscle content and drastically diminished the lipid oxidation of meat. Gene expression profiles for treatments VE and CON were clearly separated from each other in the LT and SF. Vitamin E supplementation had a dramatic effect on subcutaneous fat gene expression, showing general up-regulation of significant genes, compared to CON treatment. In LT, vitamin E supplementation caused down-regulation of genes related to intracellular signaling cascade. Functional analysis of SF showed that vitamin E supplementation caused up-regulation of the lipid biosynthesis process, cholesterol, and sterol and steroid biosynthesis, and it down-regulated genes related to the stress response. Different gene expression patterns were found between the SF and LT, suggesting tissue specific responses to vitamin E supplementation. Our study enabled us to identify novel genes and metabolic pathways related to vitamin E metabolism that might be implicated in meat quality. Further exploration of these genes and vitamin E could lead to a better understanding of how vitamin E affects the oxidative process that occurs in manufactured meat products. Vitamin E is a lipid-soluble essential component of human and animal diets due to its powerful antioxidant activity. There are eight different isoforms of vitamin E, and the most active isoform for cell protection appears to be α-tocopherol [1]. Alpha-tocopherol is a cell signaling molecule involved in a broad range of effects on cellular systems [2] and specific regulation of gene expression [2–6]; therefore, α-tocopherol can influence a number of biological functions by regulating cell signaling at both the mRNA and microRNA (miRNA) levels [7]. So far, the impact and beneficial effects of vitamin E in the prevention of chronic diseases have been mainly associated with its antioxidant properties [8]. Vitamin E is extensively used in animal diets as an antioxidant supplement. Feeding strategy is an important tool to manipulate intramuscular α-tocopherol content in animals. An increase in α-tocopherol intake can be achieved through grazing systems [9] or by feeding animals with concentrate supplemented with α-tocopherol, which can be used as an effective method to reduce the oxidative processes reported in meat products [10, 11]. During oxidative processes, the muscle haeminic pigment changes from red oxymyoglobin to brown metmyoglobin, giving the meat an undesirable brownish color [9]. Moreover, lipid oxidation results in the production of free radicals, which are linked to the formation of off-flavors and odors, a reduction in polyunsaturated fatty acids and the production of undesirable compounds, such as potentially toxic peroxides and aldehydes [12]. All of these modifications cause decreases in the freshness and quality of meat and lower consumer acceptance, resulting in considerable economic loss for the meat industry. So far, efforts to discover the genes and metabolic pathways involved in vitamin E metabolism have mainly focused on rodents. These studies have reported important long-term effects of vitamin E deficiency on liver gene expression, up-regulation of genes involved in cholesterol synthesis and steroidogenesis, lipid uptake, and anti-oxidative mechanisms [3, 13]. In addition, vitamin E in the rat brain affected genes associated with hormones, nerve growth, apoptosis, dopaminergic neurotransmission, and clearance of amyloid-α [14]. Furthermore, genes encoding for muscle structure and extra cellular matrix and those involved in anti-oxidative and anti-inflammatory processes were up-regulated in rat skeletal muscle in response to vitamin E deficiency [15]. Although nutritional science has embraced the tools of genomics, including cDNA arrays in rodent models, few attempts at large-scale or global evaluation of nutritional gene regulation have mainly used rodents as a model. Only a small number of genes are currently known to be related to vitamin E metabolism in muscle or fat. In the last few years, several studies have explored the transcriptomic adaptations of skeletal muscle in response to different nutrition variables in ruminants [16–19]. Data from these studies have allowed scientists to identify the biochemical mechanisms that could be associated with key physiological processes in animals and to define specific markers for evaluating meat quality. A better understanding of the genes and metabolic pathways associated with vitamin E metabolism is critical for identifying the key physiological processes associated with vitamin E content, oxidative stress and other metabolic pathways associated with meat quality. The main effect of vitamin E on meat is to change the lipid oxidation and thus to increase shelf-life of meat. Because lipid oxidation depends mainly on enzyme activity, post-transcriptional and post-translational changes are processes implicated in the shelf-life of meat. However, the identification of genes related to vitamin E content would be a good starting point for candidate gene selection and single nucleotide polymorphism (SNP) association studies with variations in vitamin E content and therefore implicated in meat quality. Furthermore, non-antioxidant roles of vitamin E, serving as a regulator of gene/protein, have been described. In this sense, transcriptomic analysis of skeletal muscle could identify metabolic pathways modified by vitamin E that could influence meat traits. Therefore, the main objective of this study was to investigate transcriptional changes in the L. Thoracis muscle (LT) and subcutaneous fat (SF) of lambs supplemented with vitamin E using the Affymetrix Ovine Gene 1.1 ST whole-genome array. Furthermore, we aimed to identify novel genes that could play important roles in the metabolism of vitamin E and that might be associated with meat quality traits. Alpha-tocopherol muscle content, intramuscular fat, TBARS and metmyoglobin formation Significant differences in weaning weight and slaughter age (SA), and average daily gain (ADG), from birth to weaning and from birth to slaughter, were found between treatments (Table 1). Animals from the CON group were younger at slaughter (P < 0.05). In addition, these animals had greater ADG from birth to weaning (P < 0.01) and from birth to slaughter (P < 0.05). During the experimental period, the ADG from weaning to slaughter was not significant between treatments. Average daily gain from birth to slaughter and SA were highly correlated between them (r 2 = -0.90; P < 0.01). The results of α-tocopherol content, intramuscular fat (IMF) content, thiobarbituric acid-reactive substances (TBARS) and metmyoglobin (MMb) formation in the LT muscle for each treatment are shown in Table 1. Our results showed that the content of α-tocopherol in the muscle was significantly higher in lambs that received a basal concentrate supplemented with dl-α-tocopheryl acetate (VE), while lambs fed a basal concentrate (CON) showed higher values of TBARS (mg of malonaldehyde per kg of L. Thoracis) (P < 0.05). Furthermore, metmyoglobin formation was significantly lower in VE lambs, compared to the CON group (P < 0.05). The K/S572/525 ratio decreased when the metmyoglobin content increased. Intramuscular fat (IMF) content was not different between the treatments (P > 0.05). Table 1 Effect of the dietary treatment on slaughter age and weight, growth rate, alpha-tocopherol muscle content, intramuscular fat, TBARS and metmyoglobin formation Microarray gene expression results Identification and classification of differentially expressed genes by microarray analysis in LT and SF Significance analysis of microarray (SAM) was performed to compare the VE treatment with CON. SAM identified a total of 29 genes with a false discovery rate (FDR) = 0.008, 26 down- regulated and 3 up-regulated genes (Table 2). The results of SAM regarding LT muscle are shown in Fig. 1. Table 2 The significant features identified by SAM in VE vs. CON contrast in L. Thoracis muscle Significant features identified by SAM in a VE-CON contrast in LT, and b VE-CON contrast in SF. The green circles represent features that exceed the specified threshold Regarding subcutaneous fat, when VE treatment was compared with the CON group, SAM identified a total of 330 genes with a FDR < 0.001. Among these genes, 295 were up-regulated, and 35 were down-regulated. The results of the top 50 genes identified with SAM for SF are shown in Table 3. In Additional file 1: Table S1 all of the significant genes in SF are ranked according to their fold change (FC). Notably, H1F0 gene was found to be significantly down-regulated in VE lambs in both tissues. Table 3 Top 50 genes identify with SAM in VE vs. CON contrast in subcutaneous fat Treatment-dependent multivariate analysis results of gene expression In the LT muscle, principal component analysis (PCA) of the complete set of 32 genes identified by SAM showed that the first 2 PCs covered 39.7% of the observed variance in the sample set (Fig. 2a). The PCA score plot revealed differences corresponding to lambs fed with the two different treatments. The ellipse corresponding to CON was clearly separated from the VE treatment. Partial least squares-discriminate analysis (PLS-DA) showed a clear separation of the two groups (Fig. 2b). In addition, PLS-DA allowed for the identification of the genes that were most important for the separation observed in the score plots. DEF8 gene showed the highest score, followed by ASPN and AKR7A2 (Fig. 2c). Moreover, we investigated trends or patterns in gene expression changes (Fig. 2d). For example, ABCC4, DEPTOR, IGFR1, MYLK2 and ACAT1 were positively correlated with each other in the two treatments, showing a down- and up-regulation in the VE and CON treatments, respectively. In contrast, they were negatively correlated with SAT1, ASPN, or LRRTM2. These genes, which are either positively or negatively correlated with each other, appeared to play an important role in light of the PCA and PLS-DA cluster analysis. Multivariate analysis based on gene expression profile data in LT muscle. a Principal component analysis (PCA) score plots distinguishing between the LT muscle of lambs fed concentrate (triangle), and supplemented with vitamin E in the treatment, (+). b Partial least squares-discriminant analysis (PLC-DA) based on gene expression profile data. c Important features identified by PLS-DA. The top 15 genes are ranked by VIP scores. The colored boxes on the right indicate the relative expression of the corresponding gene in each group under study. d A bar graph showing the top 25 genes correlating with diet (CON, VE). Variables with the same distance from 0 with similar positions are positively correlated. Those with the opposite direction are negatively correlated. The light blue bars indicate genes showing a negative correlation, and the light pink bars indicate those with a positive correlation with the given pattern of change of treatment Multivariate analysis results from subcutaneous fat were used to cluster the samples based on gene expression profiles of animals fed two different diets: CON and VE. The PCA of the complete set of 330 genes identified by SAM showed that the first 2 PCs covered 68% of the observed variance of the sample set (Fig. 3a). The figure shows the score plot of the two first principal components extracted in this study. PLS-DA showed that the VE and CON groups were clearly separate from each other. (Fig. 3b). In addition, PLS-DA allowed for the identification of the most important genes contributing to the separation observed in the score plots, and ALG11 had the highest score, followed by SRPBR and PPX47. Multivariate analysis based on gene expression profile data in subcutaneous fat. a Principal component analysis (PCA) score plots distinguishing between the subcutaneous fat of lambs fed concentrate (triangle), and supplemented with vitamin E in the treatment (+). b Partial least squares-discriminant analysis (PLC-DA) based on gene expression profile data. c Important features identified by PLS-DA. The top 15 genes are ranked by VIP scores. The colored boxes on the right indicate the relative expression of the corresponding gene in each group under study. d A bar graph showing the top 25 genes correlating with treatment (CON, VE). Variables with the same distance from 0 with similar positions are positively correlated. Those with the opposite direction are negatively correlated The light pink bars indicate genes with a positive correlation with the given pattern of change of treatment Moreover, we investigated patterns in gene expression changes in subcutaneous fat (Fig. 3d). For example, the gene expressions of ALG11, SRPBR, and PPX47 were positively correlated with each other, being up-regulated in VE treatment. Hierarchical clustering analysis (HCA) HCA was performed using the significant genes obtained by SAM for both contrasts. The results of HCA for LT muscle are presented in Fig. 4a. The expression profile of these genes was able to cluster and to classify correctly the samples within their corresponding groups. The heatmap shows the presence of 2 different clusters containing different genes. The responses of each variable to the two different treatments are indicated with changes in the color intensity on the heatmap. The VE and CON groups showed very different gene expression patterns. For instance, LRRTM2, ASPN and SAT1 were up-regulated in the VE group. Furthermore, a second cluster including the remainder of the genes was found to be down-regulated in the VE group. These two clusters distinguished the VE group from the CON group. These genes are involved in different metabolic processes. Hierarchical clustering analysis of gene expression in a) the L. Thoracis muscle, b) subcutaneous fat tissue of lambs receiving different treatments (CON and VE), using the most significant genes of each contrast. Cells are colored based on the signal intensity measured. Dark brown represents high gene expression levels, blue indicates low signal intensity, and gray indicates the intermediate level (see color scale above the heatmap) Regarding subcutaneous fat, the results of clustering analysis of top 50 genes are presented in Fig 4b. Analyzing the heatmap, it can be observed that the CON group showed very different gene expression patterns from the VE group. There is a general down-regulation of gene expression in the CON group and an up-regulation of gene expression in the VE group. The results of clustering analysis of the total 330 genes in subcutaneous fat were similar to the 50 genes analysis results, but one VE animal was clustered in the CON group (Additional file 2: Figure S1). More specifically, 34 genes were down- regulated in the VE group (SOD3, CLEC3B, METTL7A, IER3, PLK2, CLEC1A, HSPA1A, TNFSF10, MERTK, MLLT3, TPPP2, HMGB2, PECAM1, IFITM3, H1F0, HMG20B, GALK1, NFIL3, CDH5, ERG, CEBPA, ANKRD44, HCST, UACA, IFITM1, RPL10, PID1, LUC7L3, H3F3A, AMOTL2, PSIP1, RPL17, TRA2A, and RPS259). Functional clustering annotation In the LT muscle, the results of Database for Annotation, Visualization and Integrated Discovery (DAVID) functional annotation clustering (FAC), including the 29 significant genes in the VE-CON contrast, showed that 4 genes from the "intracellular signaling cascade" (IGF1R, DEF8, AKAP7 and CISH) had the most enrichment and were all down-regulated in the VE treatment (Additional file 3: Table S2). However, the confident enrichment scores were less than 1.3 in both cases. In subcutaneous fat, the results of DAVID FAC of 330 significant genes in the VE-CON contrast, revealed that the most significantly enriched cluster was "lipid biosynthesis process", (enrichment score of 5.38) with a total of 20 genes involved (PGAP3, EBP, CRLS1, MVD, CYP51A1, GNE, HMGCS1, DPAGT1, LSS, SIGMAR1, LPCAT3, FDFT1, DOLK, PIGM, SQLE, DHCR7, AGPAT9, LTA4H, PCYT2 and HSD17B7), all of them up-regulated in the VE group compared to the CON group. Many of these genes play roles in the cholesterol, sterol and steroid biosynthesis. In Table 4, the DAVID FAC results of the 330 genes in the VE-CON contrast are shown. Table 4 DAVID Functional Annotation Clustering of SAM genes in VE vs. CON subcutaneous fat Validation of microarrays results using qPCR Thirteen genes were selected to validate the microarray results by quantitative real-time PCR (qPCR). The gene set included 4 genes in muscle and 9 genes in subcutaneous fat. In LT muscle, the genes were selected because they were significant differentially expressed between the VE and CON treatments (CISH, ABCC4, ACAT1 and IGF1R). In SF, the significant genes in the VE-CON contrast (LDLR, SOD3, SQLE, SREBF1, MTTL1, HAX1, HMGB2, HSPB8 and IER3) were selected. Although the magnitude of FC obtained by microarray and qPCR was slightly different in some instances, the qPCR results demonstrated a similar trend compared with the microarray results of these 13 genes, demonstrating the reliability of microarray analysis (Pearson's correlation coefficient 0.99, P = 0.008 for LT muscle and 0.99, P < 0.001 for SF) (Table 5). Table 5 Real-time PCR confirmation of the microarray results The aim of the present study was to assess the effects of adding VE to the fattening concentrate, fed between weaning and slaughter, on the transcriptional changes in the LT and SF. The experimental period ended when the lambs reached the target slaughter LW (22–24 kg), according to the specifications of Ternasco de Aragón Protected Geographical Indication (Regulation (EC) No. 1107/96). The light lamb production is based on two periods: suckling and fattening. The suckling period is usually limited by the time, usually lasting approximately 45 d (in the present study, it was 48 d), while the fattening period is limited by the weight (22–24 kg LW). Thus, lambs with high ADG during lactation period spent fewer days in the fattening period than those with low ADG. To be able to evaluate the potential effects of the inclusion of VE on the transcriptome of the L. Thoracis muscle and subcutaneous fat, we planned to feed at least 30 days of VE concentrate. According to Ripoll et al. [11], supplementation with VE for 30 days was found to increase noticeably concentration of the α-tocopherol content in muscle. In the present study, the ADG during the experimental period was not different, however during the suckling period it was lower in VE treatment (p < 0.01; Table 1). This implies that the lambs of the VE treatment during the suckling period presented lower growth compared to the CON group and needed more days to reach the target weight. Moreover, there was a strong correlation between ADG from birth to slaughter and SA (r 2 =−0.9). Therefore, to overcome this unbalance between treatments ADG values were included as covariates in the statistical model used to validate gene expression differences by qPCR, thus avoiding estimation biases. We analyzed LT muscle and SF because meat cuts for human consumption include both intramuscular and subcutaneous fat [20], constituting the total amount of meat fat purchased at retail. The results related to the content of α-tocopherol in the muscle and TBARS confirm what was planned in the methodology. Vitamin E has been successfully used to increase the muscle α-tocopherol and to reduce lipid oxidation in beef and chicken meat [21]. In this study, as expected, there were significant differences between both diets in the α-tocopherol content, lipid oxidation and MMb formation in the LT muscle, as previously found by Ripoll et al. [11]. Moreover, TBARS values were lower in VE lambs which showed that the lipid oxidation process was slower in animals fed this type of diet. In the present study, we used microarray technology to study changes in gene expression profiles in LT muscle and SF in response to vitamin E supplementation in lambs. Our results, showed that vitamin E supplementation caused different responses in gene expression in LT muscle and SF, suggesting a specific response of tissue to vitamin E supplementation. In our study, we did not measure the concentration of VE in the SF, however the gene expression results might be related to the greater α-tocopherol accumulation in adipose tissues than in skeletal muscles [22, 23]. It has been reported that α-tocopherol can influence a number of biological functions by regulating cell signaling at both the mRNA and miRNA levels [7]. Indeed, our results showed that vitamin E supplementation affected the expression of 29 genes in the LT muscle. The results of functional analysis showed that genes related to the intracellular signaling cascade (CISH, IGF1R, DEF8, and AKAP7) and metabolic processes (ZNF79, MAFB, MYLK2, ACACB, ACAT1, CISH, IGF1R, PGLS, DUSP26, AKR7A2, FBXL4, AKAP7, and RSC1A1) were down-regulated. The enrichment scores were less than 1.3, likely because the number of significant genes in this contrast was low. The most down-regulated gene by vitamin E in LT was CISH (Cytokine Inducible SH2 containing protein). Chen et al. [24] reported that CISH activates protein kinase C (PKC) activity by G-protein coupled receptor protein, which is important for the activation of both the activator protein 1 (AP-1) and nuclear factor- κB (NF-κB) pathways. In a previous study Boscoboinik et al. [25], demonstrated that PKC is inhibited by α-tocopherol. NF-κB proteins are a family of transcription factors and are of central importance in inflammation, immunity and apoptosis [26]. Evidence suggests a role for reactive oxidative intermediates (ROIs) as a common and critical intermediate for various NF-κB-activating signals, based on inhibition of NF-κB activation by a variety of antioxidants [27, 28]. There is a bidirectional relationship between cytokines and oxidative stress. Exposure of myotubes to reactive oxygen species (ROS)-producing agents resulted in an increase in interleukin 6 (IL-6) release through the activation of the redox-sensitive transcription factor, NF-κB [28]. In this sense, IL-6 induces marked increases in expression of CISH, SOCS-1, SOCS-2, and SOCS-3 in tissues, which in turn result in inhibition of the signaling of wide range of cytokines [29]. Thus, CISH expression could be related to oxidative status in the muscle. In this sense, low levels of ROS and ROIs in muscle caused by α-tocopherol could be associated with low expression of CISH. In this sense, lipid oxidation in the LT muscle and metmyoglobin formation were lower when lambs were supplemented with VE. In the same manner, RSC1A, which inhibits a dynamin and PKC-dependent exocytotic pathway of SLC5A1 gene, was down-regulated in the VE group. Interestingly enough CISH and MYLK, also down-regulated in the VE treatment, are involved in inflammation mediated by chemokine and cytokines signaling pathway, which could suggest another possible role for VE that of decreased inflammation. In our study, alterations of the Ras homolog gene family, member A (RhoA) and actin cytoskeleton signaling were identified (IGF1R and MYLK2 genes). Both IGF1R and MYLK2 were down-regulated in VE treatment. Insulin-like growth hormone 1 (IGF-1) is a protein structurally similar to insulin, and it regulates tissue growth and development in several vertebrates [30]. As a main receptor of IGFs, IGF1R mediates the transduction of metabolic signals of cell proliferation, bone growth, and protein synthesis in the GH/IGF pathway [31]. In our study, IGF1R was down-regulated in VE treatment, and because of IGF1R polymorphisms have been associated to growth traits [32–36], we thought that this effect could be due to the higher ADG in CON animals. However, ADG values were included as a covariate in the statistical model used to validate expression differences by qPCR, thus avoiding estimation biases related to ADG. Therefore these results suggest that supplementation with VE causes down-regulation of IGF1R in LT muscle. Our findings are in agreement with Araujo et al. [37], who showed that VE supplementation reduces IGF1R expression by 17% in hyperthyroid of Wistar rats. In addition, Chuang et al. [38] also found that VE alone significantly and dose-dependently reduced the cell surface expression of IGFIR in HL-60 cells. Moreover, Holzenberger et al. [39] reported that Igf1r +/−mice display greater resistance to oxidative stress. In addition, vitamin E down-regulated two genes related to lipid metabolisms (ACAT1 and ACACB) in the LT muscle. ACAT1 (acetyl-coenzyme A acetyltransferase 1) encodes a mitochondrial localized enzyme that catalyzes the reversible formation of acetoacetyl- CoA from two molecules of acetyl-CoA. ACAT1 is responsible for cholesterol homeostasis and maintain appropriate cholesterol availability in cell membranes, whereas ACACB is the key regulator of the fatty acid oxidation pathways [40]. It controls fatty acid oxidation by means of the ability of malonyl-CoA to inhibit carnitine-palmitoyl-CoA transferase I (CPT1B). As in our work, Shige et al. [41] showed that vitamin E reduced the uptake of modified low-density lipoprotein (LDL) and suppressed ACAT activity, resulting in less cholesterol esterification in macrophages. Interestingly enough ABCC4, an ATP-binding cassette (ABC) transporter, AKR7A2 which is involved in the detoxification of aldehydes and ketones, and finally RSC1A1 which transport carbohydrate across the plasma membrane, were all down- regulated with VE treatment. In hepatocytes, ABCC4 was shown to be induced by oxidative stress through binding of the oxidative sensor nuclear factor E2-related factor 2 (Nrf2) to antioxidant-responsive element sequences in the promoter of ABCC4 [42]. Our results showed for the first time that vitamin E down-regulates ABCC4 expression. Because of significant differences in ADG between treatments, we validated the expression results of the CISH, ABCC4, ACAT1 and IGFR1 genes by qPCR, including in the statistical model ADG as a covariate. ADG was not significant, with a similar FC between the microarray and qPCR results (r 2 = 0.99; P = 0.008). Therefore, treatment was the main effect over gene expression. In addition, we found that the transcription factors FHL3, ZNF777 and MAFB were down-regulated. Considering all together, our results showed that supplementation with VE increased the content of α-tocopherol in the LT muscle and decreased metmyoglobin formation and lipid oxidation. We speculate that α-tocopherol in the LT muscle causes a decrease in the catalytic activity of enzymes involved in cellular transport of fatty acids and carbohydrates, and fatty acid oxidation in the mitochondria. Decreased IGF1R expression might be related to the lower lipid oxidation levels in VE animals. We also found that IGFR1, ABCC4 ACAT1, CISH, ACACB, MYLK2, ZNF777 and MAFB were positively correlated with each other and with the diet, which suggest co-expression processes of these genes. We speculate that transcription factors ZNF777, MAFB and FHL3 could be important players in mediating the effects of VE in regulating the expression of these genes. To establish whether IGFR1, ABCC4 and ACAT1, CISH are markers of meat oxidation or indirect markers of meat quality, further studies with greater numbers of animals are necessary. A most dramatic effect of VE was observed on SF gene expression. ALG11, SRPBR, DDX47, SEC23ID and TTC37 were among the most important genes in discriminate fed treatments. These genes were up-regulated and positively correlated with each other and with the diet, which might suggest co-expression processes. Four of the up-regulated genes in the VE group were related to heat shock proteins (HSPs) or chaperonin activity (TTC37, DNAJC16, HSB8, AHSA1). Some HSPs are characterized by various specific functions such as anti-apoptotic or anti-inflammatory effects [43]. In our study, these genes were up-regulated and positively correlated, suggesting putative increased stress protection in VE lambs. Surprisingly VE treatment showed general up-regulation of almost all significant genes, compared to CON treatment. Lipid biosynthetic processes were among the most enriched functional clusters with major biological significance and importance (PGAP3, EBP, CRLS1, MVD, CYP51A1, GNE, HMGCS1, DPAGT1, LSS, SIGMAR1, LPCAT3, FDFT1, DOLK, PIGM, SQLE, DHCR7, AGPAT9, LTA4H, PCYT2, and HSD17B7). Moreover, genes implicated in sterol, steroid and cholesterol biosynthesis processes (SREBF1, EBP, LDLR, MVD, CYP51A1, SQLE, DHCR7, INSIG1, HMGCS1, LSS, and FDFT1) were up-regulated in the SF of VE animals, compared to the CON group. It has been previously reported that tocopherols inhibited de novo cholesterol synthesis within enterocytes [44], and cause repression of genes (DHCR7 and HMGCS1) involved in the de novo synthesis of cholesterol in testes and adrenal glands [45]. The differences reported in previous studies and ours might be due to the different tissues analyzed. This supports even more our idea that there is a tissue specific response in response to VE supplementation. On the other hand, Wang et al. [46] found oxysterol-specific repressive effects in the CYP51A1 and FDFT1 genes, mediated via direct binding of the ligands to liver X receptor (LXR). Because of α–tocopherol and other antioxidants can inhibit the oxidation of cholesterol [47], the VE group could have a lower quantity of oxysterols and then have inhibited the repression of cholesterol biosynthesis via LXR and oxysterols and up-regulated the sterol, steroid and cholesterol biosynthesis processes. In this sense, several genes implicated in "the stress response" (SOD3, IER3, HMGB2, UACA, LUC7L3) were down-regulated in the VE group, compared to the CON group (Table 3 and Supplementary Table S1). Among them, SOD3 showed higher values of FC. This gene encodes a member of the superoxide dismutase (SOD) protein family that protects the extracellular space from the toxic effects of reactive oxygen intermediates by converting superoxide radicals into hydrogen peroxide and oxygen. This finding contradicts the results of previous studies, which suggested that grass-based treatments elevated the activity of antioxidants, such as glutathione and superoxide dismutase (SOD), compared to grain-feeding [1]. However, Kumar et al. [48] in the myocardium muscle and Strobel et al. [49] in the skeletal muscle of exercise-trained and sedentary rats, found that antioxidant supplements reduced the endogenous antioxidants SOD2 gene and protein and the glutathione peroxidase (GPx) gene and enzyme activity. Another down-regulated gene in VE treatment was IER3. IER3-deficient NCM460 cells exhibited reduced reactive oxygen species levels, indicating increased antioxidative protection [50]. In our study, IER3 was down regulated in the VE group suggesting an increase in antioxidative protection. The role of HMGB1 in recognizing aberrant or damaged DNA has been shown in multiple in vitro experiments. A recent study directly showed the accumulation of HMGB1 at sites of oxidative DNA damage in live cells, thus defining HMGB1 as a component of an early DNA damage response [51]. A similar function has been attributed to HMGB2 [52]. These authors hypothesized that HMGB1/2 proteins act as a sensor of DNA modification, and their interaction with chemically altered DNA changes the chromatin structure, thus inducing DNA damage responses. Finally, a cluster related to tRNA metabolic processes was also significant (TRNT1, METTL1, ADAT2, NSUN2, IARS, GARS, EPRS and MARS). Aminoacyl-tRNA synthetases perform an essential function in protein synthesis by catalyzing the esterification of an amino acid to its cognate tRNA (IARS, GARS, EPRS and MARS). Considering all together, we speculate that in the SF, vitamin E exerts anti-inflammatory effect and stress protection by increasing heat shock protein expression. Vitamin E reduces stress response probably as results of reduced reactive oxygen species levels. In addition animals supplemented with VE might have inhibited cholesterol oxidation in SF and enhanced sterol, steroid and cholesterol biosynthesis processes. And finally, we speculate that regulation of these gene expressions it could be mediated through tRNAs IARS, GARS, EPRS and MARS. Regarding LT, we included ADG values as a covariate in the statistical model used to validate the expression differences by qPCR to avoid estimation biases. In this case, ADG was not significant, and a similar FC between microarray and qPCR results was found (r 2 = 0.99; p < 0.0001). Thus, the treatment was also the main effect over gene expression of SF. Although we found differences in mRNA activity, it did not necessarily cause differences in metabolic processes. An increase in gene expression is not necessarily correlated with an increase in protein concentrations or enzyme activities. There are many processes between transcription and translation, including post-transcriptional, translational and protein degradation regulation, in controlling steady-state protein abundances [53]. Moreover, DNA microarray has been the technology of choice for transcriptome analysis in recent years. Nonetheless, array technology has several limitations which include: using microarray technology limits the researcher to detecting transcripts that correspond to existing genomic sequencing information; and background hybridization limits the accuracy of expression measurements, particularly for transcripts present in low abundance. This study demonstrated the beneficial effects of vitamin E supplementation during fattening period in lambs by increasing α-tocopherol content in the LT muscle and diminishing drastically the lipid oxidation of the meat. We observed a tissue-specific response to vitamin E supplementation. The gene expression profiles for VE and CON treatments were different in both LT and SF. Vitamin E supplementation had a dramatic effect on subcutaneous fat gene expression, showing a general up-regulation of genes, compared to CON treatment. Our study enabled us to identify novel genes (for example, IGF1R, ACAT1, ABCC4, ACACB, SOD3, and IER3) and metabolic pathways related to vitamin E metabolism that might be implicated in meat quality. To the best of our knowledge, this study was the first to report the effect of vitamin E supplementation on gene expression in the LT muscle and SF of lambs. Future exploration of these genes is necessary for a better understanding of how vitamin E affects the oxidative processes that occur in meat products. All experimental procedures including the care of animals and euthanasia were performed in accordance with the guidelines of the European Union and with Spanish regulations for the use and care of animals in research and were approved by the Animal Welfare Committee of the Centro de Investigación y Tecnología agroalimentaria (CITA) (protocol number 2009-01_MJT). In all cases, euthanasia was performed by penetrating captive bolt followed by immediate exsanguination. Animals and sample collection Fourteen single reared male lambs of the Rasa Aragonesa breed were weaned at 48.28 ± 0.85 days of age. Seven lambs were fed a basal concentrate from weaning to slaughter (CON treatment, 24 ± 2.62 days). The remaining 7 lambs received for 4.71 ± 2.62 days the same basal concentrate as the CON group, and thereafter until slaughter, they received a similar concentrate with the same characteristics but enriched with 500 mg dl-α-tocopheryl acetate per kg of feed (VE treatment) for 33.28 ± 1.07 days. The ingredients and chemical composition of the feedstuffs are shown in Table 6. Prior to weaning, the CON and VE lambs suckled their mothers and had free access to their concentrates. The average concentrate intake of the CON and VE lambs during the experimental period was 24.3 and 25.1 kg per lamb, respectively. The experimental procedures, management of the animals and sample details for each group are described in detail in Ripoll et al. [11]. Table 6 Ingredients and chemical composition of the feedstuffs used in the experiment All of the lambs were slaughtered when they attained 22–24 kg of slaughter weight (SW), according to the specifications of Ternasco de Aragón Protected Geographical Indication (Regulation (EC) No. 1107/96), which stipulates that lambs must be less than 90 days old with a SW between 22 and 24 kg. The lambs were slaughtered using EU laws in the same commercial abattoir, and the carcasses were hung by the Achilles tendon and chilled for 24 h at 4 °C in total darkness. The slaughter age, slaughter weight, and growth rate of the 2 management strategies are presented in Table 1. Immediately after slaughter, a piece of LT muscle from the 12th thoracic vertebra and a piece of SF between the atlas and axis cervical vertebrae were cut, frozen in liquid nitrogen and stored at−80 °C until RNA isolation. Analysis of α-tocopherol, intramuscular fat content, TBARS and metmyoglobin formation After chilling, a piece of the LT muscle between the 4th and the 6th lumbar vertebrae was vacuum-packed and kept at−20 °C in darkness until the α-tocopherol analysis. The α-tocopherol concentration was determined by liquid extraction as described in González-Calvo et al. [54]. A portion of the loin between the 7th and the 13th thoracic vertebrae was used to measure the LT muscle oxidative processes. The color (metmyoglobin content, MMb) and lipid oxidation analysis (thiobarbituric acid-reactive substance, TBARS) were quantified after 7 days of being maintained in darkness at 4 °C. The LT muscle color and LT intramuscular fat oxidation were measured as described in González-Calvo et al. [54]. Briefly, the relative content of metmyoglobin (MMb) was estimated by the K/S572/525 ratio [55]. This ratio decreases when the MMb content increases. Intramuscular fat oxidation of the M. Longissimus thoracis was determined using the procedure reported by Pfalzgraf et al. [56]. The TBARS values are expressed as milligrams of malonaldehyde (MDA) kilogram−1 of muscle. RNA isolation and assessment of RNA integrity Total RNA was extracted from approximately 500 mg of LT muscle or SF using RNeasy Tissue mini kits (QIAGEN, Madrid, Spain), following the manufacturer's protocol. Prior to microarray analysis, RNA integrity and quality were assessed by a RNA 6000 Nano LabChip on the Agilent 2100 Bioanalyzer (Agilent, Madrid, Spain) and were quantified using a nanophotometric spectrophotometer (Implen, Madrid, Spain). All RNA integrity number (RIN) values were greater than 8. Microarray hybridization and data processing RNA samples (n = 14, 7 samples from each treatment) were analyzed using Ovine Gene 1.1 ST Array Strip (Affymetrix, High Wycombe, UK). The Ovine gene 1.1 ST Array Strip allows for processing of four samples in parallel. This array contains a collection of 508538 probes that interrogate up to 26 unique sequences of each transcript (median probes/transcript = 23). These probes correspond to 22047 ovine genes. This study was part of a larger study in which we analyzed 84 samples corresponding to 3 treatments and 4 tissues (7 animals per treatment). In each strip, we hybridized the four tissues, selecting the animal tissue for each strip by random sampling. Microarray hybridization and scanning were performed at the Functional Genomics Core facility (Institute for Research in Biomedicine, IRB Barcelona, Spain), following the recommendations of the manufacturer. Scanned images (DAT files) were transformed into intensities (CEL files) by Affymetrix GeneChip Operating Software (GCOS). Overall array intensity was normalized between arrays to correct for systematic bias in the data and to remove the impact of non-biological influences on biological data. The imported data were analyzed at the gene-level, with exons summarized to genes, using the mean expression of all of the exons of a gene. Normalization was performed with the Robust Multi-Array Average (RMA) algorithm using quantile normalization, median polish probe summarization, and log2 probe transformation. The data sets supporting the results and discussed in this publication have been deposited in NCBI's Gene Expression Omnibus repository [57] and are accessible through GEO Series accession number GSE63774 (https://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?acc=GSE63774? acc = GSE63774). Validation of microarray data by qPCR One microgram of RNA from each sample were treated with DNAse (Invitrogen, Carlsbad, CA, USA), and single-stranded cDNA was synthesized using the SuperScript®III Reverse Transcriptase kit (Invitrogen, Carlsbad, CA, USA), following the manufacturer's recommendations. Specific exon-spanning primers for genes were generated and confirmed for specificity using BLAST (National Center for Biotechnology Information: http://www.ncbi.nlm.nih.gov/BLAST/). Before performing the qPCR reactions,conventional PCR was performed for all of the genes to test the primers and to verify the amplified products. The PCR products were sequenced to confirm gene identity using an ABI Prism 3700 (Applied Biosystems) with standard protocols. Homology searches were performed with BLAST (National Center for Biotechnology Information: https://blast.ncbi.nlm.nih.gov/Blast.cgi) to confirm the identity of the amplified fragments. Quantitative reverse transcriptase polymerase chain reaction (qRT-PCR) was performed using SYBR Green Master Mix: SYBR Premix Ex Taq II (Tli RNase H Plus) and an ABI Prism 7500 platform (Applied Biosystem, Madrid, Spain). Standard curves for each gene were generated to calculate the amplification efficiency through 4-fold serial dilution of cDNA pooled from the LT muscle and SF. The efficiency of PCR amplification for each gene was calculated using the standard curve method (E = 10(−1/slope)). Two "connector samples" were replicated in all of the plates to remove technical variation from this source of variability. The annealing temperatures, primer concentrations, and primer sequences for CISH, ABCC4, ACAT1, IGF1R, LDLR, SQLE, SREBF1, SOD3, HAX1, HMGB2, METTL1, HSPB8, and IER3 (genes of interest: GOIs) and the reference genes (GUSB and YWHAZ) are described in Table 7. These reference genes were chosen because in previous studies they have been shown to be the most stable in these tissues [5]. Table 7 Primers forward and reverse used in RT-PCR Statistical analysis of performance, α-tocopherol and lipid oxidation in the LT muscle Statistical analysis was performed using a general lineal model (GLM). Treatment (CON and VE) was included as the fixed factor for weaning age (WA), slaughter age (SA), slaughter weight, intramuscular fat content (IMF) and average daily gain (ADG). For muscle α-tocopherol, myoglobin and TBARS, the model also included intramuscular fat content and slaughter age as covariates. The results are expressed as least square means ± the standard error (SE) values and the differences were tested at a level of significance of 0.05 with the t statistic. Statistical analysis for the identification of differentially expressed genes by microarray analysis in LT and SF Normalized data were further analyzed using Babelomics (http://babelomics.bioinfo.cipf.es/) and MetaboAnalyst software [58]. Genes showing a statistically significant value of the Limma-test; (P < 0.01) were screened out as differentially expressed between the treatments. Significant genes were annotated based on similarity scores in blastn comparisons of Affymetrix Transcript cluster sequences against ovine sequences in GenBank. In addition, a second method, significance analysis of microarray (SAM), was used to identify and reconfirm differentially expressed genes in VE-CON contrasts. Furthermore, SAM was used to detect false positive significant genes from Limma-testing. SAM is a well-established statistical method for the identification of differentially expressed genes in microarray data analysis [58]. SAM is designed to address the FDR when running multiple tests on high-dimensional microarray data. First, it assigns a significance score to each variable based on its relative change from the standard deviation of repeated measurements. Then, it chooses variables with scores greater than an adjustable threshold Δ and compares their relative differences from the distribution estimated by random permutations of the class labels. For each Δ, a certain proportion of the variables in the permutation set will be found to be significant by chance. This number is used to calculate the FDR. Underestimation of the variability inflates the value of the statistic and can result in an increased number of false positives. Multivariate analysis of gene expression Multivariate analysis was performed using MetaboAnalyst, according to Xia et al. [58]. Principal component analysis (PCA), partial least squares discriminate analysis (PLS-DA), and variable importance of projection (VIP) were used to cluster the samples based on the selected gene expression profiles. Principal component analysis was used to reduce the large set of variables (genes) into 2 principal components (PCA 1 and 2). PLS-DA was used to enhance the separation between the groups by summarizing the data into a few latent variables that maximized covariance between the response and the predictors. The corresponding loading plot was used to determine the genes most responsible for separation in the PLS-DA score plot. Based on the PLS-DA results, genes were plotted according to their importance in separating the dietary groups and each gene received a value called the variable importance in the projection. Variable importance in the projection values >1 suggests that the variable is significantly involved in the separation of groups [59]. Variables with the highest VIP values were the most powerful group of discriminators. We also investigated trends or patterns in gene expression changes. Cluster analysis was performed using MetaboAnalyst. In (agglomerative) hierarchical cluster analysis, each sample begins as a separate cluster and the algorithm proceeds to combine them until all of the samples belong to one cluster. Two parameters must be considered when performing hierarchical clustering. The first is the similarity measure, and the other is the clustering algorithm. For distance measurements we used the Euclidian and Ward algorithm for clustering. The results are shown as a heatmap. Statistical analysis of gene expression validated by qPCR The corresponding mRNA levels were measured and analyzed by their quantification cycles (Cq). The statistical methods to analyze differences in the expression rate were performed following the method proposed by Steibel et al. [60]. The mixed model fitted was: $$ {{\mathrm{y}}_{\mathrm{rigkm}}}_{=}\mathrm{T}{\mathrm{G}}_{\mathrm{gi}} + \mathrm{b}{\left(\mathrm{I}\mathrm{M}\mathrm{F}\right)}_{\mathrm{m}} + \mathrm{b}\left(\mathrm{A}\mathrm{D}\mathrm{G}\right)\mathrm{m} + {\mathrm{P}}_{\mathrm{k}} + {\mathrm{A}}_{\mathrm{m}} + {\mathrm{e}}_{\mathrm{rigkm}} $$ where, y rigkm is the C q value (transformed data taking into account E < 2) of the gth gene (GOIs and housekeeping) from the rth well in the kth plate collected from the mth animal subjected to the ith treatment (CON, VE and ALF); TGgi is the fixed interaction among the ith treatment and the gth gene; IMFm (only used in L. Thoracis muscle tissue gene expression), and ADGm are the effects of intramuscular fat, and the average daily gain of the mth animal included as covariates; Pk is the fixed effect of the kth plate; Am is the random effect of the mth animal from which samples were collected (Am ~ (0,σ2 A)); and erigkm is the random residual. Gene specific residual variance (heterogeneous residual) was fitted to the gene by treatment effect (e rigkm ~ N (0, σ2 egi). To test differences (diff GOI ) in the expression rates of the target genes between treatments in terms of fold changes (FCs), the approach suggested by Steibel et al. [60] was used. The significance of the diff GOI estimates was determined with the t statistic. Functional annotation analyses The Database for Annotation, Visualization and Integrated Discovery (DAVID) v6.7b [61], was used to determine the pathways and processes of major biological significance and importance through the Functional Annotation Cluster (FAC) tool based on the Gene Ontology (GO) annotation function. DAVID FAC analysis was performed with the gene lists obtained after SAM analysis. Medium stringency EASE score parameters were selected to indicate confident enrichment scores of functional significance and the importance of the given pathways and processes investigated. 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The data sets supporting the results and discussed in this publication have been deposited in NCBI's Gene Expression Omnibus repository and are accessible through GEO Series accession number GSE63774. LGC and PS performed the experiments. MJ, MS and JHC designed the research and obtained funding for this research. LGC, ED, MS, JMO and JHC wrote the paper. LGC, MS, ED, MJ, RMH, JMO and JHC analyzed the data. MJ provided the animals. JHC had primary responsibility for the final content. All of the authors contributed to the manuscript discussion. All of the authors read and approved the final manuscript. All of the experimental procedures, including the care of animals and euthanasia, were performed in accordance with the guidelines of the European Union and with Spanish regulations for the use and care of animals in research and were approved by the Animal Welfare Committee of the Centro de Investigación y Tecnología Agroalimentaria (CITA) (protocol number 2009-01_MJT). In all cases, euthanasia was performed by penetrating captive bolt followed by immediate exsanguination. Unidad de Tecnología en Producción Animal, CITA, 59059, Zaragoza, Spain Laura González-Calvo, Margalida Joy, Pilar Sarto & Jorge H. Calvo University of Alberta, 116 St and 85 Ave, Edmonton, AB, T6G 2R3, Canada Elda Dervishi IMDEA-Alimentación, 28049, Madrid, Spain Roberto Martin-Hernandez Departamento de Mejora Genética Animal, INIA, 28040, Madrid, Spain Magdalena Serrano Jean Mayer-USDA Human Nutrition Research Center on Aging at Tufts University, Boston, MA, USA Jose M. Ordovás ARAID, 50004, Zaragoza, Spain Jorge H. Calvo Laura González-Calvo Margalida Joy Pilar Sarto Correspondence to Jorge H. Calvo. Additional file 1: Table S1. The significant genes identified by SAM in VE vs. CON contrast. (DOCX 62 kb) Additional file 2: Figure S1. Hierarchical clustering analysis in subcutaneous fat using 330 SAM genes. (DOCX 290 kb) DAVID Functional Annotation Clustering of SAM genes in VE vs. CON muscle L. Thoracis. Only is shown the 2 most enrichment cluster. (DOCX 16 kb) González-Calvo, L., Dervishi, E., Joy, M. et al. Genome-wide expression profiling in muscle and subcutaneous fat of lambs in response to the intake of concentrate supplemented with vitamin E. BMC Genomics 18, 92 (2017). https://doi.org/10.1186/s12864-016-3405-8 Genome-wide expression profiling Musclem Subcutaneous fat Submission enquiries: bmcgenomics@biomedcentral.com	CommonCrawl
Density estimates for vector minimizers and applications Large $s$-harmonic functions and boundary blow-up solutions for the fractional Laplacian December 2015, 35(12): 5609-5629. doi: 10.3934/dcds.2015.35.5609 Harmonic functions in union of chambers Laura Abatangelo 1, and Susanna Terracini 2, Dipartimento di Matematica e Applicazioni, Università di Milano-Bicocca, Via Cozzi, 55 - 20125 Milano, Italy Dipartimento di Matematica "Giuseppe Peano", Università degli Studi di Torino, Via Carlo Alberto 10, 10123 Torino Received March 2014 Published May 2015 We characterize the set of harmonic functions with Dirichlet boundary conditions in unbounded domains which are union of two different chambers. 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On the universal $ \alpha $-central extensions of the semi-direct product of Hom-preLie algebras Classification and simulation of chaotic behaviour of the solutions of a mixed nonlinear Schrödinger system September 2021, 29(4): 2599-2618. doi: 10.3934/era.2021003 Global stability of traveling waves for a spatially discrete diffusion system with time delay Ting Liu and Guo-Bao Zhang , College of Mathematics and Statistics, Northwest Normal University, Lanzhou, Gansu 730070, China * Corresponding author: Guo-Bao Zhang Received September 2020 Revised November 2020 Published September 2021 Early access January 2021 Fund Project: The second author is supported by NSF of China (11861056) This article deals with the global stability of traveling waves of a spatially discrete diffusion system with time delay and without quasi-monotonicity. 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Grigori Yakovlevich Perelman Leningrad, USSR (now St Petersburg, Russia) Grigori Perelman is a Russian mathematician who proved the Poincaré Conjecture and who refused to accept a Fields Medal or the $1 000 000 Clay Prize. View six larger pictures Grigori Yakovlevich Perelman's parents are Yakov Perelman, an electrical engineer, and Lubov Lvovna, who was a teacher of mathematics at a technical college. They were Jewish, which would present their son with some problems in a country where it was feared that those of Jewish descent had divided loyalty. Grigori Yakovlevich, their first child, is often known by the name Grisha. As a young child Grisha was taught to play the violin both by his mother and by a private tutor. His father also had a major influence in developing his son's problem solving skills. Speaking about his father, Perelman said (see [11]):- He gave me logical and other maths problems to think about. He got a lot of books for me to read. He taught me how to play chess. He was proud of me. His mother also helped develop his mathematical skills and, by the time he was ten, he had taken part in district mathematics competitions and shown a marked talent. Lubov sought advice about how best to develop Grisha's mathematical talents and was advised to send him to a mathematics club run by a nineteen year old coach named Sergei Rukshin. The club met twice a week at the Palace of Pioneers at the end of the school day and Rukshin, an undergraduate student at Leningrad University, had some novel ways of getting the best out of the boys who came to the club. Rukshin quickly saw Perelman's potential even though at first there was little to distinguish him from other bright children in the group. There developed a bond, an understanding, between the two with Perelman becoming Rukshin's favourite pupil. In the summer of 1980 Rukshin tutored Perelman in English so that he could enter Leningrad's Special Mathematics and Physics School Number 239 in September of that year. To allow Perelman to get this intense tuition, learning the English covered in four years of schooling in a few weeks, the Perelman family had to remain in Leningrad over the summer rather than going to the country which would have been the norm. Lessons were conducted walking round the parks of Leningrad and successfully achieved their aim. The class that Perelman entered in School 239 was unusual in that the group of highly talented mathematicians tutored by Rukshin were put into the same class. At the school Valery Ryzhik became both their class teacher and their mathematics teacher. Ryzhik was an extraordinarily talented mathematics teacher but the class containing Rukshin's collection of mathematical geniuses proved almost an impossible challenge for him. As well as mathematics, Ryzhik ran a chess club on one evening a week which Perelman attended, showing considerable talents at the game. When he was fifteen, Perelman attended the summer camp run by Rukshin. This was the first time that he had spent a night away from his mother but the bond between Rukshin and Perelman helped the potentially difficult situation. Rukshin not only trained his club boys to be the best solvers of mathematics problems but also tried to broaden their interests. Perelman was already interested in the violin and classical music but Perelman was able to broaden his musical interests. Although he would attend camps with Rukshin, Perelman never took part in the trips arranged by Ryzhik. In January 1982 Perelman was chosen as a potential member of the 1982 Soviet Mathematical Olympiad team. He attended a selection session in Chernogolovka, about 80 km north of Moscow, where in addition to the mathematical training they were subjected to stiff physical exercises in the gym. Perelman excelled and the next step was a two-day session in Odessa in April when they were given harder problems than those expected at the Olympiad competition. Perelman achieved full marks as he did at the International Mathematical Olympiad competition in Budapest in July. He received a gold medal and a special prize for achieving a perfect score. Being a member of the Soviet team gave Perelman automatic entry to university. Perelman entered Leningrad State University in autumn 1982. There he was particularly influenced by Viktor Zalgaller and Aleksandr Danilovic Aleksandrov. During his undergraduate years he assisted Rukshin as a mathematics tutor, going to summer camps, but his incredibly high standards gave even outstanding students an almost impossible time. Eventually Rukshin had to stop Perelman assisting at the summer camps. His university work, however, was exceptional and he graduated in 1987. He had already published a number of papers: Realization of abstract k-skeletons as k-skeletons of intersections of convex polyhedra in R2k−1\mathbb{R}^{2k-1}R2k−1 (Russian) (1985); (with I V Polikanova) A remark on Helly's theorem (Russian) (1986); a supplement to A D Aleksandrov's, On the foundations of geometry (Russian) (1987) in which Perelman discussed the equivalence of a Pasch-style axiom of Aleksandrov and some of its consequences; and On the k-radii of a convex body (Russian) (1987). One might imagine that his achievements would mean that he would be welcomed as a graduate student at the Leningrad branch of the Steklov Mathematics Institute with open arms. However, under Ivan Vinogradov's leadership the Steklov Mathematics Institute had accepted no Jews and, although it now had a new director, the old policies persisted. Aleksandr Danilovic Aleksandrov wrote to the director requesting that Perelman be allowed to undertake graduate work under his supervision at the Leningrad branch of the Steklov Mathematics Institute. The request, highly unusual coming from someone of Aleksandrov's high standing, was granted but, although Aleksandrov would be his official advisor, in practice it was Yuri Burago who took on the role. Perelman defended his thesis Saddle Surfaces in Euclidean Spaces in 1990. He had already published one of the main results of the thesis in An example of a complete saddle surface in R4\mathbb{R}^{4}R4 with Gaussian curvature bounded away from zero (Russian) (1989). Burago contacted Mikhael Leonidovich Gromov who had been a professor at Leningrad State University, but was at this time a permanent member of the Institut des Hautes Études Scientifiques outside Paris. He explained to Gromov that he had an outstanding student and asked if an invitation could be issued for him to spend time at IHES. The invitation allowed Perelman to spend several months at IHES working with Gromov on Aleksandrov spaces. Perelman's first major paper, written jointly with Burago and Gromov, was A D Aleksandrov spaces with curvatures bounded below (1992). Tadeusz Januszkiewicz begins a review as follows:- This is an important paper in many respects. It contains a careful and fairly detailed discussion of basic facts of the theory, including various equivalent forms of definitions. It recognizes that the home of various important theorems of Riemannian geometry is the theory of Aleksandrov spaces, that both statements and proofs become more satisfactory (but not necessarily easier) in this context, and other theorems emerge naturally to complete the picture. It develops useful tools for studying Aleksandrov spaces with curvature bounded below in full generality. Finally, it contains an ample discussion of further results and open problems. After visiting the IHES near Paris, Perelman returned to the Steklov Mathematics Institute in Leningrad but, thanks to Gromov, Perelman was invited to the United States to talk at the 1991 Geometry Festival held at Duke University in Durham, North Carolina. He lectured on the work which he had done on Aleksandrov spaces with Burago and Gromov (which had not been published at that time). In 1992 Perelman was invited to spend the autumn semester at the Courant Institute, New York University, on a postdoctoral fellowship, and the spring 1993 semester at Stony Brook, a campus of the State University of New York, again funded by a fellowship. Masha Gessen describes Perelman at this time [1]:- By the time Perelman arrived in the United states, he was twenty-six, no longer pudgy but tall and apparently fit. His beard had passed out of its extended awkward-tuft stage and was thick, black and bushy. His hair was long. He did not believe in cutting hair or fingernails ... [he wore] the same clothes every day - most notably a brown corduroy jacket ... [he ate] a particular kind of black bread that could be procured only from a Russian store in Brooklyn Beach, where Perelman walked from Manhatten. While Perelman was in the United States in 1992, his mother stayed with friends in New York, his father had earlier emigrated to Israel, and Perelman's young sister Lena was still being educated in St Petersburg (Leningrad returned to its original name of St Petersburg in 1991). He got to know Jeff Cheeger and Gang Tian, and the three of them regularly travelled to Princeton to attend seminars at the Institute for Advanced Study. Perelman attended a conference in Israel in 1993 then accepted a two-year Miller Research Fellowship at the University of California, Berkeley. He published some remarkable papers during these years. Elements of Morse theory on Aleksandrov spaces (Russian) (1993) investigates the local topological structure of Aleksandrov spaces. Manifolds of positive Ricci curvature with almost maximal volume (1994) solves a conjecture about a complete Riemannian manifold MnM^{n}Mn. If such a manifold has Ricci curvature ≥ n−1n - 1n−1 and volume close to that of the sphere then Perelman proved it is homeomorphic to the sphere. The biggest breakthrough, however, was his paper Proof of the soul conjecture of Cheeger and Gromoll (1994) which answered a question asked by Cheeger and Gromoll twenty years earlier. Perelman was invited to address the International Congress of Mathematicians in Zürich in 1994 and he gave the lecture Spaces with curvature bounded below. To understand the problems that Perelman was beginning to think about around this time, we give the description of the Poincaré Conjecture and the Thurston Geometrization Conjecture from [16]:- A 2-manifold with positive curvature can be deformed into a 2-sphere; one with zero curvature can be deformed into a torus; and one with negative curvature can be deformed into a torus with more than one hole. The Poincaré Conjecture, which originated with the French mathematician Henri Poincaré in 1904, concerns 3-dimensional manifolds, or 3-manifolds. ... Can every simply connected 3-manifold be deformed into the 3-sphere? The Poincaré Conjecture asserts that the answer to this question is yes. Just as with 2- manifolds, one could also hope for a classification of 3-manifolds. In the 1970s, Fields Medalist William Thurston made a new conjecture, which came to be called the Thurston Geometrization Conjecture and which gives a way to classify all 3-manifolds. The Thurston Geometrization Conjecture provides a sweeping vision of 3-manifolds and actually includes the Poincaré Conjecture as a special case. Thurston proposed that, in a way analogous to the case of 2-manifolds, 3-manifolds can be classified using geometry. But the analogy does not extend very far: 3-manifolds are much more diverse and complex than 2-manifolds. A possible approach to attacking the Poincaré Conjecture had been developed by Richard Hamilton who had introduced a significant idea in 1982 when he began to study a particular equation he called the Ricci flow. When Perelman was going to lectures at the Institute for Advanced Study he attended a lecture there by Hamilton and talked with him after the lecture. Perelman recalled [11]:- I really wanted to ask him something. He was smiling, and he was quite patient. He actually told me a couple of things that he published a few years later. He did not hesitate to tell me. Hamilton's openness and generosity -- it really attracted me. I can't say that most mathematicians act like that. I was working on different things, though occasionally I would think about the Ricci flow. You didn't have to be a great mathematician to see that this would be useful for geometrization. I felt I didn't know very much. I kept asking questions. When he was a Miller fellow at Berkeley, Perelman attended some further lectures by Hamilton and he began to understand why Hamilton could not make any further progress towards proving the Poincaré Conjecture using the Ricci flow. While he was in the United States, Perelman received several requests asking him to apply for professorships. These came from top institutions such as Stanford and Princeton. He was offered a full professorship, without making any application, by Tel Aviv University in Israel, but he turned down all the offers and returned to the St Petersburg branch of the Steklov Mathematics Institute after his Miller fellowship came to an end in the summer of 1995. Basically he was able to live on the savings he had made from the money paid to him in the United States which was quite considerable since he had lived exceptionally frugally. He refused to accept a European Mathematical Society prize in 1996. Perelman had realised that Hamilton was making no progress with the Poincaré Conjecture when he read a paper Hamilton published in 1995 and, in the following year, he wrote to Hamilton explaining that he might have a way round the problem and offering to collaborate with him. When he received no reply, Perelman seems to have decided to work on solving the Poincaré Conjecture alone. On 11 November 2002, Perelman put his paper The Entropy Formula for the Ricci Flow and Its Geometric Applications on the web. Although he did not claim in the paper to be able to solve the Poincaré Conjecture, when experts in the subject read it they realised that he had made the breakthrough necessary to solve the Conjecture. Quickly he received invitations to visit the Stony Brook campus of the State University of New York and the Massachusetts Institute of Technology. He began making plans for the visits and, before setting off, he posted a second paper Ricci flow with surgery on three-manifolds on the web continuing his proof. He arrived in the United States in April 2003 and went first to the Massachusetts Institute of Technology where he gave talks on his work for most days in the two weeks he was there. He spent two similar weeks at Stony Brook followed by visits to Columbia University and Princeton University where he gave lectures. He turned down all offers of professorships that were made to him, becoming annoyed at the pressure some put on him to accept. He returned to St Petersburg at the end of April 2002 and, in July, put Finite extinction time for the solutions to the Ricci flow on certain three-manifolds, the third instalment of his work, on the web. It took some time for experts in the field to convince themselves that Perelman had solved the Poincaré Conjecture and a little longer to work through the details to see that he had also solved the Thurston Geometrization Conjecture. He continued working at the Steklov Mathematics Institute in St Petersburg where he was promoted to Senior Researcher. However in December 2005 he resigned, saying that he was disappointed in mathematics and wanted to try something else. In August 2006 he was awarded a Fields medal:- For his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow. John Lott described Perelman's work leading to the award of a Fields Medal in a lecture he gave to the International Congress of Mathematicians in Zürich in August 2006 [8]. For an extract of Lott's talk, giving some technical details, see THIS LINK. (Note the careful choice of Lott's language. He says the Perelman "proved the so-called Soul Conjecture," but only that he "presented proofs of the Poincaré conjecture and the geometrization conjecture.") Perelman refused the invitation to be a plenary speaker at the 2006 International Congress of Mathematicians. He also refused the award of the Fields Medal, the first person to have done so. If his hope had been to avoid publicity he was highly unsuccessful since huge public interest was generated and he was hounded by the press. In March 2010 the Clay Mathematics Institute announced that Perelman had met the conditions for the award of one million US dollars which they had offered for the solution of the Poincaré Conjecture. In July 2010 Perelman refused to accept the million dollars, saying:- I do not like their decision, I consider it unfair. I consider that the American mathematician Hamilton's contribution to the solution of the problem is no less than mine. Let us end this biography by quoting Mikhael Gromov (see [1]):- [Perelman] has moral principles to which he holds. And this surprises people. They often say he acts strangely because he acts honestly, in a nonconformist manner, which is unpopular in this community - even though it should be the norm. A Poster of Grigori Yakovlevich Perelman M Gessen, Perfect Rigor: A Genius and the Mathematical Breakthrough of the Century (New York, 2009). 2006 Fields Medals awarded, Notices Amer. Math. Soc. 53 (9) (2006), 1037-1044. L Bessières, G Besson and M Boileau, The proof of the Poincaré conjecture, according to Perelman, in The scientific legacy of Poincaré (Amer. Math. Soc., Providence, RI, 2010), 243-255. R Ezhil K, The man who refused the Fields Medal may also refuse a million dollars, Current Sci. 98 (10) (2010), 1279-1280. A Jackson, Conjectures No More? Consensus Forming on the Proof of the Poincaré and Geometrization Conjectures, Notices Amer. Math. Soc. 53 (8) (2006). 897-901. B Kleiner and J Lott, Notes on Perelman's papers, Geometry & Topology 12 (5) (2008), 2587-2855. N Lobastova and M Hirst, World's top maths genius jobless and living with mother, The Daily Telegraph (20 August 2006). J Lott, The work of Grigory Perelman, International Congress of Mathematicians I (Eur. Math. Soc., Zürich, 2007), 66-76. D Mackenzie, Breakthrough of the year. The Poincaré Conjecture-Proved, Science 314 (5807) (2006), 1848-1849. J Mullins, Prestigious Fields Medals for mathematics awarded, New Scientist (22 August 2006). S Nasar and D Gruber, Manifold Destiny: A legendary problem and the battle over who solved it, The New Yorker (21 August 2006). A Osborn, Russian maths genius may turn down $1m prize, The Daily Telegraph (27 March 2010). D Overbye, An Elusive Proof and Its Elusive Prover, The New York Times (15 August 2006). J A Paulos, He Conquered the Conjecture, The New York Review of Books (23 December 2010). J Porti, 2006 Fields Medal: Grigori Perelman (Catalan), SCM Not. No. 23 (2007), 50-51. Press Release, 2006 Fields Medal: Grigori Perelman. J Randerson, Meet the cleverest man in the world (who's going to say no to a $1m prize), The Guardian (16 August 2006). S Robinson, Russian Reports He Has Solved a Celebrated Math Problem, The New York Times (15 April 2003). A M Vershik, J Bourgain, H Kesten and N Reshetikhin, The mathematical work of the 2006 Fields medalists, Notices Amer. Math. Soc. 54 (3) (2007), 388-404. Other pages about Grigori Yakovlevich Perelman: Perelman's work leading to the 2006 Fields Medal Other websites about Grigori Yakovlevich Perelman: NNDB Honours awarded to Grigori Yakovlevich Perelman Fields Medal 2006 (though he did not accept it) Popular biographies list Number 150 Other: Most popular biographies	CommonCrawl
Skip to main content Skip to sections Biomedical Dermatology December 2019 , 3:13 \| Cite as Difference between the biologic and chronologic age as an individualized indicator for the skin care intensity selection: skin topography and immune system state studies, parameter correlations with age difference Yurij Sukhovei Elena Kostolomova Irina Unger Andrey Koptyug Denis Kaigorodov First Online: 14 January 2020 Present research addresses the issue of skin aging and corresponding skin treatment individualization. Particular research question was on the developing of simplified criterion supporting patient-specific decision on the necessity and intensity of skin treatment. Basing on the published results and a wide pool of experimental data, we have formulated a hypothesis that a difference between biologic and chronologic age can be used as an express criterion of skin aging. In present paper, we report the results of studies with 80 volunteers between 15 and 65 years of age, linking parameters reflecting immune state, skin state, and topography to the difference between biologic and chronologic age. Facial skin topography, skin moisture, sebum level, and skin elasticity were studied using commercial devices. Blood immunology studies were performed using venous blood samples. Correlations between all measured parameters and age difference were calculated. Also, cross correlations between skin cell profile and blood immune profile parameters, and skin roughness parameters were calculated. Age dependencies of the blood immunological parameters on the biologic and chronologic age difference are less pronounced as compared to the changes in skin cell profile parameters. However, the changes in the tendencies when biologic age becomes equal to chronologic one are visible for all studied parameters. All measured skin roughness parameters show correlations with age difference, but average skin roughness and depth of the deepest profile valley have the largest correlation coefficient values. Many of the measured skin cell profile and blood immunology parameters show strong correlations with average skin roughness and deepest profile valley, with some of the coefficients exceeding 0.5–0.6. Basing on own experiments and published research results, it is possible to suggest using the difference between calculated biologic age and chronologic age as an individualized criterion supporting decisions on skin treatment strategy. Further research involving larger numbers of participants and aiming on optimizing the expressions for calculating biologic age could lead to reliable and easily available express criterion supporting the decision making for an individualized skin treatment. Skin aging Biologic and chronologic age Skin topography Immune status Individualized treatment Biologic age Blood cholesterol level Chronologic age Forced vital lung capacity NBT Nitro-blue tetrazolium polyethyleneglycol Average roughness Systolic blood pressure Arithmetic mean of the profile slope of the roughness profile Maximum stretching of the roughness profile Height of the greatest profile peak Depth of the deepest profile valley Average value of five highest peaks minus average value of five deepest valleys Urea concentration in urine Addressing of the issue on proper and timely measures against human skin aging is a complex problem for cosmetology and medicine involving among others physiological, social, and psychological aspects (Waters 1986; Koblenzer 1996; Gilchrest 2003; Gupta and Gupta 2003; Gupta and Gilchrest 2005; Matts 2008; Bhomick and Rao 2014; Konduracka et al. 2014; Zhang and Duan 2018). Low self-perception of skin quality is often forcing people to seek intense intervention, which may be not necessary or even harmful (Waters 1986; Bhomick and Rao 2014; Konduracka et al. 2014). Multiple studies have suggested objectively measurable skin properties and biochemical parameters (markers) that can be used for assessing if the skin is aging and needs certain cosmetic or medical intervention (Kwon and da Vitoria Lobo 1999; Jacobi et al. 2004; Klemera and Doubal 2006; Gruenewald et al. 2006; Naylor et al. 2011; Mann et al. 2012; Arce-Lopera et al. 2013; Porcheron et al. 2013; Freis and Perie 2014; Masuda et al. 2014; Shetage et al. 2014; Woo et al. 2014; Belsky et al. 2015; Trojahn et al. 2015; Belsky et al. 2017). Corresponding methodologies cover the analysis of skin images (e.g., Matts 2008; Kwon and da Vitoria Lobo 1999; Arce-Lopera et al. 2013), skin topography (e.g., Jacobi et al. 2004; Masuda et al. 2014; Shetage et al. 2014; Trojahn et al. 2015) and mechanical properties (e.g., Porcheron et al. 2013; Freis et al. 2014; Woo et al. 2014), skin biochemistry (e.g. Naylor et al. 2011; Mann et al. 2012), etc. So far, it is accepted that multiparameter (multimarker)-based methods are the best candidates for the development of aging criteria, in particular the criteria of skin aging (e.g., Voitenko and Tokar 1983; Alonso-Fernández and de la Fuente 2011; Castelo-Branco and Soveral 2014; Martínez de Toda et al. 2016; Kang et al. 2017; Csaba 2019; Fahy et al. 2019). Recent research makes use of an old concept of biologic age (Benjamin 1947), suggesting introduction of a cumulative factor including multiple parameters related to aging process (e.g., Voitenko and Tokar 1983; Klemera and Doubal 2006; Gruenewald et al. 2006; Alonso-Fernández and de la Fuente 2011; Castelo-Branco and Soveral 2014; Belsky et al. 2015; Belsky et al. 2017; Martínez de Toda et al. 2016; Kang et al. 2017; Csaba 2019; Fahy et al. 2019). Modern approach to the calculation of biologic age (BA) incorporates a number of objectively measurable and quantifiable parameters including body mass index, arterial pressure, different cardiorespiratory parameters, blood cholesterol levels and white blood cell counts, urea composition, etc. (e.g., Voitenko and Tokar 1983; Klemera and Doubal 2006; Gruenewald et al. 2006; Alonso-Fernández and de la Fuente 2011; Castelo-Branco and Soveral 2014; Martínez de Toda et al. 2016; Kang et al. 2017; Csaba 2019; Fahy et al. 2019). These parameters are used in formal mathematical expressions for calculating estimated BA value. Different researchers utilize different sets of parameters and different expressions, but one can outline few common conclusions. Firstly, in the groups of individuals with the same chronologic age (CA; age according to the year of birth), biologic age is covering the values from far lower to far higher than the chronologic age (Voitenko and Tokar 1983; Alonso-Fernández and de la Fuente 2011; Castelo-Branco and Soveral 2014; Belsky et al. 2015; Trojahn et al. 2015; Belsky et al. 2017; Martínez de Toda et al. 2016; Kang et al. 2017; Csaba 2019; Fahy et al. 2019). Basing on a study of calculated biologic age for individuals with the same chronologic age and significant difference of BA and CA, it was found that a pace of aging is increasing with increasing chronologic age. Our studies indicate that there is a noticeable and measurable difference in many parameters reflecting the state of human skin for the individuals with BA < CA and BA > CA (Sukhovei et al. 2019). Basing on available information, a hypothesis was formulated that a difference between the chronologic and biologic age can be used as an express indicator of skin aging. If such hypothesis is supported, it would open a pathway for developing an express criterion supporting decisions on an individualized skin treatment. In addition, it was concluded that corresponding biologic age value could be calculated using a simplified approach demanding only basic parameters that could be acquired from tests performed ambulatory or in almost every clinic. Discussed results of experimental studies on dependencies of the parameters reflecting skin state (cellular structure) and their correlations with the biologic and chronologic age difference (BA − CA) provided certain grounds for the validity of such hypothesis (Sukhovei et al. 2019). Basing on the available data, it was concluded that for stated purposes gender-specific expressions for calculating biologic age should be used. Literature studies also indicate that for chosen specific purpose of designing express criterion for the individualized skin treatment different approaches for BA calculation may be equally useful. Further studies are needed to understand if such approach is universal and does not strongly depend on the choice of particular expression of BA calculation, or certain specific formula is most relevant. In the present paper, we continue the discussion of formulated hypothesis describing the studies of parameters reflecting skin state (moisture, elasticity, and sebum level), skin topography, cellular structure, and overall body immune status of the study participants. Immune studies were added to the overall research scope reflecting the importance of the immune status changes in the aging process (Voitenko and Tokar 1983; Kiecolt-Glaser et al. 2003; Alonso-Fernández and de la Fuente 2011; Castelo-Branco and Soveral 2014; Martínez de Toda et al. 2016; Kang et al. 2017; Csaba 2019; Fahy et al. 2019). Studies were carried out with a group of volunteers between 15 and 65 years of chronologic age (40 males and 40 females) recruited predominantly from the city population. There was no pre-selection of the participants depending on the health or their skin state. Participants were thoroughly informed on the purpose of the studies and procedures involved and gave their written consent. The plans for the research and consent forms were approved by the Ethics Commission of the Institute of Immunology (IRB 1025402458740) according to the formal documents issued by the State Department of Health of Russian Federation. All procedures were conducted by the qualified personnel in accordance with principles of the Declaration of Helsinki and its amendments (World Medical Association Declaration of Helsinki 2013). The average age of the male and female participants was 39.05 ± 2.28 and 39.48 ± 2.28 years, correspondingly. Calculation of the biologic age The following expressions for the biologic age calculations were used: $$ \mathrm{for}\ \mathrm{females}\ BA=51.01+{0.84}^{\ast }\ UC-{5.53}^{\ast }\ FVC+{0.2}^{\ast }\ SBP+{0.093}^{\ast }\ BCh-{5.53}^{\ast }\ BCa $$ $$ \mathrm{for}\ \mathrm{male}\ BA=93.86+{0.44}^{\ast }\ UC-{4.92}^{\ast }\ FVC+{0.19}^{\ast }\ SBP+{0.10}^{\ast }\ BCh-{9.01}^{\ast }\ BCa $$ where FVC is the forced vital lung capacity (liter) measured using common medical spirometer, SBP is systolic blood pressure (mm Hg) measured by a cuff tonometer, UC is urea concentration in urine (mg/100 ml), and BCh is a blood cholesterol level (mg/100 ml) and BCa is a calcium level (mg/100 ml) in the blood serum. Corresponding expressions for BA calculations are common for gerontology and age-related studies in Russia (Voitenko and Tokar 1983; Beloserova 2006; Sukhovei et al. 2019). Note that these expressions give overestimated values of BA for early age and underestimated for late age, compared to the corresponding expressions used by other researchers underestimating BA in early age and overestimating it at late age (Webster and Logie 1976; Dean 1986; Borkan and Norris 1980; Dean 1998). In addition, with the approach to BA calculations used in the present research, young age is corresponding to BA > CA, which may be some counterintuitive but does not influence the purpose of present study. Biologic age was calculated for each of the participants according to expressions (1) and (2). According to the formulated hypothesis, one should be able to select the individuals that "should not need skin corrective intervention" and "may require intensive corrective intervention." Following this approach, we have identified three sub-groups for each sex corresponding to "early age," "critical age," and "late age" as reflected by the age difference BA − CA (Sukhovei et al. 2019). A group for "critical age" was defined as having this difference less than 5 years: $$ \mid \mathrm{BA}-\mathrm{CA}\mid <5\ \mathrm{years} $$ Thus, three sub-groups were chosen to have chronologic age below and above the "critical" (BA is clearly larger or clearly smaller than CA) and around the "crossover" age (BA~CA). Individual scatter of the values in BA vs CA dependences is rather significant, so basing on all experimental data acquired we have adopted a simplified approach to the "critical age" sub-group selection linked to the biologic age but basing on the chronologic one. So finally, the conditions for the three sub-group selection were chosen as follows: below 40, between 40 and 50, and above 50 years for the male subjects; and below 30, between 30 and 40, and above 40 years for the female subjects. Thus, the definition of the simplified criteria for the age sub-group selection is: $$ \mathrm{critical}\ \mathrm{chronologic}\ \mathrm{age}\ \mathrm{group},\mathrm{male}-\mathrm{between}\ 40\ \mathrm{and}\ 50\ \mathrm{years}; $$ $$ \mathrm{critical}\ \mathrm{chronologic}\ \mathrm{age}\ \mathrm{group},\mathrm{female}-\mathrm{between}\ 30\ \mathrm{and}\ 40\ \mathrm{years}; $$ Further, we refer to these groups as "early age," "critical age," and "late age" ones. Assessment of the skin topography Skin topography was measured using optical PRIMOS 3D scanner (by GF Messetechnik, Germany) on the face of the participants according to the protocol defined by the manufacturer. The following parameters of the skin topography were extracted using the embedded algorithms within PRIMOS system: Average roughness, Sa Maximum stretching of the roughness profile, Smax (difference between the highest "peak" and the deepest "valley" within the whole measured area) Ten-point height, Sz (average value of 5 highest peaks minus average value of five deepest valleys within the whole measured area) Height of the greatest profile peak, Sp Depth of the deepest profile valley, Sv Arithmetic mean of the profile slope of the roughness profile, Sda Assessment of the skin state The following parameters were measured to assess the state of the facial skin: Skin moisture—by the Corneometer® (Courage & Khazaka GmbH, Germany) Sebum level of the skin surface—by Sebumeter® SM 815 (by Courage & Khazaka electronic GmbH, Germany). Elasticity of the upper skin layer—by Cutometer® 580 MPA (by Courage & Khazaka electronic GmbH, Germany). Cutometer uses mild negative pressure that deforms the skin mechanically to measure skin displacement with the pressure. Corresponding skin elasticity parameters (R-parameters) are extracted using the embedded software. Corresponding values measured for all participants were close to the values for the corresponding age groups reported in the literature (Nedelec et al. 2016; Coltman et al. 2017). Assessment of the immune system state Blood immunology tests were conducted to assess the general health status of the participants. The following factors were chosen for the analysis: Erythrocyte count (RBC) Leukocyte common antigen (CD45) T lymphocytes (CD45+CD3+) and their sub-populations Th lymphocytes or T-helpers (CD45+CD3+CD4+CD8−) Cytotoxic Ts lymphocytes (CD45+CD3+CD4−CD8+) B lymphocytes (CD45+CD3−CD19+) Natural Killer (NK) cells (CD45+CD3−CD16+CD56+) Immunologic index (CD45+CD3+CD4+/CD45+CD3+CD8+) Immunoglobulin concentration in the blood serum (IgA, IgG, IgM, IgE) Blood macrophage and microphage activity Blood immunology was studied using venous blood samples taken using BD Vacutainer system (by Bioline, USA). Functional lymphocyte analysis was performed for untreated blood using indirect immunofluorescence with Cytomics FC500 Flow Cytometry Analyzer (Beckman Coulte Inc., USA) using monoclonal antibodies CYTO-STAT tetraCHROME CD45-FITC/CD4-RD1/CD8-ECD/CD3-PC5 and CYTO-STAT tetraCHROME CD45-FITC/CD56-RD1/CD19-ECD/CD3-PC5 (by Beckman Coulte Inc., USA). Erythrocyte samples for flow cytometry were prepared using COULTER Q-PREP Workstation and reagent system COULTER IMMUNOPREP (both by Beckman Coulte Inc., USA) according to the protocols specified by the equipment manufacturer. Skin-resident macrophage concentration and activity were measured using the same biopsy samples as used for the skin cell studies under flow cytometry according to common protocols. Blood monocyte count was measured using sample-stained glass in optical microscope. Metabolic blood monocyte activity was assessed using spontaneous and stimulated nitro-blue tetrazolium test (NBT; Freeman and King 1972; Gordon et al. 1973; Müller et al. 1981; Hart et al. 1999; Mosser and Zhang 2011; Kazanci et al. 2017). Blood monocyte phagocytic activity was assessed through the expression of FcγRIII (Fcγ receptor III, CD16) using the ingestion and attachment of the opsonized sheep erythrocytes (Mosser and Zhang 2011). Quantization of the phagocytosis of opsonized sheep erythrocytes by macrophages was done visually under optical microscope by measuring the numbers of monocytes attached to the membrane surface of opsonized sheep erythrocytes (membrane-bound monocytes) and the number of monocytes that have ingested opsonized sheep erythrocytes (monocyte-ingested erythrocytes), as a percentage of the overall monocyte numbers. Mastocyte count measurement was incorporated into the experimental procedure as their levels were shown to decrease with aging in animal experiments (Benjamin 1947; Voitenko and Tokar 1983; Hart et al. 1999; Martínez de Toda et al. 2016; Kang et al. 2017; Csaba 2019; Fahy et al. 2019). Concentrations of blood immunoglobulins were measured by turbidimetry using Modular Pre-Analytics EVO analyzer with the immunochemical module E140 (Roche, Switzerland) with the test system for nephelometry and turbidimetry by Dako, USA. Quantization of soluble immune complexes was done using precipitation by polyethyleneglycol (PEG; Chia et al. 1979; Ohlson and Zetterstrand 1985; Giaimis et al. 1992) using two different PEG concentrations (3.5 and 7 vol. %). Phagocytic activity of the blood and epidermal neutrophils was assessed using adhering/ingestion method with Saccharomyces cerevisiae (brewer's yeast, Giaimis et al. 1992). The following parameters were recorded: percentage of active neutrophils participating in active phagocytosis and phagocytosis intensity as the mean number of adhered/ingested cells per phagocytizing neutrophil after 30 and 120 min from the start of experiment. Pearson statistical and correlation analysis was carried out using the software package IBM SPSS Statistics Base v 22.0. Though the data sample size is not large enough to suggest adequate statistical analysis, one can already formulate certain preliminary conclusions. A large pool of experimental data was acquired and analyzed in the study. Here, we report on the data analysis and the most representative results for the parameters reflecting skin state and roughness, and blood immune status followed by the discussion on correlations of studied parameters with age difference BA – CA, and correlations of the skin roughness parameters with other measured skin and blood immunology status parameters. The age dependencies of the skin cell profile parameters were analyzed in a previous paper (Sukhovei et al. 2019), and it was concluded that plotting the values against the difference between biologic and chronologic age allows to clarify certain tendencies and illustrate the trend changes around BA = CA. Thus, it was of significant interest to analyze if similar tendencies will be present for the blood immunology and skin roughness parameters. Immune system status changes with the age difference BA − CA It was already shown that skin cell profile parameters often show certain interesting features when plotted against the age difference BA = CA and are quite monotonous when plotted against either chronologic or biologic age. In addition, it was noted that in some cases plotting such dependencies against the normalized age difference makes specific features more clear. Similar data processing was used for the analysis of the blood immunology profile parameters (Figs. 1 and 2). Although acquired data have significant scatter, certain hints toward the special case of BA = CA already can be observed. It should be noted that plotting the dependencies against age difference (BA − CA, as in Fig. 2a), or normalized age difference (for example, (BA − CA)/BA, as in Fig. 2b) does not change the general trends as compared to the plot against age difference BA − CA. Changes in the blood concentrations of immunoglobulin M plotted against the chronologic (a) and biologic (b) age. Squares (linear fit: double-dotted line)—male participants; diamonds (linear fit: dashed line)—female participants. Trend lines (a): female y = 0.011x + 1.185, R2 = 0.138; male y = − 0.004x + 1.770, R2 = 0.012. Trend lines (b): female y = 0.010x + 1.127, R2 = 0.097; male y = 0.011x + 1.156, R2 = 0.018 Changes in the blood concentration of immunoglobulin M plotted against a biologic and chronologic age difference BA − CA, and normalized age difference (BA − CA)/BA. Squares (second order polynomial fit: double-dotted line)—male participants; diamonds (second order polynomial fit: dotted line)—female participants. Note that large positive difference BA − CA corresponds to early age. Trend lines (a): female y = 0.0009x2 − 0.0139x + 1.6008, R2 = 0.0680; male y = − 0.0001x2 + 0.0091x + 1.6232, R2 = 0.0471. Trend lines (b): female y = − 0.890x2 + 0.549x + 1.654, R2 = 0.069; male y = − 0.890x2 + 0.549x + 1.654, R2 = 0.069 In order to validate that age difference BA = CA can be used as a simplified criterion of aging, corresponding dependencies are visualized with the cumulative data averaged for the age sub-groups corresponding to "early," "critical," and "late" chronologic age (expressions 4 and 5), similarly to the approach used previously (Sukhovei et al. 2019). As the scatter of the values in the plots against age difference is rather significant between participants, this sub-group age breakdown selection was done basing on the full set of obtained experimental data. Bar plots in Fig. 3 present averaged levels of blood immunoglobulins for the chosen age sub-groups. Three left bars in each plot correspond to female, three right bars to male participants. Though some of the trends are less pronounced, there is certain tendency to have trend changes around (BA = CA) ± 5 years. Concentrations of the blood immunoglobulins IgA, IgM, and IgG (a–c) averaged for the sub-population groups selected according to the "critical" chronologic age approach Previous studies reported contradicting trends in the immunoglobulin concentration changes. It is assumed that among the main reasons for that are the differences in the age and gender of test subjects, location of the immune cells, and study methods (Voitenko and Tokar 1983; Alonso-Fernández and de la Fuente 2011; Castelo-Branco and Soveral 2014; Martínez de Toda et al. 2016; Kang et al. 2017; Csaba 2019; Fahy et al. 2019). There are reports that the levels of IgA in saliva are increasing up to about 60 years of age followed by the decline (Castelo-Branco and Soveral 2014), which is quite similar to the trends shown in Fig. 3a. For the purpose of our research, dependencies of the blood immunoglobulin concentrations can still be used as certain argument for the formulated hypothesis. Bar plots in Fig. 4 present averaged values reflecting the metabolic monocyte activity in spontaneous (a) and stimulated (b) NBT Test, and the phagocytic activity of the monocytes (percentage of membrane-bound monocytes (c) and of monocyte-ingested erythrocytes (d)) in the opsonization tests for the chosen age sub-groups. Three left bars in each plot correspond to female, three right bars to male participants. Certain tendency to have trend changes around ((BA = CA) ± 5 years) is also pronounced. Functional activity of the blood monocytes for the sub-population groups selected according to the "critical" chronologic age approach. Results of spontaneous (a) and stimulated (b) NBT tests. Percentage of the membrane-bound monocytes (c) and monocyte-ingested erythrocytes (d), relative to the overall monocyte numbers Plots in Fig. 5 present the levels of phagocytic activity and intensity of phagocytosis of blood neutrophils 30 and 120 min of the test for the chosen age sub-groups. Again, trend changes are visible around (BA = CA) ± 5 years. Phagocytic activity of blood neutrophils after 30 (a) and 120 (b) minutes of the test and intensity of phagocytosis of blood neutrophils after 30 (c) and 120 (d) minutes of the test Previous studies generally report on the decreasing with age overall numbers of monocytes and NK cells and greater adherence of neutrophils (Alonso-Fernández and de la Fuente 2011). In general, researchers pay more attention towards the changes in the functioning of the innate immunity cells with age (Voitenko and Tokar 1983; Alonso-Fernández and de la Fuente 2011; Castelo-Branco and Soveral 2014; Martínez de Toda et al. 2016; Kang et al. 2017; Csaba 2019; Fahy et al. 2019). However, as it is with the changes in the immunoglobulin concentrations, changes in the corresponding trends of the age dependencies of the innate immunity cells can be used in support of the formulated hypotheses. Skin state and topography changes with the age difference BA – CA Measured skin moisture, elasticity, and sebum level values are in general agreement with previously reported data (Castelo-Branco and Soveral 2014). Nevertheless, as corresponding age dependence plots for these values have quite a large scatter, they cannot be used for supporting or opposing the formulated hypotheses. Data from the skin roughness measurements by the Cutometer are used for arguing and in general are in good agreement with previously reported values (Nedelec et al. 2016; Coltman et al. 2017). Initially, the parameter values were plotted against the difference between the biologic and chronologic age (BA – CA). However, it became clear that corresponding trends are becoming more pronounced if the data are plotted against "normalized age difference" (BA – CA)/CA, similar to the case for the parameters reflecting skin cell profile and blood immunology status. Large number of parameters calculated by the Cutometer show similar trends, and plots for average roughness (Sa) and maximum span of the roughness profile (Smax, difference between the highest "peak" and the deepest "valley" within the complete measured area) are presented in Fig. 6 as an example. Other measured roughness parameters have similar dependences on the age difference. Note that positive normalized age difference (BA – CA)/CA corresponds to early age, negative difference to late age participants. It should be also pointed out that corresponding dependencies on the normalized age "soften" the tendency towards increasing of skin roughness for BA < CA (late age). Average skin roughness Sa (a) and maximum stretching of the roughness profile difference between the highest "peak" and the deepest "valley" within the whole measured area) Smax (b) for all participants. In the corresponding trend lines, best fit is given by exponential curves (see Table 1). Note that positive normalized age difference (BA – CA)/CA corresponds to young, negative difference to elderly participants Similar shift in the same direction was observed for the female participants, which indicates that certain corrections into the expressions for the calculating of biologic age may be needed. Best data fit for the experimental dependencies in Fig. 6 was achieved using the exponential trend lines; corresponding expressions are given in Table 1. Trend lines for the dependencies of skin roughness parameters on the age difference (x = BA – CA) for male and female participants y = 48.80e–0.83x, R2 = 0.209 y = 565.2e–0.62x, R2 = 0.160 y = 0.181e–0.43x, R2 = 0.377 It can be noticed that the scatter in the skin roughness values presented in Fig. 6 also seems to depend on the normalized age difference. Figure 7 presents some examples for the dependencies of the modulus of the difference between the measured values and trend lines shown in Fig. 6 (expressions for the trend lines are according to Table 1) on the normalized age difference (BA – CA)/CA. Dependencies of the absolute values for the difference between measured values and trend lines (Table 1) for the skin roughness parameters Sa (a), Smax (b), and Sda (c). Values in micrometers, red squares—male participants, blue diamonds—female participants. Note that positive values of the normalized age difference correspond to young age Age dependencies of the chosen parameters for individual subjects show significant scatter of the values. Also, the dependencies of the parameters reflecting blood immunology status and skin roughness on either biologic or chronologic age (Figs. 1 and 2) do not show the trend changes around BA = CA. As in the case for the parameters reflecting skin cell profile (Sukhovei et al. 2019), analysis of the parameter plots against age difference or normalized age difference suggests that skin aging selection criterion basing on the comparison of the biologic and chronologic age has certain grounds. In the data averaged for chosen age sub-groups ("early age," "critical age," "late age," reflecting the individual differences between chronologic and calculated biologic age BA – CA) interesting trends are also visible, although the interval corresponding to "critical" age is chosen to be reasonably large (BA = CA ± 5 years) and its boundaries are chosen rather arbitrary. Firstly, there is a clear difference in the "critical age" condition (BA = CA) for male and female participants. Corresponding value trends around CA about 35 years for female and about 45 years for male participants recovered from the blood immunology and dermal and epidermis cell profile (Martínez de Toda et al. 2016) are showing very good correspondence. Such difference can be attributed to the impact of the estrogens assumed suppressors of innate immunity (Csaba 2019). For some of the blood immunity status indicators, scatter of the values are also quite high, but for many of them trend changes in the dependences on the age difference BA – CA are still pronounced and appear close to the values BA = CA. Certain general observations can also be made from the data acquired for the roughness parameters of the skin. Firstly, there are no specific trend line anomalies in the data, skin roughness parameters of all participants (either male or female) increase with the age, including the plots against the age difference (BA – CA), or normalized age difference (both (BA – CA)/CA and (BA – CA)/BA). In addition, male skin tends to be rougher than that of females one more or less for all age. Thirdly, in the "early age" group the individual differences of the skin roughness parameters between participants are not very significant. Near and above "critical age" (BA = CA) such individual skin roughness differences are becoming significant and, in some cases, extreme and continuously increase with changing BA – CA (Fig. 7). Individual differences in the male skin roughness are also much more pronounced. These observations can be used to support formulated hypothesis that "critical age point" may present certain watershed between young and aging skin helping to individualize the decisions on corresponding skin treatment. It should be stressed that average roughness parameters (like the ones given by Cutometer measurements) may be not optimal for describing surface roughness features for any specific surface, biological or technological alike, as it was shown in relation to the discussion on "optimum roughness" of metallic biomedical implants (e.g., Albrektsson and Wennerberg 2004; Löberg et al. 2010; Koptyug et al. 2014). For example, average parameters cannot adequately distinguish between surfaces with intense waviness (with large characteristic dimensions of features on the surface) having small or large micro-roughness (small scale features on the top), as average roughness values will be still dominated by the waviness (Koptyug et al. 2014). And it is suggested that data of actual measured surface profiles should be analyzed using spectral methods, reflecting the "density" of the features having certain dimensions. In technology, modern instruments allow for embedded functionality providing such analysis. However, in many situations, corresponding analysis of the surface profiles ("raw profile data") are used for the following post-processing. In case of skin roughness characterization, such approach may also be better than using averaged roughness parameters, but as far as we are aware, commercial measurement units like Cutometer do not have the option of providing raw data from the roughness profiles. Correlation analysis Even without true correlation analysis, it could be observed that for many measured parameters trends in the dependencies for the blood immunology and skin cell profiles have certain special points at the same or very similar age difference values. Figure 8 illustrates this statement for the dependencies on the normalized age difference (BA – CA)/BA of the percentages of blood and skin Ts lymphocytes (a) and Th lymphocytes (b) for male participants. It is also quite clear that special point position for male in these graphs is some shifted from BA = CA towards younger age. Visual illustration of blood and skin cell profile parameter correlations: a numbers of cytotoxic Ts lymphocytes in blood (triangles) and epidermis (squares); b numbers of Th lymphocytes in blood (triangles) and epidermis (squares) for male participants plotted against normalized age difference (BA – CA)/CA, with corresponding second order polynomial fitting curves. To help visualization blood lymphocyte relative numbers are unchanged, but all values for the skin lymphocytes are multiplied by 5. Original values are in percentage to the overall T cell counts. Note that positive age difference corresponds to the young age With all reservations due to the relatively small number of participants in the studies, basic correlation analysis of all acquired data can be useful. Pearson correlation analysis was carried out between the roughness parameters of the skin and other measured parameters for all participants (including the results discussed in Sukhovei et al. 2019). Largest correlation coefficients between the skin roughness parameters and age difference (BA – CA) were found for two of them, namely average skin roughness, Sa, and depth of the deepest profile valley, Sv (Table 2). Certain correlations between other skin roughness parameters and age difference BA – CA are also present. Correlation between skin roughness parameters and age difference BA – CA Skin roughness parameter (calculated by the Cutometer embedded software) BA – CA Sa, average roughness − 0.381* Smax, maximum stretching of the roughness profile (difference between the highest "peak" and the deepest "valley" within the whole measured area) − 0.194 Sz, ten-point height (average value of 5 highest peaks minus average value of 5 deepest valleys within the whole measured area) Sp, height of the greatest profile peak Sv, depth of the deepest profile valley 0.413** Sda, mean dale area (average value of the local profile slope in the measured plane) p < 0.05; p < 0.01 Tables 3 and 4 present the correlations of two roughness parameters Sa and Sv and skin cell and immune status parameters (see Sukhovei et al. 2019; for corresponding discussions and data analysis for the skin cell profile parameters). Corresponding correlations of the chosen skin roughness parameters (Sa and Sv) with the epidermal cell counts are rather significant on all positions (except for endotheliocytes and activated endotheliocytes II). Correlations with the skin immune parameters also exist, but on smaller number of positions as compared to the epidermal cell counts. It is not surprising taking into account that skin status and topography was measured on the face, skin cell status was assessed using the samples taken from the gluteal region, and the immunology status is assessed using venous blood samples. Correlations between two average skin roughness parameters and skin cell numbers Skin cells Keratinocytes – 0.617* + 0.689 Activated keratinocytes Fibroblasts Activated fibroblasts Endotheliocytes – 0.053 Activated endotheliocytes (I) Activated endotheliocytes (II) + 0.290 p < 0.01 Correlations between two average skin roughness parameters and skin immune status parameters Skin immune status Mastocytes Activated mastocytes – 0.407* Activated monocytes + 0.333* T lymphocytes Тh lymphocytes Ts lymphocytes B lymphocytes Characteristically, in cases of significant correlations, corresponding coefficients with Sv are positive and with Sa negative. It actually seems counterintuitive, as deeper valleys (reflected by larger Sv values) usually mean larger surface roughness (e.g., larger Sa values). Reflecting to the above discussion on the impact of extracting only averaged parameters from actual skin topography profiles, this may mean that deep skin features with small width (wrinkles) should be analyzed separately and may give better indication of skin aging. Correlations of the age difference and parameters representing epidermal cell profile (Table 5) and skin immune profile discussed in (Sukhovei et al. 2019) were also calculated (Table 6). Correlations of the age difference parameter (BA – CA) are equally significant for the same epidermal cell count parameters, as it is for the correlations of skin roughness ones. Again, there is negligible correlation with the overall number of endotheliocytes, but there is a strong correlation with the number of activated endotheliocytes II. Skin immune profile parameters also show certain correlations with age difference, with strongest correlations for epidermal T lymphocyte, Th lymphocyte, and B lymphocyte numbers. Correlation between epidermal cell profile parameters and age difference BA – CA Epidermal cell numbers 0.69 p < 0.01; *p < 0.05 Correlation between skin immune profile parameters and age difference BA – CA Epidermal immune cell numbers To complete the analysis, correlations of the skin roughness parameters (Sa and Sv) as well as the correlations of the age difference parameter (BA – CA) with the blood cell counts and blood immune profile were calculated. In the majority of cases, correlations were found to be small or insignificant. The only blood immunity parameters having correlation coefficients with Sa and Sv above 0.2 are: Immunoglobulins IgM, IgG, and IgE Parameters of monocyte tests (stimulated and spontaneous NBT test; numbers of monocytes attached to the membrane surface of opsonized sheep erythrocytes) Numbers of T lymphocytes and B lymphocytes Amount of soluble immune complexes in the tests using precipitation by 7% polyethylene glycol Largest correlation coefficients in this case were for the numbers of B lymphocytes: – 0.385 with Sv (p < 0.05) and + 0.278 with Sa. Similarly, the only blood immune parameters having correlation coefficients with (BA – CA) above 0.2 are immunoglobulins IgM (– 0.243) and IgE (0.642, p < 0.01), parameters of monocyte tests (stimulated and spontaneous NBT test, − 0.398 and − 0.353, p < 0.05) and number of T lymphocytes (– 0.279), and amount of soluble immune complexes in the tests using precipitation by 7% polyethylene glycol (0.463). Analysis of the parameter correlations supports the suggestion that dermal and epidermal cell profile, immune profile, and skin topography are inter-related (for some combinations clearly correlated) and that individual parameters (BA – CA) has a strong potential of reflecting skin vitality and state linked to its aging. At the same time, blood immunity indicators are not that strongly correlated to the skin parameters such as skin roughness, or to the age difference parameter (BA – CA). At the same time, certain links of the blood immunity profile to the skin state and age difference seems to exist. Summary of the data analysis Analysis of the epidermal cell profile, skin immune profile, and skin roughness parameter changes with age shows peculiarities in their dependence on the difference of the chronologic and calculated biologic age. Young individuals have biologic age larger than the chronologic, and in later life, it becomes smaller then chronologic one (if the biologic age is calculated using chosen expressions 1 and 2, and the boundaries of the "early," "critical," and "later age" are defined according to expression 3). It appears that dependencies of the critical parameters assumed to be relevant and reflecting skin aging process are changing trends, or having their maximum or minimum near the crossover point BA = CA (calculated biologic age is equal to the chronologic one). Skin roughness increases much more intensely for the late age (BA < CA), and parameter differences between individuals are becoming much more significant. Trend lines for the skin parameter dependencies for male and female also tend to crossover near the point BA = CA. Analysis of the blood cell profile and immune status shows similar peculiarities in the dependences on (BA – CA), though in many cases they are less pronounced than that for the ones reflecting skin roughness. There are certain correlations between BA – CA and skin roughness parameters, but much more pronounced are the correlations with epidermal cell profile and immune status parameters. The "crossover point" BA = CA is different for male and female participants (see also the results presented in Gruenewald et al. 2006; Klemera and Doubal 2006; Fahy et al. 2019), differing almost 10 years being about 35 years for female and 45 years for male participants. In line with findings from other authors and following the results of present studies, one can conclude that the difference of calculated biologic and chronologic age may indeed be used as an indicator of significant changes related to aging, and in particular, the changes in skin properties including epidermal cell and immunity profiles underlying the skin aging processes. This conclusion is well supported by the studies of the age dynamics of skin cell profile parameters, skin and blood immunology profile, skin moisture and sebum levels, and skin roughness values. The dependence of the skin roughness parameters on the biologic and chronologic age difference shows clear increase of the skin roughness for the late age (as defined by used expressions), together with significantly increasing individual differences. It also is clear that for better individualization expressions for calculating biologic age for male and female could be further adjusted. Thus, it can be concluded that available experimental data support the hypothesis that a difference of the biologic age, calculated basing on the forced vital lung capacity value, systolic blood pressure, urea concentration in urine and blood cholesterol level, and a chronologic age could be used as an individual express criterion supporting the decisions on the need and intensity of the skin treatment. Analysis of the results also indicates that it is possible to qualify the skin status according to the early age, critical age, and late age concept with the critical age boundary defined as \|BA – CA\| < 5 years. It is also suggested that using this criterion can support the decisions if a person "does not need skin treatment," "may need certain, mild treatment," and "may need more intense skin care or treatment" depending on the particular clinical case. For the particular group of subjects, it was possible to re-define this criterion, linking it to the chronologic age of participants. Taking into account relative simplicity and generally good availability of the tests needed to acquire data for calculating biologic age using chosen expressions, such criterion can become a useful tool for skin care specialists and medics in taking decisions about skin care and skin treatment in individual cases. Relatively small number of participants to certain extent restricts the validity of above conclusions, and thorough tests should be further performed with larger number of participants. It would also be important to perform a study following the same individuals for a period of time and correlating calculated biologic age with parameters related to aging and critical for taking decisions about skin treatment. It should be specifically noted that used expressions common for the geriatric research in Russia give counterintuitive values for biologic age (in this case, biologic age is larger than chronologic one for young people). In addition, additional studies should be performed to analyze if the other accepted expressions for the biologic age calculation would be equally good or better when predictors of the critical to skin aging are based on the age difference BA – CA. Authors express their acknowledgements to Professor Vladimir Kozlov from the Institute of Clinical and Experimental Immunology for fruitful discussions. Main idea of the research belongs to YS; authors of the main hypothesis were YS and AK; designing, organizing, and performing experiments were done by YS, EK, IU, and DK; data analysis was performed by AK. All authors read and approved the final manuscript. Studies were carried out within the current research program of the Institute of Clinical Immunology and no external funding was received. All participants were properly informed on the nature of studies and specific procedures and gave signed written consent to participate. The consent forms and the plans for the research were approved by the Ethics Commission of the Institute of Clinical Immunology according to the formal requirements issued by the State Department of Health of Russian Federation. All participants and authors gave their consent for the publication of the study results, and a formal consent for publication was granted by the Research Council of the Institute of Clinical and Experimental Immunology. It is also confirmed that the work conforms to the principles of WHO Helsinki Declaration. Albrektsson T, Wennerberg A. Oral implant surfaces: part 1-review focusing on topographic and chemical properties of different surfaces and in vivo responses to them. 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Typical dynamics of plane rational maps with equal degrees JMD Home This Volume An Urysohn-type theorem under a dynamical constraint 2016, 10: 339-352. doi: 10.3934/jmd.2016.10.339 On small gaps in the length spectrum Dmitry Dolgopyat 1, and Dmitry Jakobson 2, Department of Mathematics, University of Maryland, Mathematics Building, College Park, MD 20742-4015, United States Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Str. West, Montréal QC H3A 2K6 Received February 2016 Revised June 2016 Published August 2016 We discuss upper and lower bounds for the size of gaps in the length spectrum of negatively curved manifolds. For manifolds with algebraic generators for the fundamental group, we establish the existence of exponential lower bounds for the gaps. 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Channel estimation for massive MIMO TDD systems assuming pilot contamination and flat fading Felipe A. P. de Figueiredo ORCID: orcid.org/0000-0002-2167-72861, A Correction to this article was published on 13 March 2018 This article has been updated Channel estimation is crucial for massive massive multiple-input multiple-output (MIMO) systems to scale up multi-user (MU) MIMO, providing great improvement in spectral and energy efficiency. This paper presents a simple and practical channel estimator for multi-cell MU massive MIMO time division duplex (TDD) systems with pilot contamination in flat Rayleigh fading channels, i.e., the gains of the channels follow the Rayleigh distribution. We also assume uncorrelated antennas. The proposed estimator addresses performance under moderate to strong pilot contamination without previous knowledge of the cross-cell large-scale channel coefficients. This estimator performs asymptotically as well as the minimum mean square error (MMSE) estimator with respect to the number of antennas. An approximate analytical mean square error (MSE) expression is also derived for the proposed estimator. Massive multiple-input multiple-output (MIMO) antenna systems potentially allow base stations (BSs) to operate with huge improvements in spectral and radiated energy efficiency, using relatively low-complexity linear processing. The higher spectral efficiency is attained by serving several terminals in the same time-frequency resource through spatial multiplexing, and the increase in energy efficiency is mostly due to the array gain provided by the large set of antennas [1]. The expected massive MIMO improvements assume that accurate channel estimations are available at both the receiver and transmitter for detection and precoding, respectively. Additionally, the reuse of frequencies and pilot reference sequences in cellular communication systems causes interferences in channel estimation, degrading its performance. Since both the time-frequency resources allocated for pilot transmission and the channel coherence time are limited, the number of possible orthogonal pilot sequences is also limited, and as a consequence, the pilot sequences have to be reused in neighbor cells of cellular systems. Therefore, channel estimates obtained in a given cell get contaminated by the pilots transmitted by the users in other cells [2]. This coherent interference is known in the literature as pilot contamination, i.e., the channel estimate at the base station in one cell becomes contaminated by the pilots of the users from other cells [3]. The contamination not only reduces the quality of the channel estimates, i.e., increases the MSE, but also makes the channel estimates statistically dependent, even though the true channels are statistically independent. Moreover, pilot contamination does not disappear with the addition of more antennas [4]. Massive MIMO systems operating in TDD assume channel reciprocity between uplink and downlink in order to minimize pilot overhead, transmitting pilot reference signals only in the uplink. In this scenario, pilot overhead cost is proportional to the number of terminals and improved estimation quality can be achieved due to the large number of antennas [5, 6]. Base stations estimate channels usually based on least squares (LS) [3] or minimum mean square error (MMSE) [7–9] methods. Besides, inter and intra-cell large-scale fading coefficients are assumed to be perfectly known when applying the MMSE method in the great majority of works [5, 9–13]. In a real-world network deployment, although changing slowly, the large-scale fading coefficients must be estimated and updated from time to time. Additionally, the estimation error of the large-scale fading coefficients impacts significantly on the performance of uplink data decoding and downlink transmission (e.g., precoding and beamforming) [14–16]. Approaches on how to estimate the large-scale fading coefficients are presented in the following pieces of work [10, 14, 17]. The most commonly used analytical massive MIMO channel is the spatially i.i.d. frequency non-selective (flat) fading channel model. Flat fading channels are also known as amplitude varying channels and narrowband channels as the signal's bandwidth is narrow compared to channel's bandwidth [18]. In this narrowband channel model, the channel gain between any pair of transmit-receive antennas is modeled as a complex Gaussian random variable. This model relies on two assumptions: (i) the antenna elements in the transmitter and receiver being spatially well separated once the more widely spaced (in wavelengths) the antenna elements, the smaller the spatial channel correlation [19, 20], and (ii) the presence of a large number of temporally but narrowly separated multipaths (common in a rich-scattering environment), whose combined gain, by the central-limit theorem, can be approximated by a Gaussian random variable [20]. Flat fading channels present a channel response that exhibits flat gain and linear phase over a bandwidth (coherence bandwidth) that is greater than the signal's bandwidth. Therefore, all frequency components of the signal will experience the same magnitude of fading, resulting in a scalar channel response. The gain applied to the signal varies over time according to a fading distribution. In this work, we consider that the gain applied to the signal passing through this channel will vary randomly, according to a Rayleigh distribution. We additionally assume that the antenna spacing is sufficiently large so that the antennas are uncorrelated. In this paper, we deal with the channel estimation and pilot contamination problems associated with uplink training in flat Rayleigh fading channels and understand its impact on the operation of multi-cell MU massive MIMO TDD cellular systems. We propose and evaluate an efficient and practical channel estimator that does not require previous knowledge of inter/intra-cell large-scale fading coefficients (i.e., interference) and noise power. Differently from [21], we employ the maximum likelihood (ML) method to find an estimator for the interference plus noise power term in the MMSE channel estimator. We show that this estimator is not only unbiased but also achieves the Crámer-Rao lower bound. We replace this estimator back into the MMSE estimator and prove that the performance of the new channel estimator asymptotically approaches that of the MMSE estimator. Simulation results confirm that the performance of the proposed channel estimator approaches that of the ideal MMSE estimator asymptotically with the number M of antennas, i.e., M→∞. Additionally, in contrast with [21], we derive an approximate analytical MSE expression for the proposed channel estimator that is more mathematically tractable and not susceptible to numerical issues. In this section, we survey previous work on channel estimation and pilot contamination mitigation. A TDD cellular system employing BSs equipped with large numbers of antennas that communicate simultaneously with smaller numbers of cheap, single-antenna terminals through MU MIMO techniques is proposed in [3]. The author employs LS channel estimation in order to study and evaluate the problems caused by pilot contamination to such systems. He concludes that even when different sets of orthogonal pilots are used in different cells, it makes little difference to the resulting signal-to-interference ratio (SIR). This work is the first one to present the massive MIMO concept and identify its intrinsic issues, however, it fails to suggest ways to mitigate the pilot contamination problem. The impact of pilot contamination on multi-cell systems is studied in [5]. The authors adopt MMSE channel estimation for the analysis of pilot contamination and the achievable rates in a massive MIMO system suffering from such problem. They propose a multi-cell MMSE-based precoding method that mitigates the pilot contamination problem by considering the set of training sequences assigned to the users in the solution of an optimization problem that minimizes the error seen by users in the serving cell and the interference seen by the users in all other cells. Simulation results show that the proposed approach has significant gains over certain single-cell precoding methods such as zero-forcing. In summary, the authors address the pilot contamination problem through a precoding technique and assume that the large-scale fading coefficients are known to all BSs. MMSE channel estimation is used in [7] to derive approximations of the achievable uplink and downlink rates with several linear precoders and detectors for realistic system dimensions, i.e., systems where the number of antennas is not extremely large compared to the number of users. Simulation results show that the approximations are asymptotically tight, but accurate for realistic systems. The authors do not propose any approach to mitigate the pilot contamination problem, however, they study and evaluate its impact on the achievable rates. The impact of pilot contamination effect on the achievable uplink ergodic rate when using linear detection in multi-cell MU massive MIMO systems under a more realistic physical channel model is assessed in [8]. The authors assume that the channel vectors for different users are correlated, or not asymptotically orthogonal due to the antennas not being sufficiently well separated and/or the propagation environment not offering rich enough scattering. Moreover, they assume that the BS performs MMSE channel estimation based on training sequences received on the uplink and a priori knowledge of the large-scale fading coefficients. In [9], the polynomial expansion (PE) technique is applied to channel estimation of massive MIMO systems in order to approximate the MMSE estimator and thereby obtain a new set of low-complexity channel estimators. Conventional MMSE estimators present cubic complexity due to an inversion operation while the estimator proposed in [9] reduces this to square complexity by approximating the inverse by a L-degree matrix polynomial. The proposed estimator achieves near-optimal MSE with low polynomial degrees. However, statistical knowledge of channel and disturbance parameters at the receiver is assumed in this paper. Outer multi-cellular precoding is employed in [10] to devise a method used to eliminate pilot contamination in massive MIMO systems. Each BS performs two levels of precoding, firstly it estimates and shares only the large-scale fading coefficients with a central entity (network controller) which computes the precoding matrices and sends them back to the BSs, i.e, outer precoding. Next, each BS performs local precoding using estimates of the fast-fading vectors, i.e., inner precoding. The proposed approach is shown to completely mitigate the pilot contamination problem, making it possible to construct interference and noise free multi-cell massive MIMO systems with frequency reuse one and infinite downlink and uplink signal-to-interference-plus-noise ratios (SINRs). The proposed method employs MMSE channel estimation, however, the effectiveness of this method lies in the estimation accuracy of the shared large-scale fading coefficients from each BS. The authors also propose a method to estimate the large-scale fading coefficients. As this approach needs to share the large-scale coefficients with the network controller for outer precoding computation, it presents a higher computational complexity than non-cooperative approaches. The authors in [11], adopt a massive MIMO system model that is based on spatially correlated channels. They devise a covariance aided channel estimation method which exploits the covariance information of both desired and interfering user channels. The Bayesian method is used to derive two different channel estimators (it is also shown that the Bayesian estimators coincide with the MMSE estimators), one for all channels from users in all cells to the target cell and the other one for the channels from users within the target cell. Results show that in the ideal case, where the desired and the interference covariance matrices span distinct subspaces, the pilot contamination effect tends to vanish in the large antenna array case. As a consequence, users with mutually non-overlapping angle of arrival (AoA) hardly contaminate each other. Based on the results, the authors propose a coordinated pilot assignment strategy which assigns carefully selected groups of users to identical pilot sequences. A semi-blind iterative space-alternating generalized expectation maximization (SAGE) based channel estimation algorithm for massive MIMO systems with pilot contamination is proposed in [13]. The proposed method does not assume a priori knowledge on the large-scale fading coefficients of the interfering cells, employing an estimate obtained from the received signal. The method updates the pilot based MMSE channel estimates iteratively with the help of the SAGE algorithm, which improves the initial estimate with the help of pilot symbols and soft information of the transmitted data. However, as it refines the channel estimates over some iterations starting from an initial MMSE channel estimation, it presents a computational complexity that is higher than the one presented by pure blind and linear estimators. After surveying the literature on channel estimation and pilot contamination mentioned above, it is clear that, for clarity, in the great majority of studies the authors always assume complete knowledge on large-scale fading coefficients, i.e., path-loss and shadow fading, of the interfering cells, which is not the case in practical deployments of MU Massive MIMO systems. Furthermore, several studies propose solutions that present additional computational complexity in order to mitigate the pilot contamination problem. The main contribution of our work is the proposal and assessment of a simple and practical channel estimator used to mitigate the pilot contamination problem. The proposed estimator does not assume a priori knowledge of the large-scale fading coefficients of the interfering cells. Moreover, it does not require the heavy overhead created by their estimation once it obtains them from the received signal. The remainder of this work is divided into four parts: First, we present the problem structure, signal model adopted for this study and briefly discuss two well-known channel estimators, namely, LS and MMSE linear estimators. Then, we introduce the proposed channel estimator for flat Rayleigh fading channels. Later, some numerical results are presented in order to support the effectiveness of the proposed estimator against the well-known linear estimators. Finally, we present our conclusions. Problem structure Let us assume as illustrated in Fig. 1 a multi-cell system with L cells, where each cell has a BS at its center with M co-located antenna elements and K randomly located single antenna users. Let us also assume Rayleigh fading channels being independent across users and antennas. Let g ilkm represent the complex gain of the channel from the kth user in the lth cell to the mth BS antenna in the ith cell. We can write $g_{ilkm} = \sqrt {\beta _{ilk}} h_{ilkm}$ where $\sqrt {\beta _{ilk}}$ is the large-scale coefficient encompassing both path loss and log-normal shadowing. We assume the same large-scale coefficient value for all BS co-located antennas, and h ilkm is the small-scale coefficient with a circularly symmetric complex normal distribution $\mathcal {CN}(0,1)$. We assume that the large-scale fading coefficients do not depend on the frequency as well as on the antenna index m of a given BS because typically, the distance between a user and a BS is significantly larger than the distance between the BS antennas [10]. Therefore, between a BS and a user, there is only one large-scale fading coefficient. Moreover, these coefficients only change when a user considerably change its geographical location. The wireless channels are considered static during the channel coherence time (i.e., channel estimates are effective only in this time interval) and independent across users and antennas. The M×1 channel vector from the kth user in the lth cell to the M antennas at the ith BS is defined by g ilk =[gilk1,gilk2,⋯,g ilkM ]T. The overall M×K channel matrix G il is obtained by column concatenating vectors g ilk for all cell users, that is, G il =[gil1,gil2⋯g ilK ]. For detection and precoding, BS i needs to know the channels of the users in cell i, namely {g iik ,∀k}. The same way as in the literature, we treat {β ilk } as being deterministic during the channel estimation [1, 6, 8, 13]. As described, the overall channel matrix G il can also be defined directly by the channel coefficients, $$ \mathbf{G}_{il} = \left[\begin{array}{cccc} g_{il11} & g_{il21} & \cdots & g_{ilK1} \\ g_{il12} & g_{il22} & \cdots & g_{ilK2} \\ g_{il13} & g_{il23} & \cdots & g_{ilK3} \\ \vdots & \vdots & \ddots & \vdots \\ g_{il1M} & g_{il2M} & \cdots & g_{ilKM} \\ \end{array} \right]. $$ Based on the assumption of channel reciprocity, we adopt the TDD protocol depicted in Fig. 2 and proposed in [22]. Due to the reciprocity principle, only the uplink channels need to be estimated while the downlink channels are equal to the transpose of the uplink channels. It is important to note that the length of the TDD frames is limited by the channel coherence time [22, 23]. According to the TDD protocol, first, all users in all cells send their uplink training sequences synchronously. After that, the BSs use the training sequences to estimate the uplink channels. Next, the users send uplink data signals. Then, the BSs use the estimated channels to detect uplink data and generate precoding matrices used to transmit downlink data. TDD transmission protocol Uplink training Each user transmits an uplink training sequence so that the user serving BS can estimate the channels per antenna and subsequently detect the transmitted user data. We assume that users in different cells transmit data at the same time-frequency resource (a typical scenario in massive MIMO) and that the pilot reuse factor is one, the worst possible use case scenario [3]. As all BSs reuse the same set of pilots and transmit at the same time-frequency resource, the pilot contamination problem arises, consequently, all the other BSs will also receive the pilots sent by users being served by other BSs, limiting the quality of the channel estimation [24]. The pilot signals of K users are represented by a N×K matrix S of the form S=[s1,s2,⋯,s K ], where N is the length of the pilot sequences. Each pilot sequence is of the form $\mathbf {s}_{k} = \left [ s_{k}^{0}, s_{k}^{1}, \cdots, s_{k}^{N-1}\right ]^{T}$. The pilot matrix, S, exhibits orthogonal property SHS=NI K . The pilots are created by applying cyclic shifts to Zadoff-Chu (ZC) root sequences with length N, where N is a prime number. These sequences exhibit some useful properties: (i) cyclically shifted versions of themselves are orthogonal to each other, (ii) constant amplitude, (iii) zero auto-correlation, (iv) flat frequency domain response, and (v) cross-correlation between two ZC sequences is low [25]. Some of the reasons why they are adopted in communication systems like long-term evolution (LTE) are (i) channel estimation at receiver is made simpler due to their small variation in frequency, (ii) inter-cell interference is reduced as they present low cross-correlation, (iii) high peak to average power ratio (PAPR) is reduced due to their small variation in time. ZC sequences are used in this work due to the properties mentioned above [25]; however, any other sequences could be used as long as they exhibit the required orthogonal property. Additionally, we assume that N≥K in order to avoid underdetermined systems. The received uplink training sequences at the ith BS can be represented as a M×N matrix defined as $$ \mathbf{Y}_{i} = \sqrt{q} \sum^{L}_{l=1}{ \mathbf{G}_{il} \mathbf{S}^{H} + \mathbf{N}_{i}}, $$ where q is the uplink power or transmit signal to noise ratio (TX SNR) and N i is a M×N noise matrix with independent and identically distributed elements following $\mathcal {CN}(0,1)$. Equation (2) can also be written as showed below, which clearly highlights the coherent inter-cell interference caused by users employing the same pilot sequences in other BSs. $$ \mathbf{Y}_{i} = \underbrace{ \sqrt{q} \mathbf{G}_{ii} \mathbf{S}^{H} }_{\text{Desired pilot signals}} + \underbrace{\sqrt{q} \sum^{L}_{l=1, l \neq i}{ \mathbf{G}_{il} \mathbf{S}^{H}}}_{\text{Undesired pilot signals}} + \underbrace{\mathbf{N}_{i}}_{\text{Noise}}. $$ LS channel estimator For estimation of the channel g ilk at BS i, a sufficient statistic [26–28] is given by $$ \begin{aligned} \mathbf{z}_{ik} &= \frac{1}{\sqrt{q}N} \mathbf{Y}_{i} \mathbf{s}_{k} = \sum_{l=1}^{L}{\mathbf{g}_{ilk}} + \frac{\mathbf{N}_{i}\mathbf{s}_{k}}{\sqrt{q}N} \\ &= \underbrace{ \mathbf{g}_{iik} }_{\text{Desired channel}} + \underbrace{ \sum_{l=1, l \neq i}^{L}{\mathbf{g}_{ilk}} }_{\text{Inter-cell interference}} + \underbrace{ \frac{\mathbf{N}_{i}\mathbf{s}_{k}}{\sqrt{q}N}}_{\text{Noise}}. \end{aligned} $$ where z ik is a column vector with a $\mathcal {CN}(\mathbf {0}_{M},\zeta _{ik}\mathbf {I}_{M})$ distribution and $$ \zeta_{ik} = \sum_{l=1}^{L}{\beta_{ilk}} + \frac{1}{qN}. $$ Additionally, the term corresponding to noise in (4) has a $\mathcal {CN}\left (\mathbf {0}_{M},\frac {1}{qN}\mathbf {I}_{M}\right)$ distribution. Therefore, the least square estimator is given by [26] $$ \hat{\mathbf{g}}_{iik}^{\text{LS}} = \mathbf{z}_{ik}. $$ The MSE per antenna of the LS estimator is given by $$ \eta_{ik}^{\text{\text{LS}}} = \frac{1}{M} \mathbb{E} \left[ \left\\| \hat{\mathbf{g}}_{iik}^{\text{LS}} - \mathbf{g}_{iik} \right\\|^{2} \right] = \zeta_{ik} - \beta_{iik}. $$ As known, the LS estimator has larger MSE than the MMSE estimator; however, it does not need prior knowledge of the large-scale fading coefficients, {β ilk }. Due to pilot contamination, as q→∞, $\eta _{ik}^{\text {LS}} \to \sum _{l=1,l \neq i}^{L}{\beta _{ilk}} $. MMSE channel estimator A great number of massive MIMO works adopt the MMSE estimation method to obtain channel knowledge [5, 8]. Those works assume that all large-scale fading coefficients, i.e., {β ilk ,i≥1,l≤L,1≤k≤K}, are perfectly known. In practice, this assumption might not be reasonable. In case we consider the coefficients {β ilk } perfectly known at the BS, the ideal MMSE estimator is given by [26] $$ \hat{\mathbf{g}}_{iik}^{\text{MMSE}} = \frac{\beta_{iik}}{\zeta_{ik}}\mathbf{z}_{ik}, $$ where $\hat {\mathbf {g}}_{iik}^{\text {MMSE}} \sim \mathcal {CN}\left (\mathbf {0}_{M},\frac {\beta _{iik}^{2}}{\zeta _{ik}}\mathbf {I}_{M}\right)$ and the MSE of MMSE estimator is given by $$ {}\eta_{ik}^{\text{MMSE}} = \frac{1}{M} \mathbb{E} \left[\! \left\\| \hat{\mathbf{g}}_{iik}^{\text{MMSE}} - \mathbf{g}_{iik} \right\\|^{2} \right] = \beta_{iik}\left(1 - \frac{\beta_{iik}}{\zeta_{ik}} \right). $$ Due to pilot contamination, as q→∞, $\eta _{ik}^{\text {mmse}} \to \beta _{iik} \left (1 - \frac {\beta _{iik}}{\sum _{l=1}^{L}{\beta _{ilk}}} \right)$. Proposed channel estimator In this work, we employ the ML method to estimate the parameter ζ ik [26]. Applying the ML method to $f(\mathbf {z}_{ik};\zeta _{ik}) \sim \mathcal {CN}(\mathbf {0}_{M},\zeta _{ik}\mathbf {I}_{M})$, we find the following estimator for ζ ik given the observation z ik $$ \hat{\zeta_{ik}} = \frac{\lVert \mathbf{z}_{ik} \rVert^{2} }{M}. $$ This estimator has $\mathbb {E} \left [ \hat {\zeta _{ik}} \right ] = \zeta _{ik}$, which shows that the ML estimator is unbiased, and $ \text {var}\left \{ \hat {\zeta _{ik}} \right \} = {\zeta _{ik}^{2}}/{M}$. In order to assess the efficiency of the estimator we derive the Cramér-Rao bound as [26] $$ \text{var} \left(\hat{\zeta_{ik}} \right) \geq \frac{\zeta_{ik}^{2}}{M}. $$ Therefore, the ML estimator derived for ζ ik is the minimum variance unbiased estimator (MVUE), i.e., it is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter [26]. This simple and effective estimator is derived based on the observation that the MMSE estimator does not need to know the individual large-scale fading coefficients, {β ilk }, as assumed in the existing literature, but just ζ ik suffices. The proposed estimator for ζ ik makes the acquisition of inter-cell large-scale fading coefficients unnecessary. The task of gaining knowledge of those coefficients may be unjustifiable in practice due to the excessive, e.g., in case there are L cells serving K users in each one of them, each BS needs to acquire (L−1)K inter-cell large-scale coefficients. Swapping ζ ik with $\hat {\zeta _{ik}}$ in (8) produces the proposed channel estimator, which is defined by $$ \hat{\mathbf{g}}_{iik}^{\text{prop}} = M \beta_{iik} \frac{\mathbf{z}_{ik}}{ \lVert \mathbf{z}_{ik} \rVert^{2} }. $$ This estimator approaches the ideal MMSE estimator asymptotically with respect to M. The estimator has $\mathbb {E} \left [ \hat {\mathbf {g}}_{iik}^{\text {prop}} \right ] = \mathbf {0}_{M}$ and variance given by $$ \text{Var}\left[ \hat{\mathbf{g}}_{iik}^{\text{prop}} \right] = \mathbb{E} \left[ \hat{\mathbf{g}}_{iik}^{\text{prop}}\left(\hat{\mathbf{g}}_{iik}^{\text{prop}}\right)^{H} \right] = \left(\frac{M^{2}}{M-1}\frac{\beta_{iik}^{2}}{\zeta_{ik}}\right) \mathbf{I}_{M}. $$ As can be seen by analyzing equation (13), as $M \rightarrow \infty, \text {Var}\left [\hat {\mathbf {g}}_{iik}^{\text {prop}}\right ] \rightarrow \frac {\beta ^{2}_{iik}}{\zeta _{ik}}$. An approximation to the MSE per antenna of this estimator is given by $$ {}\eta_{ik}^{\text{\text{prop}}} = \frac{1}{M} \mathbb{E} \left[ \lVert \hat{\mathbf{g}}_{iik}^{\text{prop}} - \mathbf{g}_{iik} \rVert^{2} \right] \approx \beta_{iik} \left[ 1 - \frac{(M-2)\beta_{iik}}{(M-1)\zeta_{ik}} \right]. $$ The approximate MSE in (14) for the proposed estimator decreases with increasing transmitting power q, increasing M or decreasing β iik , which means smaller interference level from other cells, i.e., smaller pilot contamination. Due to pilot contamination, as q→∞ and M→∞, $\eta _{ik}^{\text {prop}} \to \beta _{iik} \left (1 - \frac {\beta _{iik}}{\sum _{l=1}^{L}{\beta _{ilk}}} \right)$. Remark 3 clearly shows that the MSE of the proposed estimator tends to that of the MMSE estimator when both q and M→∞. The proof for the approximation of the MSE is given in Appendix A. For the sake of clarity, we reproduce below the closed-form MSE equation (9) presented in [21]. $$ \eta_{ik}^{\text{prop(closed-form)}} = \frac{M}{M-1}\frac{\beta_{iik}^{2}}{\zeta_{ik}} + \beta_{iik} - 2 \beta_{iik}\theta_{ik} $$ $$ \begin{aligned} \theta_{ik} = \int_{0}^{1} \int_{-1}^{1} \frac{k_{ik}^{2}(1-t)+k_{ik}w\sqrt{t(1-t)}}{k_{ik}^{2}(1-t)+2k_{ik}w\sqrt{t(1-t)}+t} \\. f_{T}(t)f_{W}(w)dwdt \end{aligned} $$ with $k_{ik} = \sqrt {\frac {\beta _{iik}}{\zeta _{ik}-\beta _{iik}}}$, and f T (t) and f W (w) are given by $$ \begin{aligned} f_{T}(t) = \frac{\Gamma(2M)}{(\Gamma(M))^{2}}(t(1-t))^{M-1}, 0 < t < 1 \end{aligned} $$ $$ \begin{aligned} f_{W}(w) = \frac{M}{\pi} B\left(\frac{1}{2},M\right) (1-w^2)^{M-\frac{1}{2}}, \|w\| < 1. \end{aligned} $$ The difference between the closed-form, given by Eq. (9) in [21], and the approximated MSE expressions are defined by $$ {}\eta_{ik}^{\text{prop (closed-form)}} - \eta_{ik}^{\text{prop (approx.)}} = 2 \beta_{iik} \left\lbrace \frac{\beta_{iik}}{\zeta_{ik}} - \theta_{ik} \right\rbrace, $$ where θ ik is defined in [21]. As both q and M→∞, $\theta _{ik} \to \frac {\beta _{iik}}{\zeta _{ik}}$ and then, $\eta _{ik}^{\mathrm {prop (closed-form)}} - \eta _{ik}^{\mathrm {prop(approx.)}} \to 0$. We find Remark 4 by using Remark 3 and equaling the closed-form and approximated MSE expressions. This remark shows that the difference between the closed-form and the approximated MSE expressions decreases, tending to 0, as both uplink power, q, and number of receiving antennas, M, increase. The average normalized squared Euclidean distance between $\hat {\mathbf {g}}_{iik}^{\text {prop}}$ and $\hat {\mathbf {g}}_{iik}^{\text {MMSE}}$ is given by $$ \frac{1}{M} \mathbb{E} \left[ \left\\| \hat{\mathbf{g}}_{iik}^{\text{prop}} - \hat{\mathbf{g}}_{iik}^{\text{MMSE}} \right\\|^{2} \right] = \frac{1}{M-1} \frac{\beta_{iik}^{2}}{\zeta_{ik}}. $$ The proof of (20) is given in Appendix B. From (5) and (20), it is easily noticeable that the average distance decreases with increasing M, decreasing q, increasing β ilk ,i≠l, and decreasing β iik . In this section, we compare the performance of the proposed channel estimator with that of the MMSE and LS estimators. We adopt a typical multi-cell structure as the one shown in Fig. 1 with L=7 cells (one central cell surrounded by 6 other cells), K=10 users in each cell, frequency reuse factor of 1 and N=K pilot symbols. We consider two different types of setups for {β ilk }, one with fixed values and other with random values. For the fixed case, we set β iik =1 and β ilk =a,∀ l≠i, where a represents the cross-cell interference level. The value selected for a in the fixed case is 0.05, and it is chosen so that there is moderate cross-cell interference level from users being served by other BSs, i.e., not being served by the central cell. For the random case, users in each cell are uniformly distributed within a ring with radii d0=100 m and d1=1000 m respectively. The large-scale fading coefficients {β ilk } are independently generated by $\beta _{ilk} = \psi / \left (\frac {d_{ilk}}{d_{0}}\right)^{v}$, where v=3.8, $10 \ \text {log}_{10}(\psi) \sim \mathcal {N}\left (0,\sigma _{\text {shadow, dB}}^{2}\right)$ with σshadow, dB=8, and d ilk is the distance of the kth user in the lth cell to the ith BS. Both, the path loss exponent, v, and the standard deviation of the log-normal shadowing, σshadow, dB, are common values for outdoor shadowed urban cellular radio environments [18, 29]. The results in Fig. 3 show MSE versus SNR (uplink pilot power q) performances for a=0.05 and M=70. As can be seen, analytical, approximated, and simulation MSEs match for all estimators. With the increase of SNR, MSEs of all the estimation methods decrease. There are MSE floors for all the three estimators due to pilot contamination (see Remarks 1, 2, and 3). At low SNR, the MSE of the proposed estimator is very close to that of the ideal MMSE estimator. On the other hand, as can be noticed, with the increase of the SNR, the gap between the ideal MMSE estimator and the proposed one increases (see Remark 5). Channel estimation MSE versus uplink pilot power In Fig. 4, we compare MSE versus the number of BS antennas M under the setting of a=0.05 and TX SNR q=10 dB. With the increase of M, the MSE of the proposed estimator approaches that of the ideal MMSE, while the MSE of LS estimator does not change. Due to numerical issues, the closed-form MSE expression presented in [21] does not produce values for M>85. During our simulations, comparing the closed-form expression given by equation (15) and the approximated MSE expression given by (14), we noticed that the Γ(2M) function in the numerator of equation (16) grows without bound, reaching values that are greater than the largest possible finite floating-point number represented by the IEEE double precision format, i.e., 1.7977e+308 [30], for values of M greater than 85. A double precision variable goes to +Inf after the largest possible number [30]. On the other hand, as can be seen in Fig. 4, the approximate analytical MSE expression (14) does not present the same problem and, therefore, can be used to evaluate the MSE for any number of antennas, M without any numerical issue. MSE performance versus number of BS collocated antennas, M In Fig. 5, we compare MSE performance with respect to various levels of cross-cell interference, a, with q = 10 dB and two different number of antennas, M = 30 and M = 90. We can see that when a increases (the effect of pilot contamination increases), the estimation performance degrades. At a low cross-cell interference level, LS presents a slightly better MSE when compared to the proposed estimator. This difference disappears as M increases, as can be noticed in the plot with M = 90. As the interference level increases, the proposed method outperforms the LS estimator substantially and approaches the ideal MMSE performance (see Remark 5). Channel estimation MSE versus cross-cell interference level In Fig. 6, we evaluate the MSE performance under random large-scale fading coefficients {β ilk } with M = 30. The results are obtained by averaging MSEs over 10000 realizations of {β ilk }. As can be observed, simulation MSE matches with the analytical MSE. Additionally, the sensitivity of the proposed estimator against inaccuracy of β iik by using an estimate $\beta _{iik} = \beta _{iik}\left (1 + \mathcal {N}\left (0,\sigma ^{2}\right)\right)$ is investigated. The performance degradation for σ2=0.1 is noticeable at high SNR but for σ2=0.01, it is insignificant. The proposed estimator still outperforms the LS estimator significantly. Average channel estimation MSE under random {β ilk } In Fig. 7, we compare the distance between the proposed and MMSE channel estimators for different number of antennas, M, with a = 0.05. As the Remark 5 states, the distance is small at low SNR, increasing with SNR until a ceiling is reached. As can be also noticed, the ceiling value decreases with the number of antennas, M. Distance between proposed and MMSE estimators (Remark 5) In Fig. 8, we compare the absolute distance between the approximated MSE expression presented in (13) and the analytical (closed form) MSE expression presented in [21] for various SNR and M values with a = 0.05. The distance between the MSE expressions is small at low SNR, increasing with SNR until a ceiling value is reached. As can be noticed, the ceiling value decreases with the number of antennas, M. For M = 50, the ceiling distance is smaller than 1e−4, showing that the approximated MSE expression can replace the one presented in [21]. Absolute distance between closed form and approximated MSE expressions In this work, we have introduced a simple and practical channel estimator for massive MIMO TDD systems with pilot contamination in a flat channel environment. The proposed estimator replaces the combined interference plus noise power term in the ideal MMSE estimator with a maximum likelihood estimator for that term. Moreover, the proposed estimator presents MSE results that are very close to that of the ideal MMSE estimator without requiring previous knowledge of noise and interference statistics. Additionally, we have derived an approximate analytical MSE expression for the proposed estimator which can be useful in system design and performance evaluation. We have also shown that the MSE expression presented here asymptotically approaches that of the MMSE estimator. Finally, the simpler approximate analytical MSE expression presented here can be used instead of the more complex and susceptible to numerical issues one presented in [21]. For the proof of the approximate MSE of the proposed estimator, we need to present a few Lemmas. Lemma 1 If $X_{m} \sim \mathcal {CN}\left (0,\sigma ^{2}\right) \ \forall m$ are independent, then $\sum _{m=1}^{M}{\lVert X_{m} \rVert ^{2}} \sim \Gamma \left (M,\sigma ^{2}\right)$. If X∼Γ(k,θ) and $\frac {1}{X} \sim \Gamma ^{-1}(k,\theta)$, i.e., the inverse-gamma distribution, then $\mathbb {E} \left \lbrace \frac {1}{X} \right \rbrace = \frac {1}{\theta (k-1)}$. Let μ X and μ Y be the expectations of X and Y, $\sigma _{Y}^{2}$ be the variance of Y, and σ XY be their covariance. Then, the expectation, $\mathbb {E} \{X/Y \}$, can be approximated by $$ \mathbb{E} \left\lbrace \frac{X}{Y} \right\rbrace \approx \frac{\mu_{X} }{ \mu_{Y}} - \frac{\sigma_{XY}}{\mu_{Y}^{2}} + \frac{\mu_{X}}{\mu_{Y}^{3}} \sigma_{Y}^{2}. $$ For a function that depends on two variables, x and y, the second order Taylor expansion series about the point (a,b) is given by $${} \begin{array}{ll} g(x,y) = &g(a,b)+g_{x}(a,b)(x-a) + g_{y}(a,b)(y-b) \\ &+\frac{1}{2!} \left(g_{xx}(a,b)(x-a)^{2} \!+ 2g_{xy}(a,b)(x-a)(y-b)\right.\\ &\left.+ g_{yy}(a,b)(y-b)^{2} \right), \end{array} $$ where the subscripts denote the respective partial derivatives. The partial derivatives are defined by g y =−X/Y2, g yy =2X/Y3, g x =1/Y, g xx =0, and g xy =−1/Y2. Applying the derivatives into (22), the second order Taylor expansion of g(X,Y)=X/Y around the mean point (μ X ,μ Y ), the following is obtained $$ \begin{array}{ll} \frac{X}{Y} \approx &\frac{\mu_{x}}{\mu_{y}} - \frac{\mu_{x}}{\mu_{y}^{2}}(Y - \mu_{y}) + \frac{1}{\mu_{y}}(X - \mu_{x})\\ &+\frac{1}{2!} \left(\frac{2\mu_{x}}{\mu_{y}^{3}}(Y - \mu_{y})^{2} - \frac{2}{\mu_{y}^{2}}(Y - \mu_{y})(X - \mu_{x}) \right). \end{array} $$ Finally, applying the expectation operator, $\mathbb {E} \left \lbrace.\right \rbrace $, to (23) concludes the proof. □ Proof of the approximate MSE, $\eta _{ik}^{\text {prop}}$ For the proof of the approximate MSE, we expand it as $$ \begin{aligned} \eta_{ik}^{\text{\text{prop}}} = &\frac{1}{M} \mathbb{E} \left[ \lVert \hat{\mathbf{g}}_{iik}^{\text{prop}} \rVert^{2} \right] + \frac{1}{M} \mathbb{E} \left[ \lVert \mathbf{g}_{iik} \rVert^{2} \right] \\ &- \frac{2}{M} \mathbb{E} \left[ \mathfrak{R} \left[ \left(\hat{\mathbf{g}}_{iik}^{\text{prop}} \right)^{H} \mathbf{g}_{iik} \right] \right], \end{aligned} $$ and find these three expectations. From (12), the first expectation can be written as $$ \begin{aligned} \frac{1}{M}\mathbb{E} \left[ \lVert \hat{\mathbf{g}}_{iik}^{\text{prop}} \rVert^{2} \right] &= M \beta_{iik}^{2} \mathbb{E} \left\lbrace \frac{\lVert \mathbf{z}_{ik} \rVert^{2}} { [ \lVert \mathbf{z}_{ik} \rVert^{2} ]^{2}} \right\rbrace \\ &= M \beta_{iik}^{2} \mathbb{E} \left\lbrace \frac{1} { \lVert \mathbf{z}_{ik} \rVert^{2}} \right\rbrace. \end{aligned} $$ From Lemma 1, we know that ∥z ik ∥2∼Γ(MP,ζ ik ). Then, applying Lemma 2 to (25), we figure out that $\mathbb {E} \left \{ 1 / \lVert \mathbf {z}_{ik} \rVert ^{2} \right \} = 1/ \zeta _{ik} (M - 1)$ and consequently, the first expectation term is defined as $$ \frac{1}{M}\mathbb{E} \left[ \lVert \hat{\mathbf{g}}_{iik}^{\text{prop}} \rVert^{2} \right] = \frac{M \beta_{iik}^{2}}{\zeta_{ik}(M-1)}. $$ The second expectation term is defined as $$ \frac{1}{M} \mathbb{E} \left[ \lVert \mathbf{g}_{iik} \rVert^{2} \right] = \frac{1}{M} \sum_{m=1}^{M} \mathbb{E} \left[ \lVert g_{iikm} \rVert^{2} \right] = \beta_{iik}. $$ Finally, in order to find the expected value of the third term, first, we use (4) and (12) to rewrite it as $${} \begin{array}{ll} -2\beta_{iik} \mathbb{E} \left\lbrace \mathfrak{R} \left[ \frac{ \mathbf{z}_{ik}^{H} \mathbf{g}_{iik} }{ \lVert \mathbf{z}_{ik} \rVert^{2}} \right] \right\rbrace = &-2 \beta_{iik} \left\lbrace \mathbb{E} \left[ \mathfrak{R} \left[ \frac{\sum_{l=1}^{L} \mathbf{g}_{ilk}^{H} \mathbf{g}_{iik}}{ \lVert \mathbf{z}_{ik} \rVert^{2}} \right] \right] \right. \\ &\left. + \mathbb{E} \left[ \mathfrak{R} \left[ \frac{\mathbf{w}_{ik}^{H} \mathbf{g}_{iik}}{ \lVert \mathbf{z}_{ik} \rVert^{2}} \right] \right] \right\rbrace \end{array} $$ where $\mathbf {w}_{ik} = {\mathbf {N}_{i}\mathbf {s}_{k}}/{\sqrt {q}N} \sim \mathcal {CN}\left (\mathbf {0}_{M},\frac {1}{qN}\mathbf {I}_{M}\right)$. In order to avoid the numerical issues mentioned earlier in this work and find a simpler and more tractable equation for the MSE of the proposed channel estimator, we find approximations to the two ratios of random variables in (28). It is possible to approximate the moments of a function g(X,Y) using Taylor series expansions, provided g is sufficiently differentiable and that the moments of X and Y are finite. Therefore, applying Lemma 3 separately to each one of the terms in the second and third lines of (28), we are able to find an approximation to the third expectation, which is defined as $${} \begin{array}{ll} - \frac{2}{M} \mathbb{E} \left[\! \mathfrak{R} \left[ \left(\! \hat{\mathbf{g}}_{iik}^{\text{prop}} \right)^{H}\! \mathbf{g}_{iik}\! \right] \right] \!\approx\!\! &-2 \beta_{iik} \left\lbrace\! \left[\! \frac{\beta_{iik}}{\zeta_{ik}} \left(\! 1 \,-\, \frac{\sum_{l=1}^{L}{\beta_{ilk}}}{M\zeta_{ik}} \,+\, \frac{1}{M}\! \right)\! \right] \right.\\ &\left. + \left[ \frac{-\beta_{iik}}{M\zeta_{ik}^{2}qN} \right] \right\rbrace = -\frac{2 \beta_{iik}^{2}}{\zeta_{ik}}. \end{array} $$ After finding the three expectations, (26), (27), and (29), by substituting them back in the expansion of $\eta _{ik}^{\text {\text {prop}}}$, we complete the proof. Here, we present proof for (20). First, we expand the normalized Euclidean distance between $\hat {\mathbf {g}}_{iik}^{\text {prop}}$ and $\hat {\mathbf {g}}_{iik}^{\text {MMSE}}$ as $$ \begin{array}{ll} \frac{1}{M} \mathbb{E} \left[ \left\\| \hat{\mathbf{g}}_{iik}^{\text{prop}} \right\\|^{2} \right] &+ \frac{1}{M} \mathbb{E} \left[ \left\\| \hat{\mathbf{g}}_{iik}^{\text{MMSE}} \right\\|^{2} \right] \\ &- \frac{2}{M} \mathbb{E} \left[ \mathfrak{R} \left[ \left(\hat{\mathbf{g}}_{iik}^{\text{prop}}\right)^{H} \hat{\mathbf{g}}_{iik}^{\text{MMSE}} \right] \right]. \end{array} $$ Then, we compute these three different expectations. The first one is given by (26), $\frac {1}{M} \mathbb {E} \left [ \left \\| \hat {\mathbf {g}}_{iik}^{\text {prop}} \right \\|^{2} \right ] = M \beta _{iik}^{2} / \zeta _{ik}(M-1)$. Next, by recalling that $\hat {\mathbf {g}}_{iik}^{\text {MMSE}} \sim \mathcal {CN}\left (\mathbf {0}_{M},\frac {\beta _{iik}^{2}}{\zeta _{ik}}\mathbf {I}_{M}\right)$, we have that $\frac {1}{M} \mathbb {E} \left [ \left \\| \hat {\mathbf {g}}_{iik}^{\text {MMSE}} \right \\|^{2} \right ] = {\beta _{iik}^{2}} / {\zeta _{ik}}$. For the last expectation term, using (8) and (12), we can write it as $${} \begin{array}{ll} - \frac{2}{M} \mathbb{E} \left[ \mathfrak{R} \left[ \left(\hat{\mathbf{g}}_{iik}^{\text{prop}}\right)^{H} \hat{\mathbf{g}}_{iik}^{\text{MMSE}} \right] \right] &= -\frac{2 \beta_{iik}^{2}}{\zeta_{ik}} \mathbb{E} \left\lbrace \mathfrak{R} \left[ \frac{\lVert \mathbf{z}_{ik} \rVert^{2} }{ \lVert \mathbf{z}_{ik} \rVert^{2}} \right] \right\rbrace \\ &= - \frac{2 \beta_{iik}^{2}}{\zeta_{ik}}. \end{array} $$ Finally, by substituting these results back into the expansion, we arrive at (20). 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IEEE 754-2008, IEEE 754Ű2008: Standard for Floating-Point Arithmetic (Institute of Electrical and Electronics Engineers, August, 2008). This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors. Department of Information Technology, Ghent University, Technologiepark-Zwijnaarde, 15, Gent, 9052, Belgium FAPdF is the main author and is responsible for the conception, simulation, interpretation of data and wrote the paper. FACMC revised equations, helped writing the introduction, and critically revised the paper. IM critically revised the paper and proofread it. GF supervised the research and approved the version to be published. All authors read and approved the final version of the manuscript. The original version of this article was revised: Several corrections. corrected publication March 2018 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. de Figueiredo, F., Cardoso, F., Moerman, I. et al. Channel estimation for massive MIMO TDD systems assuming pilot contamination and flat fading. J Wireless Com Network 2018, 14 (2018). https://doi.org/10.1186/s13638-018-1021-9 Massive MU-MIMO Channel estimation Flat fading Pilot contamination	CommonCrawl
The Dantzig selector: Statistical estimation when p is much larger than n 22 March, 2008 in math.ST, update \| Tags: compressed sensing, Dantzig selector, estimation, lasso selector, linear programming, mean square error, restricted isometry property Over two years ago, Emmanuel Candés and I submitted the paper "The Dantzig selector: Statistical estimation when is much larger than " to the Annals of Statistics. This paper, which appeared last year, proposed a new type of selector (which we called the Dantzig selector, due to its reliance on the linear programming methods to which George Dantzig, who had died as we were finishing our paper, had contributed so much to) for statistical estimation, in the case when the number of unknown parameters is much larger than the number of observations. More precisely, we considered the problem of obtaining a reasonable estimate for an unknown vector of parameters given a vector of measurements, where is a known predictor matrix and is a (Gaussian) noise error with some variance . We assumed that the predictor matrix X obeyed the restricted isometry property (RIP, also known as UUP), which roughly speaking asserts that has norm comparable to whenever the vector is sparse. This RIP property is known to hold for various ensembles of random matrices of interest; see my earlier blog post on this topic. Our selection algorithm, inspired by our previous work on compressed sensing, chooses the estimated parameters to have minimal norm amongst all vectors which are consistent with the data in the sense that the residual vector obeys the condition , where (1) (one can check that such a condition is obeyed with high probability in the case that , thus the true vector of parameters is feasible for this selection algorithm). This selector is similar, though not identical, to the more well-studied lasso selector in the literature, which minimises the norm of penalised by the norm of the residual. A simple model case arises when n=p and X is the identity matrix, thus the observations are given by a simple additive noise model . In this case, the Dantzig selector is given by the hard soft thresholding formula The mean square error for this selector can be computed to be roughly and one can show that this is basically best possible (except for constants and logarithmic factors) amongst all selectors in this model. More generally, the main result of our paper was that under the assumption that the predictor matrix obeys the RIP, the mean square error of the Dantzig selector is essentially equal to (2) and thus close to best possible. After accepting our paper, the Annals of Statistics took the (somewhat uncommon) step of soliciting responses to the paper from various experts in the field, and then soliciting a rejoinder to these responses from Emmanuel and I. Recently, the Annals posted these responses and rejoinder on the arXiv: Bickel compared these results with recent results on the lasso selector by Bunea-Tsybakov-Wegcamp and Meinshausen-Yu, commented on the naturality of the constraint (1), raised the issue of collinearity (which is precluded by the RIP hypothesis, but can of course occur in practice), and proposed the use of tools such as cross-validation to estimate the quantity appearing in the constraint (1). Efron, Hastie, and Tibshirani performed numerics to compare the accuracy of the Dantzig selector and the lasso selector, the performance was broadly rather similar, but the Dantzig selector appeared to have some artefacts arising from the constraint (1). Cai and Lv asked whether the factor in (1) was too conservative in the case when p was extremely large compared to n, leading to an overly sparse model ; similarly, they raised the question of whether the logarithmic losses in (2) were sharp. Concerns were also raised about the verifiability of the RIP condition in this case (which is also the case in which collinearity becomes likely). There were also some issues raised concerning speed and robustness of the implementation of the Dantzig selector. Ritov raised a more philosophical point, as to whether the prediction error (which is essentially in this model) is a better indicator of accuracy than the loss . Meinshausen, Rocha, and Yu compared our results with similar (though not perfectly analogous) existing results for the lasso selector, as well as an comparative analysis in low-dimensional situations. Their numerical experiments also suggest that the parameter in (1) needs to be tuned by cross-validation, and that the Dantzig selector has particular difficulties with collinearity. Friedlander and Saunders focused on the speed of implementation of the Dantzig selector, concluding that using general-purpose linear algebra solvers (e.g. the simplex method) was moderately computationally intensive in practice. Finally, Candès and myself gave a rejoinder to these responses. Our main points were: Regarding collinearity (which in particular implies breakdown of the RIP), an accurate estimation of the parameters is essentially hopeless no matter what selector one uses, and it is indeed more profitable to instead focus on estimating instead, but our selector is focused on applications (such as imaging, ADC conversion, or genomics) in which is the variable of interest rather than . It is certainly of interest to relax the RIP hypothesis, however, and to see whether one can still obtain good estimates for in this case. (The canonical selector always gives a near-optimal estimate for , but is NP-hard (and thus infeasible in practice) to compute.) We agree with the points made that the parameters in (1) need to be tuned further to optimise performance, and in particular that cross-validation is an eminently sensible idea for this purpose. Note that in many applications (e.g. imaging), the variance can be specified from the design of the application. The mean-square error for the Dantzig selector does tend to underperform that for the the lasso selector slightly in many cases, but (as noted in our original paper) this can be compensated for by using a slightly more complicated Gauss-Dantzig selector in which the Dantzig selector is used to locate the "active" parameters, to which one then applies a classical least-squares regression method. Running time of off-the-shelf implementations of the Dantzig selector are indeed somewhat of a concern for large data sets (e.g. measurements). But the same could have been said of the lasso selector when it was first introduced, and we expect to see faster ways to implement the algorithm in the future. It was an interesting and challenging new experience for Emmanuel and myself to engage in a formal discussion over one of my papers in a journal venue; I suppose this sort of thing is more common in the applied sciences such as statistics, but seems to be rather rare in pure mathematics. Incidentally, after this rejoinder was submitted, more recent work has appeared showing that the lasso selector enjoys similar performance guarantees to the Dantzig selector: see this paper of Bickel, Ritov, and Tsybakov. Also, a nice way to perform cross-validation for general compressed sensing problems via the Johnson-Lindenstrauss lemma was noted very recently by Ward. [Update, Mar 22: The journal issue (Vol. 35, No. 6, 2007) in which all these articles appear can be found here.] [Update, Mar 29: I have learned also of the recent paper of James, Radchenko, and Lv, which introduces a new "DASSO" algorithm for computing the Dantzig selector in time comparable to that of the best known Lasso algorithms, and provides further theoretical connections between the two selectors.] Jed Harris I'd like to read the articles you reference at arXiv, but all the commentary and your own response are embargoed. I don't know if there is anything you can do about that. Oops… these articles should be available within about 24 hours (Sun 8pm EST, to be precise). I guess I posted too soon… On the other hand, the articles are available from Project Euclid (if your institution has a subscription), at http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.aos/1201012955 John Sidles Many of the topics on the (wonder-full) weblog — like parameter estimation, compressive sampling, and even Ricci flow — share the common theme of order reduction (the reduction or approximation of complex systems as simpler systems). That is why this is one of my favorite blogs … order reduction is the essence of engineering. It can happen, however, the underlying mathematical state-space seems either too restrictive (the linear framework of compressive sampling) or too general (the coordinate-free manifolds of Ricci flow). In practice, the state-spaces that we engineers really like tend to be the the nonlinear yet computationally tractable state-spaces of algebraic geometry. For us, these state-spaces are "the porridge that is not too hot and not too cold." Speaking only for myself, it is quite challenging to develop an appreciation for what is known, and what is not yet known, in this mathematical area. That is why posts in this area are always very welcome. And, thanks to all who contribute to this fine weblog. Gabriel Peyré Small typo : "Hard thresholding" should be replaced by "Soft thresholding". Thanks for the correction! Zhou Fang Are you aware of the work by Gareth James on his 'DASSO' algorithm? It's a LARS modification, so substantially faster for full-solution path calculation. (e.g . for CV) Though it's somewhat slower than lasso/lars (since the Dantzig path seems to have more break points), it looks pretty close to optimal. Thanks for the reference, which I was unaware of! It now seems, in view of recent literature, that the Dantzig selector and LASSO selector are in fact extremely close cousins of each other in many respects. David Molnar Gareth James also has a more recent paper with P. Radchenko on "A Generalized Dantzig Selector with Shrinkage Tuning" listed on his web page. He also includes code for the method in R, in case anyone wants to try it: http://www-rcf.usc.edu/~gareth/research/gdscode "The journal issue (Vol. 35, No. 6, 1997)" you mean 2007, of course. Dear anonymous: thanks for the correction! sounak Do you think a Bayesian Dantzig selector based on the "loss likelihood duality" principle will be an interesting study. I know directly constructing the likelihood from L-infinity loss may be not very reasonable, but how about some continuous approximations of the L-infinity norm. Connie Leung Hi there, I am a student at the University of Southampton, UK. I chose to study subset selection and shrinkage methods techniques in order to see which of the 13 covariates are best to model property values. Of these methods, one of the methods I have chosen to look at is the Dantzig Selector but cannot find the codes for this method. Is there any chance that you could send me what the code would be? (I will acknowledge you in my report! :) ) Many thanks! Connie My co-authors developed the l1-Magic package at http://users.ece.gatech.edu/~justin/l1magic/ to do these sorts of computations, though my understanding is that nowadays there are significantly faster methods available than this one. Many thanks! I understand there are probably faster methods but my study is on this method so this would be useful – thank you! Prof Terence Tao : Could you please comment on this fundamental problem : https://math.stackexchange.com/q/2249528/2987 Alexander Davis I don't think you should jump from "X is colinear" to "estimation of β is essentially hopeless". It depends on the loss function. Consider the changepoint problem. A piecewise constant vector Y is equal to Lβ, where L is a lower triangular matrix of 1's and β is sparse. In the presence of noise you can't find an estimate β* which will perfectly recover β. But you consider it a job well-done if the non-zero entries of β* are near the non-zero entries of β. This suggests a loss function something like $$\sum_{i=1}^p (\beta^_i – a_i)^2 + \\|\beta\\|_0$$ $$a_i = \frac{1}{11}\sum_{k=i-5}^{i+5} \beta_i$$ This problem has a sequential structure, and there are similar problems with more complex structures. For example, here's a similar problem with a tree structure. You are given a phylogenetic tree of $n$ species, and for each species $i$, you are given $y_i$, the copy number of a certain gene in the genome of that species. Where, on the phylogenetic tree, did this gene undergo duplications and deletions? My own statistical work involves a sort of hybrid between these two problems, where we have a sequence of identical trees, and each node is linked to the corresponding node in the next tree. So, here's a general problem that might appeal to you as a mathematician. It includes the case of estimating β, the case of estimating Xβ, and all the cases above. Given a system Xβ+ε = y, with unknown sparse β, find an estimate β to minimize the loss function \|\|Aβ – Αβ\|\|*. (And if you know anyone that has studied this, please link me to the papers.) « Lewis lectures Dvir's proof of the finite field Kakeya conjecture »	CommonCrawl
Zhang's Theorem on Bounded Gaps Between Primes by Dan Goldston In late April 2013 Yitang Zhang of the University of New Hampshire submitted a paper to the Annals of Mathematics proving that there are infinitely many pairs of primes that differ by less than 70 million. The proof of this amazing result was verified with high confidence by several experts in the field and accepted for publication. A public slightly revised version of the paper should be available shortly. Before describing the proof, we make the caveat: As with any major result, the proof needs to be widely examined for errors before it can be completely accepted as correct. In this case the 55 page paper is detailed and precise, and the probationary period will probably be a few months. Zhang's theorem is a huge step forward in the direction of the twin prime conjecture. We now know for the first time that there are actually infinitely many pairs of primes that differ by some fixed number. The proof does not specify any specific number, only that there is at least one that is less than 70 million. (We actually expect that every even number will occur as the difference of two primes infinitely often.) Since the average spacing of primes around $x$ is $\log x$ which grows to infinity slowly, this sequence of pairs defy this isolating trend. If not twins, then certainly siblings. Zhang's proof makes use of a modified version of the 2005 method of Goldston, Pintz, and Yildirim (GPY). Consider the tuple $(n+h_1,n+h_2, \ldots , n+h_k)$, where the $h_i$'s are specified integer shifts, and $n$ runs through the positive integers. The Hardy-Littlewood $k$-tuple conjecture states that there are infinitely many $n$ where every component of the tuple is simultaneously prime, except for $h_i$'s where this is clearly impossible. Thus $(n,n+1)$ is only a prime tuple for $(2,3)$ since one of $n$ or $n+1$ is even and divisible by 2. Similarly $(n,n+2,n+4)$ only is a prime tuple for $(3,5,7)$ since one component is divisible by $3$. On the other hand $(n,n+2)$ and $(n,n+2,n+6)$ have no such obstruction and we expect them to be prime tuples infinitely often; the former giving the twin primes. A tuple without the obstruction that some prime always divides one of its components is called admissible. How GPY works is to apply a sieve, actually the Selberg sieve, to a given tuple when $n$ runs over positive integers $\le x$ . Roughly speaking, the sieve removes the tuples where any component has a small prime factor and leaves only tuples where all the components have only large prime factors. Therefore the tuples left have relatively few prime factors distributed among their components, and we obtain a sequence where we are likely to find primes close together. If for example we had a 10-tuple where the components together have at most 18 prime factors this would force at least two components of the tuple to be prime and we would have produced two primes whose difference is at most the width of the tuple. Sieves never work this well or we would have solved most of the problems concerning primes long ago. Despite this, the Selberg sieve applied to larger $k$-tuples is still highly effective at producing "almost prime" tuples. We need to use some further idea in order to detect the primes in the tuple, and what we use is the level of distribution of primes in arithmetic progressions. The prime number theorem says that the number of primes $\le x$ is asymptotically $x/\log x$ as $x\to \infty$. This was proved in 1896 by Hadamard and de la Vallèe-Poussin, and in 1899 de la Vallèe-Poussin extended the result to prove the prime number theorem for arithmetic progressions. Thus for example if we look at the three arithmetic progressions modulo 3 we have no primes except 3 in $3, 6, 9, 12, \ldots$ but asymptotically half of all the primes will occur in $1, 4, 7, 10, \ldots$ and the other half occur in $2, 5, 8, 11, \ldots$. The principle is that for the $q$ progressions modulo $q$ the primes will flow evenly into the progressions that allow primes, namely those for which there is no prime dividing every term in the progression. There are $\phi(q)$ such progressions, where $\phi(q)$ is the Euler phi-function equal to the number of integers $a$, $1\le a \le q$ for which $a$ and $q$ are relatively primes. Hence each progression gets asymptotically $1/\phi(q) \times x/\log x$ primes. For applications we usually need to have $q$ be a function of $x$, and for this our knowledge is extremely limited. For example, if $q=x^\alpha$ then there is no $\alpha >0$ known for which the asymptotic formulas are always true. Assuming the Generalized Riemann Hypothesis (GRH) this is know for any $\alpha < 1/2$. A major advance in the field occurred in 1965 when Bombieri and independently Vinogradov proved that the asymptotic formula is true for $\alpha < 1/2$ for "almost all" progressions. Since in many applications we break our expression up over lots of progressions, the Bombieri-Vinogradov Theorem has exactly the same strength as GRH for these applications. If in place of $1/2$ we assume that almost all progressions satisfy the prime number theorem for arithemtic progressions for $q=x^\alpha$ and $\alpha <\theta$ then we say the primes have level of distribution $\theta$. It is conjectured that the primes have level of distribution 1, which is called the Elliott-Halberstam conjecture, but it appears very difficult to go beyond the know level of distribution $1/2$, and GRH does not help with this either. With this preparation we return to GPY and take the sequence of almost prime tuples produced by the Selberg sieve and freeze (or twist) one of the components to be a prime. We can compute this proportion because the sieving is implemented through multiples of any divisors of the other components, and we then count how often the frozen prime component occurs in these arithemtic progressions. We can freeze individually each of the $k$ components to be a prime and we get the same result in each case. If the amount we get when we freeze one component to be a prime is greater than $1/k$ times the contribution of all the almost prime tuples, then the $k$ events where one component is frozen to be a prime cannot all be disjoint from each other and there must be some overlap where two of the components are primes simultaneously. This produces two primes in the given tuple. Therefore the success of the method relies on the ratio of the almost primes tuples produced by the Selberg sieve to the almost prime tuples produced where one component is a prime. The Selberg sieve coefficients need to be chosen appropriately, and while the optimal choice is not clear, it isn't too hard to make a natural and very good choice. In evaluating the twisted sum the size of the numbers we use in sieving is limited by the level of distribution, and therefore the sieving is improved by a larger level of distribution. The result of this procedure obtained in GPY is the following. If the level of distribution $\theta >1/2$ then you actually win and obtain two primes in your tuple for sufficiently large $k$. Thus you get bounded gaps between primes under this unproved assumption. If we assume a level of distribution 1, the Elliot-Halberstam Conjecture, then we get two primes infinitely often in every admissible $6$-tuple. The smallest admissible $6$-tuple is $(n, n+4, n+6, n+10, n+12,n+16)$ which gives pairs of primes with difference $\le 16$. Since we only know level of distribution $1/2$, GPY fails to get 2 primes in any tuple unconditionally. However not all is lost, and by separate arguments one can still produce two primes significantly closer than the average spacing between primes. However these small gaps between primes are unbounded and grow to infinity. The most tantalizing question left by GPY was whether one could edge over the level of distribution barrier at $\theta =1/2$ to get bounded gaps between primes. Soundararajan showed that improving the choices in the Selberg sieve could not succeed, and that shifted the question onto the level of distribution error terms that arise in the method. In the early 1980's Fouvry and Iwaneiec were able to obtain results connected to primes in arithmetic progressions with a level of distribution greater than 1/2. During 1985-90 Bombieri, Friedlander, and Iwaniec wrote three well-known papers where they obtained many results which go beyond level of distribution 1/2. In particular these papers obtain results beyond what GRH implies, and require estimates from the spectral theory of automorphic forms. Their results in some cases corresponding to a level of distribution $4/7$. One limitation of these methods is that they do not apply directly to sums of absolute value of the errors terms in the progressions, but rather to weighted sums of the error terms, where the weights have a fair degree of flexibility. Since in applications the error terms also come weighted by various arithmetic functions, these new results have found a number of important uses. For example, Brian Conrey's proof that more than 2/5's of the zeros of the Riemann zeta-function are on the half-line uses this analysis. In the case of GPY however, despite attempts by a number of mathematicians, no one was able use these techniques to deal with the error terms generated by the method. Now Zhang has found how to break this barrier. The first step is a modification in the GPY method. Zhang shows that in using the Selberg sieve one can restrict the sieving to divisors with no large prime factors. This of course decreases the effectiveness of the sieve, but in GPY he shows that this decrease has a surprisingly small effect on the method. Next, he increase the sieving range corresponding to a level of distribution $1/2 + 1/584$. This turns out to be large enough to overcome the loss from removing the large prime factors above and give bound gaps between primes, provide all the error terms can be controlled. This leads to a very intricate analysis using the methods of Bombieri, Friedlander, and Iwaniec. Of crucial importance is that the divisors in the sieving have no large prime factors and therefore may themselves be factored into factors of various sizes with considerable flexibility. Ultimately it is shown that all the error terms are controlled and the result follows. It should be noted that this does not provide a proof that the primes themselves have a level of distribution greater than 1/2 according to our definition of level of distribution above. It is too early to see how Zhang's method may be used in other applications. Zhang's proof ends up proving that every admissible $k$-tuple with $k=3,500,000$ contains 2 primes. It is not easy to find the smallest such admissible tuple, but a good choice is to take the shifts $h_i$ to be the first $k$ primes that are larger than $k$. Using a math package and rounding up to the nearest 10 million gives the size $70,000,000$ for the width of the tuple and thus the difference between the two primes. (Actually 60,000,000 seems to work here.) This number has attracted attention, but it has no intrinsic significance. In working out a complicated proof, one often uses whatever numbers make the argument work out reasonably simply. No doubt much smaller numbers will be found in later papers of greater complexity as the limits of the method are explored. At the moment it is hard to predict even the rough size of the ultimate answer by this method. On the other hand, it would be nice to have simpler and shorter proofs which make no attempt to get any specific number.	CommonCrawl
On inverse-trig integration When faced with something like $\int \frac{1}{\sqrt{1+x^2}} \dx$, my first instinct has usually been to panic, and then to try trig (or hyperbolic) substitutions more or less at random. But is there a better way? There are six such integrals altogether: $\int \frac{1}{\sqrt{1-x^2}} \dx = \arcsin(x) + C$ $\int \frac{-1}{\sqrt{1-x^2}} \dx = \arccos(x) + C$ $\int \frac{1}{\sqrt{1+x^2}} \dx = \arsinh(x) + C$ $\int \frac{1}{\sqrt{x^2-1}} \dx = \arcosh(x) + C$ $\int \frac{1}{1+x^2} \dx = \arctan(x) + C$ $\int \frac{1}{1-x^2} \dx = \artanh(x) + C$ It sort of looks like there's a pattern… but then there isn't. How do we go about spotting what's going on? Sketch the integrand I'm going to leave the $\arctan$ and $\artanh$ integrals for later and focus on the ones that have a square root on the denominator. The square roots are extremely useful: they tell you where things are defined. For example: when the integrand is $\frac{\pm 1}{\sqrt{1-x^2}}$, this is only defined when $1-x^2 \ge 0$, so $-1 \le x \le 1$. What functions do we know that have a range like that? That's right, the sines and cosines - so these two must correspond to the arcsine and arccosine functions. Which way round? Think about the gradients: $\arccos(-1) = \pi$ and $\arccos(1) = 0$, so arccosine has a negative gradient; it must correspond to the negative integrand. You can make a similar argument for arcsine. How about the others? When the integrand is $\frac{1}{\sqrt{1 + x^2}}$, that's clearly defined for all values of $x$ - arsinh fits the bill there. We can also use Osborn's Law, which says that 'if you have a trigonometric identity involving squares, replacing $\sin^2(x)$ with $-\sinh^2(x)$ and $\cos^2(x)$ with $\cosh^2(x)$ will give you a corresponding hyperbolic identity. In this case, this means 'flipping the signs on the $x$ in the arcsine integral - it works! Meanwhile, $\frac{1}{\sqrt{x^2-1}}$ is only defined for $\|x\|\ge1$ - and $\cosh(x)$ is the function that fits the bill there. The tangents Lastly, we can note that $\tanh(x)$ gives an output between $-1$ and $1$, which suggests that its derivative must be $\frac{1}{1-x^2}$ - rather than $\frac{1}{1+x^2}$, which is defined everywhere. Again applying Osborn's Law, we can see that that has to be arctangent. There are other, less exciting ways to tackle these, obviously. But as a quick-and-dirty check of what's going on, I find asking "what could the domain be?" saves a bit of substitution and makes one look like a ninja. Brathwaite's Law Ask Uncle Colin: Why is it not 4? Why $17 \times 24$ isn't 568 Why SOH CAH TOA is stupid (and what you can do instead)	CommonCrawl
Probabilistic metabolite annotation using retention time prediction and meta-learned projections Constantino A. García ORCID: orcid.org/0000-0002-9739-22521, Alberto Gil-de-la-Fuente1,2, Coral Barbas2 & Abraham Otero1,2 Retention time information is used for metabolite annotation in metabolomic experiments. But its usefulness is hindered by the availability of experimental retention time data in metabolomic databases, and by the lack of reproducibility between different chromatographic methods. Accurate prediction of retention time for a given chromatographic method would be a valuable support for metabolite annotation. We have trained state-of-the-art machine learning regressors using the 80, 038 experimental retention times from the METLIN Small Molecule Retention Tim (SMRT) dataset. The models included deep neural networks, deep kernel learning, several gradient boosting models, and a blending approach. 5, 666 molecular descriptors and 2, 214 fingerprints (MACCS166, Extended Connectivity, and Path Fingerprints fingerprints) were generated with the alvaDesc software. The models were trained using only the descriptors, only the fingerprints, and both types of features simultaneously. Bayesian hyperparameter search was used for parameter tuning. To avoid data-leakage when reporting the performance metrics, nested cross-validation was employed. The best results were obtained by a heavily regularized deep neural network trained with cosine annealing warm restarts and stochastic weight averaging, achieving a mean and median absolute errors of $39.2 \pm 1.2\; s$ and $17.2 \pm 0.9\;s$, respectively. To the best of our knowledge, these are the most accurate predictions published up to date over the SMRT dataset. To project retention times between chromatographic methods, a novel Bayesian meta-learning approach that can learn from just a few molecules is proposed. By applying this projection between the deep neural network retention time predictions and a given chromatographic method, our approach can be integrated into a metabolite annotation workflow to obtain z-scores for the candidate annotations. To this end, it is enough that just as few as 10 molecules of a given experiment have been identified (probably by using pure metabolite standards). The use of z-scores permits considering the uncertainty in the projection when ranking candidates, and not only the accuracy. In this scenario, our results show that in 68% of the cases the correct molecule was among the top three candidates filtered by mass and ranked according to z-scores. This shows the usefulness of this information to support metabolite annotation. Python code is available on GitHub at https://github.com/constantino-garcia/cmmrt. Metabolite annotation remains the main bottleneck in untargeted metabolomics [1, 2], with the vast majority of metabolites being left as unidentified [3]. Beyond the molecule's mass, other molecule's properties such as Retention Time (RT), collision cross section, or the fragmentation spectrum can be very valuable during the metabolite annotation process [4, 5]. The most common approach to annotate metabolites is to query a metabolomics database for compounds that have a mass compatible with the experimental masses. Often this query returns multiple annotation candidates for the same mass. Next, the researcher tries to discard, or score according to plausibility, the candidate annotations using other molecule's properties [1]. Liquid Chromatography Mass Spectrometry (LCMS) remains the most common platform used in untargeted metabolomics. In addition to m/z ratio, it provides information about the Retention Time (RT), the time at which metabolites elute from the chromatographic column. By using hyphenated setups (MS/MS), the fragmentation spectra of the molecules may be obtained [6]. These spectra are very useful for ruling out candidate annotations, and they are necessary to achieve the highest confidence levels of the Metabolomics Society in metabolite annotation (levels 0 and 1 [7]). However, obtaining them requires hyphenated setups which are more expensive and complex. Even when this type of instrumentation is used, the fragmentation spectrum of every molecule of interest is not always available due to instrumentation limitations or time constraints for the analysis. Also, sometimes the amount of sample available is not sufficient for MS/MS analysis. Hence, especially in pilot untargeted studies where unambiguous identification is not crucial (that is, where confidence level 2 of the Metabolomics Society is enough), often the fragmentation spectra are not available, and the annotation has to be done with just m/z ratios and RTs. Obtaining molecule's properties experimentally (such as the Retention Time (RT) or the fragmentation spectrum) requires the analysis of pure standards, which is a long, tedious and expensive process. Therefore, metabolomic databases often lack this information, especially for new metabolites that are still being discovered. Furthermore, the variability of the experimental setups means that different values are often obtained for these features in different setups [6, 8]. The reliable prediction of these features from the structures of molecules using machine learning techniques is therefore a compelling alternative to their experimental generation [9,10,11,12]. Computational prediction of the Retention Time (RT) has been shown to be useful for molecule annotation in proteomics [13, 14] and lipidomics [15, 16]. However, until recently the prediction of small molecules Retention Time (RT) remained a challenge due to the small size (usually a few hundreds) of the publicly available Retention Time (RT) datasets [17]. This size prevented the training of machine learning models capable of accurately predicting the Retention Time (RT) of the large variety of small molecules involved in the typical metabolomic study, being the efforts in this direction limited to the prediction of the Retention Time (RT) of some concrete type of small molecules [14, 16, 18], or of the order of elution of the molecules [19, 20]. This situation changed recently with the publication of more than 80,000 experimental RTs collected through reversed-phase Liquid Chromatography Mass Spectrometry (LCMS) from the METLIN Small Molecule Retention Time (SMRT) dataset [21], which has renewed interest in the Retention Time (RT) prediction of small molecules [17, 22,23,24,25,26]. In this paper we have tested the performance of several state-of-the-art machine learning models for the task of Retention Time (RT) prediction using the SMRT dataset. In the evaluation presented in [21] the molecules that were not retained by the column were excluded. In our evaluation, both retained and non-retained molecules will be considered. Non-retained molecules are typically ignored in metabolomics experiments. However, the ultimate goal of the machine learning model would be the computational prediction of the RTs of a set of molecules present in a metabolomics database based on their chemical structures, to confirm or discard candidate metabolite annotations. In this scenario, it is unknown in advance whether a molecule of the database is going to be retained or not, and therefore it is desirable to predict as accurately as possible the RTs of the non-retained molecules. Hyperparameter search for the models was performed with the Tree-structured Parzen Estimator (TPE) algorithm [27], and a nested cross-validation was used in the evaluation. The best model was a Deep Neural Network (DNN) trained using molecular fingerprints, which improved the performance of the best previous models to predict Retention Time (RT) [24, 26]. Having a machine learning model capable of accurately predicting the Retention Time (RT) would enable filtering out annotations with similar mass but different RTs. However, note that a model trained on the SMRT dataset can only accurately predict RTs for a Chromatographic Method (CM) identical to the one employed to collect this data. Since laboratories usually customize the Chromatographic Method (CM) for the needs of each experiment, a SMRT-based model cannot be directly applied to experimental data from other laboratories, or even other experiments conducted in the same laboratory. However, if CMs are similar, elution order is largely preserved [8], which enables the construction of a projection function that maps RTs in one Chromatographic Method (CM) to RTs in another Chromatographic Method (CM). Figure 1 illustrates both the dependency of the RTs with the Chromatographic Method (CM), and the conservation of the elution order. To build such a projection function, a set of known molecules whose RTs is known in both CMs is needed. RTs measured in different CMs (y-axis) compared with the predictions of a machine learning model trained on SMRT (x-axis). The figure also shows the RTs of the same molecule (PubChem ID 10742) in the different CMs (shown with the star shapes), which illustrates the variability in the times measured with different experimental configurations. Since the model has been trained on a single Chromatographic Method (CM), the experimental RTs on different CMs do not match its predictions (dashed line). This figure illustrates the need for a projection method able to translate the predictions of a model trained on a specific Chromatographic Method (CM) to different CMs Figure 2 shows a possible workflow to exploit the Retention Time (RT) predictions of a machine learning model and a projection method during the metabolite annotation process. Although not explicitly shown in the figure, we assume that RTs are used in conjunction with the m/z ratio. In the center of Fig. 2 there is a large database containing molecule identities and their main chemical properties, including RTs. The RTs stored in the database are computed using the predictive model trained on the SMRT dataset (step 1). The creation of a database (step 2) avoids running complex predictive models in real-time. Also, note that this database may include molecules not observed in the SMRT dataset. To use this database, a researcher provides the experimental RTs (as measured in his/her Chromatographic Method (CM)) of a few molecules whose identity is known (step 3). These molecules will typically be pure metabolite standards added to the sample. The molecule identities are then used to retrieve the corresponding predicted RTs from the database, which will be subsequently used to create pairs of experimental-predicted RTs (step 3). A projection function mapping predicted RTs to experimental RTs is learned from these pairs (step 4). The researcher then provides experimental m/z (not shown in the figure to avoid clutter) of the molecules he/she is trying to identify. The m/z ratios are used as a first filter to obtain candidate annotations from the database. The predicted RTs of the filtered molecules are then projected to experimental RTs to create a "projected database" (step 5). Note that the projected database is much smaller than the original one due to the m/z filtering, which makes the projection computationally efficient. The researcher finally uses the experimental RTs to query the projected database (step 6). The results retrieved from it would enable scoring candidates with similar m/z but different RTs (step 7). Illustrative workflow to exploit a machine learning model trained on a large dataset (here, SMRT) to annotate metabolites. Steps 1-2: a RTs database is created using a predictive model trained on the SMRT dataset. Step 3: to use this database, a researcher provides the experimental RTs of a few molecules whose identity is known. The molecule identities are then used to retrieve the corresponding predicted RTs from the database to create pairs of experimental-predicted RTs. Step 4: a projection function mapping predicted RTs to experimental RTs is learned from these pairs. Step 5: the researcher then provides experimental m/z (not shown in the figure) of the molecules he/she is trying to identify. Molecules are filtered using the m/z ratio and the predicted RTs of those molecules are then projected to experimental RTs to create a "projected database". Step 6: the researcher finally uses the experimental RTs to query the projected database. Step 7: the results retrieved from it would enable scoring candidates with similar m/z but different RTs To make this workflow practical, it is desirable that the projection function can be learned from a very small dataset, so that the researcher only has to identify a small set of molecules. To that end, this work proposes a Bayesian meta-learning approach to project the predicted RTs to a specific Chromatographic Method (CM) based on just a few identified molecules. This approach has the advantage of being able to generalize from a small training set while providing confidence intervals for the Retention Time (RT) projections between CMs, and not only a point estimate. We demonstrate the ability of the proposed projection method to learn from few samples by testing not only its predictive accuracy, but also its ability to rank the correct metabolite identity among the top three candidates based on their RTs. The METLIN Small Molecule Retention Time (SMRT) dataset consists of the experimental retention times of 80,038 small molecules from the METLIN library [21]. All RTs were obtained using reverse-phase chromatography with high-performance liquid chromatography-mass spectrometry (HPLC-MS). The dataset has a wide variety of small molecules analysed under the same conditions, including metabolites, natural products and drug-like small molecules. It also includes non-retained molecules; these are compounds that are not retained in the column and elute before gradient starts, typically within the first minute. Hence, RTs of the non-retained molecules are considerably smaller than RTs of the retained molecules. Although some authors ignore the non-retained molecules when validating machine learning models, the whole dataset was used for both training and validating the regressors of this paper. The rationale for this is that these machine learning models are going to be used to predict RTs of metabolites in a database (see Fig. 2). Then, these predictions could be used to filter and rank experimental data. If a regressor is trained without non-retained RTs it will only be able to predict retained RTs, even for a non-retained metabolite A in the database. If in an experiment there is an unidentified metabolite B with a similar m/z and whose RT is close to A's (wrongly) predicted Retention Time (RT), the system will propose metabolite A as a candidate annotation for B. Hence the interest in training the regressors with both retained and non-retained molecules. The SMRT dataset has been made public including the PubChem numbers and SDF files representing their chemical structure [28], together with their experimental RT information. In this work, these chemical structures were used to obtain a wide variety of features describing relevant properties of the molecules. These features were computed using alvaDesc [29, 30] and include both fingerprints and molecular descriptors. Specifically, alvaDesc permits the computation of MACCS166 fingerprints, Extended Connectivity Fingerprints (ECFP) [31] and Path Fingerprints (PFP), making a total of 2, 214 fingerprints. Additionally, the 5, 666 molecular descriptors supported by alvaDesc were also generated; the complete list can be seen in [32]. All the descriptors and fingerprints obtained with alvaDesc were used to feed the regressors. Following [21], we also used the PredRet database [8] for validating the projections from predicted to experimental RTs. The PredRet is a database of experimental RTs from different chromatographic systems commonly used for building and testing projection models between pairs of CMs. First we shall describe the different machine learning models used to predict the RTs, and then we shall present our Bayesian approach to project the RTs to a given Chromatographic Method (CM). Prediction of retention times with machine learning Several state of the art machine learning regressors were tested for predicting the RTs using three different sets of features: fingerprints only, descriptors only and fingerprints+descriptors. Parameter search was used for tuning all models with the exception of CatBoost-based regressors (see "Gradient boosting" Section for the rationale). We have also created an ensemble with all the trained models to attempt to further improve Retention Time (RT) prediction [33]. Some of the choices for the regressors can be understood by the need of having diversity in their predictions to increase the chances of the ensemble improving their individual performances (see "Blending" Section). Preprocessing of descriptors and fingerprints Descriptors were first standardized and imputed using median imputation when alvaDesc was not able to generate some descriptor. If imputation was needed, a missing indicator was added, enabling the regressors to account for missingness despite the imputation. Features with 0 variance were removed. Highly correlated features were also eliminated (correlation $> 0.9$); this conservative threshold was not tuned since all tested regressors are robust against collinearity. The main benefit of removing correlated features is memory saving. The only preprocessing applied to the fingerprint features was removing those with low variance. Treating each feature X as a binary Bernouilli random variable, the variance threshold was selected using $\text {Var}[X]=p (1-p)$, were p is a parameter to be tuned (see "Bayesian hyperparameter search" Section) which is usually set to a high value (typically $>0.9$). Taking inspiration from [24], an additional binary feature was added to each molecule representation indicating whether the molecule is retained or not. Since in a real world application this information would not be available, this feature must also be predicted. To that end, we trained a eXtreme Gradient Boosting (XGBoost) classifier. As suggested by Fig. 3, a molecule was considered non-retained if its Retention Time (RT) was smaller than 5 minutes. The XGBoost classifier was tuned using the same procedure described in "Bayesian hyperparameter search" Section for the regressors, although the metric to be maximized in this case was the F1 score. Preliminary results suggested that using fingerprints, descriptors, and fingerprints+descriptors yielded similar results, so we used only fingerprints as features for speed. Histogram of the RTs in the SMRT dataset. The distribution is clearly bimodal due to the presence of non-retained molecules. In this paper, a molecule is considered as non-retained if its Retention Time (RT) is smaller than 300s Gradient boosting Gradient Boosting Machines (GBMs) have already been considered in state of the art methods for Retention Time (RT) prediction [24]. In this work, several GBMs were tested, using slightly different approaches for the hyperparameter search. In addition to the interest of comparing several GBMs, the use of different combinations of GBMs and tuning options was partially motivated by the need of having diversity in the predictions for building a good ensemble (see "Blending" Section). Specifically, we tested: XGBoost [34]: it is probably the most-commonly used GBM, and it was employed for Retention Time (RT) prediction in [24]. Bayesian search was applied on different regressors fed using fingerprints, descriptors and fingerprints+descriptors. Among the tuned parameters, the most relevant ones include the number of boosting rounds, the maximum depth of the trees, subsampling parameters (either by column, by tree or by level), regularization parameters (such as $L_1$ and $L_2$ regularization) and parameters controlling the conservativeness of the algorithm (usually referred as $\gamma$ and minimum child weight). Gradient Boosting Machine (lightGBM) [35]: it is a well-known alternative to XGBoost, with optimizations for speed and memory usage (hence, its name). Furthermore, stepwise optimization methods particularly designed for lightGBM can be used. This avoids the need for Bayesian search, further reducing tuning times by exploiting heuristics. The hyperparameters were selected in the following order: $L_1$ regularization, $L_2$ regularization, maximum number of leaves, proportion of randomly selected features on each tree, bagging fraction, bagging frequency (it controls the number of iterations between bagging) and the minimum number of samples in the leaves. CatBoost [36]: an interesting question regarding the non-retained molecules is if their inclusion as training data improves the performance of the regressors. To investigate this question, the performance of a regressor when trained with different weights for the retained and non-retained molecules can be evaluated. Different weights for both types of molecules can also help with the unbalance between retained and non-retained molecules. Since the ratio of non-retained to retained molecules is approximately 1/40 in the SMRT dataset, the weight of the retained molecules was set to 1, whereas the weight of the non-retained molecules was varied between $10^{-6}$ (effectively ignoring them) and 80 (hence the global influence of the non-retained molecules is approximately twice the influence of the retained ones). However, using the same approach as with previous regressors would require a full Bayesian search for each weight of the non-retained molecules. Instead of tuning parameters for each weight, we looked for a regressor able to provide good performance with its default parameters. CatBoost was selected for this reason [36]. Note that CatBoost regressors not only permit studying the influence of the non-retained molecules in the predictions, but they also provide a useful context that may enable the meta-regressor of the ensemble to distinguish between retained and non-retained molecules (see "Blending" Section). Deep neural network Together with GBMs, DNNs usually achieve the best results in machine learning competitions [37, 38]. DNNs were used for Retention Time (RT) prediction in [21], where a DNN with 4 layers and regularization was proposed. Regularization is key for achieving good generalization, since even a small shallow neural network can overfit the SMRT dataset in a few epochs. Driven by this observation, we used a DNN with just 3 layers, regularized using large dropout rates. The sizes of the hidden layers, the dropout rates and the non-linear activations were determined using Bayesian hyperparameter search. To improve the generalization ability of the DNN and to accelerate its training, we used cosine annealing warm restarts [39]. The number of restarts and the length of the cosine annealing were also subject to hyperparameter search. After the training with warm restarts, we employed Stochastic Weight Averaging (SWA) using a constant learning rate schedule. With this setting, SWA just consists of training the DNN for a few extra epochs (whose optimal value is to be determined during hyperparameter search), and then averaging the weights of the DNN along the trajectory followed during optimization. In [40], the authors suggest that SWA leads to wider minima, which is hypothesized to result in better generalization than conventionally trained DNN. Finally, quantile transformation was applied to RTs before fitting. The method transforms RTs to follow a standardized normal distribution. This may facilitate learning since the last layer does not need to learn large weights to match the untransformed RTs. Kernel methods Support Vector Machines (SVMs) have already been considered for a wide variety of applications related to metabolites, including elution order prediction [19]. Although we tested SVMs with both descriptors and fingerprints, performance of both regressors was poor. As an alternative to this classic kernel method, we considered Deep Kernel Learning (DKL) [41]. DKL can be interpreted as a DNN whose last layer has been substituted by a Gaussian Process (GP). This permits leveraging both the ability of deep learning for extracting relevant features from the raw-inputs, and the non-parametric flexibility of GPs. The combination of the DNN and the GP kernel can also be viewed as a new flexible kernel which can be used as a drop-in replacement for standard kernels. DKLs were tested using fingerprints, descriptors and fingerprints+descriptors. Following the observations from "Deep neural network" Section, we employed a highly regularized DNN. Besides dropout, we also considered batch-normalization [42], not only because of its regularization capabilities, but also because it keeps activations from the network within a predictable range. This eases the use of kernel interpolation (specifically, KISS-GP [43]) to approximate the GP kernel, which enables fast computations. Quantile transformation was also applied to the RTs. DKL was trained using early stopping, and the learning rate was tuned during parameter search. Similar to the DNNs from "Deep neural network" Section, the specific architecture and regularization were subject to parameter search. Learning rate scheduling was used, reducing the learning rate when validation loss was stacked in a plateau. The patience argument before decreasing the learning rate was also tuned. Finally, three kernels were considered during hyperparameter tuning: the squared exponential kernel, the linear kernel and a spectral mixture kernel with four components [44]. A full list of the mathematical expressions of the kernels used in this paper can be found in Section S3 of Additional file 1. We tested if the combination of the different regressors could improve their individual predictions. We used blending [45] to build a meta-regressor which learns to combine the predictions of the so-called base-regressors. Blending is a popular alternative to stacked generalization (or stacking) [46] which has lower computational demand and it is simpler, resulting in less likelihood of information leakage. With large datasets like SMRT, blending and stacking usually yield similar results. Hence, since the meta-regressor is also subject to parameter tuning, blending was used for faster training. To train a meta-regressor with blending, a holdout set is created using a small subset of the training set. In our experiments, we used a 80-20% split. The base-regressors are trained on the 80% of the data, and their predictions for the holdout dataset are stored. The meta-regressor then learns to combine the predictions of the base-regressors using the predictions on the holdout dataset. Note that an instance on the original training data is only used just once for training, either on the base-regressors or in the meta-regressor, avoiding information leakage. This procedure for training the meta-regressor is also outlined in Fig. S1 of Additional file 1. A random forest was used as meta-regressor, tuning its main parameters through Bayesian optimization. The parameters tuned were the number of trees, the maximum depth of each tree, the maximum number of features considered at each split, the minimum number of samples before considering a split and the minimum number of samples at a leaf. Bayesian hyperparameter search Most regressors with the exception of lightGBMs (tuned using iterative search for speed tuning) and CatBoosters (not tuned due to its good default values) were tuned using Bayesian hyperparameter search. The p parameter controlling the thresholding of binary features was also optimized (see "Preprocessing of descriptors and fingerprints" Section). The parameters were tested following the predictions of a TPE algorithm [27]. The TPE algorithm works by suggesting the parameters that maximize the expected improvement in the score being maximized, which in this paper was the negative of the MEDian Absolute Error (MEDAE). This permits balancing exploration versus explotation, obtaining a set of hyperparameters with good performance in fewer iterations than other approaches like grid search. In our experiments each model performed 50 iterations of the Bayesian search. Regarding the optimization of the blended regressor, it should be noted that it proceeds greedily. That is, base-regressors are tuned individually, and the predictions of the best performing parameters are then used to create the training set for the meta-regressor. Finally, the parameters of the latter are optimized. It may be argued that this approach is suboptimal, since the base-regressors cannot be tuned to complement each other. However, jointly optimizing all base-regressors and the meta-regressor is difficult due to the dimensionality of the search space. Furthermore, this approach would not permit drawing conclusions from the performance of the base-regressors, which is part of the objectives of this work. Validation procedure To avoid data-leakage when reporting the performance of the different models, nested stratified cross-validation was used. Nested cross-validation guarantees that different data is used to tune model parameters and to evaluate its performance by means of outer and inner cross-validation loops [47]. In the outer loop, train/test splits are generated, which are then used for averaging the test scores over several data splits. In the inner loop, the train set is further split in train/validation subsets. The best parameters are selected by minimizing the MEDAE on the validation splits. We used 5-folds and 7-folds stratified cross-validations in the outer and inner loops, respectively. To ensure that the distribution of RTs is representative of the population in all folds, stratification was performed by separating the target variable (RTs) into 6 different bins. The validation procedure is also summarized in Fig. S1 of Additional file 1. The Bayesian hyperparameter search ("Bayesian hyperparameter search" Section) and the validation procedure described in this section approximately required 2.5 months of computational time in a computer with an AMD Ryzen Threadripper 2970WX with 24 cores at 1.85 Gz, and a NVIDIA GeForce RTX 2080 GPU. Projection between chromatographic methods Machine learning models trained on a given Retention Time (RT) dataset (SMRT in this work) cannot be directly used to predict experimental RTs from other Chromatographic Method (CM)s due to the variability of the experimental setups. To exploit the knowledge of a predictive model trained on the SMRT, a second model projecting the predicted RTs to the specific Chromatographic Method (CM) used in an experiment is needed. Given a specific Chromatographic Method (CM), the projection function can be learned if some of the experimental metabolites have been identified, and therefore both their experimental and predicted RTs are known (step 3 in Fig. 2). For the workflow in Fig. 2 to be practical, it is desirable that the projection function can be learned from a small dataset (tens of molecules) so that the researcher has to identify just a few molecules. In practice, this would probably be accomplished by adding pure metabolite standards to the sample. The more standards that need to be used, the more time and money will be required. Hence the interest in minimizing their number. Bayesian methods are particularly well suited to solve classification/regression problems when data is scarce. This is due to their ability to incorporate prior knowledge about the problem. If the prior provides useful inductive biases for the task at hand, only a few samples may be needed to learn a proper solution to the problem [48]. Hence, under the Bayesian paradigm, the issue of learning from few data becomes how to specify a suitable prior for the problem. Meta-learning has recently arose as a possible solution for acquiring useful prior knowledge. In meta-learning, knowledge is gained by solving a set of tasks (meta-tasks), which is then exploited to solve a closely-related but different task (target-task). In the Bayesian setting, meta-tasks are used to learn a useful prior distribution, which is then used as starting point to solve the target-task. This is done by incorporating new evidence provided by the target-task into the prior, which results in the so-called posterior distribution. Hence, we propose the use of meta-learning to solve the problem of learning from few samples. The outline of the approach is shown in Fig. 4. We shall consider that the set of meta-tasks $\mathcal {M}$ consists of m datasets $\mathcal {M}=\{\mathcal {D}_i\}_{i=1}^m$, each corresponding to a different Chromatographic Method (CM). Each dataset $\mathcal {D}_i$ contains predicted RTs $\mathbf {x}^i$, as well as the experimental RTs obtained with a specific Chromatographic Method (CM), $\varvec{y}^i$. Hence, $\mathcal {D}_i=\{\mathbf {x}^i, \varvec{y}^i\}$ is a single meta-task and we would like to map $\varvec{x}^i$ to $\varvec{y}^i$ using a smooth function $f(\cdot )$. The predicted RTs are obtained by using the best predictive model from "Prediction of retention times with machine learning" Section. In our problem, meta-tasks are used to learn a prior distribution p(f) over the functions $f(\cdot )$ translating predicted RTs to experimental RTs of different CMs. Let us consider that we have gathered experimental RTs using the CMs A, B and C. During meta-learning, the projection functions $$\begin{aligned} f_A(\varvec{x}^A) \approx \varvec{y}^A, f_B(\varvec{x}^B) \approx \varvec{y}^B, \text { and } f_C(\varvec{x}^C) \approx \varvec{y}^C, \end{aligned}$$ will be constructed. These functions should be considered as samples drawn from the same distribution p(f). The aim of meta-learning is to learn a plausible prior p(f) that explains all observed samples $f_A(\cdot ), f_B(\cdot )$ and $f_C(\cdot )$. Overview of the meta-learning approach to RTs projection. 1) The meta-tasks consist of creating projection functions mapping predicted RTs to experimental RTs in several Chromatographic Method (CM)s. Each target Chromatographic Method (CM) is a different meta-task. 2) During meta-learning a prior distribution $p_{\theta }(f)$ on the projection functions is learned. This prior contains the learned projection functions in the meta-tasks (shown in color), and also any other function with similar properties to those observed in the dataset (shown in gray). 3) To solve a target-task, the prior distribution $p_{\theta }(f)$ is updated with new evidence provided by the target training set, resulting in the so-called posterior distribution. 4) The posterior distribution is used to evaluate the performance on a target test set In addition to the the meta-tasks we have the target-task $\widetilde{\mathcal {D}}=\{\varvec{\tilde{x}}, \varvec{\tilde{y}}, \varvec{\tilde{x}^}, \varvec{\tilde{y}^}\}$. Again, a single target-task is comprised of data from a single Chromatographic Method (CM). Intuitively, the target training points $\{\varvec{\tilde{x}}, \varvec{\tilde{y}}\}$ represent molecules whose identity is known (step 3 in Fig. 2) whereas the target test points $\{\varvec{\tilde{x}^},\varvec{\tilde{y}^}\}$ are molecules whose identity is to be discovered (step 6 in Fig. 2). We assume that the number of annotated molecules is small (indeed, this is the main difference between a meta-task and a target-task). Note that, when solving the target-task, the prior distribution p(f) learned during meta-learning is updated with the new evidence $\{\varvec{\tilde{x}}, \varvec{\tilde{y}}\}$, which should enable the prediction/ranking of $\{\varvec{\tilde{x}^},\varvec{\tilde{y}^}\}$. GPs are particularly suited as projection model: they represent a distribution over functions, they can perform regression on smalls amount of data, and they can incorporate prior knowledge using the Bayesian framework. Hence, we shall consider: $$\begin{aligned}&f(\cdot ) \sim \mathcal {GP}\left( m_{\varvec{\theta }_m}(\cdot ), k_{\varvec{\theta }_k}(\cdot , \cdot )\right) \text { or equivalently}\\&p_{\varvec{\theta }}(f)= \mathcal {GP}\left( f \mid m_{\varvec{\theta }_m}, k_{\varvec{\theta }_k}\right) ,\qquad \varvec{\theta }=[\varvec{\theta }_m, \varvec{\theta }_k] \end{aligned}$$ where the mean and kernel functions of the GP are parametrized with $\varvec{\theta }_m$ and $\varvec{\theta }_k$, respectively. Hence, the whole prior is parametrized with $\varvec{\theta }=[\varvec{\theta }_m, \varvec{\theta }_k]$. These parameters are learned by minimizing the negative Leave One Out (LOO) log predictive probability on the meta-tasks (see Algorithm 1, where $\varvec{y}^i_{-j}$ means all targets but the j-th item). The use of the LOO-based loss instead of the usual log marginal loss is based on the observation that cross-validation procedures (such as LOO) should be more robust against possible model misspecifications [49, Section 4.8]. Once the parameters have been learned, they can be used to specify a prior that is expected to generalize well on the target-task. Indeed, to avoid overfitting, $\varvec{\theta }$ is not optimized while solving the target-tasks. The only parameter estimated with target-task data is the variance of the residuals. This is done by maximizing type II maximum likelihood during 250 epochs with an Adam optimizer with learning rate set to 0.01. It is worth noting that the proposed meta-learning method fits well the Retention Time (RT)-based filtering workflow shown in Fig. 2. In this scenario, a query from a researcher corresponds to a target-task, which exploits the information provided by a previously meta-learned prior. Furthermore, although computing new predictions with the projection function scales quadratically with the training data, it will typically train on tens of RTs. Hence, it would only take tenths of a second to map experimental RTs to predicted RTs. Next sections present the data preprocessing and the parameter ($m_{\varvec{\theta }_m}$, $k_{\varvec{\theta }_k}$) selection process used to devise our projection method. Experimental setup and data preprocessing In [21] the non-retained molecules were ignored for validating the projection method, and we adopt the same methodology here. The rationale for this is that in an experiment is easy to know if a molecule has been retained or not, and a researcher would not use a RTs database to try to annotate non-retained metabolites. To avoid data-leakage during validation, we ensured that the meta-tasks data, target training data, and target test data did not overlap. To that end, we used a leave-one-Chromatographic Method (CM)-out approach. That is, data from a specific Chromatographic Method (CM) could only be used as either part of the meta-tasks or as the target-task. Hence, when using a Chromatographic Method (CM) as target-task, meta-learning was used on the remainder of CMs. Following [21], the following CMs were used to create the target-tasks: FEM long (342 molecules), FEM orbitrap plasma (133), LIFE old (148) and RIKEN (271). The number of molecules in the remainder of CMs is 2418. For a specific target-Chromatographic Method (CM) (one of the four above mentioned), and after meta-learning on the meta-tasks, the target training data is created by subsampling the Chromatographic Method (CM) data (and the remainder of RTs are used as target test data). To obtain a good projection, researchers are expected to add standards spanning the whole range of the experimental RTs. To mimic this behaviour, stratified sampling was used. Sampling was repeated 10 times for each number of training points to obtain error estimates. To study the robustness of the projection method when only a few metabolites are known, the number of training points was varied between 10 and 50; 50 was the number of molecules used in [21]. All GP models share the same preprocessing steps despite their mean and kernel functions. RTs are transformed to log space using $$\begin{aligned} \bar{\varvec{x}} = \log (1 + \varvec{x}) \qquad \text { and } \bar{\varvec{y}} = \log (1 + \varvec{y}), \end{aligned}$$ where $\varvec{x}$ and $\varvec{y}$ may belong to any meta-task $\mathcal {D}_i$ or any target-task $\widetilde{\mathcal {D}}$. The motivation for using this transformation is twofold. On one hand, RTs take only positive values. Without any transformation, the model has to learn this restriction on its own, which may be difficult in the scarce data scenario. By using the transformed RTs $\bar{\varvec{y}}$, the model learns to predict a target without any restriction. Then, the inverse transformation maps back $\bar{\varvec{y}}$ to the positive interval, forcing positiveness in the projected RTs. On the other hand, by also applying the transformation to $\varvec{x}$, the non-linear relationship between $\varvec{x}$ and $\varvec{y}$ linearizes, which could enable the use of simpler kernels. After the log-transformation, and since the software used to implement GPs is geared towards using inputs normalized to [0, 1] and outcomes normalized to $[-1, 1]$, data is further scaled using robust statistics. We used $$\begin{aligned} \bar{\bar{x}} = \left( \frac{\bar{x} - \text {median}(\bar{x})}{0.741\cdot \text {IQR}(\bar{x})} + 3\right) / 6 \qquad \text { and } \qquad \bar{\bar{y}} = \left( \frac{\bar{y} - \text {median}(\bar{y})}{0.741\cdot \text {IQR}(\bar{y})}\right) / 3, \end{aligned}$$ where $\text {IQR}$ denotes the interquartile range. The constant 0.741 is used because, for normal populations, the standard deviation fulfills $\sigma \approx 0.741 \cdot \text {IQR}$. Hence, under the normality assumption, 99.7% of the transformed $\bar{\bar{x}}$ will be on the [0, 1] range and 99.7% of the transformed $\bar{\bar{y}}$ will be on the $[-1, 1]$ range. Despite the different last preprocessing step for predicted ($\varvec{x}$) and experimental ($\varvec{y}$) RTs, both transformations are learned using the predicted RTs. Thus, there is no Chromatographic Method (CM)-dependent scaling. Comparison of meta-learned GP models We evaluated the performance of the different meta-learned GPs models arising from various choices of their two parameters: Mean function $m_{\varvec{\theta }_m}(\cdot )$: a typical parametrization of a GP when no prior information is available about the mean is $f(\cdot ) \sim \mathcal {GP}\left( 0, k_{\varvec{\theta }_k}(\cdot , \cdot )\right)$; that is, $m_{\varvec{\theta }_m}(\cdot )=0$. The underlying assumption is that all relevant prior information can be incorporated into the kernel parameters $\varvec{\theta }_k$. However, [50] shows that learning a mean function $m_{\varvec{\theta }_m}(\cdot )$ (either alone or combined with kernel learning) can outperform kernel learning alone. We tested this in our problem by studying GPs with a constant mean function, and GPs with a mean function parametrized with a neural network. In our experiments, we used a neural network with two hidden layers with 128 units and leaky-ReLU activations. Kernel function $k_{\varvec{\theta }_k}(\cdot , \cdot )$: different kernels result in different properties of the projection function. We compared the commonly used kernels and combinations of them. Specifically, we tested the squared exponential kernel, Matérn kernels with $\nu =1.5$ and $\nu =2.5$, the polynomial kernel of degree 4, a linear combination of two squared exponential kernels, a linear combination of a linear kernel and a squared exponential kernel, and a linear combination of a squared exponential kernel and a polynomial kernel of degree 4. A full list of the mathematical expressions for these kernels can be found in Section S1 of Additional file 1. The experimental setup described in "Experimental setup and data preprocessing" Section is used. We focused on the performance of the models in the low-data regime using just 10 training data points. For a single target-task $\widetilde{\mathcal {D}}=\{\varvec{\tilde{x}}, \varvec{\tilde{y}}, \varvec{\tilde{x}^}, \varvec{\tilde{y}^}\}$, the predictive marginal log-likelihood $$\begin{aligned} \mathcal {L}_{\mathcal {D}} = p(\varvec{\tilde{y}^} \mid \mathcal {D}, \varvec{\tilde{x}}, \varvec{\tilde{y}}, \varvec{\tilde{x}^}) = \int p \left( \varvec{\tilde{y}^} \mid f(\varvec{\tilde{x}^}) \right) p\left( f(\varvec{\tilde{x}^}) \mid \mathcal {D}, \varvec{\tilde{x}}, \varvec{\tilde{y}}, \varvec{\tilde{x}}^\right) d f. \end{aligned}$$ was used as metric of the model's performance. To obtain a single metric while taking into account the possible differences in the scales of the marginal log-likelihoods for the different CMs, each $\mathcal {L}_{\mathcal {D}}$ was compared with the marginal log-likelihood of a reference model $\mathcal {L}_{\mathcal {D}}^{\text {ref}}$: $\Delta \mathcal {L}_{\mathcal {D}} = \mathcal {L}_{\mathcal {D}}-\mathcal {L}_{\mathcal {D}}^{\text {ref}}$. We used as reference model a GP with constant mean and squared exponential kernel trained on the target-task without meta-learning. This model was trained by optimizing type II maximum likelihood during 500 epochs using an Adam optimizer with learning rate set to 0.01. The final metric $\Delta \mathcal {L}_{\text {avg}}$ was obtained by averaging across the four test-tasks and repetitions. Values $\Delta \mathcal {L}_{\text {avg}} > 0$ correspond with models that perform better (in average) than the reference one. Note that this not only permits the comparison of different meta-learned GP-models, but it also assesses the usefulness of the meta-learning approach. Additional experiments studying the influence of the number of meta-tasks in the performance of the GP were also carried out. They are discussed in Section S3 of the Additional file 1. Predictive performance of the projection function We compared the best GP-model from "Comparison of meta-learned GP models" Section with monotonic Generalized Additive Models (GAMs) [8], robust polynomial regression [21] and piecewise polynomial regression [24]. Unfortunately, it is not possible to compute the predictive marginal likelihood for all these models. Hence, we evaluated the performance of the models attending to both their predictive accuracy as well as their ability to generate proper prediction intervals. To test the predictive accuracy of the meta-learning approach we computed the median relative error, Mean Absolute Error (MAE) and MEDAE for the target test set. To test the prediction intervals we used the interval score [51] $$\begin{aligned} S(\varvec{\ell }, \varvec{u}, \varvec{\tilde{y}^})&= \frac{1}{\text {len}(\varvec{\tilde{y}^})}\sum _{i=1}^{\text {len}(\varvec{\tilde{y}^})} S(\ell _i,u_i,\tilde{y}^_i) \qquad \text { with }\nonumber \\ S(\ell _i,u_i,\tilde{y}^_i)&= (u_i-\ell _i)+\frac{2}{\alpha }(\ell _i-\tilde{y}^_i)\mathbbm {1}(\tilde{y}^_i<\ell _i)+\frac{2}{\alpha }(\tilde{y}^_i-u_i)\mathbbm {1}(\tilde{y}^_i>u_i), \end{aligned}$$ where $\varvec{\ell }$ and $\varvec{u}$ are the lower and upper ends of the prediction interval generated for the test target points $\varvec{\tilde{y}^}$, $\mathbbm {1}$ is the indicator function, and $\alpha$ is the coverage that the models are aiming for. We used $\alpha =0.95$ in all experiments. Equation (2) can be understood by noting that a proper prediction interval should reach a tradeoff between being as small as possible ($l_i$ should be close to $u_i$) and covering the observed values ($l_i \le \tilde{y}^_i \le u_i$). The first term of Equation (2) just measures the length of the interval, while the second and third terms penalize having observed values outside the prediction interval (moreover, the further apart an observation is from the interval, the larger the penalty). Note that the interval score has the same units as the RTs in $\varvec{\tilde{y}^}$. To obtain an adimensional metric and facilitate the comparison of different target CMs, we define the scaled interval score as $S(\varvec{\ell },\varvec{u},\varvec{\tilde{y}^}) / \text {median}\left( [\varvec{y^}, \varvec{\tilde{y}^}]\right) .$ Ranking annotations based on the projection function We have tested the ability of the projection method to rank and filter candidate annotations in metabolomic experiments based on mass search and RT predictions. The test implements a similar workflow to that described in Fig. 2. We collected the Retention Time (RT) predictions of the best-performing model from "Prediction of retention times with machine learning" Section for the 6,823 molecules with KEGG number in the Human Metabolome DataBase (HMDB) [52]. This simulates the database used to rank candidate annotations in Fig. 2. We used the leave-one-Chromatographic Method (CM)-out approach described in "Experimental setup and data preprocessing" Section for meta-training and target-tasks evaluation. After learning a projection function on the target training set, we simulated queries against the HMDB database to annotate the molecules on the target test set. For each molecule in the target test set, an accurate mass search (10 ppm mass error, the same as [21]) was performed to retrieve all compatible molecules from HMDB. To mimic real experimental conditions, we simulated experimental errors in the mass measurement by adding random noise to the mass of the unknown molecule. The random noise had a normal distribution with zero mean and a standard deviation of 10/3 ppm so that $99.7\%$ of the errors were between $[-10 \text { ppm}, 10 \text { ppm}]$. Random noise below $-10$ ppm or above 10 ppm was truncated to guarantee that the mass search always returned the correct molecule as a candidate (note that the mass search is based on the noisy mass and not the real one). Then, the molecules were ranked using Retention Time (RT) information according to a z-score computed as $$\begin{aligned} z=\frac{\mid \tilde{y}^ - \mu (\tilde{x}^)\mid }{\sigma (\tilde{x}^)}, \end{aligned}$$ where $\mu (\tilde{x}^)$ and $\sigma (\tilde{x}^)$ represent the GP's mean and standard deviation for the predicted-experimental Retention Time (RT) pair $(\tilde{x}^, \tilde{y}^)$. The intuition for the usage of the z-score as ranking metric is to take into account not only the agreement between the real experimental Retention Time (RT) and the projected value, but also the uncertainty in the projection. We focused on mass queries returning more than three candidates and computed the percentage of results where the true molecule was ranked among the top three candidates after z-scoring. To facilitate the interpretation of the results, a baseline performance for metabolite annotation when using only mass information was also computed. In this case, if several candidates with the same mass were returned, ties were randomly broken. Retention time prediction with machine learning MAE results for all tested regressors are summarized in Fig. 5. The MEDAE results are qualitatively similar to MAE ones, and can be found in Fig. S3 of Additional file 1. Both MAE and MEDAE are also reported in Tables 1, 2 and 3. Figure 5 shows that the DNN models outperform the other models, with the exception of the blender, which has similar results. Specifically, the DNN trained with fingerprints achieves a MEDAE of $17.2 \pm 0.9\;s$ and a MAE of $39.2 \pm 1.2\; s$ when considering all molecules, and a MEDAE of $17.2 \pm 0.9\;s$ and a MAE of $34.0 \pm 0.9\; s$ when considering retained molecules only. To the best of our knowledge, the previous top performing models achieved a MAE of $45.6 \pm 0.4\;s$ for all molecules [24], and $39.87\;s$ when only using retained molecules [26]. MAE results in seconds. The different estimators have been grouped by families, which are also highlighted with different colors, and approximately sorted by performance. The different panels indicate which molecules where considered for evaluating the performance: all includes all molecules, non-retained includes only those molecules considered as non-retained (Retention Time (RT) smaller than 5 minutes), and retained includes only retained molecules. The different shapes indicate the features used for feeding the regressors (in the legend, fgp and desc indicate fingerprints and descriptors, respectively). In the case of the blender, the features represented are descriptors+fingerprints since it is using all predictions from the base-regressors (i.e, it is using predictions from regressors using fingerprints, regressors using descriptors, and regressors using both). Error bars correspond to the 99% confidence interval of the MAE. In the figure, XGBoost, lightGBM and CatBoost have been shortened to XGB, LGB and CB, respectively. The numbers near the CB regressors correspond to the total contribution of non-retained molecules compared to retained molecules during training. For example, assigning a weight of 80 to each non-retained molecule (see "Gradient boosting" Section) results in these molecules influencing the loss function 80 times more than the retained ones. Since the relative abundance is 1/40, this leads to non-retained molecules having twice the influence of retained molecules during learning, which is shown as CB 2/1 Table 1 MAE and MEDAE results for the top 4 performing regressors (mean ± standard error) Table 2 MAE and MEDAE results for LightGBM and weighted CatBoost regressors with small overall weights for non-retained molecules (0, 1/80 and 1/40) Table 3 MAE and MEDAE results weighted CatBoost regressors with large overall weights for non-retained molecules (1/2, 1/1 and 2/1) Regarding the other models, they can be sorted from lower to higher errors as follows: DKL, XGBoost, and lightGBM and CatBoost algorithms, which have similar MAE. It is worth noting that DKL obtains similar results to those reported in [24] ($45.6 \pm 2.4$ and $40.8\pm 2.4\;s$ using fingerprints for all molecules and retained molecules, respectively) and [26] ($39.87\;s$ for retained molecules only). The differences in the regressors' performance originate from the prediction of the RTs for the retained molecules since the MAE for non-retained molecules is quite similar for all models. Computing the projection between chromatographic methods Figure 6 shows the averaged differences in predictive marginal log-likelihood $\Delta \mathcal {L}_{\text {avg}}$ for different combinations of means and kernel functions. Since the median of all models is $>0$, the meta-learning provides some advantage with respect to directly fitting a GP to the target-task data. Using a flexible mean function parametrized by a DNN does not seem to offer any advantage compared to the simpler constant mean. Regarding the influence of kernels, although there is no clear winner, the combination of a squared exponential kernel and a linear kernel (which has the largest median $\Delta \mathcal {L}_{\text {avg}}$), and the polynomial kernel of degree 4 (which has the lowest variability) stand out. Since having a low variability is particularly important in the context of training from few points, we shall use a GP parametrized with a constant mean, and a polynomial kernel of degree 4. That is $$\begin{aligned} f(x) \sim \mathcal {GP}\left( c, (xx' + \gamma )^4\right) . \end{aligned}$$ Averaged differences in predictive marginal log-likelihood $\Delta \mathcal {L}_{\text {avg}}$ for different combinations of means and kernel functions. SE refers to a squared exponential kernel and poly to a polynomial kernel of degree 4 Performance of the projection function Figures 7 and 8 show the MAE and scaled interval scores for the projections to four CMs from the PredRet database when using different models. MEDAE results show a similar behaviour to those obtained with MAE, and hence are shown in Fig. S4 of Additional file 1. Table 4 shows these three metrics and the median relative error (in %) for the meta-learned GP. Regarding the accuracy of the model (MAE and MEDAE), all methods perform similarly. However, GPs consistently rank among the two best results for most combinations of Chromatographic Method (CM) and number of training points. Figure 7 is particularly revealing since all methods but GPs show some large fluctuation (note the large error bars) for 10 or 20 training points, which suggests that they are more sensitive to the presence of outliers. MAE for projections between the predicted RTs and different CMs when using different projection models. GP refers to a GP with constant mean and polynomial kernel of degree 4, GAM refers to monotonic Generalized Additive Models [8], RLM refers to robust polynomial regression of order 4 [21], and PLM refers to piecewise polynomial regression [24]. The GAM value for RIKEN and 10 training points is a large outlier and hence it is not shown Scaled interval score (the lower, the better) for projections between the predicted RTs and different CMs when using different projection models. See Fig. 7 for the meaning of the acronyms Table 4 Scaled interval score, Median relative error (in %), MAE and MEDAE for projections between the predicted RTs and different CMs Regarding the scaled interval scores, piecewise liner regression and meta-learned GPs show a better overall performance than the other methods, specially when compared to GAMs. Meta-learned GPs have the best performance in three of four CMs, while piecewise linear regression performs better in one of four. An illustrative example of the projection function built using just 10 training points is shown in Fig. 9. Projections from the predicted RTs to four different CMs from the PredRet database using the proposed meta-learning approach. Red points and blue crosses indicate train and test points respectively. The black line is the predictive mean of the GP while the grayed region indicates the predictive 95% interval Ranking candidate annotations with the projection function Table 5 shows the percentage of the results where, using the Retention Time (RT) projection function, the true molecule was ranked among the top three candidates for those queries with more than three candidates. A comparison with the baseline values when only mass information is used (shown between parentheses in Table 5) reveals that the use of Retention Time (RT) information always improves ranking accuracy. Reported results in [21] for 50 training points were 66.7%, 67.9%, 69.7% and 71.9% for FEM long, FEM orbitrap plasma, LIFE old and RIKEN, respectively. Considering the standard error, when using 50 annotated molecules our DNN+meta-learning approach outperforms [21] in the FEM long system, while it has lower performance in the LIFE old system. The DNN+meta-learning approach reaches a global mean of $70\%$ for 50 annotated molecules. The number of training points affects both the ranking accuracy and its variability (standard errors). When using as few as 10 training points, the global performance decreases to $68\%$. Table 5 Percentage of results where the true molecule was ranked among the top three candidates using the meta-learning method In this paper we have trained several state-of-the-art machine learning regressors to predict small molecules Retention Time (RT) using the 80,038 experimental RTs from the SMRT dataset. The regressors included DNNs, DKL, XGBoost, lightGBM, CatBoost, and a blending approach. The models were trained using only molecular descriptors, only fingerprints, and both types of features simultaneously. Descriptors and fingerprints were generated with the alvaDesc software. Furthermore, we have proposed a meta-learning approach to learn projection functions between different CMs from a few training points. Retention time prediction Deep learning models, regardless the input features used for training, clearly outperform the other models. When using fingerprints, the DNN achieves a MAE of $39.2 \pm 1.2\; s$ when considering all molecules, and a MAE of $34.0 \pm 0.9\; s$ when considering retained molecules only; the previous top performing models achieved a MAE of $45.6 \pm 0.4\;s$ [24] on all molecules, and $39.87\;s$ when only using retained molecules [26]. This suggests that DNNs are better suited for Retention Time (RT) prediction than other models. Note that the DKL models, which should also exploit the benefits of DNNs, also achieve similar results to previously top-performing models, although they do not reach the performance of DNN. This may imply that the use of recent techniques intended for improving the generalization capabilities of DNNs (e.g. warm-restarts and SWA) were key for their performance. Although meta-models are expected to improve the base-regressors' performance, the blender built using all regressors has similar performance to that obtained by DNNs (see Fig. 5). To achieve an improvement, the base-estimators of the blender should have similar performance and be as diverse as possible, providing complementary information to be exploited by the meta-regressor. In our blender, the predictions of the meta-regressor are mostly influenced by the DNNs, since they have the best performance. The fact that the blender cannot improve the predictions of the DNNs implies that their predictions are almost the same. Indeed, the predictions of the three different DNNs are highly correlated (e.g., the correlation between the fingerprints' DNN and the descriptors' DNN is $0.972 \pm 0.003$). Since the fingerprints' DNN has similar performance and can be trained much faster, we can conclude that the use of blending has not provided any value for Retention Time (RT) prediction. Figure 5 shows that models that did not employ Bayesian search (lightGBM and CatBoost) perform worse, which suggests the usefulness of this procedure. These were also the models that benefited from using both descriptors and fingerprints; in the other models using both types of features together had a performance similar to using only the descriptors. In the literature there are both works reporting that fingerprints outperform molecular descriptors (e.g., [21]) and works claiming just the opposite (e.g., [24]). Our results slightly favor the usage of fingerprints, although it cannot be ruled out that the best type of feature depends on the machine learning regressor used. Regarding the experiments where the weights of the non-retained molecules were varied within the CatBoost regressor, Fig. 5 shows that increasing the importance of these molecules (large weights) yields worse MAE results for the retained molecules. As expected, large weights yield some improvement in the performance of the non-retained molecules (see Fig. 5). However, the large values of MAE for the non-retained molecules indicate that the regressors are not able to reliable distinguish non-retained molecules from retained ones. This also explains why the usage of different weighted CatBoosters did not have the expected impact on the blender: it was expected that the blender would match the performance of the best regressor for non-retained molecules. However, this has not been observed probably because the regressors fail to identify non-retained molecules and they tend to predict RTs as if the molecule was retained, even if it is not. This can be confirmed by inspecting the performance of the classifier trained to predict if a molecule will be retained or not (see "Preprocessing of descriptors and fingerprints" Section). Although the classifier has large specificity ($0.9953 \pm 0.0005$), precision and recall are low ($0.74 \pm 0.03$ and $0.512 \pm 0.016$, respectively), which highlights the difficulty in properly identifying non-retained molecules. Meta-learning-based projections The experiments suggest that the method to project the predicted RTs to a specific Chromatographic Method (CM) is able to provide proper projections using as little as 10 or 20 training points. In this range of training points, the accuracy of the meta-learned-GP shows similar or slightly better MAE and MEDAE than other state-of-the-art methods (Fig. 7). Regarding the prediction intervals, it has the best performance in three of the four CMs (Fig. 8). Being able to train the projection model from a few training points is key for real world applications, since it avoids the need to identify a large number of molecules. Note that in this small-data regime, the predictions are mainly driven by the prior learned during meta-learning. This can be seen by looking at the upper confidence interval for the FEM long Chromatographic Method (CM) in Fig. 9, which seems larger than needed. With more training points, the GP is flexible enough to reduce uncertainty around the training points, adjusting to the actual dispersion of the Chromatographic Method (CM), as shown by the trend for the FEM long system in Fig. 8. Remarkably, and although the scaled interval scores tend to decrease with the number of training points, they are quite stable for the other systems. The ability of GPs of generating credible prediction intervals for the projections can be used to obtain probabilistic scores for the putative annotations, as shown in "Ranking candidate annotations with the projection function" Section. Table 5 shows that, when using 50 training points, our projection method ranks the correct identity among the top three candidates in $70\%$ of the cases, at a similar level than other projection methods [21]. When decreasing the number of training points to just 10 samples, the percentage is $68\%$, while with 30 is $69\%$. This shows that meta-learning enables the creation of projection functions from just a few known metabolites. However, Table 5 also reveals large standard errors, which suggest that the projection functions are highly dependent on the training inputs. An accurate predictive model and a projection function that can be learned from as few as 10 identified metabolites permit building a tool to support metabolite annotation following the scheme presented in Fig. 2. We intend to integrate such a tool into CEU Mass Mediator [5], a metabolite annotation platform that has 332,665 metabolites in its database, of which approximately 250,000 have no RT information in the SMRT dataset. When RTs are available, it will only be necessary to use the projection function to map the experimental Retention Time (RT)s of the database to the Retention Time (RT) of the Chromatographic Method (CM) of a given experiment. When no Retention Time (RT) is available in the database, it will also be necessary to predict it using the best model achieved in this work (the DNN trained with fingerprints). The user of CEU Mass Mediator will only need to provide (1) the experimental RTs of the known molecules, whose identity should also be specified (by indicating their PubChem ID, InChI Key or similar), and (2) both the m/z and experimental RTs of the molecules to be annotated. This information can be uploaded to the tool's web page using text format. CEU Mass Mediator will then return the annotations compatible with the experimental data, ranked accordingly to their z-scores. Note that the use of the CEU Mass Mediator database avoids running the DNN in real-time. On the other hand, the projection method is highly efficient thanks to the meta-learning approach: the learning of the GP prior parameters is accomplished in an offline task, and the target-task that has to be executed online to compute the posterior distributions runs in just tenths of seconds. Hence, both the predictive model and the meta-learned projection function can be integrated into the workflow of Fig. 2 with negligible computational overhead. Furthermore, that workflow could be combined with an in silico MS/MS-based annotation approach when MS/MS data is available. In that scenario, the top predicted candidates by the model could be feed into tools that match them to the experimental MS/MS data, followed by a reranking based on both RT and MS/MS predictions. The software supporting the conclusions of this article is available in the constantino-garcia/cmmrt Github repository (https://github.com/constantino-garcia/cmmrt)."The sofware is distributed as a Python 3 package (platform independent) and also provides a Makefile for running most important actions (i.e, installing dependencies, train and validate regressors, and train and validate projections). 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Nucleic Acids Res 46(D1):608–617 This work was supported by Ministry of Science, Innovation and Universities of Spain (MICINN) and FEDER funds (Ref. RTI2018-095166-B-I00). Department of Information Technology, Escuela Politécnica Superior, Universidad San Pablo CEU, Campus Montepríncipe, Boadilla del Monte (Madrid), 28688, Spain Constantino A. García, Alberto Gil-de-la-Fuente & Abraham Otero Centre for Metabolomics and Bioanalysis (CEMBIO), Facultad de Farmacia, Universidad San Pablo CEU, Campus Montepríncipe, Boadilla del Monte (Madrid), 28688, Spain Alberto Gil-de-la-Fuente, Coral Barbas & Abraham Otero Constantino A. García Alberto Gil-de-la-Fuente Coral Barbas Abraham Otero CAG contributed to the conceptualization of work, software development, literature review, critical discussion, and paper writing. AGDLF contributed to the software development, critical discussion, and paper reviewing. CB contributed to the conceptualization of work, critical discussion, and paper reviewing. AO contributed to the conceptualization of work, critical discussion, and paper writing. All authors read and approved the final manuscript. Correspondence to Constantino A. García. Additional details on the experiments. Section S3 provides a brief description of the kernels tested with the DKL methods and the meta-learned GPs. Section S2 illustrates the training and validation procedures for all Retention Time (RT) regressors. Section S3 describes an additional experiment studying the influence of the number of meta-tasks in the performance of meta-learned GPs. Section S3 shows the performance of the machine learning models used to predict RTs using the MEDAE metric. Section S4 shows the performance of different projection methods using the MEDAE metric. García, C.A., Gil-de-la-Fuente, A., Barbas, C. et al. Probabilistic metabolite annotation using retention time prediction and meta-learned projections. J Cheminform 14, 33 (2022). https://doi.org/10.1186/s13321-022-00613-8 Bayesian methods	CommonCrawl
SGLSim: tool for smart glazing energy performance analysis Proceedings of the Energy Informatics.Academy Conference 2022 (EI.A 2022) Md Anam Raihan1, Kuntal Chattopadhyay1, Aviruch Bhatia2, Vishal Garg1 & Aftab M. Hussain3 A tool Smart Glazing Simulator (SGLSim), has been developed to perform parametric simulation analysis of different window systems with several window-to-wall ratios and orientations to compute and compare the annual energy performance. The net annual energy performance of the building is based on the electricity consumption in heating, cooling, interior lighting, and appliances, along with the electricity generation by the photovoltaic (PV) glazing, which is used to evaluate the energy performance of smart glazing. Performing parametric energy simulations and calculating the net annual electricity consumption of different combinations requires building modeling and energy simulation expertise. A web-based parametric tool can assist the user in carrying out the desired studies without requiring extensive technical knowledge. A case study is prepared for India's warm and humid climatic zone. This study examines the benefits of double pane semi-transparent photovoltaics (STPV) glazing, STPV glazing with dynamic internal blind, and electrochromic (EC) glazing over other traditional glazing systems. The study shows that the optimal net annual electricity consumption in the case of STPV windows is 10–12% less than the optimal value obtained in a simple glazing case. Additionally, the result suggested that glare-controlled interior blinds in the STPV window further reduce the net annual electricity consumption by up to 15% compared to conventional glazing. Similarly, installing the EC glazing reduces the yearly electricity consumption by up to 5% compared to standard glazing. Building energy consumption depends on the electricity consumed in heating, cooling, lighting, and other electrical appliances. Due to affordability and increased comfort requirements in recent years, buildings now account for a more significant portion of total energy use. The window regulates 20 to 40 percent of the total energy consumption of the building and provides the occupants with the ability to control the local environment (Cheng et al. 2018; Bülow-hübe 2001). The window orientation and window-to-wall ratio (WWR) are significant factors in determining a building's energy usage. A large or small WWR can cause overheating or underheating in the indoor environment, seriously impacting thermal comfort, human health, and building energy consumption. Newer technologies such as building-integrated photovoltaics (BIPV), dynamic blinds, and electrochromic (EC) glazing have been deployed in building facades or windows to conserve energy consumption and maintain the occupants' thermal and visual comfort. In the recent decade, solar photovoltaics (PV), which convert sunlight directly into electricity, have been more widely used (Zhang and Lu 2019). Due to limited land resources, integrating PV modules into buildings, such as roofs, facades, and skylights, to construct BIPV systems is one of the most effective ways to promote sustainable energy. In addition, unlike wind energy which requires enormous wind farms, PV installation is easy-going in urban areas. Moreover, dynamic blinds in buildings reduce building energy consumption while providing a desirable indoor environment for building occupants. Similarly, EC glazing is another dynamic technology that changes its tint to improve occupant comforts, maximize daylight access and reduce energy consumption. In general, windows are passive components, but the addition of these technologies transformed these windows into active systems. These systems are smart windows in this research. The performance of a window system depends on the glazing's optical, thermal, and electrical parameters. These properties affect the building energy demand, and in the case of the semi-transparent photovoltaic (STPV) system, it affects the power generation capabilities of the module (Miyazaki et al. 2005; Olivieri et al. 2014). An STPV window with low transparency may produce high electrical energy; however, it may increase the lighting load of the building. In contrast, a highly transparent STPV window allows more visible light to enter interior spaces, thereby reducing the lighting load of the building. Moreover, the high solar component in the infrared and ultraviolet range may increase the building's cooling load besides generating less electrical energy. Blinds, on the other hand, affect interior lighting loads, space heating, and cooling loads by regulating the quantity of daylight and incoming solar radiation via the window. Integrating dynamic internal blinds with STPV glazing further reduces the building energy consumption by reducing the solar heat gain. Similarly, EC glazing reduces the building energy consumption by changing its tint, thereby reducing the solar heat transmission inside the building based on some control parameters. To conduct parametric energy simulations of STPV, STPV with dynamic blind, and EC glazing requires proficiency in building simulation, which is repetitive and error-prone. A miscalculation in any energy simulation step can drastically alter the results. Hence, there is a need for a tool that can perform parametric simulations for multiple window systems using the inputs the user provides with the least amount of error. In this research, a web tool is developed to take the users' input about the building and simulate different window systems in EnergyPlus for various orientations and WWR. After completing all the simulations, it sends the graphical results back to the users to make an informed decision. This study aims to develop a tool for performing parametric simulations of several types of smart glazings, such as EC, STPV with dynamic blind, and STPV glazing. The parametric energy simulation is performed to compute, analyze, and assess the impact of smart glazing on the net annual electricity consumption of the building. To perform the comparative energy performance analysis of smart glazing with traditional glazing, annual energy simulations with varying envelope variables, WWR, and orientation are necessary. The variation in glazing parameters, direction, and WWR helps comprehend the impact of different glazing and dwelling parameters on building energy performance. It also helps identify the optimal operating condition (WWR, orientation, window type) under different climatic zones. Evaluation of smart glazings such as building-integrated STPV, STPV with dynamic blinds, and EC glazing is performed using a parametric annual energy simulation-based methodology. To understand the impact of smart windows on energy consumption and find the optimal building configuration, building energy modeling (BEM) is essential. EnergyPlus v9.2 (EnergyPlus 2021a) is used in this study because it has been validated under the ASHRAE standard 140-2017 validation test, a traditional comparative method for evaluating building energy analysis computer programs. It is the third-generation dynamic building energy simulation engine developed by the United States Department of Energy for simulating building, heating, cooling, lighting, ventilation, and other energy flows. The program was established in the 1990s using the BLAST and DOE-2 simulation engines. A significant portion of the building energy consumption depends on the glazing installed in the building. Glazing can alter the solar heat gain inside the room and light transmittance, which can increase/decrease the energy consumption in cooling/heating depending upon the season, i.e., summer or winter. EnergyPlus requires the window system's optical and thermal performance indices (i.e., U-values, SHGC, and VLT) to model traditional glazing in a window. The building energy performance depends on the opto-thermal parameters. Moreover, PV glazing impacts the net annual electricity consumption of the building by generating electricity. The generated electricity from the STPV system is accounted as well in EnergyPlus. Post modeling, the annual energy simulation for a window system is performed in various orientations and WWR. The energy performance of a system depends on the electricity benefits it provides. The net annual electricity consumption depends on electricity generation and consumption of the building. It is the summation of all the electricity consumption and generation in the building whereas the values corresponding to the electricity consumption are positive, and electricity generation is negative. The lower the net annual electricity consumption value compared to the baseline, the better the glazing performance. The SGLSim tool performs a parametric simulation of different window systems. It calculates and compares the net annual electricity consumption of the selected window system in different configurations. Finally, it provides a straightforward graphical interpretation of results describing the energy-saving potential of various glazing systems to the end-user. Development of the tool A web-based tool called SGLSim has been developed to perform parametric simulations of the different window systems. The software details and architecture has been described in this section. The tool gives a simple interface to the users to model the building and window as per their requirements. It then computes and compares the net annual electricity consumption of the selected glazing systems in different configurations. Finally, it provides a graphical interpretation of results demonstrating the energy-saving potential of various glazing systems to the end-user. No other open-source tool exists which supports the same functionality and feature as provided by SGLSim. Energy enthusiasts, researchers, and building simulation engineers can use this easy-to-use tool to determine the efficiency of different glazing systems. This tool is the first of its kind and can be used for energy analysis of conventional glazing with PV systems. The software stack helped in building a convenient and user-friendly application. The tool requires computation memory and storage for running EnergyPlus parametric simulation and saving the results with both web application and simulation server running on the same instance. It provides the user with graphical results comparing the net annual electricity consumption of different window systems. It also provides users with tabular yearly energy consumption data. Python-based software development has become popular owing to its simplicity, flexibility, and ease of learning. Python (https://www.python.org/) has extensive library options, which can help a lot in the automation of various tasks. Also, unlike most other modern programming languages, python is much more user-friendly and reliable. The entire web application is built in Flask (https://flask.palletsprojects.com/en/2.1.x/). It is a lightweight web server gateway interface (WSGI) web application framework and offers much flexibility in structuring the application. Redis (Redis 2021) list allows to push and pop items from both ends using commands. Thus, it creates a first-in, first-out queue that maintains the task queues. MySQL database was used to store user data, and Flask SQL Alchemy was used to implement and communicate with the database. Table 1 shows the technologies used in the development of the tool. Table 1 Tech stack Tool architecture The entire application architecture consists of three parts: (1) Front End or web client, which includes a user interface that allows users to register, log in, and submit the required parameters for the simulation. (2) A Flask app interconnects the database, task queues, web client, and simulation server. (3) A Simulation server generates an EnergyPlus input data file (IDF), performs energy simulation, generates results, and sends it back to the user. Figure 1 shows the system design of the tool. Each component of the system has been explained in detail in this section. System design of the tool The web client consists of web pages that act as an interface to submit the simulation parameters and construct the building model. The user interface and the simulation form were developed using the technologies such as HTML, CSS, JavaScript, and Bootstrap. The simulation parameters consist of two different types: Fixed and Parametric. WTForms (https://wtforms.readthedocs.io/en/3.0.x/) is used for form validation as it is a flexible forms validation library for Python web development. It notifies the user if any field is incorrectly filled, and in case all the fields are correct, the tool sends the data to the Flask app using a POST API request. Figure 2 shows a screenshot of the user interface of the SGLSim tool. Since the simulation usually takes a long time, the user is redirected to the home page after successfully submitting the simulation parameters. Meanwhile, the simulation is performed on the server; post-completion, the results are mailed to the user by the tool using python-emails (email PyPI 2022), a python library for emails. The results include the building's net annual electricity consumption for different window systems and configurations and tabular load consumption data. User interface of the tool Flask app Flask is a python-based web application framework with a simple and scalable core. It's a micro-framework built on the Werkzeg WSGI toolkit and the Jinja2 template engine. Werkzeug is a WSGI toolkit that implements requests, response objects, and utility functions and allows for creating a web frame. Jinja2 is a popular python template engine that enables you to create dynamic web pages. It does not provide an Object Relational Manager (ORM); however, Flask SQLAlchemy is used as an ORM to communicate with the database. Both Flask app and simulation server is hosted on the same server in different instance. Flask app renders pages for the web client. When the application receives a simulation request, it validates to check for any errors. It then serializes the user input into a JSON object and stores it in the task queue. After successfully storing the input data, the application redirects the user back to the home page. Simulation server The simulation server is the standalone and most crucial component of the tool. The core of the simulation server is developed in python using various open-source libraries such as Eppy (eppy PyPI 2022), NumPy (NumPy 2022), Pandas (https://pandas.pydata.org/), etc. Eppy is a scripting language for EnergyPlus input and output files. It is written in the python programming language; hence, it fully utilizes the rich data structure and idioms offered in python. NumPy and Pandas were used during the post-processing of results. The simulation server connects the Flask app with the building simulation software EnergyPlus. It takes the input from the task queues using the first-in, first-out (FIFO) algorithm and then deserializes it to generate the simulation's EnergyPlus input data files. As soon as file generation is completed, it starts simulating the IDF files, successively storing the net annual electricity consumption for the various parametric combination of the building model. This annual energy consumption is later graphically plotted using Plotly (https://plotly.com/) and sent back to the user. Figure 3 shows the working of the tool. Since the parametric simulation can take a long time, all the essential steps are performed in the server, so the web client is free to take requests from the users and store them in the task queue. The application allows the user to install different kinds of glazing and PV on windows and observe their effect on annual electricity consumption. The tool has a primary input data file on which all these user inputs are appended. Working of the tool The tools aim to automate the entire process of comparative energy analysis of different glazing systems, such as PV, Low-E, and standard glazing. It provides the net annual electricity consumption of the same building model with various window systems, which can help the user understand the optimal orientation, WWR, and glazing for a particular climatic zone. A sample of graphical results sent by the tool is shown in Fig. 4, a graph of the net annual electricity comparison of two glazing systems A and B in West orientation. Table 2 shows the number of features developed in this tool. Graphical comparison of net annual electricity consumption between two window systems Table 2 Features of the tool The input to the SGLSim tool consists of all the parameters required to construct a single-zone model with the smart window functionalities. The input can be categorized into fixed and variable parameters, as shown in Table 3. The fixed parameters include the building name, location, dimension, blind control, building type, daylight control, heating, ventilation, and air conditioning (HVAC) type. In contrast, the variable parameters are orientation, WWR, and glazing properties such as solar heat gain coefficient (SHGC), thermal transmittance (U-value), visible light transmittance (VLT), and PV generator properties. Further details about the other parameters can be found in the EnergyPlus input–output reference guide (EnergyPlus 2021b). Table 3 Fixed and variable parameters Window geometry and construction The building model has a window in one of the walls to install the glazing and to study the effect of changes in WWR on the net annual electricity consumption of the building. The WWR of the building changes by modifying the dimension of the window. In EnergyPlus, calculating the window parameters such as length, height, starting X coordinate, and Z coordinate is necessary for making changes in the WWR. The window dimensions and the starting X and Z coordinates of the window are calculated before each IDF generation to change the WWR of the model. The Z coordinate represents the sill height of the window. The offset is 50 cm on each side and represents the minimum distance between the wall and window in the horizontal direction. L and H denote the length and height of the building model. The following equations show how the window dimensions and coordinates are calculated before IDF generation. $$Area\;of\;the\;wall\;(A)=L \times H$$ $$Area\;of\;the\;window\;(A_{w})=\frac{A \times WWR}{100}$$ $$Length\;of\;the\;window\;(l)=L-2 \times Offset$$ $$Height\;of\;the\;window \;(h)=\frac{A_{w}}{l}$$ $$X\;coordinate\;of\;the\;window=\frac{L-l}{2}$$ $$Z\;coordinate\;of\;the\;window=\frac{H-h}{2}$$ Modeling STPV glazing STPV glazing generates electrical power based on the fraction of sunlight on the window surface absorbed by the panel, which otherwise would have penetrated the room. Increasing the coverage area of the STPV glazing may increase power generation, but the daylight entering the room reduces, thereby increasing artificial lighting consumption. As a result, solar cells on the glass minimize transmitted solar heat gain, potentially resulting in a higher heating load in the winter and a lower cooling load in the summer than standard glazing. When the glazing has STPV, it generates electricity that the building can use, and therefore, it is deducted from the total electricity consumption. The double-pane semi-transparent CdTe PV glazing was modeled using the Sandia model as a PV performance object. It uses PV panel coefficients to calculate the electrical production capabilities of the STPV window. Sandia model is intrinsically linked to the surface heat equilibrium and uses surface temperature as the operating temperature of the solar cell (Peng et al. 2015). The PV arrays are connected to a single electric load center containing a list of electric power generators required in the simulation and an inverter that converts direct current (DC) to alternating current (AC) and has a fixed efficiency. The study compares the energy performance of double-pane STPV glazing systems with standard glazing. The window configuration and electrical properties of the selected STPV glazing are referred from earlier study (Raihan et al. 2022), as shown in Table 4 and Table 5. The conventional glazing is assumed to have the same U-factor, SHGC, and VLT as in Table 4 without the electrical parameters of the STPV. Table 4 Window parameters Table 5 Electrical parameter of STPV Modeling STPV glazing with dynamic blind Blinds control the amount of sunlight entering the room. Depending on how it is mounted on the window, blinds can be classified into three categories: external, internal, and intermediate. There are two kinds of blind control: Static and Dynamic. Static blind control is always on or off and manually operated by the occupants. A dynamic blind system allows control of the blinds based on the room's dynamics. EnergyPlus allows more than fifteen control types for the blinds based on solar radiation, horizontal solar radiation, slat angle, outdoor temperature, zone temperature, glare, and zone cooling, depending upon the requirements of the building. In EnergyPlus, a blind is modeled as a window material integrated into the window as a construction layer. Further, to dynamically control the blind, window shading control is used to fix the setpoint, schedule, and shading control type. This study modeled a dynamic internal blind with glare control in EnergyPlus. The blind lowers if the glare at the zone's first daylighting reference point from the window exceeds the maximum glare index specified in the daylighting input for the building. Modeling electrochromic glazing In EnergyPlus, Electrochromic (EC) glazing can be modeled as a switchable glazing shading device that allows electrochromic glazing to switch from clear (high transmittance) to dark (low transmittance) based on user-defined control type and setpoint. EnergyPlus allows various control types based on temperature, solar radiation, glare, and cooling. As reported in multiple studies, EC control based on daylight illuminance and solar radiation has resulted in maximum energy saving (Sullivan et al. 1994; Maria et al. 2000). The limitation of this modeling method is that it allows only two states; however, current EC glass allows intermediate conditions between the clear and fully tinted state. Another method to model EC glazing is through Energy Management System (EMS) program in EnergyPlus. It is developed to incorporate many control algorithms with the previous generation of the Building Performance Simulation (BPS) program. EMS uses a programming language called EnergyPlus Runtime Language (ERL) to describe the control algorithms. EMS program broadly contains two kinds of objects: Sensor and Actuator. The sensor object declares an ERL variable that uses the standard EnergyPlus variable to calculate the parameter used in the control algorithm. In contrast, the actuator overrides the predefined construction states assigned to specific components such as surface constructions, thermostat setpoints, and internal shades (Crawley et al. 2007). This study evaluates a 4-tint states SAGE EC product (SAGEGLASS®) with a control algorithm modeled using the EMS program. The spectral properties of the EC glazing are available in the electrochromic parameter folder in the GitHub repository. The sensor object used in the EMS program calculates the solar radiation falling per unit area on the window. This variable is used in the control algorithm to determine the tint state of the window. EMS Actuator object contains the name of the component controlled and its type. It also specifies the control type since some elements have more than one control type, such as flow rate or temperature. For our case, we have used the surface actuator with the control types of construction state (Dutta 2018). EMS construction index variable declares an EMS variable that identifies a construction. The default construction assigned is clear, which has the highest transmittance. The following two represent the intermediate states, and the last depicts the darkest tint. Algorithm 1 Electrochromic glazing control Result: Switching tint of the EC window while building is operating do if solar radiation falling on window ≤ 200 then Set Tint 1 else if solar radiation falling on window ≤ 500 then The simulation model for the case study was referred from earlier study (Raihan et al. 2022). Input parameters for the case study are mentioned in Tables 6 and 7, showing the fixed and variable parameters of the case study, respectively. Table 6 Fixed parameter for the case study Table 7 Variable parameter for the case study Climate of Kolkata Kolkata (22.5726° N, 88.3639° E) has a warm and humid climate with hot and humid summer and pleasant winter. The Bay of Bengal heavily influences its environment. Kolkata has three seasons- summer, monsoon, and winter. The annual mean temperature is 26.8 °C, whereas the monthly mean temperature ranges from 15 to 30 °C. Summer has a monthly mean temperature of 30 °C, but the maximum temperature often exceeds 40 °C, whereas, during winters, the temperature dips to 12 °C between December and January. Most of the city's annual rainfall is brought by the Bay of Bengal rains, which lash the city between June and September. Figure 5 shows the dry bulb temperature and relative humidity of Kolkata. Dry bulb temperature and relative humidity of Kolkata The net annual electricity consumption of the STPV and standard window systems in the four primary orientations in Kolkata is shown in Fig. 6. The dashed black line denotes the PV window system, whereas the solid red line indicates the performance of the traditional glazing system. Comparison of net annual electricity consumption of STPV with standard glazing The graphs show that the PV window system is energy efficient compared to the standard glazing system. The lowest net annual electricity consumption was achieved in the North orientation due to less solar radiation, causing a low cooling load, as shown in Table 8. The West orientation is the next optimal orientation for PV installation in Kolkata. Table 8 Solar radiation in different orientations The minimum net annual electricity consumption achieved by the window systems in different orientations and the corresponding WWR has been mentioned in Table 9. The table shows the best performance of window systems in various configurations and orientations. It also shows that the optimal net annual electricity consumption in the case of STPV windows is less than 10–12% compared to the standard glazing having the same optical and thermal characteristics. Moreover, it shows that with the help of the STPV window, a larger WWR is possible. Table 9 Optimal WWR at minimum net annual electricity consumption for W1 window Figure 7 shows a window system's comparative energy performance analysis in three different configurations. Dashed blue and solid red lines denote the STPV and standard glazing, respectively, whereas the dotted green line represents the STPV with a dynamic internal blind. The glare-controlled dynamic interior blind installation with STPV further reduces the net annual electricity compared to the STPV window systems. With the increase in WWR, the difference in net annual electricity between the STPV window system and STPV with dynamic blind increases. The STPV, with an active internal blind window system, achieved the lowest annual electricity in the North orientation. The glare-controlled dynamic internal blind can save up to 4% compared to the STPV window system and up to 14% net annual electricity consumption compared to a simple window system. Net annual electricity consumption of STPV with dynamic blind Figure 8 shows the comparative energy performance analysis of EC and standard glazing. The solid red line represents the standard glazing system W1, whereas the EC glazing is denoted by the black dashed line. The EC glazing consumes less electricity compared to conventional glazing. The installation of EC glazing results in more than 3% annual electricity savings compared to a simple window system. In this graph, the W1 system represents the standard glazing without any electrical properties for energy generation. Comparison of net annual electricity consumption of EC glazing with standard glazing A web-based tool has been developed for parametric simulations for different glazing systems to find the optimal window-to-wall ratio, orientation, and glazing type for a particular climate zone. The tool allows users to compare two glazing systems with or without an STPV on the window. Some of the benefits of the SGLSim tool are: The optimal window-to-wall ratio and orientation can be calculated easily for different glazing systems for a selected city. It reduces the time to perform parametric simulations of various glazing systems as the program automates the entire simulation process. It reduces the error in various calculations, such as the window-to-wall ratio. It provides the user with graphical results. The application of the tool is shown through case studies in India's warm and humid climatic zone. The study suggests that the North orientation has the lowest net annual electricity consumption for Kolkata compared to other directions. In the North orientation, the window with WWR up to 90% can be installed. Moreover, West is the next optimal orientation for installing PV facades, with the lowest annual electricity achieved at WWR between 40 and 70%. The study further suggests that installing glare-controlled dynamic blinds in an STPV system avoids the glare problem and reduces the net annual electricity consumption compared to STPV and simple window systems. An adequately modeled dynamic blind system can result in an additional 15% more annual electricity reduction than conventional glazing while maintaining the glare throughout the room. Finally, installing the EC glazing saves up to 5% net annual electricity consumption compared to the traditional window. The datasets generated and analyzed during the current study are not publicly available due to currently more research going on the datasets but are available from the corresponding author on reasonable request. The basic version of the tool can be accessed from the GitHub link—https://github.com/iamar7/SGLSim. Alternating current ASHRAE: The American Society of Heating, Refrigeration and Air-Conditioning Engineers BIPV: Building Integrated Photovoltaic BPS: Building Performance Simulation CdTe: Cadmium telluride Direct current EC: Electrochromic ERL: EnergyPlus Runtime Language FIFO: First in first out Hypertext Markup Language HVAC: IDF: Input data file ORM: Object Relational Manager SGLSim: Smart Glazing Simulator SHGC: Solar heat gain coefficient STPV: Semi-transparent photovoltaic U-Value: Thermal transmittance VLT: Visible light transmittance WSGI: Web server gateway interface WWR: Window to wall ratio Bülow-hübe H (2001) Energy-efficient window systems: effects on energy use and daylight in buildings. Lund University, Lund, p 248 Cheng Y, Gao M, Dong J, Jia J, Zhao X, Li G (2018) Investigation on the daylight and overall energy performance of semi-transparent photovoltaic facades in cold climatic regions of China. Appl Energy 232:517–526 Corsi M, Zmeureanu R, Fazio P (2000) Modeling of electrochromic glazing switching control strategies in Micro-DOE2.1E, Centre for Building Studies, Concordia University Crawley DB, Ellis PG, Torcellini PA (2007) Simulation of energy management systems in EnergyPlus. Build Simul Dutta R (2018) Modeling an electrochromic window using a multi-criteria control strategy. In: Proceedings of the building performance analysis conference and simbuild co-organized by ASHRAE and IBPSA-USA. Chicago, IL, USA, pp 149–156 Email PyPI (2022) https://pypi.org/project/email/. Accessed 7 June 2022 EnergyPlus (2021a) https://energyplus.net/. Accessed 14 Oct 2021 EnergyPlus (2021b) EnergyPlusTM input output reference. https://energyplus.net/documentation. Accessed 12 Oct 2021 Eppy PyPI (2022) https://pypi.org/project/eppy/. Accessed 7 June 2022 Miyazaki T, Akisawa A, Kashiwagi T (2005) Energy savings of office buildings by the use of semi-transparent solar cells for windows. Renew Energy 30:281–304 NumPy (2022) https://numpy.org/. Accessed 7 June 2022 Olivieri L, Caamaño-Martin E, Olivieri F, Neila J (2014) Integral energy performance characterization of semi-transparent photovoltaic elements for building integration under real operation conditions. Energy Build. 68:280–291 Pandas—Python Data Analysis Library. https://pandas.pydata.org/. Accessed 7 June 2022 Peng J, Lu L, Yang H, Ma T (2015) Validation of the Sandia model with indoor and outdoor measurements for semi-transparent amorphous silicon PV modules. Renew Energy 80:316–323 Plotly: the front end for ML and data science models. https://plotly.com/. Accessed 7 June 2022 Raihan MA, Chattopadhyay K, Bhatia A, Garg V, Hussain AM (2022) Energy analysis of semi-transparent building integrated photovoltaic window in Hyderabad, India using automated parametric simulations. IOP Conf Ser Earth Environ Sci 1050:012022 Redis (2021) https://redis.io/. Accessed 14 Oct 2021 SAGEGLASS®. https://www.sageglass.com. Accessed 10 May 2022 Sullivan R, Lee ES, Papamichael K, Rubin M, Selkowitz SE (1994) Effect of switching control strategies on the energy performance of electrochromic windows. In: Wittwer V, Granqvist CG, Lampert CM (eds) Optical materials technology for energy efficiency and solar energy conversion XIII. SPIE, Bellingham, pp 443–455 Welcome to Flask—Flask documentation (2.1.x). https://flask.palletsprojects.com/en/2.1.x/. Accessed 7 June 2022 Welcome to Python.org. https://www.python.org/. Accessed 7 June 2022 WTForms—WTForms documentation (3.0.x). https://wtforms.readthedocs.io/en/3.0.x/. Accessed 7 June 2022 Zhang W, Lu L (2019) Overall energy assessment of semi-transparent photovoltaic insulated glass units for building integration under different climate conditions. Renew Energy. 134:818–827 The authors would like to acknowledge the contributions of Md Aamir Raihan, who provided writing reviews during the paper preparation. This article has been published as part of Energy Informatics Volume 5 Supplement 4, 2022: Proceedings of the Energy Informatics Academy Conference 2022 (EI.A 2022). The full contents of the supplement are available online at https://energyinformatics.springeropen.com/articles/supplements/volume-5-supplement-4. This research was partly funded by the Ministry of Electronics and Information Technology (MEITY) under Grant No. 3070665 (2020) as part of the Smart City Living Lab project and Department of Science and Technology (DST), Government of India (GOI) under the project "Development and Performance analysis of double pane semi-transparent solar photovoltaic window/facade system (DPSTSP)." Center for IT in Building Science (CBS), International Institute of Information Technology, Hyderabad, 500032, India Md Anam Raihan, Kuntal Chattopadhyay & Vishal Garg Department of Sustainable Engineering, TERI School of Advanced Studies, New Delhi, 110070, India Aviruch Bhatia Center for VLSI and Embedded Systems Technology (CVEST), International Institute of Information Technology, Hyderabad, 500032, India Aftab M. Hussain Md Anam Raihan Kuntal Chattopadhyay Vishal Garg MAR: developed SGLSim, investigation, writing—original draft, visualization, formal analysis, methodology. KC: investigation, formal analysis, validation. AB: writing—review and editing, methodology, validation, supervision. VG: conceptualization, supervision, project administration. AMH: supervision. All authors read and approved the final manuscript. Correspondence to Md Anam Raihan. Raihan, M.A., Chattopadhyay, K., Bhatia, A. et al. SGLSim: tool for smart glazing energy performance analysis. Energy Inform 5 (Suppl 4), 40 (2022). https://doi.org/10.1186/s42162-022-00226-3 Smart glazing Energy performance Parametric simulations	CommonCrawl
Editing the content of questions Suppose a user asks a question on the main site, and he makes several mistakes in his question. Then the editing crew shows up to fix those mistakes. So far so good. If he made typos, we fix them. If the layout is messed up, we try to make it look better. But what if there are small and/or big mistakes in the content of the question? In other words: Should we ever edit the (mathematical) content of questions? I would say that it is not our job to fix any content whatsoever. The mistakes are part of the question, and help us understand what the user knows and what he does not know, and where he may have gone wrong. But recently I ran into a question where a mistake in the content (even though it was just a tiny mistake) was edited and fixed by another user. Would it be wrong for me to say that that mistake should not have been fixed? In this particular case, the mistake was irrelevant to the question itself, e.g. fixing "I know 1+1=3, but do we also have $\int \frac{1}{x}=\log x + C$?" to "I know 1+1=2, but do we also have $\int \frac{1}{x}=\log x + C$?". Even then I'd say we should leave the "1+1=3" there and let others tell the user in the comments that he is wrong, so that he can learn from it. TMMTMM $\begingroup$ I usually indicate the errors through comments, to see if it was a typo or an actual mistake. If it is a typo, it can be corrected (either by the OP or by editors). If it was a mistake, then IMHO it should be addressed (e.g., in answers) even if it is irrelevant to the rest of the question... $\endgroup$ – Arturo Magidin May 19 '12 at 20:12 No, I agree that we should not correct mathematical errors by editing the question. I also think that this is true for answers, for the most part. I would prefer that users comment to point out mathematical errors (or include the correction in an answer if the error is in the question, as Arturo commented). Here is a related post. Jonas MeyerJonas Meyer $\begingroup$ Agreed, but you can't win. I recently pointed out a couple of borderline typos/errors in an answer, and was asked by the poster why I didn't just edit them myself instead of announcing them to everyone. Sometimes, it's a judgement call, and sometimes different people will make different judgements. $\endgroup$ – Gerry Myerson May 20 '12 at 7:12 $\begingroup$ I disagree with Jonas (in the abstract): there are mathematical errors and there are mathematical errors. A few missing minus signs which do not matter in the grand scheme of the argument is, technically, a mathematical error. But in this case it would be much quicker and effective to treat them like a simple typo. I would say the same to TMM's example in the question: typing $1+1 = 3$ is much more likely a fat-finger mistake (easily made on mobile devices even). A truly mathematical "mistake" for which I'd agree with Jonas would be something like "I know $\pi + e$ is rational..." $\endgroup$ – Willie Wong May 21 '12 at 7:38 Not the answer you're looking for? Browse other questions tagged discussion editing . What is to be edited? Treatment of multiple answers by same user to same question When does editing become over editing? Questions concerning editing of wikipedia articles How much is it acceptable to partially answer a post within an edit of that post? User that never shows work Should I refrain from editing older questions/answers? If so, why? Should \dfrac be edited in? Down voting a question for not showing a correct attempt? Editing Other's Answers Etiquette Answers that are wrong, but useful? + Editing out your mistakes?	CommonCrawl
Chapter 6 Short Answer/Critical Application cmtrentx What is the major function of muscle? To contract or shorten. To cause movement. Compare skeletal, smooth, and cardiac muscles in regard to their microscopic anatomy, location and arrangement in body organs, and function in the body Skeletal muscle: Long, cylindrical, striated, multinucleate cells; attached to bones and crossing joints; forms the "flesh" of the body and is responsible for all voluntary movement. Cardiac muscle: Branching, striated cells containing a single nucleus; interdigitate with one another at tight junctions called intercalated disks; found only in the heart, arranged in spiral bundles; contraction of the heart propels blood into the blood vessels. Involuntary movement. Smooth muscle: Fusiform, uninucleate cells, no striations; generally found in cell layers (or sheets) arranged at right angles to one another (one running longitudinally and the other circularly) within the walls of hollow organs; causes substances to move through internal body tracts (digestive, urinary, reproductive, respiratory). Involuntary movement. What two types of muscle tissue are striated? Skeletal and cardiac muscle. Why are the connective tissue wrappings of skeletal muscles important? Name these connective tissue coverings, beginning with the finest and ending with the coarsest. They protect, reinforce, and strengthen the delicate muscle tissue. Endomysium, perimysium, and epimysium. What is the function of tendons? Tendons attach muscle to bone. Define neuromuscular junction, motor unit, tetanus, graded response, aerobic respiration, anaerobic glycolysis, muscle fatigue, and neurotransmitter. Neuromuscular junction: The junction of a motor neuron's axon terminals and the sarcolemma of a muscle cell. Motor unit: One motor neuron and all the muscle cells it stimulates. Tetanus: The smooth, sustained contractions of a muscle with no evidence of relaxation. Graded response: Different degrees of contraction in response to different levels of stimulation (changes in both the stimuli frequency and number of muscle cells stimulated). Aerobic respiration: Metabolic pathways that use O2 to generate ATP. Anaerobic glycolysis: Metabolic pathway that breaks down glucose into pyruvic acid (without using O2) to generate ATP. Muscle fatigue: The inability of a muscle to contract even though it is still being stimulated; usually a result of a lack of oxygen and the accumulation of lactic acid in the muscle tissue. Neurotransmitter: A chemical substance released by a neuron when the nerve impulse reaches its axon terminals. Describe the events that occur from the time calcium ions enter the axon terminal at the neuromuscular junction until muscle cell contraction occurs. Acetylcholine is released; it diffuses through the synaptic cleft and attaches to receptors on the sarcolemma; sarcolemma permeability to sodium ions increases briefly; sodium ions rush into the muscle cell, reversing the electrical conditions of the resting sarcolemma (depolarization of the membrane); the action potential is initiated and sweeps over the entire sarcolemma eventually reaching the sarcoplasmic reticulum deep inside the cell; calcium ions are released from the sarcoplasmic reticulum; attachment of calcium ions to the thin/actin filaments exposes binding sites for myosin. Myosin heads bind to actin, triggering their inward sliding; contraction occurs. How do isotonic and isometric contractions differ? Isotonic contractions: Muscle tension remains the same, and the muscle shortens. Isometric contractions: Muscle tension increases, but the muscle cannot shorten. Muscle tone keeps muscles healthy. What is muscle tone, and what causes it? What happens to a muscle that loses its tone? Muscle tone is a state of continuous, partial contraction of muscles resulting from discontinuous but systematic stimulation of different motor units by the nervous system . A muscle without tone is paralyzed (unable to contract) due to destruction of the nerve supply, and becomes flaccid and can eventually atrophy. A skeletal muscle is attached to bones at two points. Name each of these attachment points, and indicate which is movable and which is immovable. Origin: Immovable (or less movable) end. Insertion: Movable end; when contraction occurs, the insertion moves toward the origin. List the 12 body movements studied in this chapter, and demonstrate each. Flexion, extension, abduction, adduction, rotation, circumduction, pronation, supination, inversion, eversion, dorsiflexion, plantar flexion. How is a prime mover different from a synergist muscle? How can a prime mover also be considered an antagonist? A prime mover is a muscle that has major responsibility for causing a particular movement; for example, the gastrocnemius is the prime mover of plantar flexion. Synergist muscles aid prime movers by causing the same movement (but less effectively) or by stabilizing joints or bones over which the prime mover acts; for example, the peroneus muscles (which promote plantar flexion) are synergists of the gastrocnemius muscle. The tibialis anterior muscle causes dorsiflexion of the foot; thus, the gastrocnemius (prime mover for plantar flexion) is its antagonist. If you were alternately contracting and relaxing your masseter muscle, what would you be doing? Name three other muscles of the face, and give the location and function of each. Chewing food, grinding your teeth, or just opening and closing the jaw. Frontalis: covers the frontal bone; allows you to raise your eyebrows and wrinkle your forehead. Orbicularis oculi: found in circles around eyes; functions to close eyes, squint, blink, and wink. Orbicularis oris: circular muscle of the lips; closes mouth and protrudes lips (kissing motion). Buccinator: runs horizontally across the cheek and inserts into the orbicularis oris; flattens cheek and aids in chewing. Zygomaticus: extends from corner of mouth to cheekbone; raises corners of mouth upward for smiling. Temporalis: overlies the temporal bone; closes jaw. The sternocleidomastoid muscles help to flex the neck. What are their antagonists? Trapezius muscles. Name two muscles that reverse the movement of the deltoid muscle. Anteriorly, the pectoralis major. Posteriorly, the latissimus dorsi. Name the prime mover of elbow flexion. Name its antagonist. Prime mover: Biceps brachii. Antagonist: Triceps brachii. Other than acting to flex the spine and compress the abdominal contents, the abdominal muscles are extremely important in protecting and containing the abdominal viscera. What is it about the arrangement of these muscles that makes them so well suited for their job? The four muscles (or muscle pairs) are arranged so their fibers run in different directions, much as sheets of different wood grains are compressed together to make plywood. Like plywood, the abdominal wall musculature is extremely strong for its thickness; it is well constructed for its function as an abdominal girdle. The hamstring and quadriceps muscle groups are antagonists of each other, and each group is a prime mover in its own right. What action does each muscle group perform? Hamstrings: Extend hip and flex knee. Quadriceps: Flex hip (rectus femoris only) and extend knee. What two-bellied muscle makes up the calf region of the leg? What is its function? Gastrocnemius: Plantar flexion. What happens to muscles when they are exercised regularly? Exercised vigorously as in weight lifting? Not used? Muscles that are exercised regularly are healthy (with increased endurance), firm and free of superficial fat, and perhaps larger in size (depending on the type of exercise). Resistance- type exercises, such as weight lifting, cause muscles to hypertrophy to meet the increased demands placed on them. Muscles that are not used will atrophy (lose mass) and become weak. What is the effect of aging on skeletal muscles? With aging, skeletal muscle tissue mass decreases and the relative amount of connective tissue in the muscles increases, causing the muscles to become sinewy. As the muscles decrease in mass, they also decrease in strength. Loss in muscle mass may be partially prevented by regular exercise. Should a triathlete engage in aerobic or resistance training? Explain. He or she should engage in aerobic training. Training aerobically increases the amount and activity of enzymes within the aerobic metabolic pathways to make ATP for repeated muscular contractions whereas anaerobic training increases the amount and activity of enzymes within the glycolytic metabolic pathways. Muscles that are stronger, more resistant to fatigue, and flexible are the result of aerobic types of exercise. Name three muscles or muscle groups used as sites for intramuscular injections. Which is most often used in babies? Deltoid, gluteus maximus, gluteus medius, vastus lateralis, and rectus femoris. The vastus lateralis and rectus femoris is used more often for babies because their gluteus muscles are poorly developed. While jogging, Mr. Ahmadi was forced to jump out of the way of a speeding car. He heard a snapping sound that was immediately followed by pain in his right lower calf. A gap was visible between his swollen calf and his heel, and he was unable to plantar flex that foot. What do you think happened? He ruptured his Achilles tendon, which attaches the gastrocnemius to the heel bone. This accounts for the gap between the calf and the heel, as well as the inability to plantar flex the foot. Susan fell off her bicycle and fractured her right clavicle. Treatment prescribed by the emergency room physician included using a sling to immobilize the clavicle and speed its healing. What muscles are temporarily "out of business" as a result of this injury? Any muscle that inserts on the clavicle-trapezius. The muscles of her arm would also be immobilized by the sling. When Eric returned from jogging, he was breathing heavily and sweating profusely, and he complained that his legs ached and felt weak. On the basis of what you have learned about muscle energy metabolism, respond to the following questions: Why is Eric breathing heavily? What ATP-harvesting pathway have his working muscles been using that leads to such a breathing pattern? What metabolic product(s) might account for his sore muscles and his feeling of muscle weakness? Eric's oxygen intake has not been adequate to keep his muscles supplied with the oxygen they needed to support prolonged aerobic activity. His heavy breathing will supply oxygen to repay the oxygen deficit. His muscle cells were relying on aerobic metabolism, and their oxygen consumption led to breathlessness. When the oxygen ran out, anaerobic metabolism took place, leading to lactic acid accumulation, short-term muscle fatigue, and muscle soreness. Chapter 6 Critical Thinking Questions katherine_bower Essentials of Human Anatomy & Physiology Ch 6 Musc… madelinesmith7 A & P - Unit 5: Skeletal & Muscular macy_ambrose Neuro System short answer questions E_Forgione Sets found in the same folder Nervous System Review Questions courtneyrose1316 Chapter 8 Short Answer/Critical Thinking Natasha_Kruelski9 Chapter 6 The muscular System mustangfusion71 Review Questions - Final Exam Questions Chapter 12 Short Answer/Critical Thinking List what are the three main types of landforms. You are working as a nuclear physicist and are performing research on mirror isobars. Mirror isobars are pairs of nuclei for which $Z_{1}=N_{2}$ and $Z_{2}=N_{1}$ (the atomic and neutron numbers are interchanged). You wish to investigate the independence of nuclear forces on charge by comparing binding-energy measurements in the laboratory on mirror isobars against a theoretical value for the difference in binding energies. You first find the theoretical difference in binding energies for the two mirror isobars $_{8}^{15} \mathrm{O}$ and $_{7}^{15} \mathrm{N}$. In a semiclassical model of the hydrogen atom, the electron orbits the proton at a distance of 0.053 nm. a. What is the electric potential of the proton at the position of the electron? b. What is the electron's potential energy? Why are the OMZs expanding and what are the likely impacts on nutrient cycles? 13th Edition•ISBN: 9780073378275David N. Shier, Jackie L. Butler, Ricki Lewis 1,402 solutions Essentials of Anatomy and Physiology 3rd Edition•ISBN: 9781264398621Kenneth Saladin, Robin McFarland 1st Edition•ISBN: 9781938168130 (1 more)OpenStax Anatomy and Physiology: The Unity of Form and Function 9th Edition•ISBN: 9781260973587Kenneth S Saladin Principles of Radiographic Exposure II E… tristaboevePlus HWC Final 1 rosie_salzer social policy under Elizabeth I: the Poor Q0_0	CommonCrawl
Calculating π with atan2() Obtuse axiomatization of category theory Philadelphia Slaughterhouse Hotel The New York City passport office About ten years ago I started an article, addressed to my younger self, reviewing various books in category theory. I doubt I will ever publish this. But it contained a long, plaintive digression about Categories, Allegories by Peter Freyd and Andre Scedrov: I keep this one around on the shelf just so that I can pick it up ever few months and marvel at its opacity. It is a superb example of the definition-theorem-remark style of mathematics textbooks. I have heard that this was a style pioneered by a book you are already familiar with, John Kelley's General Topology of 1955. If so, all I can say is, sometimes it works, and sometimes it doesn't. It worked for Kelley in 1955 writing about topology. Here is an example of what is wrong with this book. Everyone who knows anything about category theory knows that a category is a sort of abstraction of a domain of mathematical objects, like sets, groups, or topological spaces. A category has a bunch of "objects", which are the sets, the groups, or the topological spaces, and it has a bunch of "morphisms", which are maps between the objects that preserve the objects' special structure, be it algebraic, topological, or whatever. If the objects are sets, the morphisms are simply functions. If the objects are groups, the morphisms are group homomorphisms; if the objects are topological spaces, the morphisms are continuous maps. The basic point of category theory is to study the relationships between these structure-preserving maps, independent of the underlying structure of the objects themselves. We ignore the elements of the sets or groups, and the points in the topological spaces, and instead concentrate on the relationships between whole sets, groups, and spaces, by way of these "morphisms". Here is the opening section of Categories, Allegories : 1.1 BASIC DEFINITIONS The theory of CATEGORIES is given by two unary operations and a binary partial operation. In most contexts lower-case variables are used for the 'individuals' which are called morphisms or maps. The values of the operations are denoted and pronounced as: !!□x!! the source of !!x!!, !!x□!! the target of !!x!!, !!xy!! the composition of !!x!! and !!y!!, The axioms: !!xy!! is defined iff !!x□ = □y!!, !!(□x)□ = □x!! and !!□(x□) = x□!!, !!(□x)x = x!! and !!x(x□) = x!!, !!□(xy) = □(x(□y))!! and !!(xy)□ = ((x□)y)□!!, !!x(yz) = (xy)z!!. In light of my capsule summary of category theory, can you figure out what is going on here? Even if you already know what is supposed to be going on you may not be able to make much sense of this. What to make of the axiom that !!□(xy) = □(x(□y))!!, for example? The explanation is that Freyd has presented a version of category theory in which the objects are missing. Since every object !!X!! in a category is associated with a unique identity morphism !!{\text{id}}_X!! from !!X!! to itself, Freyd has identified each object with its identity morphism. If !!x:C\to D!!, then !!□x!! is !!{\text{id}}_C!! and !!x□!! is !!{\text{id}}_D!!. The axiom !!(□x)□ = □x!! is true because both sides are equal to !!{\text{id}}_C!!. Still, why phrase it this way? And what about that !!□(x(□y))!! thing? I guessed it was a mere technical device, similar to the one that we can use to reduce five axioms of group theory to three. Normally, one defines a group to have an identity element !!e!! such that !!ex=xe=x!! for all !!x!!, and each element !!x!! has an inverse !!x^{-1}!! such that !!xx^{-1} = x^{-1}x = e!!. But if you are trying to be clever, you can observe that it is sufficient for there to be a left identity and a left inverse: There must be an identity !!e!! such that !!ex=x!! for all !!x!!, and for each !!x!! there must be an !!x^{-1}!! such that !!x^{-1}x=e!!. We no longer require !!xe=x!! or !!xx^{-1}=e!!, but it turns out that you can prove these anyway, from what is left. The fact that you can discard two of the axioms is mildly interesting, but of very little practical value in group theory. I thought that probably the !!□(x(□y))!! thing was some similar bit of "cleverness", and that perhaps by adopting this one axiom Freyd was able to reduce his list of axioms. For example, from that mysterious fourth axiom !!□(xy) = □(x(□y))!! you can conclude that !!xy!! is defined if and only if !!x(□y)!! is, and therefore, by the first axiom, that !!x□ = □y!! if and only if !!x□ = □(□y)!!, so that !!□y = □(□y)!!. So perhaps the phrasing of the axiom was chosen to allow Freyd to dispense with an additional axiom stating that !!□y = □(□y)!!. Today I tinkered with it a little bit and decided I think not. Freyd has: $$\begin{align} xy \text{ is defined if and only if } x□ & = □y \tag{1} \\ (□x)□ & = □x \tag{2} \\ (□x)x & = x \tag{3} \\ □(xy) & = □(x(□y)) \tag{4} \end{align} $$ and their duals. Also composition is associative, which I will elide. In place of 4, let's try this much more straightforward axiom: $$ □(xy) = □x\tag{$4\star$} $$ I can now show that !!1, 2, 3, 4\star!! together imply !!4!!. First, a lemma: !!□(□x) = □x!!. Axiom !!3!! says !!(□x)x = x!!, so therefore !!□((□x)x) = □x!!. By !!4\star!!, the left-hand side reduces to !!□(□x)!!, and we are done. Now I want to show !!4!!, that !!□(xy) = □(x(□y))!!. Before I can even discuss the question I first need to show that !!x(□y)!! is defined whenever !!xy!! is; that is, whenever !!x□ = □y!!. But by the lemma, !!□y=□(□y)!!, so !!x□ = □(□y)!!, which is just what we needed. At this point, !!4\star!! implies !!4!! directly: both sides of !!4!! have the form !!□(xz)!!, and !!4\star!! tells us that both are equal to !!□x!!. Conversely, !!4!! implies !!4\star!!. So why didn't Freyd use !!4\star!! instead of !!4!!? I emailed him to ask, but he's 83 so I may not get an answer. Also, knowing Freyd, there's a decent chance I won't understand the answer if I do get one. My plaintive review of this book continued: Another, briefer complaint about this book: Early on, no later than page 13, Freyd begins to allude to "Lazard sheaves". These are apparently an important example. Freyd does not define or explain what "Lazard sheaves" are. Okay, you are expected to do some background reading, perhaps. Fair enough. But you are doomed, because "Lazard sheaves" is Freyd's own private coinage, and you will not be able to look it up under that name. Apparently some people like this book. I don't know why, and perhaps I never will. [Other articles in category /math] permanent link Earlier this week I reported on a good visit I had had to the Philadelphia offices of the Social Security Administration. Philadelphia government offices, in my experience, are generally better than those I have visited elsewhere. I've never been to the New York DMV office (do they even have one?) but the Philadelphia ones are way better than the New Jersey ones I used to use. Instead of standing in line for forty-five minutes, you get a number and sit down until your number is called. The passport office was the biggest surprise. I first went in to deal with some passport thing shortly after I arrived in Philadelphia, maybe 1990 or so. The office was clean and quiet, the line was short, I got my business done quickly. None of those is the case in the New York passport office. The New York passport office. Wow. Where to begin? I want to say that it defies description. But, I learned later, it has been described by no less a person than Samuel Beckett: The abode is a flattened cylinder with rubber walls fifty meters in circumference and eighteen meters high. It is constantly illuminated by a dim, yellow light, and the temperature fluctuates between 5°C to 25°C, sometimes in as small an interval as four seconds. This leads to extremely parched skin, and the bodies brush against each other like dry leaves. Kisses make an "indescribable sound" and the rubber makes the footsteps mostly silent. There are 200 inhabitants, or one per square meter. Some are related to each other. Some are even married to each other, but the conditions make recognition difficult. Here's a story of the New York passport office told to me by a friend many years ago. He stood in the line for forty-five minutes, and when he reached the window, he handed over his forms. The clerk glared at him for a few seconds, then, without a word, pushed them back. "Is something wrong?" asked my friend. There was a long pause. The clerk, too disgusted or enraged to reply immediately, finally said "They're not stapled." "Oh," said my friend. "I see you have a stapler on your desk there." "You're supposed to staple them." "May I use your stapler?" "No, your stapler is on the table at the back of the room." At this point my friend realized he was dealing with a monster. "Okay, but I can come right back to the window afterward, right?" "No, you have to wait, like everyone else." At that moment my friend felt a tap on his shoulder. A man a few places behind him in line reached into his suit pocket and handed him a stapler. My friend says that as he stapled his papers and turned them in, the look on the clerk's face was of someone whose whole day had just been ruined. "Thanks so much," said my friend to Stapler Man. "Why did you happen to have a stapler in your pocket?" "Oh," said Stapler Man. "I do a lot of business at the passport office." [Other articles in category /misc] permanent link Sun, 07 Jul 2019 [ I wrote this in 2007 and forgot to publish it. Or maybe I was planning to finish it first. But if so I have no idea what I was originally planning to say, so here we are. ] In computer programs, it's quite common to need a numerical value for π. Often you see something like: #define PI 3.141592654 This has the drawback of not representing π as exactly as possible. But to do that in C probably requires putting in 16 digits after the decimal point, and most people don't have so much memorized. And anyway, you don't really know at compile time what the floating-point precision will be; some platforms support quad-width floats. So you can do better, maybe, by using the math library to calculate π. And people do: static double pi = 4atan2(1,1); The atan2(y, x) function produces the (almost-)unique value θ from the range !![-\pi, \pi]!! such that a ray from the origin, passing through point (x, y), makes angle θ with the x-axis. Note that the arguments have y first and x second. For example, atan2(17, 0) returns !!\frac\pi 2!!, because a line at angle !!\frac\pi 2!! passes through the point (0, 17). Similarly, atan2(-17, 0) returns -!!\frac\pi 2!!. You can use atan2 to calculate π, by using !!4·{\operatorname{atan}}2(1,1)!!, as I mentioned above. Many people do; Google searching finds hundreds of examples. The manual for the standard Perl module constant.pm mentions this example. But this is a bit strange. Why is this so well-known? Why calculate 4atan2(1,1) when $$\pi = {\operatorname{atan}}2(0,-1)$$ produces the same result and is simpler? (Obligatory IEEE 754 complaining: atan2 should return an always-unique value from !!(-\pi, \pi]!!, but I have to say "almost-unique" because as usual IEEE 754 fucks everything up, this time with its stupid distinction between 0 and -0.) [ Addendum: Leah Neukirchen suggests that the atan2(1,1) is a translation from earlier systems that provide a single-argument atan function but no atan2. In those systems, there is no workable analogue of atan2(0, -1) because the transformation !!{\operatorname{atan}}2(y, x)\Rightarrow {\operatorname{atan}}\left(\frac yx\right)!! gives !!{\operatorname{atan}}(0)!!, which doesn't work for this application as it yields !!0!! instead of the desired !!\pi!!. And similarly in languages with atan but not atan2 there is no analogue of !!\pi = 2·{\operatorname{atan}}2(1, 0)!!. So the simplest thing you can do is pi = 4 * atan(1), and after the transformation above one gets !!\pi = 4·{\operatorname{atan}}2(1,1)!!. ] [Other articles in category /prog] permanent link More information about the mysterious slaughterhouse hotel has come to light, thanks to Chas. Owens, Pete Krawczyk, and this useful blog post by D.S. Rosenstein. Most important, the perplexing "hotel" is not intended for humans. "Hotel" is apparently stockyard jargon for a place where livestock are quartered temporarily just prior to slaughter. I am so glad to have this cleared up. Also, M. Rosenstein has a photograph of the fancy abattoir with the spires: They don't make industrial buildings like they used to. Check out the ornamental pattern in the bricks on the lower floor and the baluster along the riverside façade. More details here. [ Addendum: Josh Bevan of Hidden City Philadelphia on When Cattle Men Reigned In The West (of Philadelphia). ] [Other articles in category /history] permanent link Yesterday on my other blog I posted about the most hilariously mislocated hotel I've ever heard of. It's the hotel that in 1910 was located in the Philadelphia stockyards, just the other side of the railroad tracks from the hog pens, between the slaughter house and the abbatoir: I thought that would be the end of it, but Chas. Owens did a little digging around and found a picture of the hotel, provided by the Greater Philadelphia GeoHistory Network. It's from R. Hexamer's insurance survey of 1877. At that time, the building was partly a hotel and partly the offices of the Philadelphia Stock Yard Company. The survey includes a map of the site and a description of the facilities. Here's the detailed plan of the hotel: The full image is 105 MB: None of these buildings is still standing. (As I mentioned yesterday, the site is now occupied by the Cira Centre.) But the neighborhood's history as the center of Philadelphia's meatpacking district is not completely lost. According to this marvelous article from Hidden City Philadelphia, in 1906 the D.B. Martin company built a new combination office building and slaughterhouse only two blocks away at 3000 Market Street. Here's my favorite detail from the article: Five hundred head of cattle at a time would be held on the rooftop cow pens, right above the heads of the company's executives, That building still stands, although I believe it's no longer used as a slaughterhouse. [ Addendum 20190702: The "hotel" is explained: it is a temporary residence for livestock, not for humans. ]	CommonCrawl
Why we don't always punish: Preferences for non-punitive responses to moral violations Crowdsourcing punishment: Individuals reference group preferences to inform their own punitive decisions Jae-Young Son, Apoorva Bhandari & Oriel FeldmanHall Direct and indirect punishment of norm violations in daily life Catherine Molho, Joshua M. Tybur, … Daniel Balliet Children punish third parties to satisfy both consequentialist and retributive motives Julia Marshall, Daniel A. Yudkin & Molly J. Crockett A computational account of how individuals resolve the dilemma of dirty money Jenifer Z. Siegel, Elisa van der Plas, … M. J. Crockett Diffusion of punishment in collective norm violations Anita Keshmirian, Babak Hemmatian, … Fiery Cushman Social threat indirectly increases moral condemnation via thwarting fundamental social needs Robert K. Henderson & Simone Schnall Increasing altruistic and cooperative behaviour with simple moral nudges Valerio Capraro, Glorianna Jagfeld, … Iris van de Pol Motivated misremembering of selfish decisions Ryan W. Carlson, Michel André Maréchal, … Molly J. Crockett Increased generosity under COVID-19 threat Ariel Fridman, Rachel Gershon & Ayelet Gneezy Joseph Heffner ORCID: orcid.org/0000-0001-6757-33971 & Oriel FeldmanHall1,2 Scientific Reports volume 9, Article number: 13219 (2019) Cite this article Human behaviour While decades of research demonstrate that people punish unfair treatment, recent work illustrates that alternative, non-punitive responses may also be preferred. Across five studies (N = 1,010) we examine non-punitive methods for restoring justice. We find that in the wake of a fairness violation, compensation is preferred to punishment, and once maximal compensation is available, punishment is no longer the favored response. Furthermore, compensating the victim—as a method for restoring justice—also generalizes to judgments of more severe crimes: participants allocate more compensation to the victim as perceived severity of the crime increases. Why might someone refrain from punishing a perpetrator? We investigate one possible explanation, finding that punishment acts as a conduit for different moral signals depending on the social context in which it arises. When choosing partners for social exchange, there are stronger preferences for those who previously punished as third-party observers but not those who punished as victims. This is in part because third-parties are perceived as relatively more moral when they punish, while victims are not. Together, these findings demonstrate that non-punitive alternatives can act as effective avenues for restoring justice, while also highlighting that moral reputation hinges on whether punishment is enacted by victims or third-parties. Punishment is pervasive throughout many societies1. Decades of research in behavioral economics and psychology empirically demonstrate that humans exhibit a strong desire to punish when deciding how to restore justice, even when it is costly2. However, more recent work reveals that if non-punitive alternatives are made available, punishment is not always systemically endorsed3,4,5. This suggests that preferences for punishment may be limited, perhaps to contexts where it is the only available option for restoring justice. Although the desirability of punishment has been questioned6,7,8, it remains unclear what features of a moral transgression motivate a punitive versus non-punitive response. Here, we explore this question, investigating when—and why—punishment is preferred as an instrument for restoring justice. The desire to punish appears to lie either in its ability to change unjust behavior through deterrence9 or alleviate negative emotions triggered from being treated unfairly10,11. In either case, punishing a transgressor can reap positive benefits. There are, however, several negative consequences associated with responding punitively. For example, punishment can erode cooperation by turning prosocial cooperators into antisocial punishers2,12,13. In other cases, perceived unjustified punishment leads individuals to retaliate with retributive behavior, and this cycle of retribution collectively reduces the welfare of the group14,15. These findings together suggest that punishment may have mixed desirability depending on the context, and thus may not be a uniformly preferred method for restoring justice. In contrast, non-punitive options have shown to be powerful motivators for restoring justice16,17,18. These non-punitive options typically address the victim's needs through compensation (operationalized within the laboratory by endowing the victim with money) instead of focusing on punishing the perpetrator. Compensating the victim has many real-world analogues. For example, insurance companies pay reimbursement for stolen or damaged goods, and programs such as the Office for Victims of Crime allocate money (e.g., more than $2 billion in 2016) to help more than 5 million victims who have been impacted by crime19. Furthermore, monetarily rewarding good behavior—compared to sanctioning norm violators—appears to be one effective route for promoting cooperation20,21,22. Other research examining how rewards and sanctions differentially encourage cooperation reveals that rewards can produce better outcomes for the group compared to punishment alone3. Although these results suggest that, depending on the context, non-punitive measures may be viable alternatives, the boundary conditions (i.e., is there a tipping point for how much compensation is required before punishment is no longer desired?) remain unknown. This inconsistent evidence naturally begs the question of when punishment is the preferred avenue for restoring justice. One possibility is that the decision to punish hinges on the context of the moral infraction23. One naturally-occurring context that may shape punishment preferences is when punishment is decided by a victim versus an impartial third-party5,24. In these cases, it is conceivable that different moral signals are generated depending on the perspective of the person deciding to punish, such that the act of punishing can either reap reputational benefits or damage one's reputation. For example, when deciding to restore justice as a victim, punishment (such as gossiping about or publicly blaming norm violators, deciding to ostracize transgressors, etc.) may be perceived as retributive or vindictive while non-punitive responses may embody the doctrine of "turning the other cheek", conveying that one values forgiveness25. If so, the reputational information gleaned from a victim deciding not to punish may signal that an individual has a positive moral character. In contrast, if a third-party member fails to punish, it may be interpreted as condoning the transgression, which would result in missing out on potential reputational advantages associated with punishing26,27. Simply put, punishment may act as a conduit for signaling different moral values depending on the context in which it arises and the perspective of the punisher. To test these hypotheses and identify the social contexts in which preferences for punitive responses (as opposed to non-punitive alternatives such as compensation) are preferred, we leverage both behavioral economic games and crime vignettes. We fully parameterize the decision space to precisely measure the point at which people make trade-offs between punishment and compensation. If punishment is not a preferred method for restoring justice, then it should be less appealing as the victim's needs are met through compensation. Indeed, it is possible that once the victim's needs are sufficiently met, no amount of punishment—however small—will be preferred. In contrast, only when the victim's monetary needs are not met should punishment become the preferred response. Additionally, we predict that the reputational value associated with decisions to punish will be modulated by the situation (i.e., deciding as a victim or a third-party). If punishment provides a greater positive reputational moral signal when deciding as a third-party, then third-party punishers should be preferred compared to punitive victims. Experiment 1: Compensating the Victim Abolishes Preferences to Punish Perpetrator 150 participants (48 women, 1 participant whose gender was unknown; age = 33.1 years, SD ± 10.6) were recruited through Amazon's Mechanical Turk28 (AMT) to play a modified Justice Game5 (JG) and were paid $1.50 for completing the task, as well as a bonus determined from their decision on one randomly selected trial. For all experiments: (1) participants played anonymously over the Internet and were not allowed to participate in more than one experimental session; (2) all studies were approved by Brown University's Institutional Review Board; (3) all the methods were performed in accordance with the relevant guidelines and regulations of the institution, and informed consent of all participants was obtained; (4) we only analyzed the data of subjects who had unique Internet protocol addresses to avoid duplicate respondents; (5) all analyses were conducted in R29 and mixed-effects models were made with lme430. (6) the desired sample sizes recruited for all studies were calculated using GPower 3.131. For all studies employing an economic game (Experiments 1, 2, and 4), our sample sizes were based on effect sizes (Cohen's d = 0.28) observed in previous studies using a similar design5, which suggest than an approximate sample size of 110 participants (alpha = 0.05, beta = 0.90) was sufficient to detect preferences for compensation over punishment; (7) We collected a variety of post-experimental questionniares that were not analyzed for this manuscript. These include: Interpersonal Reactivity Index32, Social Value Orientation33, Delayed Discounting34, Intolerance of Uncertainty Scale35, and demographic data. For all studies we have reported all measures, manipulations, and participant exclusions. Finally, (8) we used Amazon's Mechanical Turk to recruit all participants, whose subject pool has been shown to be representative of the broader population in the United States36. Participants played a modified version of a well-vetted economic paradigm known as the Justice Game5,37 (JG). In the JG, participants are paired with a unique anonymous player every trial and the two players must agree on how to split a sum of money. As the first mover, Player A is endowed with one dollar and proposes a division of this money with the participant, Player B (Player A: $1-x, Player B: x), in increments of $0.10 (prior work reveals incentive size—$1 versus $10—does not affect behavior5). We restrict offers from Player A (unbeknownst to participants, predetermined offers from a computer) to varying levels of unfairness, equally ranging from moderately unfair ($0.60, $0.40) to highly unfair splits ($0.90, $0.10). On each trial, participants, as Player B, respond by choosing between two options: (1) compensation: a non-punitive option where the victim deserves recompense—such that Player B is compensated some monetary amount while Player A's payout remains unaffected; and (2) punishment: a 'just deserts' option where the perpetrator deserves punishment for the wrong committed—such that Player A is punished through monetary reduction while Player B is compensated38. Accordingly, there are two trial types: partial compensation and partial punishment. In partial compensation trials, participants (Player B) must choose between maximal punishment to Player A and some amount of compensation to oneself (Fig. 1a). As an example, after receiving a highly unfair offer ($0.90, $0.10), the partial compensation option could increase Player B's payout to some amount greater than $0.10, while not changing Player A's payout ($0.90). This option is always pitted against maximal punishment, which fully reduces Player's payout (to $0.10) and fully enhances Player B's payout (to $0.90). In other words, participants choose between maximally punishing Player A at no cost to themselves, versus accepting some amount of compensation to avoid punishing Player A. Intuitively, when presented with these options, maximal punishment should be treated as the default, and thus this first experiment seeks to answer the question of how much compensation is required to shift people away from punishing? Partial Compensation Trials. (a) Game Tree. Player A (denoted in red) is endowed with one dollar and proposes a split with Player B. Participants, as Player B (denoted in blue), are informed of the proposed split and choose between two options to determine the final payouts of both players: (1) maximal punishment, an option which reverses the monetary payouts by fully reducing Player A's payout (e.g., from $0.90 to $0.10) while also fully increasing the monetary payout for themselves (e.g., from $0.10 to $0.90), and (2) partial compensation, an option which partially increases the payout for themselves (varying on each trial) while Player A's payout remains the same. (b) Results. We compute selection of maximal punishment juxtaposed against all partial compensation options. For example, the first data point shows a trial where participants chose between maximal punishment ($0.10, $0.90) and minimal compensation ($0.90, $0.10). Each data point represents a $0.10 increase in compensation. The point of indifference indicates a 50% chance of choosing punishment and the shaded area visualizes the area where punishment is the preferred option. Error bars reflect the standard error of the mean (SEM). Conversely, in partial punishment trials, Player B has the option to enhance their own payout while only partially reducing Player A's payout. Effectively, they can choose to punish Player A for an unfair offer (partial punishment) or receive maximal compensation and forgo any punishment towards Player A. Critically, Player B's payout is constant in these trials regardless of their choice and the only aspect that differs is how much punishment could be applied to Player A (ranging from minimal to maximal). This task structure allows us to determine the preference placed on applying punishment to Player A versus compensating oneself. Because partial punishment trials vary the amount of punishment available, the question is simply how much punishment is required (if any) to restore justice? Participants completed 80 fully randomized, one-shot, self-paced trials: 20 partial compensation trials and 20 partial punishment trials deciding as the victim (Player B) and the same 40 trials deciding as a third-party (a within-subject design; see supplement for task instructions, full methodological details, and results of the third-party condition which show a similar pattern of behavior). Preferences shift from punishing the perpetrator to compensating the victim Given that punishment has been shown to be a highly preferred response to severe fairness violations1, we initially restricted our analysis to the most unfair offers ($0.90, $0.10). Using a logistic mixed-effects model, we tested our hypothesis based on previous work5,37 that increasing compensation for the self would result in less punitive behavior towards Player A (we report maximal models for all analyses39,40). In partial compensation trials with minimal compensation, participants unsurprisingly prefer maximal punishment since that option maximizes one's own payout (Fig. 1b). However, participants become significantly less punitive as compensation to themselves increases ($Odds\,Rati{o}_{compensation}$ = 0.40; Table 1). In fact, once maximal compensation is available, the endorsement of punishment drops by almost 50 percentage points (Fig. 1b). This illustrates that participants' preferences to punish a perpetrator attenuates as their own compensation increases. Replicating previous work5,37, once participants are fully compensated, punishment is no longer the most preferred response. This effect was observed for all fairness levels (see supplement). Table 1 Greater compensation for victim leads to less punishment to perpetrator. $Punis{h}_{i,t}={{\rm{\beta }}}_{0}+$ ${{\rm{\beta }}}_{1}Compensatio{n}_{i,t}+{\rm{\varepsilon }}$. Preferences to punish do not increase if there is ample compensation We next tested whether manipulating the degree of punishment in partial punishment trials can shift participants' preferences in the wake of a fairness violation. That is, if a victim's needs are already met through the maximal compensation option, how much punishment (if any) is endorsed? Contrary to the idea that there are appropriate amounts of punishment specific to certain degrees of infraction38 (i.e., a $0.90, $0.10 offer), we observed no increased desire to punish so long as participants received maximal compensation ($Odds\,Rati{o}_{punishment}$ = 0.91; Fig. 2b; Table 2). Simply put, given a specific infraction, participants were insensitive to the degree of punishment toward Player A, even in the face of highly unfair offers ($0.90, $0.10; see supplement for the results for other fairness levels, which all mirror the same behavioral pattern). These results indicate that the preference for punishment is non-dominant as long as one is sufficiently compensated, even when punishment is free and easy to implement. Partial Punishment Trials. (a) Game Tree. Player A is endowed with one dollar and proposes a split of that money with Player B. Participants, as Player B, are informed of the proposed split and choose between two options to determine the final payout of both players: (1) partial punishment, an option which reduces the monetary payout of Player A to some amount between $0.10 and $0.80 (varying on each trial), while also fully increasing the monetary payout for themselves, and (2) maximal compensation, an option where the payout to Player A remains the same ($0.90) but the payout to oneself is maximally increased ($0.90). (b) Results. We compute selection of maximal compensation juxtaposed against all partial punishment options. For example, the final data point on the right of the graph shows a trial where participants choose between maximal compensation ($0.90, $0.90) and minimal punishment ($0.80, $0.90). Each data point represents a $0.10 decrement from maximal punishment (Player A receives only $0.10) to minimal punishment (Player A receives $0.80). The point of indifference indicates a 50% chance of choosing punishment and the shaded area visualizes the area where punishment is the preferred option. Error bars are ± 1 SEM. Table 2 Minimal preference to punish if victim's needs are met. $Compensat{e}_{i,t}={{\rm{\beta }}}_{0}+{{\rm{\beta }}}_{1}Punishmen{t}_{i,t}+\,{\rm{\varepsilon }}$. Experiment 2: Compensation is Preferred in an Unconstrained Decision Space Experiment 1 revealed that once one's monetary needs are fully met, punishing Player A for making an unfair offer is no longer the dominant response. While Experiment 1 fully parameterized the possible punitive and compensatory decision space in the JG, it is possible that these observed behavioral patterns are an artifact of the forced choice design. If given an opportunity to freely express their own redistribution preferences, participants might demonstrate alternative behavioral patterns. Accordingly, we designed Experiment 2 to allow participants to express preferences for compensation and punishment independently by determining the final outcomes for both Player A and themselves (in $0.10 increments). Rather than pitting discrete choice pairs against one another, participants could choose to maximize (or minimize) punishment to Player A and maximize (or minimize) compensation to the self—or any combination in between. This experimental design does not force participants to select specific redistribution preferences operationalized by the researchers, and instead allows us to test whether—in an unconstrained decision space—participants naturally redistribute money in ways that increase compensation for the self and attenuate punishment towards the perpetrator. 200 participants (73 women, 1 participant whose gender was unknown; age = 32.8 years, SD ± 8.8) were recruited through Amazon's Mechanical Turk. Participants were paid $0.50 for completing the task, as well as a bonus determined from their decision on one randomly selected trial. As in Experiment 1, participants play the Justice Game but this time they use a sliding visual analogue scale (VAS) to decide the final monetary outcomes of both Player A and themselves (Player B). The monetary amounts on the VAS depend on the fairness of the original offer, such that if Player A proposes an unfair split of ($0.90, $0.10) then the VAS's maximum endpoint would be $0.90 (see Fig. 3a). This design ensures that the redistribution space is fully indexed according to the original offer from Player A. Participants can keep the proposed split the same (e.g., $0.90 for Player A, $0.10 for themselves), or, decrease or increase Player A's payout as well as their own payout without restriction. Participants are explicitly told that the total monetary amounts of both players do not have to add up to one dollar. Unconstrained Redistribution Trials. (a) Game Tree. As before, Player A makes a split of one dollar with Player B. Participants, as Player B, determine the final monetary payouts using a visual analog scale (VAS). The monetary range of the VAS depends on the proposed offer, such that if Player A offered an unfair split ($0.90, $0.10) then the VAS would range from $0 to $0.90 for both players. This allows participants access to the full range of punitive and compensatory redistribution possibilities associated with each offer. The schematic shows an example where the participant chose to redistribute $0.50 to Player A and $0.70 to themselves after receiving an unfair offer ($0.90, $0.10). (b) Redistributions. Average monetary redistribution is plotted for Player A (in red) and Player B (in blue) as a function of the unfairness of the proposed offer. (c) Redistributions accounting for offer unfairness. The absolute difference between the final redistribution and original offer is plotted for compensation decisions (in purple) and punishment decisions (in green) as a function of the unfairness of the proposed offer. Error bars are ±1 SEM. Participants completed four one-shot, self-paced trials as the victim in response to offers ranging from relatively fair ($0.60, $0.40) to highly unfair ($0.90, $0.10). They also completed four trials as a third-party member (see supplement for task instructions, full methodological details, and results of the third-party condition). Trials were fully randomized. Examining decisions to re-allocate money across all fairness infractions reveals that participants consistently redistributed approximately $0.50 to Player A (Fig. 3b; Table S5), which can be perceived as a form of minimal punishment (compared to taking away all of their money). However, when taking the unfairness of the original offer into account, we can calculate the amount of punishment toward Player A and compensation for oneself, by taking the absolute value of the final redistribution minus the original offer. This analysis reveals that participants increase both their own compensation and punishment toward Player A as unfairness increases (Cohen's d = 1.21; Table 3). Critically, an interaction between decision type (compensation or punishment) and the unfairness of the original offer reveals that participants compensate themselves more relative to punishing Player A as unfairness increases (Cohen's d = 0.50; Table 3; Fig. 3c). Together, these results reveal that while punishment does increase with unfairness, compensation for oneself as a means of justice restoration increases even more as a function of the violation. Table 3 Participants compensate relatively more than punish as unfairness increases. Redistribution Accounting for $Offe{r}_{{\rm{i}},{\rm{t}}}={{\rm{\beta }}}_{0}+{{\rm{\beta }}}_{1}\,Decision\,Typ{e}_{{\rm{i}},{\rm{t}}}\times {{\rm{\beta }}}_{2}\,Original\,Offe{r}_{{\rm{i}},{\rm{t}}}+{\rm{\varepsilon }}$. Experiment 3: Preferences for Compensation Generalize to Severe Moral Transgressions In Experiment 2, when participants were given full control over the final redistribution outcomes, we again found evidence that they preferred to compensate themselves more than punish the perpetrator. However, it remains unclear if these preferences exist only in contexts where there are relatively minor violations (i.e., unfair splits of one dollar in one-shot economic games), or if they generalize to other more egregious transgressions. In Experiment 3, we explore this question, investigating whether preferences to punish and compensate scale with increasingly severe moral transgressions. While past research illustrates that people endorse the doctrine of "proportional punishment" (such that punishment scales with the severity of the crime committed38), it remains unknown whether compensation to the victim also scales as moral violations become increasingly pernicious. Given our findings in Experiments 1–2 that compensation can rebalance the scales of justice, we posited that people should increasingly endorse compensation as transgressions become more severe. 271 participants (163 women; age = 32.8 years, SD ± 10.1) were recruited through Amazon's Mechanical Turk. Our sample size for the data reported in the manuscript (responding as the victim, N = 134) was based on the large effect size of punishment judgments (Cohen's d = 1.18) observed in previous studies using a similar design38. However, because it is unknown whether compensation judgments would have a similar effect size as punishment, we used a conservative medium effect size41 (Cohen's d = 0.50;) which suggested that a sample size of N = 36 is sufficient to observe an effect of moral severity on compensation judgments with 90% power (α = 0.05). Participants were paid $2.50 for completing the task. To test whether judgments of punishment and compensation generalize to more severe moral violations, we developed a series of crime vignettes. We wanted naturalistic descriptions of crimes which contained enough details to justify judgments of moral condemnation without providing extraneous or nuanced aspects of each crime. Accordingly, we pulled crime examples from the "Uniform Crime Reporting Handbook" published by the Federal Bureau of Investigation42, a publication which establishes uniform definitions for crimes based on a hierarchical classification procedure. The crime vignettes ranged from disorderly conduct to murder (see supplement for all crime descriptions). Vignettes were selected and minimally altered to include one perpetrator and one victim, which ensured that judgments of punishment and compensation could be constrained to a single individual across all crimes. Participants were presented with short vignettes of a variety of crimes and were asked to rate the degree of compensation for the victim and punishment for the perpetrator. For example, a crime involving robbery stated: "You were walking down the street when an assailant grabbed you and held a knife to your throat. The assailant removed your wallet from your pocket and ran." After reading each vignette, participants answered three questions using a continuous Likert scale ranging from none (−50) to a lot (50): (1) "How much should you be compensated for the crime?" (No compensation – a lot of compensation); (2) "How much should the perpetrator be punished for the crime?" (No punishment – a lot of punishment); and (3) "Please rate the moral severity of the crime" (Not severe – Very severe). The ends of the scales were purposely left ambiguous (e.g., 'a lot of punishment'), so that subjects were free to infer their own subjective idea of what punishment should be levied on the perpetrator. This allowed us to directly compare subjective rates of punishments against compensation, while also extending our findings from Experiments 1–2, which used objective punitive and compensatory responses (i.e., money). Participants responded to 29 crime vignettes either from the perspective of the victim or from the perspective of a third-party observing the crime (a between-subject design). For the third-party condition, a crime involving robbery stated: "A man was walking down the street when an assailant grabbed him and held a knife to his throat. The assailant removed the victim's wallet from his pocket and ran". The order of trials was fully randomized (see supplement for task instructions, full methodological details, and results of the third-party condition). To examine how participants' punishment and compensation judgments varied across vignettes, we conducted a linear mixed-effects regression predicting amount of punishment or compensation as a function of judgment type (punishment or compensation) and degree of moral severity. Because participants likely would have different perceptions of the severity of the same crime, we included moral severity as a predictor. Results revealed that both compensation and punishment judgments scaled upwards as the crime became more morally severe (Cohen's d = 3.47; Fig. 4a; Table 4). Participants gave harsher punishments to the perpetrator and more generous compensation to themselves (the hypothetical victim) as their perceived moral severity of the crime increased. A similar pattern was observed when participants responded as a third-party, see supplement for details. Crime Vignettes. (a) Results. Amount of compensation or punishment is plotted for compensation judgments (in purple) and punishment judgments (in orange) as a function of perceived moral severity. Plot lines reflect parameter fits based on trial-wise mixed-effects regressions. Shaded error bars reflect 95-percent confidence intervals. (b) Results grouped by crime. For each crime vignette, we averaged participants' judgments of moral severity, compensation, and punishment. Average amount of compensation and punishment allotted is plotted as a function of the perceived moral severity of each crime. A subset of the 29 crimes are labeled. Table 4 Compensation and punishment scale with moral severity. $Amoun{t}_{{\rm{i}},{\rm{t}}}={{\rm{\beta }}}_{0}+{{\rm{\beta }}}_{1}Moral\,severit{y}_{{\rm{i}},{\rm{t}}}\times $ ${{\rm{\beta }}}_{2}Judgmen{t}_{{\rm{i}},{\rm{t}}}+{\rm{\varepsilon }}$. We further observed an interaction between the amount of punishment or compensation and moral severity such that participants increased the amount of punishment relative to compensation for more morally severe crimes (Cohen's d = 1.56; Fig. 4a; Table 4). Aggregating ratings of moral severity for each vignette, participants judged crimes such as murder and forcible rape as the most severe and thus allocated the most punishment and compensation for these crimes (Fig. 4b). While these results indicate that, at least in hypothetical judgments, participants increase punishment and compensation as crime severity increases (and prefer punishment more than compensation for the most egregious crimes), it also reveals that compensation is a desirable method for restoring justice for crimes that are not too severe (e.g., disorderly conduct or stolen property). Overall, these results suggest that the preference to compensate the victim generalizes to moral transgressions observed in the real world, and both compensatory and punitive preferences increase as the crime increases in moral severity. Experiment 4: Non-punitive Responses can Confer Positive Moral Reputation In Experiment 3, when participants were asked to imagine being the victim in a series of crime vignettes, we found evidence that participants compensate themselves for both minor and severe moral violations. However, pressing questions remain; namely, why are decisions to compensate sometimes the preferred option for restoring justice, especially when punishment is free and easy to enact? We explore this question in Experiment 4, investigating whether decisions to punish play a different role in signaling a set of moral values depending on the perspective of the person deciding how to restore justice. Specifically, we predict that victims who chose the non-punitive, prosocial redistribution option will be associated with a positive moral signal because it will be akin to "turning the other cheek." In contrast, third-party members who fail to punish will be perceived as condoning the transgression. Thus, the punitive option should only be associated with a positive moral signal when deciding as a third-party. 200 participants (84 women, 4 participants whose gender was unknown; age = 34.9 years, SD ± 10.5) were recruited through Amazon's Mechanical Turk to play a new variant of the JG and two partner selection tasks. Participants were paid $2.50 for completing the task, as well as a bonus determined from their decision on one randomly selected trial. Participants played a two-stage economic game, which began with a variant of the JG. In this version of the JG, after Player A makes an offer, Player B can reapportion the money by choosing between two randomly selected options drawn from the following six options (Fig. 5a): (1) Accept: agree to the proposed split ($1-x, x); (2) Equity: split the monetary pie equally so that both players receive half of the initial endowment ($0.50, $0.50); (3) Compensate: increase Player B's own payout to equal Player A's payout, thus enlarging the pie to maximize both players' monetary outcomes ($1-x, $1-x); (4) Punish: reduce Player A's payout to the original amount offered to Player B (x, x); (5): Reverse: reverse the proposed split, the 'just deserts' motive where Player A deserves punishment proportional to the unfairness of the offer; and finally, (6): Reject: both players receive nothing ($0, $0). The first three options can be considered more prosocial in nature, with little or no punishment of Player A; while the last three options can be considered more antisocial in nature, where punishment acts as a key ingredient for restoring justice. By adding the Reject option (which was not available in the original JG version5), we ensure that there is an equal probability of being presented with a prosocial option (Accept, Equity, and Compensate) or antisocial option (Punish, Reverse, and Reject). In other words, because Player A does not know which two options will be given on any given trial, having an equal number of prosocial and antisocial options buffers against any interpretation that Player A could be strategically giving unfair offers. Here, we use these labels—prosocial and antisocial—to differentiate options not involving punishment versus those that do (although these labels were never presented to the subjects). Participants are only given two options on any trial, such that each option is randomly paired with one alternative option, resulting in every combination pair for a total of 15 unique pairs. In this first phase of the game, we have participants play the JG so they can learn all the psychological motivations behind each redistribution option. Two-Stage Economic Game. (a) Justice Game Phase. Player A makes a split of one dollar with Player B. Participants play the game either as Player B or Player C (between-subjects design). When playing as Player C, participants are a third-party who decide on behalf of an anonymous Player B such that the final payouts are for Player A and Player B. On each trial, participants pick between two randomly presented options from the six available options. The game is constructed such that there are three prosocial options (Compensate, Equity, and Accept) and three antisocial options (Reject, Punish, and Reverse). Participants are told that other participants (their future partners) also completed this task. (b) Partner Selection Phase. Participants are instructed to select a partner for the Trust Game (TG) and the Dictator Game (DG; order counterbalanced). Participants make a forced choice between two partners, labeled by their most endorsed option in the Justice Game Phase. Here, we show an example trial in the TG where one potential partner most endorsed Compensate (i.e., 'Compensator') in the JG and the other potential partner most endorsed Reverse (i.e., 'Reverser'). In the DG example, an 'Accepter' is pitted against a 'Punisher'. Participants completed all possible forced choice pairings (15 trials) for both the TG and DG. In a subsequent partner selection phase (Fig. 5b), participants are informed they will be choosing their partner for two future economic games (unknown to participants, the experiment concludes after the partner selection phase ends). The only information participants are given to inform their choice is their potential partners' past behavior in the JG. For example, participants might be informed that a partner's most endorsed option was "Reverse", while another partner preferred "Equity". Unlike the previous experiments, here, we label each of the options (i.e., Accept, Equity, Compensate, Punish, Reverse, and Reject) to reduce the cognitive load on having to infer the option name from monetary redistributions. Using a between-subjects design, participants either completed the two-stage economic game from the perspective of the victim, in which participants play the game as Player B, or from the perspective of an impartial third-party, termed Player C. When playing as Player C, participants are asked to make decisions on behalf of an anonymous Player B. Unlike decisions as the victim, third-party decisions are non-costly and non-beneficial since the final choice only influences the monetary outcomes of Players A and B. The critical test is whether those who punished would be selected as a social partner at the same rate regardless if they made the decision as a victim or a third-party. In addition, we were interested in examining the boundary conditions for when punishment would be perceived as a positive moral signal. We posited that third-party punishers may not always be systematically preferred as social partners, and that this preference will depend on the demands of the social situation. Accordingly, participants were tasked with selecting partners for both the Trust Game43 (TG) and the Dictator Game44 (DG). For the Trust Game, participants were selecting partners who would be the second mover, which indexes the perceived trustworthiness of their partner. When selecting partners for the Dictator Game, participants chose partners who would be the first mover, which indexes the perceived generosity of their partner. We chose these two games on the assumption that the reputational benefits associated with punishing might shift between these different social contexts. Take for example previous work illustrating that third-party decisions to punish are taken as a positive signal of one's trustworthiness23: those who are willing to punish norm violators are seen as more likely to observe the norm of reciprocity (i.e., reciprocating trust) in the Trust Game. There may be other social contexts, however, in which punishing is not perceived as a desirable behavior. It is possible that punitive partners would not be preferred in contexts that require generosity or altruism because the original punishment may construed as spiteful45. Rather, someone who behaved prosocially in the Justice Game—for example, by equally redistributing the money or compensating without punishing—would be more highly sought after than someone who punished the perpetrator. To test this, we utilized a similar pairwise comparison design used in Experiment 1 and fully parameterized the space by comparing each partner type against all others. All participants completed 15 self-paced partner selection trials for the TG and 15 self-paced partner selection trials for the DG, and the order of these games was counterbalanced. When deciding as a victim, punishment is a poor signal of trustworthiness We compute partner selection by the number of times a partner who preferred a particular option (e.g., a Compensator) is chosen for a Trust Game compared to every possible alternative partner (i.e., Accepter, Equity Maximizer, Punisher, Reverser, and Rejecter). Participants showed a strong preference for engaging with victims who responded prosocially (i.e., selected Accept, Equity, or Compensate options, compared to the other three antisocial partners; Friedman's test, χ2(1) = 88.36, p < 0.001, Wilcoxon Signed-Rank test post-hoc effect size r = 0.93; Fig. 6a), with an especially strong desire for engaging with those who Compensated in the wake of a fairness violation (80%). In contrast, participants least preferred to play with partners who Rejected offers as a victim (11%). These findings offer evidence that choosing prosocial actions as a victim confers strong reputational benefits and offer one possible explanation for why non-punitive decisions may be preferred. Prosocial partners are preferred over antisocial partners. Partner preference is computed as the frequency an option is selected from all available trials, such that each option's endorsement rate is out of 100%. (a) Partner selection for the TG when responding as the victim. (b) Partner selection for the TG when responding as a third-party. (c) Partner selection for the TG collapsed across prosocial and antisocial responses as victim and third-party. (d) Preference for partners who selected one of the antisocial options in the JG (punish, reverse, or reject) for the Trust Game (TG) compared to Dictator Game (DG) when responding as a third-party (see supplement for all data). Error bars are ± 1 SEM. When deciding as a third-party, punishment is a relatively better signal of trustworthiness Although participants still showed an overall preference for third-party Compensators (82%), when directly comparing preferences for partners who responded antisocially (collapsing Punish, Reverse and Reject options) as the victim versus as a third-party, we observed a stark difference in how punitive responses shaped subsequent engagement (Fig. 6c). Partners who selected the antisocial, punitive option as a third-party were more likely to be selected as partners for a Trust Game than those who responded punitively as the victim (Welch's t-test, t(147.32) = 6.98, p < 0.001, g = 0.98). Interestingly, there was a steep and significant reduction in preferring third-parties who 'Accepted' an unfair offer on behalf of another (45%; Fig. 5b) compared to victims who did the same (73%; Fig. 5a: Kruskal Wallis test, χ2(1) = 38.54, p < 0.001, r = −0.44). While there is a dominant preference for prosocial third-party partners who compensate, these findings suggest that punishment can send a relatively better moral signal of one's trustworthiness when that decision is enacted by a third-party compared to a victim. Context modulates perception of third-party punishment We next examined whether the reputational benefit for third-party punishment is stable across different social contexts. While a similar overall preference for prosocial over antisocial partners was also observed in contexts valuing generosity (i.e., in the Dictator Game; see supplement for DG results), there were significant differences in how frequently antisocial third-parties were selected in the TG compared to the DG. Third-parties who chose either to Punish, Reverse, or Reject in the JG (the antisocial options) were less preferred as partners in the DG compared to the TG (paired t-test on combined data from all three antisocial partners, t(99) = −4.47, p < 0.001, g = −0.38; Fig. 6d). When examining each option separately, Bonferroni-corrected post-hoc analysis showed that only third-parties who punished were significantly less preferred in the DG than the TG (paired t-test, t(99) = −8.11, p < 0.001, g = −0.82; Fig. 6d), and there were no contextual differences for those who chose Reverse or Reject. These results reveal that the reputational value of third-party punishment is not stable but shaped by the context of the situation. In other words, there is a significant decrease in preferring punitive partners when the situation values altruistic tendencies (i.e., generous offers in the DG), suggesting that punishment is not always interpreted as a signal of good moral character. In contexts which have strong social norms of reciprocity, such as the TG, it is possible that those who punish send a signal that they would be willing to uphold and enforce these norms. Experiment 5: Lenient Victims and Punitive Third-Parties are Perceived as Moral Experiment 4 demonstrated that victims who punish are not preferred as social exchange partners, especially compared to victims who refrain from punishing. For those who do decide to punish, third-parties are preferred to victims. However, it is unclear whether third-parties and victims who punish are actually perceived as more or less moral, respectively. Accordingly, we ran a final experiment to probe whether those who punish as third-parties and those who refrain from punishing as victims are perceived as moral. In contrast, we posited that third-parties who fail to punish and victims who desire punishment should be perceived as similarly immoral. 189 participants (117 women; age = 31.3 years, SD ± 10.2) were recruited through Amazon's Mechanical Turk. Participants were paid $0.50 for completing the task. Our sample size was based on the effect size (Cohen's d = 0.26) observed in previous studies examining third-party punishment5, which indicated that a sample size of N = 129 is sufficient to observe this effect with 90% power (α = 0.05). Similar to Experiment 3, we used a crime vignette to test the reputational effects of a victim or third-party deciding to punish (or not punish) a perpetrator. We adapted a fictional case about vigilantism which details a shoplifting crime46. Using a 2 × 2 between-subjects design, participants read one of the following four vignettes: (1) the victim (store owner) monetarily punished the perpetrator for shoplifting; (2) the victim chooses not to punish; (3) a third-party (judge) monetarily punishes the perpetrator; or (4) the third-party chooses not to punish (see supplement for full descriptions of each vignette). Participants only made a single judgment where they rated the moral character of the victim or third-party, ranging from −50 (Immoral) to 50 (Moral) on a continuous Likert scale. To examine how participants' perceptions of moral character differed as a function of who was deciding to punish, we conducted a linear regression where moral character is predicted by role (victim/third-party) and action (punish/did not punish). Results reveal an interaction between role and action: A judge who punishes is perceived to be significantly more moral compared to a victim who punishes, and victims who refrain from punishing are perceived as significantly morally superior to judges who fail to punish (Cohen's d = 0.60; Fig. 7; Table 5). Both judges who do not punish and victims who do punish are perceived as having neutral moral characters (statistically not different from 0 = 'neutral moral character', one sample t-test against 0 for third-party: t(48) = 1.39, p = 0.17; for victim: t(47) = −0.18, p = 0.86). Furthermore, judges who punish and victims who refrained from punishing—both of whom were perceived to be high in moral character—were indistinguishable from one another (Welch's t-test, t(92.26) = 1.04, p = 0.30, g = 0.21). These results accord with the hypothesis that the perception of one's moral character hinges on whether they are deciding as a victim or third-party: a victim who turns the other cheek, when they could alternatively enact vigilante justice, signals a positive moral character, while a judge gets a positive moral boost by punishing. Perceptions of the punisher's moral character depends on their role. Mean moral character judgments as a function of role (victim or third-party judge) and action (punish or not punish). Moral character ranges from −50 (Immoral) to 50 (Moral). Error bars are ±1 SEM. Table 5 Moral character of punisher depends on role. $Moral\,characte{r}_{{\rm{i}},{\rm{t}}}={{\rm{\beta }}}_{0}+{{\rm{\beta }}}_{1}Rol{e}_{{\rm{i}},{\rm{t}}}\times {{\rm{\beta }}}_{2}Actio{n}_{{\rm{i}},{\rm{t}}}+{\rm{\varepsilon }}$. Open practices The data and analysis scripts that support the findings of these studies are avaliable online at the Open Science Framework at the following URL: https://osf.io/ft9bv/ Until now, it was unknown when—and under what conditions—people preferred punishment as a means of restoring justice. Our findings are twofold. First, dovetailing with previous work5,37 we demonstrated that once a victim's needs are sufficiently met through monetary compensation, there is little desire to punish (Experiment 1). Even in a non-constrained decision space, participants freely decide to compensate themselves and administer relatively low amounts of punishment to the perpetrator—despite being able to fully reduce the perpetrator's payout (Experiment 2). Furthermore, preferences for compensation appear to be a viable method of justice restoration for even the most egregious crimes, and is equally preferred to punishment when the infraction is not too severe (Experiment 3). Second, we observed that the reputational benefits associated with non-punitive and punitive measures are modulated by the perspective of the deciding agent (Experiment 4). Choosing not to punish as a victim sends a positive moral signal that one is likely to be both trustworthy and altruistic. In contrast, punitive responses are preferred when made by a third-party compared to similar punitive responses made by a victim. However, punishing as a third-party is not ubiquitously perceived as a positive moral signal: when a social situation emphasizes generosity, preference for third-party punishment declines. Moreover, lenient victims and punitive third-parties are perceived as having similar positive moral character, while third-parties who fail to punish are perceived as being more immoral (Experiment 5). Together, these results elucidate the boundary conditions of when justice preferences shift between punitive and non-punitive responses, while also providing a mechanism for why punishment is not systematically endorsed across all social contexts. Our data suggest that there are only some situations where punishment is preferred over non-punitive options. Even if punishment is free and easy to enact, people are less motivated to punish if they are already amply compensated. Moreover, so long as compensation is available, decisions (but not judgments) to punish are largely not proportional to the degree of infraction. While this stands in stark contrast to the large amount of evidence illustrating that people have a strong desire to punish11,38, it is possible that previous work may have inflated punitive preferences because participants were not able to select non-punitive options for restoring justice. Our results suggest that when the transgression is relatively minor, punishment may not be preferred nor needed when non-punitive alternatives are available to rectify the fairness violation. However, future research—such as field experiments—can explore whether preferences for compensation extend to severe moral transgressions that are not hypothetical in nature. Dovetailing with evolutionary accounts about reputation47,48, we find that how one decides to restore justice can signal information about one's moral (or immoral) character. Individuals who endorse prosocial responses to moral infractions are perceived as more valued social partners than those who express antisocial preferences for restoring justice. Indeed, endorsing prosocial responses may have an effect on positive emotions and overall wellbeing49. However, the reputational impact of these decisions is modulated by the perspective of the deciding agent. When people decide to punish on behalf of another individual, they are more desired as social partners and are perceived as having better moral character than individuals who punish as a victim. This likely because third-party observers are adhering to and upholding fundamental moral norms, in this case punishing fairness violations23,26,27. Future studies leveraging manipulations can more directly examine whether this relationship is causal in nature. In contrast, failing to punish or taking no action as a third-party (e.g., accepting the unfair offer without any attempt at restoring justice) may be interpreted as condoning the transgression, such that the individual is neither aware nor willing to uphold moral norms. In these cases, failing to act is perceived as a signal of a questionable moral character. In a similar vein, not wanting to engage with victims who punished perpetrators suggests that such antisocial behaviors are perceived in a negative moral light. For instance, it is possible that victims who punish are perceived as trying to get 'payback' or acting on vindictive motives. Together, these results demonstrate that the reputational value associated with punishment is malleable, and critically changes depending on the perspective of the individual enacting justice. Even the reputational signal of third-party punishment, however, seems to hinge on the social context. In situations where different moral values such as altruism and generosity are prioritized, we find that third-party members who punish are preferred less compared to those who responded in a prosocial manner. One possibility for why third-party punishers are not selected as social partners in a Dictator Game is because decisions to punish provide little information about whether a person values altruism. For example, there does not seem to be a relationship between real world altruistic generosity and decisions to punish50, and recent work illustrates that punishing can either be construed as altruistically enforcing a social norm or spitefully responding to a perpetrator45. Thus, in these cases, punishment may be sending an ambiguous signal about an individual's moral character. In contrast, endorsement of other choices in the Justice Game likely sends more informative signals about a person's altruistic tendencies and what they care to uphold. For example, choosing compensation or equity could signal that the person clearly, and unambiguously, cares about prosocial values, including altruism or generosity. These results provide compelling evidence that third-party punishment is only perceived as a positive moral signal in limited social contexts. Decades of research have examined people's preference for punishment and its suggested role in enforcing normative behavior. 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Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Heffner, J., FeldmanHall, O. Why we don't always punish: Preferences for non-punitive responses to moral violations. Sci Rep 9, 13219 (2019). https://doi.org/10.1038/s41598-019-49680-2 Children as assessors and agents of third-party punishment Julia Marshall Katherine McAuliffe Nature Reviews Psychology (2022) Daniel A. Yudkin Molly J. Crockett Nature Human Behaviour (2020)	CommonCrawl
RUS ENG JOURNALS PEOPLE ORGANISATIONS CONFERENCES SEMINARS VIDEO LIBRARY PACKAGE AMSBIB Mechenov, Alexander S. Statistics Math-Net.Ru Total publications: 5 Scientific articles: 4 This page: 156 Abstract pages: 452 Full texts: 230 References: 59 Candidate of physico-mathematical sciences (1977) Speciality: 01.01.07 (Computing mathematics) Birth date: 5.03.1944 Keywords: total least squares, errorsin variables. Confluent analysis, Ill-posed problems. Main publications: Mechenov Alerxander S., Pseudosolutrion of linear functional equations, Math. Appl. (N. Y.), 576, Springer, New York, 2005 http://www.mathnet.ru/eng/person52793 List of publications on Google Scholar List of publications on ZentralBlatt https://mathscinet.ams.org/mathscinet/MRAuthorID/317095 Publications in Math-Net.Ru 1. A. S. Mechenov, "The effect of rounding errors for systems of linear algebraic equations", Zh. Vychisl. Mat. Mat. Fiz., 34:10 (1994), 1520–1523 ; Comput. Math. Math. Phys., 34:10 (1994), 1313–1316 2. A. S. Mechenov, "Partially approximate systems of linear algebraic equations", Zh. Vychisl. Mat. Mat. Fiz., 31:6 (1991), 790–798 ; U.S.S.R. Comput. Math. Math. Phys., 31:6 (1991), 6–12 3. V. A. Andrianov, M. G. Kozin, A. Yu. Pentin, V. S. Shpinel', A. S. Mechenov, V. P. Gor'kov, "Molecular field distribution and ferromagnetic clusters in dilute $\mathrm{PdFe}$ alloys: mossbauer study of the paramagnetic phase", Fizika Tverdogo Tela, 30:11 (1988), 3243–3252 4. V. A. Andrianov, M. G. Kozin, A. Yu. Pentin, V. S. Shpinel', V. P. Gor'kov, A. S. Mechenov, "Percolation nature of spontaneous magnetization in the doped ferromagnet $\underline{\mathrm{Pd}}\mathrm{Fe}$", Fizika Tverdogo Tela, 29:8 (1987), 2339–2344 5. A. S. Mechenov, "Erratum: "Partially approximate systems of linear algebraic equations"", Zh. Vychisl. Mat. Mat. Fiz., 33:6 (1993), 976 Terms of Use Registration to the website Logotypes © Steklov Mathematical Institute RAS, 2022	CommonCrawl
Theories of Everything: Ideas in Profile Ideas in Profile. Small introductions to big topics is a series published by Profile Books that give short introductions to important socio-cultural or scientific topics. The book under review is the only one so far on a mathematical-physical topic: the theories of everything (note the plural!). This has been a popular, yet undeniably difficult, subject in the media since the successes of Einstein's relativity and the mind boggling consequences of quantum physics originating in the previous century. Frank Close is an emeritus physics professor from Oxford University and he has quite some experience in science communication. So he is the right choice to author a book of this kind. A theory of everything is a theory that tries to explain everything within the realm of inanimate physics. It should not be speculation but a scientific theory, which means that it should be verifiable in some way by experimental observation. What is illustrated in this book is that the different theories of everything adapt to the scale at which one makes the observation, the scale of the mass, distance, or energy. With more powerful methods usually requiring higher energies, the definition of 'everything' has changed in the course of centuries. We are now even arriving at a point where 'theories' are developed that can probably never be verified by observation since that would require all the energy present in many galaxies. And that is certainly not going to happen in the near future. However, such an 'experiment' has taken place once already, namely at the time of the Big Bang. So our only hope is to rely on cosmic observations. Other theories propose multiverses, and since communication between these is impossible, one could ask whether this can still be called a scientific 'theory' in the usual sense. Newton's mechanics could explain what happens to men-size objects on earth. His theory of gravity even explains how planets move around the sun or the moon around the earth, but problems arise when more than three bodies are involved. When many particles are involved, this gives rise to thermodynamics, from which follows the notion of entropy which in turn explains the arrow of time. The electric and magnetic theory were unified in the Maxwell equations. With light as an electromagnetic phenomenon, Einstein introduced his relativity theory which linked space and time in a four-dimensional space-time universe where mass and energy are essentially the same. By joining Maxwell's theory to Dirac's quantum theory the quanta radiating at an atomic scale (1eV) can be described in accordance with general relativity. It took however quantum electrodynamics (QED) to match experiments properly. This insight was only possible after it was understood that terms in a seemingly divergent series cancelled so that it did converge indeed. It is all depending on mathematics after all. While QED describes the exchange of energy, quantum flavourdynamics (QFD) includes the exchange of electrical charge. However, when looking at a subnuclear particle scale (108−109 eV = 100MeV-1GeV), we are dealing with a strong nuclear force, and then the appropriate quantum field theory is quantum chromodynamics (QCD). Like we live in an electromagnetic field, it was conjectured in the 1960's that we are also surrounded by an electroweak plasma. This is only recently proved by the detection of the Higgs boson, which is its quantum excitation. Its energy is about 125 GeV, which is just within reach for the Large Hadron Collider (LHC) in CERN. This brings us to the so called standard model, and this is where the present theories of everything are conceived. Now we are dealing with the next step up the scale, which is the Planck scale (energy: $1.25\times 10^{19}$GeV, length: $1.6\times 10^{−35}$m, time: $0.5\times 10^{−43}$sec). Both relativity theory and quantum theory have reached their limits here. In the core theory gravity does not matter because it is 40 orders of magnitude less than its electromagnetic counterpart and hence not observable. Observations with this amount of energy are not conceivable and it would imply weird situations, since black holes would be created making observations impossible and quantum theory predicts an unmeasurable space-time foam of black holes. The big challenge to combine quantum field theory and general relativity is to understand dark matter, and to know what prevents the fluctuation of the Higgs field. Possible ways out are string theory (but there turn out to be many), superstring theory (based on symmetry considerations), and multiverses (not verifiable but it would postulate the precise values of the fundamental constants just right for us to exist). In a final chapter Close hints that some answers could be found in cosmological observations and that the quantum theory, built on the Heisenberg uncertainty principle, is only an approximation. If one could apply energies well above the Planck scale, observations could be made at smaller intervals of space and time and these would decrease indefinitely as the energy keeps increasing. But this is of course speculation as most theories at this scale are for the moment. Close has done a good job, faithful to the objective of the series. No formulas and no technical details. No mathematics either, although it is clear that it is the driving force in the background of all these theories. I do not think that this is the place where you should learn what relativity theory or what quantum theory really is. When it comes to particle physics, it would be difficult to keep track of all the terminology of the different actors if you never heard of them before. Thus I think, you should not start reading this booklet unprepared. The point that Close makes quite clear is that the quest for the theory of everything is chasing a moving target. As long as one stays within a certain interval of the scale, some phenomena are perfectly negligible, and a theory of everything within that interval can be designed that matches the observations. However close to the boundary of that interval, deviations can be seen and things get mixed up like for example space and time are connected or mass and energy when the speed of light is approached. Then a new, more general theory, has to be designed that explains the phenomena on a much larger interval of the scale. Close guides the reader at a high level to the cliff where we are now standing. The cliff where gravity at a Planck scale has to be incorporated is the competing theories of relativity and quantum dynamics. And he sheds some light on what might be possible roads to a solution. For those interested in this topic, note that other physicists have published books that were written with the intention. They all explain in their own way to the interested non-specialists the evolution that has brought us from the discovery of relativity theory and quantum physics in the previous century to the current state of the art in mathematical physics. Often these emphasize the personal view of the author. Here are just a few (in alphabetical order). Michio Kaku, Hyperspace. A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension (1994) Roger Penrose, The Emperor's New Mind. Concerning Computers, Minds, and the Laws of Physics (1989) Roger Penrose. Fashion, Faith, and Fantasy in the New Physics of the Universe (2016) Ian Stewart, Calculating the Cosmos. How Mathematics Unveils the Universe (2016) Max Tegmark, Our mathematical universe. My quest for the ultimate nature of reality (2014) Frank Wilczek, A Beautiful Question. Finding Nature's Deep Design (2015) Anthony Zee, Fearful Symmetry. The Search for Beauty in Modern Physics (1986) Adhemar Bultheel Close explains how a theory of everything has evolved since Newton detected gravity. He illustrates how such a theory is valid within a certain interval of the scale at which physics is considered. As soon as one shifts to a different scale, a new, broader theory has to be developed. He brings the reader up to the point where modern physics is facing the problem of incorporating phenomena at a Planck scale which is out of reach for observations in any foreseeable future. Physicists have therefore no indication in what direction the solution can be found and how gravitation can be incorporated in quantum physics, while not contradicting general relativity. Close gives a glimpse of possible directions in which to look for a solution. Frank Close 978-1781257517 (pbk) £8.99 (pbk) https://profilebooks.com/theories-of-everything-ideas-in-profile.html  Submitted by Adhemar Bultheel \|  20 / Apr / 2017	CommonCrawl
Please use this identifier to cite or link to this item: https://doi.org/10.1109/LPT.2013.2278994 Title: Pilot-aided channel equalization in RGI-PDM-CO-OFDM systems Authors: Li, X. Zhong, W.-D. Alphones, A. Yu, C. Keywords: Orthogonal frequency division multiplexing pilot-aided channel equalizer polarization division multiplexing Citation: Li, X., Zhong, W.-D., Alphones, A., Yu, C. (2013). Pilot-aided channel equalization in RGI-PDM-CO-OFDM systems. IEEE Photonics Technology Letters 25 (19) : 1924-1927. ScholarBank@NUS Repository. https://doi.org/10.1109/LPT.2013.2278994 Abstract: A pilot-aided channel equalizer (PACE) is proposed to mitigate the impairments caused by the polarization mode dispersion and laser phase noise simultaneously in reduced-guard-interval polarization-division-multiplexing coherent-optical orthogonal-frequency-division-multiplexing (RGI-PDM-CO-OFDM) transmission systems. Since PACE updates the channel state information symbol-by-symbol, it enables us to track the drifts in the optical channel. Adaptive PACE (APACE) and boosted PACE (BPACE) are then proposed to further improve the performance of PACE. Numerical simulations are carried out to compare the performance of APACE and BPACE with a conventional training symbols aided channel equalizer (TSACE) and adaptive decision-direct channel equalizer for a 108-Gb/s (56-GS/s) RGI-PDM-CO-OFDM system. It is revealed that both APACE and BPACE offer superior performances over the other two equalizers in the presence of laser phase noise, and they can tolerate lasers with a line width around $β=2000~{\rm k}$ ($2\π\β T-{s}=2.24\times 10$ when it is normalized to the symbol rate $1/Ts). We also show that only small additional computation efforts are required for APACE and BPACE when compared with TSACE. © 2013 IEEE. Source Title: IEEE Photonics Technology Letters DOI: 10.1109/LPT.2013.2278994	CommonCrawl
Can general relativity be explained by equations describing a fabric of space embedded in a flat 5-dimensional Minkowski space? Does such a set of equations exist or does our universe have an intrinsic curvature that can't be explained by an embedding in a flat Minkowski space of 1 higher dimension? Even if general relativity can be explained by such equations, it still doesn't prove our universe is embedded in a flat Minkowski space of higher dimension. general-relativity differential-geometry Qmechanic♦ 141k1919 gold badges325325 silver badges16751675 bronze badges TimothyTimothy $\begingroup$ From Whitney's embedding theorem, you might need as many as $2n$ dimensions to embed a manifold of dimension $n$, so you will need at least 8 dimensions if you want to do this $\endgroup$ – Slereah Jul 13 '16 at 20:37 $\begingroup$ @slereah: Whitney's embedding theorem is doubly irrelevant here. First, there is no reason to think that the embeddings guaranteed by Whitney preserve the metric, so you might need a whole lot more than 8 dimensions. Second, if you ignore the metric, Whitney's bound is a worst-case scenario, and it's perfectly possible that the requirements of general relativity allow you do even better --- so you might need a whole lot less than 8 dimensions. $\endgroup$ – WillO Jul 13 '16 at 20:53 $\begingroup$ Oh yes, I meant "at most", not "at least" $\endgroup$ – Slereah Jul 13 '16 at 20:54 $\begingroup$ @sleareah: "At most" and "at least" are equally wrong. $\endgroup$ – WillO Jul 13 '16 at 20:55 $\begingroup$ @Slereah They certainly don't guarantee the metric. Why? Don't ask me, I've tried to understand the Nash embedding theorem but its proof is well beyond me. I find that absolutely maddenning that I can't given that I can understand the proof of the Whitney theorem, and that, on the face of it, would seem a harder (more general thing) to prove, yet the reality for me is very much the other way around. $\endgroup$ – Selene Routley Jul 14 '16 at 0:19 For Riemannian manifolds, I believe the best result currently known is that a manifold of dimension $n$ can be isometrically embedded in a euclidean space of dimension $2(2n+1)(3n+7)$. So, for example, a 3-dimensional spacelike slice of spacetime can be embedded in a flat euclidean space of at most 224 dimensions. Maybe in low-dimensional cases like this one can do better, but if so I'm not aware of it. So much for space. If you want to embed all of spacetime, I think the best known result is that every Lorentzian manifold can indeed be embedded in a flat Lorentzian manifold, but I don't think any bound is known on the necessary number of dimensions. Edited to add: I see by the reference I posted in the comments that there is in fact a known bound for Lorentzian manifolds: $2(2n+1)(2n+6)$. So you can imbed all of (four dimensional) spacetime in a copy of $R^{252}$, with signature $(126,126)$ WillOWillO $\begingroup$ ??? Really? Is it that bad? I knew it was more than ten, but that's an insane bound. Could you link to the theorem, please? I was always looking for something like that. $\endgroup$ – CuriousOne Jul 13 '16 at 23:10 $\begingroup$ @CuriousOne: Reference here: ams.org/journals/bull/1969-75-06/S0002-9904-1969-12407-9/… . I briefly posted a comment saying one can in fact do better, but that comment was mistaken and I've deleted it. $\endgroup$ – WillO Jul 13 '16 at 23:27 $\begingroup$ @CuriousOne: As far as it being "that bad", I don't think that's known. This is an upper bound, but there might be a much better upper bound that hasn't yet been discovered. $\endgroup$ – WillO Jul 13 '16 at 23:31 $\begingroup$ @CuriousOne Incidentally, these theorems were highly important in the history of mathematics, since mathematicians, including Cartan, often liked to think of manifolds as embedded in higher dimensional flat spaces but the modern definition is much easier to work with. Everyone worked under the conjecture that the two notions were ultimately the same, however it wasn't until the the 1940s Whitney embedding theorem that people knew they were the same. $\endgroup$ – Selene Routley Jul 14 '16 at 0:04 $\begingroup$ @WetSavannaAnimalakaRodVance: I am fully aware of the importance of these theorems, but I have yet to see a nice enumeration of them in a textbook. They seemed to be scattered in the literature some 20+ years ago, when I looked at the matter the last time (could be 30+, by now), depending on the individual author's needs. I'll take a look at the citation by WillO. The general case is insanely bad, for sure. $\endgroup$ – CuriousOne Jul 14 '16 at 0:08 This is an afternote to WillO's answer which cites: Robert E. Greene, "Isometric Embeddings," Bull. AMS 1969 which addressed known bounds on the dimension required of flat Euclidean / Minkowsian space if it is to be an embedding for a solution of the Einstein field equations, which of course is a four-dimensional signatured manifold. It's worth noting that important special cases one can be embedded in much lower dimensions than the insanely loose bounds defined by the Nash embedding theorem and its Lorentzian equivalents. Such simplifications happen in cases of high symmetry. For example, the large scale homogeneous/ isotropic universe defined by the Friedmann–Lemaître–Robertson–Walker (FLRW) metric can indeed be thought of as being embedded in five dimensional space, with signature $(1,\,4)$, because it can be partitioned into foliations of space, with the foliations indexed by a universal time co-ordinate, and the spatial foliations are isometric to three dimensional spheres / hyperboloids in $\mathbb{R}^4$ with only the scale factor and energy / pressure evolving over time. Indeed, the lecture notes: Balša Terzić, Lecture notes for PHYS 652, Old Dominion University take the unusual approach of lifting well known 19th century geometry results on the hypersphere / hyperboloid and linking them to a homogeneous, isotropic stress energy tensor. The Ricci tensor is of course diagonal in this case, so the student is relieved of the full complexity of GR and gets to see the direct link between stress energy (in the diagonal case) and curved spaces. Lawrence B. Crowell's answer cites two other examples very like FRLW which can be split into spatial foliations such that the whole spacetime is embedded in 5 dimensions with a $(1,\,4)$ signature - the de Sitter and anti-de Sitter spaces, which are like FLRW but with no matter and pressure (vacuum solution) and a special value for the cosmological constant. Selene RoutleySelene Routley $\begingroup$ Unfortunately such an important case as the Schwarzschild black hole requires at least 6 dimensions. $\endgroup$ – Ruslan Feb 11 '20 at 20:40 $\begingroup$ Note Lawrence B. Crowell's answer has one embedding in 1+4 and one in 2+3 dimensions. Also this paper claims that FLRW can require up to 2+4 dimensions, though I think 1+4 is enough when $ρ\ge0$ and $Λ\ge0$. $\endgroup$ – benrg Oct 2 '20 at 22:10 General relativity in four dimensions does not need to be embedded in a larger space of any sort. Curvature in general relativity is completely defined according to curvatures that are intrinsic induced by parallel translation of vectors. One does not need to have the spacetime in four dimensions embedded in some higher dimension spacetime. There is general relativity in five dimensions with the flat metric $$ ds^2~=~dt^2~\pm~du^2~-~dx^2~-~dy^2~-~dz^2. $$ The constraint $$ t^2~\pm~u^2~-~x^2~-~y^2~-~z^2~=~\alpha^2 $$ defines hyperboloids embedded in this flat spacetime. The condition $\pm u^2$ defines the anti-deSitter $(+du^2)$ and de Sitter spacetimes $(-du^2)$. The constant $\alpha$ defines the cosmological constant. So this is a special case of what you are talking about. Lawrence B. CrowellLawrence B. Crowell To start with, a manifold is not always able to be embed in higher dimension, especially when singularity (black hole) involves. I would more agree if it is described by a 3-d gravity-free field theory. This is similar to the idea named AdS/CFT duality. Of course here is not AdS space, but the spirit is similar, I think. But I'm not an expert in this, so... RoderickLeeRoderickLee $\begingroup$ I don't see why the singluarity couldn't travel faster than light in the higher dimensional space without the fabric of space itself travelling faster than light. The only problem I see with the embedding is that the equations also for a black hole of any mass no matter how small. $\endgroup$ – Timothy Jul 13 '16 at 20:58 $\begingroup$ @user46757 First, I never say anything related to light speed. Second, flat spacetime has a simple zero curvature while singularities have divergent. That's the reason it cannot be embed in higher flat spacetime. $\endgroup$ – RoderickLee Jul 13 '16 at 21:05 $\begingroup$ Think of the region near the singularity as a cone where its sperical cross sections are shrimking slower than light. That could still cause the tip of the cone to travel faster than light. Maybe the fabric of space is rapidly accelerating and Einstein's field equations are an approximation of the correct equations that predict that a sufficienly small mass if compressed enough will form a black hole and disappear at the singularity which will cease to stay a singularity destroying the black hole. $\endgroup$ – Timothy Jul 13 '16 at 21:18 $\begingroup$ You can still embed the open manifold with the singularities excised; indeed that is the only meaningful way to treat them in the manifold framework. $\endgroup$ – Selene Routley Jul 14 '16 at 1:20 $\begingroup$ @WetSavannaAnimalakaRodVance I see, after read some reference other answers recommend. $\endgroup$ – RoderickLee Jul 14 '16 at 1:22 Maybe our universe is a uniformly accelerating fabric embedded in a 5-dimensional Minkowski space and doesn't actually obey the laws of general relativity. If gravity is entirely the result of objects making a dent in it with their weight, then for objects with an escape velocity much slower than the speed of light like Earth, the gravitational time dilation is exactly the amount general relativity predicts. The emission of a gravitional wave from merging black holes which we detected is also consistent with this theory of gravity. If that really is how our universe works, an object in free fall will still follow a geodesic of the fabric of space but there will be no gravitomagnetism and an object of sufficiently low mass if it's compressed dense enough might form a singularity then disappear at it and then the singularity will rush towards the rest of the fabric of space faster than light and cease to exist once its speed goes down to the speed of light, destroying matter and its gravitational field. Maybe at the quantum level, the information of what went into the singularity is preserved as disordered vacuum fluctuations outside the fabric of space. How do we know our universe follows the laws of general relativity if we haven't made detailed enough measurements of the behaviour of objects in a gravitational field or observed gravitomagnetism? Why should general relativity be true? Just because angular momentum has been proven to be conserved according to simplified laws of physics doesn't mean it's also conserved in the formation of a black hole. The gravitational constant is determined by the acceleration of the fabric and its resistance to bending but we already know what the gravitational constant is. Given what the gravitation constant is, the faster the fabric is accelerating, the lower the minimum mass that can be compressed to form a permanent black hole. Although Einstein's field equations are probably the simplest possible equations that are consistent with observations and are preserved at any point at any velocity below c at any orientation and are consistent with observations, there's no reason to be sure the universe isn't an embedded fabric whose equations do not simplify to such simple equations that described only the space itself According to https://en.wikipedia.org/wiki/Binary_star#Cataclysmic_variables_and_X-ray_binaries, one member of a binary system is believed to be a black hole. It's probably because of detection of movement of the other stat in the system that it's believed that there's a black hole in the system. If our universe does work the way I described, the existence of a black hole of that mass rules out the possibility that the fabric is accelerating below a certain acceleration. Not the answer you're looking for? Browse other questions tagged general-relativity differential-geometry or ask your own question. Extrinsic Description of spacetime curvature, is it possible? How many dimensions would we need? Can a non-Euclidean space be descripted through an Euclidean space of higher dimension? So why use non-Euclidean? We know there is no aether, so what is being dragged in frame dragging? Does the shape of the Universe refer to the curvature of spacetime in 5-dimensional space? Going from four to five dimensions can we overlook the entirety of time? Is there any physical interpretation of Nash embedding theorem? Is general relativity a background dependent theory in five dimensions? How should one interpret the de Sitter slicings? Is the universe 5 dimensional space-time or 4? Which curvilinear coordinate systems can I use to describe flat space-time? Can a flat space have nonzero torsion? What is intrinsic curvature? A manifold that is not embedded? Manifold definition in general relativity by Robert Wald General Relativity: is Tangent Space Always Flat?	CommonCrawl
Isosceles Obtuse Triangle – Characteristics and Examples Isosceles obtuse triangles are triangles that have two sides of the same length and an angle greater than 90 degrees. These triangles meet the conditions for an isosceles triangle and an obtuse triangle at the same time. Recall that an isosceles triangle has two sides that have the same length and two angles that have the same measure. On the other hand, an obtuse triangle is characterized by having an internal angle that measures more than 90 degrees. Learning about the isosceles obtuse triangle. See characteristics Characteristics of obtuse isosceles triangles Important isosceles triangle formulas Examples with answers of isosceles triangle problems Isosceles triangles – Practice problems Obtuse isosceles triangles have the following characteristics: Two sides of the triangle are congruent (they are equal in length). The side that does not have the same length is called the base of the triangle. An internal angle of the triangle is obtuse, that is, it has more than 90 degrees. Angles on opposite equal sides are also equal and acute. The angle different from the other two is called the apex angle. The apex angle is the obtuse angle. The height is the line perpendicular to the base and joining the apex angle. The height divides the base into two equal parts, as well as the apex angle. The height divides the triangle into two congruent right triangles. With the following formulas, we can solve a large number of problems related to isosceles triangles. Isosceles triangle perimeter formula The perimeter of any geometric figure is calculated by adding the lengths of the sides of the figure. The formula for the perimeter of isosceles triangles considers the fact that two sides of the triangle are equal: $latex p=b+2a$ where b is the length of the base and a is the length of the congruent sides. Isosceles triangle area formula The formula to calculate the area of any triangle is as follows: $latex A= \frac{1}{2} \times b \times h$ where b represents the length of the base and h represents the length of the height. Formula for the height of isosceles triangles The height formula is derived from the Pythagorean theorem, where we use the lengths of the base and the congruent sides: $latex h= \sqrt{{{a}^2}- \frac{{{b}^2}}{4}}$ where a is the length of the congruent sides and b is the length of the base. An isosceles triangle has a base with a length of 15 m and its congruent sides are 12 m. What is its perimeter? Solution: From the question, we get the following values: Base, $latex b=15$ m Sides, $latex a=12$ m Using the perimeter formula, we have: $latex p=15+2(12)$ $latex p=15+24$ $latex p=39$ The perimeter is 39 m. What is the area of a triangle that has a base of 20 m and a height of 15 m? Solution: We recognize the following values: Height, $latex h=15$ m We use the area formula with these values: $latex A= \frac{1}{2}bh$ $latex A= \frac{1}{2}(20)(15)$ $latex A=150$ The area is 150 m². An isosceles triangle has a base of length 16 m and congruent sides of length 10 m. What is its height? Solution: We have the following values: We use the height formula with these values: $latex h= \sqrt{{{10}^2}- \frac{{{16}^2}}{4}}$ $latex h= \sqrt{100- \frac{256}{4}}$ $latex h= \sqrt{100-64}$ $latex h= \sqrt{36}$ $latex h=6$ The height of the triangle is 6 m. If an isosceles triangle has a base of length 6m and congruent sides of length 7m, what is its perimeter? $latex p=19m$ A triangle has a base with a length of 12m and a height of 15m. What is its area? $latex A=90{{m}^2}$ $latex A=120{{m}^2}$ What is the height of a triangle that has a base with a length of 12m and congruent sides of length 15m? $latex h=13.75m$ Interested in learning more about isosceles triangles? Take a look at these pages: Area of an Isosceles Triangle – Formulas and Examples Perimeter of an Isosceles Triangle – Formulas and Examples Height of an Isosceles Triangle – Formulas and Examples What are the characteristics of isosceles triangles? Isosceles Acute Triangle – Characteristics and Examples	CommonCrawl
Subjective Problems of Heat Transfer A rod is composed of two section whose length are $L_1$ and $L_2$ and heat conductivities are $K_1$ and $K_2$ respectively.One end of the rod is kept at $T_1$ and other end is kept at $T_2$.The rod is enclosed in a thermally insulating sheath. a. Find the temperature of the interface. b. Find the equivalent thermal conductivity of the system. c. Find the heat current in the rod Solution-1 Let T be the temperature of the interface. Then in equilibrium Heat flowing from left= heat flowing in the right $K_1 \frac {(T_1-T)}{L_1}=K_2 \frac {(T-T_2)}{L_2}$ or $T= \frac {K_1T_1/L_1+K_2T_2/L_2}{K_1/L_1+K_2/L_2}$ $K_1 \frac {(T_1-T)}{L_1}=K_2 \frac {(T-T_2)}{L_2} =K \frac {(T_1-T_2)}{L_1+L_2}$ $K= \frac {L_1+L_2}{L_1/K_1+L_2/K_2}$ Heat current. $Q=K \frac {(T_1-T_2)}{L_1+L_2}$ $Q= \frac {T_1-T_2}{L_1/K_1+L_2/K_2}$ An 1 mole of a gas whose adiabatic coefficient is 1.4 is at an initial temperature $T_0$ ,is enclosed in a cylindrical vessel fitted with a light piston. The surrounding temperature is $T_s$ and atmospheric pressure is $P_a$.Heat may be conducted between the surrounding and gas through the bottom of the cylinder. The bottom has surface area A, thickness is $L_1$ and thermal conductivity K.Assuming all the changes to be slow and ($T_s > T_0$). a. find the temperature of the gas as a function of the time t. b. Find the distance moved by the gas as function of the time t. Heat will be transferred to the gas through the bottom of the cylinder and as the temperature of the gas increased, it will displace piston(Volume increase) since pressure is constant(atmospheric pressure) Let x be the distance moved the piston at time t Let T be the temperature of the gas at that moment. Suppose an amount of heat dQ is transferred in time dt. $dQ=C_P dT$ Also $\frac {dQ}{dt}=\frac {KA(T_s-T)}{L_1}$ $C_P dT=\frac {KA(T_s-T)}{L_1}$ ----1 Also let $V_0$ is the initial volume of the gas. Then $P_a V_0=RT_0$ or $V_0=\frac {RT_0}{P_a}$ Let V be the volume at time t $ \frac {V}{T}=\frac {V_0}{T_0}$ as Pressure remains constant throughout the process Substituting V0 from last expression $V= \frac {RT}{P_a}$ $V_0 + Ax= \frac {RT}{P_a}$ $ \frac {RT_0}{P_a}+ Ax= \frac {RT}{P_a}$ $T=T_0 + \frac {P_aAx}{R}$ Differentiating both sides $Adx=\frac {RdT}{P_a}$ Putting this is 1 $C_PAP_aL_1dx=KAR[T_s-T_0-(\frac {P_a Ax}{R})]dt$ $KRdt = \frac {C_P P_a L_1 dx}{T_s - T_0 - (P_a A x/R)}$ Integrating both sides with right side as upper and lower limit (t,0) and left side as upper and lower limit (x,0) $\int_{0}^{t} KRdt = \int_{0}^{x} \frac {C_P P_a L_1 dx}{T_s - T_0 - (P_a A x/R)}$ $ \frac {kAt}{L_1C_P}=ln[\frac {(T_s-T_0)}{(T_s-T_0-P_aAx/R)}]$ or $\frac {T_s-T_0}{T_s-T_0-P_aAx/R}= e^{kAt/L_1C_P}$ or $T_s-T_0-(P_aAx/R)=(T_s-T_0)e^{-kAt/L_1C_P}$ $x= \frac {R(T_s-T_0)(1-e^{-2kAt/7L_1R})}{P_a A}$ from ----1 $ \frac {2KAdt}{7RL_1}=\frac {dT}{(T_s-T_0)}$ Integrating both sides with right side as upper and lower limit (t,0) and left side as upper and lower limit (T,$T_0$) $ln \frac {T_s-T_0}{T_s-T}=\frac {2KAt}{7RL_1}$ or $T=T_s-(T_s-T_0)e^{-2KAt/7RL_1}$ A body A of heat capacity s is kept in a surrounding where temperature is $T_a$.It cools down according Newton laws of cooling. The mass of the body is m and the body initial temperature is $T_0$. a. Find the value of constant k if the temperature at time $t_1$ is $T_1$ b. finds the maximum heat body can lose. c. Find the time at which body loses 80% of the total heat loss. d. plots the graph for the logarithm of the numerical value of the temperature difference of the body A and its surrounding with respect to time t. We have according to Newton laws of cooling. $ \frac {dT}{dt}=-k(T-T_a)$ $ \frac {dT}{(T-T_a)}=-kdt$ Integrating both sides with right side as upper and lower limit ($T_1$,$T_0$) and left side as upper and lower limit ($t_1$,0) $ \int \frac {dT}{(T-T_a)}= \int -kdt$ $ln [\frac {(T_1-T_a)}{(T_0-T_a)}]=-kt_1$ $k = \frac {ln [(T_1-T_a)/(T_0-T_a)]}{t_1}$ The body continues to lose heat till it temperature becomes equal to surrounding. So maximum heat body can lose $\Delta Q_m=ms(T_0-T_a)$ Now if the body loses 80% of this heat in time $t_2$ and temperature is $T_{80}$ $.80 \Delta Q_m=ms(T_0-T_{80})$ $.8(T_0-T_a)=(T_0-T_{80})$ $T_{80}=.2T_0+.8T_a$. Now again from Newton law of cooling Integrating both sides with right side as upper and lower limit (T80,T0) and left side as upper and lower limit ($t_2$,0) $ \int \frac {dT}{(T-T_a)}=\int (-k)dt$ $ln \frac {(T_{80}-T_a)}{(T_0-T_a)}=-kt_2$ Substituting the value of k and T80 $t_2=ln( \frac {5}{k})$ $T- T_a=(T_1-T_a)e^{-kt}$ Taking logarithm on both sides $ln(T- T_a)=ln(T_1-T_a) -kT$ which is similarly to y=mx+c So graph will be a straight line. A rod of length l with thermally insulated lateral surface consists of a material whose heat conductivity coefficient varies with temperature given below $K=\alpha T^{1/2}$ where α is constant. The end of the rod are kept at the temperature $T_1$ and $T_2$ where $T_1 > T_2$. Find the function T(x) where x is the distance from end where the temperature is $T_1$ And the heat flow through the rod Q=-αAT1/2dT/dx Minus sign is there Temperature decreases with distance from the end $T_1$ Qdx=-αT1/2dT---1 Integrating both sides with right side as upper and lower limit (l,0) and left side as upper and lower limit ($T_2$,$T_1$) ∫Qdx=-∫αAT1/2dT $Q=\frac {2 \alpha A(T_1^{3/2}-T_2^{3/2})}{3l}$ Now again Integrating equation 1 with right side as upper and lower limit (x,0) and left side as upper and lower limit (T,$T_1$) $Qx= \frac {2 \alpha A(T_1^{3/2}-T^{3/2})}{3}$ Substituting the value of Q from last expression $T^{3/2}=T_1^{3/2} +( \frac {x}{l})(T_2^{3/2}-T_1^{3/2})$ or $T=T_1[1+(x/l)[(\frac {T_2}{T_1})^{3/2} -1]]^{2/3}]$ Six identical rods AB,BC,BD,CE,and DF are joined as shown in figure. The length ,cross-sectional area of each rod is A and L. The thermal conductivities of the rods are as below AB->K BC and BD -> K/2 CE ,DE and EF ->K The ends A and F are maintained at the temperature $T_1$ and $T_2$.Assuming no loss of heat to the atmosphere, find a. Thermal resistance of the six rods b. Thermal resistance of the whole system c. The temperature at the points TB,TC,TD,TE d. The heat flow ratio among the path BCE and BDE. Thermal Resistance of Rod AB=(L/KA) Thermal Resistance of Rod BC=(2L/KA) Thermal Resistance of Rod BD=(2L/KA) Thermal Resistance of Rod CE=(L/KA) Thermal Resistance of Rod DE=(L/KA) Thermal Resistance of Rod EF=(L/KA) Now Rod BC and CE are in series So Total Thermal resistance RBCE=RBC+RCE =(3L/KA) Similarly BD and DE are in series RBDE=RBD+RDE Now Rod BCE and BDE are in parallel, so Net thermal resistance between ends B and E (1/R)=(KA/3L)+(KA/3L) R=(3L/2KA) Now AB ,BE and EF are in series ,so net thermal resistance of the system is R=(L/KA) + (3L/2KA) + (L/KA) So Net heat flow through the system Q=(T_1-T_2)/R Q=(2KA/7L)(T_1-T_2) Now heat flow in Rod AB Q=KA(TB -T_1)/L Substituting the value of Q from equation 1 TB=(9T_1-2T_2)/7 Similarly for the heat flowing rod EF Q=KA(TE -T_2)/L TE=(2T_1+5T_2)/7 Now Heat flow through rod BC =Heat flow through rod CE (KA/2L)(TB-TC)=(KA/L)(TC-TE) Substituting the values of TB and TE we get TC=(13T_1+8T_2)/21 Similarly the temperature at D TD=(13T_1+8T_2)/21 Ratio of heat transfer =1:1 A spherical shell has inner and outer radii as a and b respectively. And temperature at the inner and outer surface area are Ta and Tb And Ta > Tb.K is the thermal conductivity of the spherical shell. Find the heat current through the shell Let us draw two spherical shell with radii r and r+dr concentric with given system and Let T and T +dT be the temperature at them the heat flow through it Q=-K(4πr2)(dT/dr) -4πKdT=Q(dr/r2) Integrating both sides with right side as lower and Upper limit (Ta,Tb) and left side as Lower and upper limit (a,b) 4πk(Ta-Tb)=Q[(1/a)-(1/b)] $Q= \frac {4\pi kab(T_a-T_b)}{b-a}$ A rod of length l as shown is figure above with thermally insulated lateral surface is made of two material whose thermal conductivities are $K_1$ and $K_2$ respectively. The cross-sectional area is a square having edge d. Temperature at the ends are $T_1$ and $T_2$($T_1 > T_2$) a, Find the heat flow b. Equivalent thermal conductivity of the Rod Considering a small portion of rod at distance x of thickness dx from the end whose temperature is T1 Heat flow through the portion of the Rod is Q=-K2(d2x/l)(dT/dx) -K1d(d -dx/l)(dT/dx) as the edge at the portion at x for K2 is given by dx/l -Q=dT/dx[K2(d2x/l) +K1d2 -K1(d2x/l)] $-dT = \frac {Qdx}{K_2^2d^2x/l +K_1d^2 -K_1d^2x/l} Integrating both sides with right side as lower and Upper limit (T1,T2) and left side as lower and upper limit (0,l) $Q = \frac {d^2(T_1-T_2)(K_2-K_1)}{l[ln (K_2/K_1)]}$ Now Q is also given by Q=Kd2(T1-T2)/l where K is the equivalent thermal conductivity of the system So comparing K=(K2-K1)/ln (K2/K1) A cubical Block of mass 1 kg and edge 5 cm is heated to 227 °C.It is kept in a chamber which is maintained at the temperature 27 °C. Assuming the cubical block is having value of e=.5 a. Find the amount of radiation falling on the block. b. Find the net amount of heat flow outside the block. c. Find the rate at which temperature decrease at the beginning if specific heat=400J/kg-K d. if the chamber is maintained at the same temperature as the block. Find the heat absorbed and heat radiated by the block. σ=6.0 x 10-8 W/m2-K4 Amount of the radiation by the block $=e \sigma AT_b^4$ where Tb is body temperature. Substituting all the values Amount of the radiation by the block=28.12 W Amount of radiation absorb from the surrounding $=e \sigma AT_s^4$ where Ts is surrounding temperature. Amount of the radiation absorb from the surrounding =3.64 W Net heat flow outside the block=Amount of the radiation by the block - Amount of radiation absorb from the surrounding =24.38 Now $ms \frac {dT}{dt}=24.38$ $ \frac {dT}{dt}=\frac {24.38}{ms}$ =.06 °C/sec If the chamber is at the same temperature as the block. then Heat absorbed=28.12 W Heat radiated=28.12 W One end of the rod of length L is inserted in furnace which is maintained at temperature $T_1$.The sides of the rod are covered with insulating material. Other end emits radiation with emissivity e. The temperature of the surrounding $T_s$.Let $T_2$ is the temperature of the end in steady state. a. Find the thermal conductivity of the Rod b. Find the heat flow in the Rod. Let k be the Thermal conductivity of the Rod. Heat flow through conduction in the Rod=Heat radiation from the Rod $ \frac {KA (T_1-T_2)}{L}=e \sigma A(T_2^4-T_s^4)$ $K= \frac {e \sigma L(T_2^4-T_s^4)}{(T_1-T_2)}$ br /> Also $Q=e \sigma A(T_2^4-T_s^4)$ A Rod is initially at a uniform temperature at $T_1$.One end is kept at $T_1$ and other end is kept in a furnace maintained at temperature at $T_2$.($T_2 > T_1$).The Surface of the rod is insulated so that heat can flow lengthwise along the rod.Lenght of the Rod is L, area A and thermal conductivity of the Rod is K.Consider a short cylindrical element of the rod of unit lenght.If the temperature gradient at the one end of the element is K'.Find the rate of flow across the element. Q=KAK' The tungsten element of the electric lamp has as surface area A and Power is P and emissivity is .4 a. Find the temperature of the filament b. if the tungsten filament behave like black-body ,find the % increase in power required to maintain the same temperature. $P=e \sigma AT^4$ $T=(\frac {P}{e \sigma A})^{1/4}$ If the body behaves like black-body. $P_1= \sigma AT^4$ Substituting the value of T from last expression $P_1= \frac {P}{e}$ % increase in Power $ =\frac {P/e -P}{P} \times 100 = 150$ % A sphere, a cube and a circular plate have the same mass and are made of same material. All of them are at the same temperature T.Which one will have maximum rate of cooling. For the same volume, Surface area of circular plate is maximum and Sphere is minimum. Now rate of cooling is $=e \sigma AT_2^4$ So rate of cooling will be maximum for circular plate then the cube and it will be minimum for sphere. A hole of radius $R_1$ is made centrally in a circular disc of thickness d and radius $R_2$.The inner surface is maintained at temperature $T_1$ and other surface is maintained at $T_2$ ($T_1 > T_2$).Thermal conductivity of the circular plate is K. a. Find the temperature as a function of radius from center b. Find the heat flow per unit time $Q=-K \times 2 \pi r d \times (\frac {dT}{dr})$ $\frac {Qdr}{r}=-2 \pi k d dT$ Integrating both sides with right side as lower and Upper limit ($R_1$,$R_2$) and left side as lower and Upper limit ($T_1$,$T_2$) $\int \frac {Qdr}{r}= \int (-2 \pi kd)dT$ $Q ln(\frac {R_2}{R_1})=2 \pi kd (T_1-T_2)$ $Q= \frac {2 \pi kd(T_1-T_2)}{ln(\frac {R_2}{R_1})}$ Now Integrating (1) both sides with right side as lower and Upper limit ($R_1$,R) and left side as lower and upper limit ($T_1$,T) $Q ln (\frac {R}{R_1})=2\ pi kd(T_1-T)$ Substituting the value of Q $T=T_1 -(T_1 -T_2) \frac {ln (R/R_1)}{ln (R_2/R_1)}$ Two metallic sphere X & Y are made of same material and have identical surface finish. Let $m_1$,$m_2$ are the masses of the spheres X & Y respectively. Both the sphere is at the same temperature. Both the sphere is placed in the same room having lower temperature. But they are thermally insulated from each other. Also $(\frac {m_1}{m_2})=n$. If the initial rate of cooling of sphere X to Y is (1/4)1/3.Find the value of n. Rate of heat loss $ms \frac {dT}{dt}=4 \pi r^2 \sigma(T^4 - T_s^4)$ Initial rate of cooling $\frac {dT}{dt}= \frac {4 \pi r^2 \sigma(T^4 - T_s^4)}{ms}$ So $\frac {dT}{dt}$ is proportional to $ \frac {r^2}{m}$ For sphere X $(\frac {dT}{dt})_X= \frac {kr_1^2}{m_1}$ For sphere Y $(\frac {dT}{dt})_Y= \frac {kr_2^2}{m_2}$ Now let D be the density of the material $m_1=\frac {4}{3} \pi r_1^3 D$ $r_1=(\frac {3 \pi D m_1}{4})^{1/3}$ $r_2=(\frac {3 \pi Dm_2}{4})^{1/3}$ Ratio of initial rate of cooling $R= \frac {r_1^2 m_2}{r_2^2 m_1}$ $R=\frac {m_1^{2/3} m_2}{m_2^{2/3} m_1}$ $R= =(\frac {m_2}{m_1})^{1/3}$ $=(\frac {1}{n})^{1/3}$ Comparing from the given expression A system is shown in figure. It is made of semicircular Rod (AXB) which is joined at its ends to a straight rod AB of same material and the same cross-section .The straight Rod form a diameter of the other rod. Similarly semicircular Rod (BYD) which is joined at its ends to a straight rod of same material and cross-section area. a. Find the ratio of heat transfer across AXB and AB b. Find the ratio of heat transfer across BYD and BD Ratio of heat transfer AXB and AB $=\frac { \frac {KA(T_a -T_b)}{\pi r}}{ \frac {KA(T_a-T_b)}{2r}}$ $= \frac {2}{\pi} $ Similarly for BYD and BD $=\frac {2}{\pi}$ <a href="https://physicscatalyst.com/heat/heat-transfer-problems.php">Heat transfer Problems for Class 11, JEE and NEET</a>	CommonCrawl
International Journal of Health Geographics Gardening in the desert: a spatial optimization approach to locating gardens in rapidly expanding urban environments Elizabeth A. Mack1, Daoqin Tong2 & Kevin Credit1 International Journal of Health Geographics volume 16, Article number: 37 (2017) Cite this article Food access is a global issue, and for this reason, a wealth of studies are dedicated to understanding the location of food deserts and the benefits of urban gardens. However, few studies have linked these two strands of research together to analyze whether urban gardening activity may be a step forward in addressing issues of access for food desert residents. The Phoenix, Arizona metropolitan area is used as a case to demonstrate the utility of spatial optimization models for siting urban gardens near food deserts and on vacant land. The locations of urban gardens are derived from a list obtained from the Maricopa County Cooperative Extension office at the University of Arizona which were geo located and aggregated to Census tracts. Census tracts were then assigned to one of three categories: tracts that contain a garden, tracts that are immediately adjacent to a tract with a garden, and all other non-garden/non-adjacent census tracts. Analysis of variance is first used to ascertain whether there are statistical differences in the demographic, socio-economic, and land use profiles of these three categories of tracts. A maximal covering spatial optimization model is then used to identify potential locations for future gardening activities. A constraint of these models is that gardens be located on vacant land, which is a growing problem in rapidly urbanizing environments worldwide. The spatial analysis of garden locations reveals that they are centrally located in tracts with good food access. Thus, the current distribution of gardens does not provide an alternative food source to occupants of food deserts. The maximal covering spatial optimization model reveals that gardens could be sited in alternative locations to better serve food desert residents. In fact, 53 gardens may be located to cover 96.4% of all food deserts. This is an improvement over the current distribution of gardens where 68 active garden sites provide coverage to a scant 8.4% of food desert residents. People in rapidly urbanizing environments around the globe suffer from poor food access. Rapid rates of urbanization also present an unused vacant land problem in cities around the globe. This paper highlights how spatial optimization models can be used to improve healthy food access for food desert residents, which is a critical first step in ameliorating the health problems associated with lack of healthy food access including heart disease and obesity. The World Bank notes that developing countries have large amounts of unused land, which run the risk of marginalizing a growing number of urban poor [1]. Cities in countries around the globe including Afghanistan [2], India [3] and Brazil [4] are urbanizing rapidly and experiencing symptoms of rapid growth including lack of food access and unused vacant land. Urban agriculture initiatives are a promising solution to the vacant land and food security problem in global cities, and urban residents around the world are pursuing urban gardening initiatives [5]. These gardening initiatives are not only important for establishing communities that are more connected and have better access to food systems, they also represent an important piece of the puzzle in solving the growing global health issue of obesity given the link between lack of access to quality food and health [6,7,8,9]. The United Nations estimates that in 2014, 54% of the world's population lived in urban areas, and this number is projected to increase to 66% by 2050 [10]. Rising rates of urbanization mean diminished connections to food sources as agricultural land disappears [3] and local food sources disappear in favor of superstores that meet consumer demand for standardized, unblemished food products [11,12,13]. The shift in size, scale, and location of food outlets over the past 60 years—from small, urban neighborhood stores to large suburban superstores—is a global phenomenon that is increasingly prevalent in the food economics of the developed world [12]. Locales where residents do not have access to and/or cannot afford healthy food are commonly referred to as "food deserts". While there has been a wealth of research dedicated to understanding the location of food deserts [14, 15] and the benefits of urban gardens [16,17,18] few studies have linked these two strands of research together to analyze whether urban gardening activity may be a step towards addressing issues of food access for residents of food deserts. To better understand the neighborhood context of urban gardening activity and its spatial linkages with food deserts, this study analyzes the locations of food deserts and urban gardening activity. The key contribution of the study is the use of a garden siting technique, the maximal covering location model, to propose alternative urban garden sites and improve food access for area residents. The potential utility of this type of analytical approach is demonstrated for Phoenix, Arizona, which is rapidly urbanizing and has a vacant land problem. This technique can be applied however to any urban environment where the necessary data are available. In this respect, siting gardens on vacant land is a particularly promising tool for improving food access and urban food security in cities around the globe. Background: food access and food deserts Food access is a precursor to healthy food consumption and healthy food consumption is associated with better health [19,20,21,22]. While the food environment is not the sole driver of food consumption practices, studies do find linkages between healthy food access and the quality of human health [7, 8, 23, 24]. Given the health implications associated with food access, several studies have endeavored to identify neighborhoods, especially low-income neighborhoods, with inadequate access to healthy food [25]. These studies find that changes in food retailing practices, with small independent retailers slowly replaced by large superstores, have changed the landscape of food access [26, 27], leaving urban residents with fewer food choices. This retailing change makes suburban locations more attractive because of the land area required for larger stores and the reduced expense of land in suburban areas [26]. It is important to note that this consolidation of food outlets also impacts rural residents when local neighborhood stores close due to competition from larger retailers [15]. While a majority of the literature on food deserts emphasizes this issue in an urban context [28,29,30], more recent work has uncovered that the hinterlands of metropolitan areas have residents that suffer from lack of access to healthy food [25], as well as residents in suburban [31] and rural areas [15, 26, 32]). Sharkey et al. [33] note that food access in rural locations is particularly important to analyze given the compounding challenges of distance and transportation access in rural environments. Work also highlights the importance of considering temporal aspect of food access related to changes in public transportation schedules and the operating hours of food stores [34]. Farber, Morang, and Widener [35], note that the operating hours of public transportation can impact travel times, which then impacts peoples' ability to patronize food outlets. Despite the amount of attention dedicated to food access, there is a lack of consensus on the definition of food deserts [26, 36, 37]. Table 1 provides several examples of food desert definitions, and highlights the sources of variation in how these are defined. Some definitions define a particular distance that constitutes good food access [14, 38, 39]. Some definitions explicitly refer to low-income neighborhoods or groups [15, 30, 40] while others do not [14, 38]. Other sources of variation in food desert definitions include the explicit mention of transit times [41] and/or specific mention of a particular type of food outlet used to determine food access. Table 1 Definitions of food deserts used in previous studies In addition to variations in food desert locations and counts stemming from basic definitional issues, Bao and Tong [42] point out inconsistencies in the findings of food desert studies that are related to differences in the spatial scale and level of data aggregation. Studies have also found that the choice of study area matters, and that not all locations have a food desert problem. For example, Apparicio et al. [43] found no evidence of a food desert problem in Montréal, which suggested the need for other mechanisms beyond improved healthy food access to resolve diet-related health problems for Montréal residents. Background: urban gardens Several studies of alternative means of food access have analyzed small food stores as a means of solving the food desert problem [6, 41, 44]. Mobile vans have also been suggested as a means of providing food insecure neighborhoods with fresh fruits and vegetables [45]. Other studies have suggested that building a strong local food economy through farmer's markets and direct sales from farms could be an important strategy in the fight against obesity [46]. This approach includes the use of community gardens as a mechanism for providing access to nutritious foods [47]. Locally grown food has a long history as an alternative means of food access in urban environments, and studies have noted that in the United Kingdom and the United States, gardens are a notable feature of the urban landscape, although the intensity of gardening activities varies over time [48]. Throughout the history of the United Kingdom, allotment gardens served as an important source of employment and food [48]. In the United States, urban gardens were part of the social reform movements in the 1890s, and were also an important source of food during the Great Depression [49, 50]. In both World Wars, urban gardens served as an alternative food source. During World War II in particular, "victory gardens" were an important source of fresh food for U.S. residents so food stuffs could be sent to troops abroad [49]. Post-WWII, urban gardening efforts experienced a comparative lull until the 1970s, when gardens become a component of urban revitalization efforts [49]. Starting in the 1970s, federal programs such as the United States Department of Agriculture's (USDA) Urban Garden Program continued to support gardening activities in urban environments [48]. Today, in cities around the globe—from Puerto Maldonado, Peru to Canberrra, Australia to Mumbai, India—organizations and urban residents are now growing food in urban environments [5]. Because of rising rates of urbanization and growing interest in urban food production globally, studies have begun to incorporate farmer's markets and community gardens into analyses of food deserts. It has been noted that studies that do not consider these sources of fresh foods will overestimate inequities in food access [51]. Studies have also found that community gardens are a viable source of food for low-income people and can provide additional benefits to neighborhoods by improving the attitudes and outlooks of residents [16, 17]. As regards access and consumption of healthy food, Litt et al. [17] found that community gardeners were more likely to consume fruits and vegetables than were home gardeners and non-gardeners. Given the importance of local, healthy food sources, researchers have also begun to examine the potential for cultivating food within urban environments [52, 53]. These studies use a wide range of tools including geographic information systems (GIS), remote sensing, and site suitability techniques. For example, Kremer and DeLiberty [52] combined GIS and remote sensing techniques to examine the availability of urban land in Philadelphia, Pennsylvania for garden activity. Site suitability analysis was used to propose locations for urban gardens in cities ranging from Hanoi, Vietnam [54] and Chittendon County, Vermont [55]. In Portland, Oregon and Vancouver, Canada, Mendes et al. [56] conducted a visual assessment of parcels, including tree canopy and built environment characteristics, to identify the most suitable government-owned land on which to pursue urban agriculture projects. Finally, participatory mapping has been used to visualize relationships in local food systems [57] and locate healthy food retail outlets [58]. This approach draws upon the knowledge of experts to understand and restructure aspects of local food systems. While these techniques represent important advancements to understanding and improving urban food systems, they are not without drawbacks. Studies have found that remote sensing techniques do not accurately identify garden locations because of their small size and heterogeneous layouts, which produce non-uniform visual patterns [53]. Site suitability techniques are an improvement over remote sensing techniques because they are capable of incorporating multiple variables above and beyond land use, but are perhaps more accurately viewed as an initial screening process that helps to find suitable areas for gardens. From this perspective, spatial optimization models represent a potential improvement over site suitability analyses. This brand of optimization model can be viewed as a type of site selection analysis with additional considerations, that include: (1) the number of gardens to site due to budget constraints, (2) a more accurate way to account for multiple factors, and (3) the spatial relationship among gardens (and between neighborhoods and gardens). Thus, spatial optimization models not only have the site-identifying capacity of site suitability analyses, but they also have the added capability of providing information about the spatial configuration of sites, in conjunction with a sense of tradeoffs about the number of gardens to be cited and the population of interest serviced by these gardens. Because of the enhanced analytical capabilities of these models, they can be used to analyze how urban gardens may be distributed better to resolve issues of access for food desert residents. Maricopa County, which contains the majority of the Phoenix metropolitan area, is the study area for this analysis. Figure 1 depicts the distribution of urban, suburban, and rural areas across the metropolitan area. Dark colors represent the most tracts while lighter colors represent comparatively rural tracts. These 2010 Rural–Urban Commuting Area (RUCA) categories of the urban–rural continuum were obtained from the United States Department of Agriculture (USDA) and contain 10 categories of tracts ranging from the most urbanized (code 1) to the most rural tracts (code 10). Based on this classification scheme, the majority of tracts (95%) across Phoenix are classified as part of the metropolitan area core. Only two tracts are classified as rural. Interestingly, tracts that are classified as having high levels of commuting to the urban core are located mostly in the West Valley of Phoenix in communities such as Glendale, El Mirage, and Surprise. Urban–rural classification of Phoenix, Arizona census tracts These high commuting tracts highlight the sprawling nature of the metropolitan area [59, 60], which means that residents are more likely to drive to everyday activities than residents in older, more walkable metropolitan areas. In this context, several locations across Maricopa County represent less centrally located communities, where issues of adequate access to healthy foods are perhaps exacerbated [25]. This issue of sprawl is not unique to Phoenix but is characteristic of cities across the globe. Another feature of the metropolitan area that is characteristic of rapidly urbanizing cities is a vacant land problem [61,62,63] with over 10,000 acres of unused land [63]. While a lot of this land is on the urban fringe, satellite imagery also highlights many examples of vacant lots in built-up portions of the study area. Recently, City of Phoenix officials have attempted to find temporary uses for vacant land and community gardens represent one of these proposed land uses [61]. For example, as part of the Phoenix Renews project, a 15-acre vacant lot at the intersection of Central Avenue and Indian School Road was proposed as the location of an urban community farm. Unfortunately, the owner of the lot defaulted on payments and had to return the land to the U.S. Department of the Interior [64]. This closure means that local gardeners who started growing crops will lose their plots, and must find a location elsewhere. Given the potential for gardens to alleviate poor access to healthy foods, finding suitable locations for community gardens is no easy task, but perhaps a necessary step to move towards a more comprehensive resolution to the vacant land problem in Phoenix, and to simultaneously improve food access for residents. Given the complex swathe of factors to consider in siting gardens, this study will analyze current sites of urban gardening activities with an emphasis on their neighborhood context. It will then propose new locations for urban gardening activity to improve access for food desert residents. To provide a more comprehensive perspective on urban garden locations, several variables are used to characterize the neighborhood environment. To do this, a variety of data including housing, land use, zoning, demographic, and socio-economic characteristics were collected at the census tract level based on the precedent of prior studies [25, 30, 43]. From this perspective, special attention was devoted to collecting information about economic disadvantage given the link between socio-economic status (SES) and access to healthy food [25, 28, 39]. Table 2 contains summary information about these data. Table 2 Description of data and data sources Garden data Urban garden locations are derived from a list obtained from the Maricopa County Cooperative Extension (MCCE) office at the University of Arizona which provided the name and address for gardens across the county. Information from this database was verified from aerial imagery on Google Maps, which provided historical images of garden locations in some cases. When necessary, contacts with garden managers were also used to verify the start and end date of the gardens to ascertain whether they were active or inactive. The address of active gardens was also verified because some gardens had moved since their initial start date. When garden managers could not be contacted, in-person visits were made to the address for the garden listed in the database to verify the status of the garden. Above and beyond information in this database, efforts were made to triangulate and supplement data from the MCCE list with information from the American Community Garden Association (ACGA) website and city government websites. Out of the 99 garden locations identified, 77 gardens locations were verified within the boundaries of the Phoenix metropolitan area. Of these 77 gardens, 68 were active at the time the data were collected. However, both active and inactive gardens will be used in the analysis that follows to understand both past and current trends in garden locations given the transient nature of urban gardening activity [49]. Once the addresses of garden locations were verified, they were geocoded and matched to their relevant census tract in order to integrate garden data with data collected from other sources. Census tracts were then assigned to one of three categories: tracts that contain a garden, tracts that are immediately adjacent to a tract with a garden, and all other non-garden/non-adjacent census tracts. The adjacency category was used to identify tracts that are proximal to a tract with a garden, as opposed to a binary breakdown of tracts into those with and without a garden. This category is important to consider because these tract residents are still nearby a source of fresh fruits and vegetables. In the analysis that follows, 75 of the 77 garden sites were located in Census tracts that fell within the boundaries of Phoenix area neighborhoods. Thus, these 75 gardens will serve as the basis for the ANOVA comparison of garden-oriented neighborhoods and non-garden oriented neighborhoods. For the spatial optimization analysis, all 77 gardens will be used because the analysis assigns gardens to tracts based on a threshold distance of 1 mile (1.61 km). Food outlet and food desert information In addition to information about garden locations, healthy food outlet information from the ESRI Reference USA dataset was compiled using the definition of food outlets from Raja et al. [41]. Based on this study, point-level information about outlets selling healthy food was compiled and aggregated to census tracts. These data include the following types of food outlets: supermarkets, natural food stores, meat and fish stores, specialty food stores, and fruit and vegetable stores.Footnote 1 Bakeries and dairy stores were excluded from the analysis because their food offerings could not be classified as healthy: most of the dairy stores in this database were verified as selling frozen yogurt. Census tract information about food deserts was obtained from the United States Department of Agriculture (USDA). Since the USDA provides several definitions of food deserts, the definition used in this study defines food deserts as Census tracts with low access to supermarkets or larger grocery stores where low access means residents are more than 1 mile (1.61 km) from food outlets in urban areas and more than 10 miles (16.09 km) from food outlets in rural areas [65]. Demographic and socio-economic data Contextual information about the demographic and socio-economic profile of Phoenix area residents was compiled from the National Historic Geographic Information System (NHGIS) Database, which contains American Community Survey (ACS) estimates for census tracts between 2010 and 2014. Demographic information collected from this database includes information about race/ethnicity, educational attainment, as well as the poverty status and income level of households. Housing, land use and zoning information Housing and land use information were also collected to provide a sense of the types of housing and land uses in and around tracts with gardens. Information about home value and occupancy status were obtained from the NHGIS archive of ACS data 2010–2014 5-year estimates. Parcel level information about land use across the metropolitan area was obtained from the Maricopa Association of Governments (MAG) database as of 2014. A critical aspect of this database is the information about vacant developable land, which is important to identify given the vacant land problem discussed above, and because these vacant land parcels represent potential urban garden locations. Parcel data were aggregated to the census tract level to get a sense of the amount of a particular land use (in square miles) within each census tract. To incorporate information about travel time for residents, tract-level data from the ACS 2010–2014 5-year estimates on commuting mode and travel time to work were also gathered. Analytical approach Analysis of variance (ANOVA) is used to determine whether there are statistical differences between the three categories of tracts described above (contain a garden, adjacent to a garden, not adjacent/does not contain a garden) based on the contextual data summarized in Table 2. This portion of the analysis is needed to test the following three hypotheses: Households in tracts with a garden, or nearby a garden, will have higher socioeconomic status than households in tracts without gardens. Tracts with gardens, or nearby a garden, will have different land uses than tracts without a garden. Tracts without gardens will have poor access to other types of food sources than tracts with gardens, or nearby a garden. These hypotheses are important to test, because they can help characterize important economic, land use and food access differences between the three types of tracts. If for example, there are no differences in food access between the three categories of tracts, a reconfiguration of current garden locations is not necessary to improve access for residents. After analyzing the neighborhood context of urban gardens, location models are used to identify potential sites for future garden activity. Here, it is important to remember that this analytical approach is different from prior remote sensing and site suitability techniques for identifying garden locations because it not only identifies potential sites for gardens based on particular criteria, but it also provides a sense of the number of gardens needed to cover a given population of interest (in this case, residents of food deserts). Location analysis and modeling has been used to support locational decisions in a wide range of applications [66], including emergency service planning [67, 68], school district design [69, 70] and wireless device placement [71] to name a few. Building on the fact that food deserts are demarcated based on distance thresholds, and the goal of the analysis is to service the food desert population, two covering models were considered for this particular study: the location set covering problem [67] and the maximal covering location problem [72]. Different from other types of location models, covering models examine service efficiency using a coverage standard that is often based on travel distance or time: demand is considered covered if it is within the coverage standard of a service provider. Recently, Bao et al. [42] developed a variant of the maximal covering location model to strategically site independent food stores for addressing food desert issues. In our study, coverage provided by a community garden will be assessed based on whether a food desert is located within the 1-mile travel distance as defined by the USDA. The location set covering model can be used to produce output that would specify the minimum number of gardens needed to ensure that no food desert is left uncovered, while the maximal covering location problem can be used to prescribe the spatial configuration of urban gardens that maximizes the coverage of food deserts when the number of gardens to site is fixed due to a budget constraint. The model selected to implement in this paper is the maximal location covering problem [72], because it is infeasible to cover all food deserts due to the limited vacant land available. The output of the maximal covering location model is the location of and coverage of food desert residents provided by a given number of gardens. The output from this spatial optimization model also provides geographic information about proposed garden sites, and a tradeoff curve which contains the number of gardens to be sited on the x-axis and the population residing in food deserts covered by the specified number of gardens on the y-axis. From this tradeoff curve, it is possible to understand tradeoffs in the number of gardens located and the percentage of food desert residents covered. Given the potential for urban gardens to serve as an affordable source of fresh fruits and vegetables for residents in food deserts, the goal of the optimization analysis will be to locate gardens based on two criteria: to cover as many residents in food deserts as possible and to locate these gardens on vacant land within the Phoenix metropolitan area. The location model is specified below. Maximal covering location problem $$ {\text{Maximize}}\,\sum_{i} w_{i} y_{i} $$ $$ \sum\limits_{{j \in N_{i} }} {x_{j} } \ge y_{i} \quad \forall i $$ $$ \sum\limits_{j} {x_{j} } = p $$ $$ x_{j} \in \left\{ {0,1} \right\}\quad \forall j $$ $$ y_{i} \in \left\{ {0,1} \right\}\quad \forall i $$ where i index of food deserts, j index of vacant land, w i population in food desert i $$ x_{j} = \left\{ {\begin{array}{{20}l} 1 \hfill &\quad{{\text{if}}\,{\text{vacant}}\,{\text{land}}\,j\,{\text{is}}\,{\text{selected}}\,{\text{for}}\,{\text{the}}\,{\text{conversion}}\,{\text{to}}\,{\text{a}}\,{\text{community}}\,{\text{garden}}} \hfill \\ 0 \hfill &\quad{\text{otherwise}} \hfill \\ \end{array} } \right. $$ $$ y_{i} = \left\{ {\begin{array}{{20}l} 1 \hfill &\quad {{\text{if}}\,{\text{food desert}}\,i\,{\text{is covered}}} \hfill \\ 0 \hfill &\quad {\text{otherwise}} \hfill \\ \end{array} } \right. $$ N i = {j\|d ij ≤ D} consists of all the candidate site j that if converted can serve food desert i (i.e., the travel distance from i to j is within D the low-access threshold used for defining food deserts). p: the number of community gardens to site Objective (1) aims to maximize the food desert population to be covered. Constraint (2) specifies that a food desert is considered covered only when there is at least one urban garden that is located within the coverage threshold D. Given that the food deserts in this study are located in urban areas, we define the coverage threshold D to be 1-mile (1.61 km) travel distance in order to be consistent with the definition of food deserts provided by the USDA. Constraint (3) specifies the number of urban gardens to be sited. Constraints (4) and (5) impose binary integer conditions on decision variables x and y that dictate whether vacant land is selected or not, and whether a food desert is covered or not, respectively. Before undertaking the spatial optimization analysis to pinpoint proposed garden sites, an analysis of the location of past and present gardens sites is conducted. This portion of the analysis is important because it provides information about the spatial distribution of garden sites, their neighborhood context, and their proximity to food desert locations across the metropolitan area. Figure 2 displays the locations of existing gardens (see Additional file 1 for a shapefile of these gardens). This graphic highlights that the majority of gardens (66%) are located in the city limits of Phoenix in areas that include the historic Encanto district, Maryvale, and South Mountain. Other cities, including Tempe, Mesa, and Chandler, also have garden activity, but the majority is highly centralized in the old urban core. Figure 2 also shows the hotspots of healthy food outlets by census tract, which was produced by aggregating the healthy food outlet point locations from the ESRI Reference USA database to census tracts. The local Moran [73] was used to identify hot-spots of healthy food outlets. These are tracts with a high level of healthy food outlet clustering.Footnote 2 Healthy food outlets and urban garden locations While the figure does not present a formal test of spatial dependence between garden locations and healthy food outlet hotspots, it does provide some support for prior work showing that gardens cluster near healthy food outlets [51]. As the ANOVA results below indicate, these areas are also more likely to be commercial neighborhoods that are zoned to allow retail uses. This means the current locations of gardens do not help residents in food deserts because they are already located in areas with access to healthy food stores. In general, the majority of gardens are located near the central city areas of Phoenix, Tempe, and Mesa. There are also several gardens in the more residential areas of North Phoenix, Scottsdale, and Mesa that are not located near clusters of healthy food outlets, but these are generally the exception. Neighborhood context of garden locations These differences in garden locations raise questions about the neighborhood context of garden sites. To provide some resolution on the extent that neighborhoods with gardens are different from those without gardens, analysis of variance (ANOVA) was conducted to statistically test for neighborhood differences based on five sets of characteristics: demographics, socio-economic status, land use characteristics, housing type, food outlet type, and commuting characteristics. Given the relatively low number of garden-containing census tracts (75 out of 880 in the study area, or 8.5% of tracts), garden-adjacent census tracts were also included in the analysis (34.3% of tracts) in order to evaluate the neighborhood context of communities with gardens. Garden-adjacent tracts are also important to identify since they are closer to garden locations—and thus more likely to receive some supplementary benefit—than other tracts in the metropolitan area. Table 3 presents summary results of this analysis and highlights significant differences between census tracts with gardens, tracts adjacent to those with gardens, and tracts without gardens. Detailed ANOVA results may be found in Additional file 2 included at the end of this paper. In terms of interpreting the information in Table 3, each variable is listed next to the tract type with the highest value of that variable; for example, industrial, neighborhood commercial, educational, office, and medical land uses are all statistically different between the tract types, and have higher percentages in garden-containing tracts. Similarly, garden-adjacent tracts show the highest percentage of multi-family residential land use. In terms of demographics, urban garden tracts and tracts adjacent to gardens are more racially and ethnically diverse; tracts with gardens have a higher percentage of Black and Hispanic residents than do non-garden tracts. They also have lower levels of educational attainment. In terms of other measures of socio-economic status, garden tracts and tracts adjacent to gardens have a higher percentage of persons who are unemployed, on food stamps, and without healthcare. Table 3 Highest values of various characteristics for no garden, garden-adjacent, and garden-containing tracts Aside from demographic and socio-economic differences, there are also interesting differences in land uses amongst the three categories of tracts analyzed, particularly for tracts with gardens and tracts adjacent to garden tracts. These tracts have less land dedicated to residential land, but more land area dedicated to medical, office, and educational uses than tracts without gardens. As for the characteristics of nearby food outlets, gardens and tracts neighboring garden tracts have higher access to a variety of food outlets including restaurants, supermarkets, and convenience stores. Interestingly tracts with gardens also had the lowest share of workers commuting to work by driving alone, the highest share of workers commuting by non-auto modes (transit, walking and cycling), the highest percentage of residents with a commute under 15 min, and the lowest percentage of residents with a commute of 30 min of more. Figure 3 displays the locations of gardens and food deserts in the metropolitan area. It highlights that many gardens are not located in food deserts; in fact, only 24 out of the 75 gardens (32%) are located in food desert tracts. Also, of the 68 active urban gardens identified at the time of this analysis, only nine cover food deserts with a population of 27,290, corresponding to just 8.4% of all food desert residents. Several of the uncovered food deserts are located in exurban locations to the West of downtown Phoenix in neighborhoods such as El Mirage and Glendale. Uncovered food deserts are also evident in the east of the metropolitan area in Mesa. Based on this distribution of gardens, it appears future garden sites could be located more strategically to cover residents in food desert locations. Urban garden and food desert locations Siting urban gardens To analyze how gardens could be distributed better, a maximal covering spatial optimization model was used to identify gardens sites to provide better coverage for food desert residents. To do this, only vacant land classified as developable was considered; military and native community lands were excluded. Land considered too small for community gardens (< 5000 ft2) was also excluded. This threshold of 5000 ft2 is based on recommendations that to achieve a critical mass of gardeners, the total size of a garden should be a minimum of 3000–3500 ft2 so that it may contain 10–12 good sized garden plots [74]. A size of 5000 ft2 would accommodate this number of plots and also provides space for a toolshed and community garden activities. The analysis resulted in 5947 pieces of vacant land selected to serve as potential urban garden sites. The coverage assessment was performed based on the travel distance from a food desert to a candidate garden site using ESRI's Network Analyst and the region's street network. During the distance calculation, vacant land was represented using the geometric centroids and food deserts were converted to points using their population centers. The maximal covering location problem introduced in the previous section was then solved to identify which vacant land sites can serve the food deserts not served currently by existing gardens. Figure 4 presents a tradeoff curve that summarizes the results of this analysis. On the x-axis of this graph is the number of gardens, and the y-axis represents the percentage of food desert residents covered by siting p number of community gardens. The tradeoff curve provides important insights for planners and government agencies to better allocate limited funds for food project planning. Similar to many other maximal coverage location problem applications, marginal coverage achieved decreases with the number of facilities sited. For example, siting 25 urban gardens achieves coverage of about 65% of the food desert population whereas an increase of gardens to twice that number (50 gardens), achieves 30% more coverage. Constrained by the location of the vacant land available, it is infeasible to achieve complete coverage of all 68 food deserts not covered by existing gardens. This is because three food deserts are left uncovered due to the lack of available land closer to food desert sites. The best coverage possible can be obtained by siting 53 urban gardens, providing maximal coverage of 65 food deserts with 96.4% of the food desert population covered (Additional file 3). This is a vast improvement over the current distribution of gardens; the 68 active community garden sites only cover 8.4% of food desert populations. A map of the 53 proposed garden sites along with food desert locations is shown in Fig. 5. Several of the proposed sites (45%) are located in the city limits of Phoenix. Proposed garden sites to the west of Phoenix include the communities of El Mirage, Glendale, Sun City, and Peoria. To the southeast of Phoenix, other proposed garden sites are located in Tempe, Chandler, and Mesa. Tradeoff curve of garden numbers and food desert coverage Proposed garden sites and food desert locations Across the world, urbanization continues at a rapid pace. As agricultural land is converted to other uses and people become disconnected from traditional food sources, access to healthy food is a growing issue for urban residents worldwide. Given the health implications associated with the lack of access to healthy food [9, 75, 76], this study set out to demonstrate how spatial optimization models may be used to better locate urban gardens to improve access for residents and to resolve the issue of unused vacant land simultaneously. This technique is demonstrated here for the Phoenix Arizona metropolitan area but can also be applied to any city globally where food access and vacant land issues are present. As mentioned previously, several cities in countries around the globe, such as Afghanistan, India, and Brazil, are currently experiencing similar problems associated with rapid rates of urbanization. Analytical results reveal important demographic, socio-economic, and land use differences between tracts with or near urban gardens and tract without or not near urban gardens. Tracts with or near gardens are more racially and ethnically diverse and also contain characteristics of low socio-economic status such as lower levels of educational attainment and higher rates of unemployment compared to non-garden tracts. These results are encouraging because they indicate that residents perhaps most in need of healthy food are often within close proximity to urban gardening activity. Unfortunately, an analysis of the spatial distribution of food deserts and urban gardens reveals that the distribution of urban gardens at the time of this analysis covered less than 10% of food desert residents, which highlights that an alternative distribution of urban gardening activity would improve access to these sources of fresh fruits and vegetables. Spatial optimization models are used to suggest alternative locations of urban gardens using vacant land. These model results suggest an alternative arrangement of 53 gardens that would provide coverage of 96.4% of the food desert population. That said, it is important to note some limitations of this analysis. First, there are additional considerations beyond the availability of land and lack of food access that will need to be investigated further in the proposed garden sites. One of these considerations is the quality of soil, which prior work has noted is a potential issue for urban gardening activity [77, 78]. Thus, it is recommended that the soil quality in the proposed sites be tested for contaminants before planting commences. A second consideration is the potential volume of food that could be produced at garden sites. Prior studies have noted that the food production capacity of urban gardens may be insufficient to provide food in the necessary quantities needed [51]. However, other studies have noted that coordinated planning efforts to foster urban gardening activity can produce a large proportion of local food needs [79]. To account for this concern, the gardens sited in this analysis ensure that at least 5000 ft2 are used for gardening activity. However, additional steps will need to be taken from a garden management perspective to ensure proper crop rotation and to ensure that the volume of fruits and vegetables grown is as such, that it may serve as a good supply of healthy foods for garden participants and the surrounding community. Third, once established, a concentrated and enduring effort to maintain urban gardens sites is needed to preserve these spaces. Gardens are a notoriously transient urban activity [49] and preservation plans are needed so as not to upend activity once it is commenced. This was the case with a large urban garden started as part of the Phoenix Renews project, which was shut down due to financial issues with the land on which the garden was placed [64]. Fourth, although citing gardens can reduce the physical distance to food, it may not reduce the temporal distance. Low-income people are more likely to be multiple job holders and may lack the time and also the knowledge to cook fresh vegetables. Finally, it is important to note that the mere provision of access to fresh fruits and vegetables is not enough to resolve dietary problems and the health issues stemming from poor diets. Studies of the built environment and health have uncovered a range of factors that influence obesity from land-use mix, crime, type of food outlets present, and urban design that is pedestrian oriented [80]. Thus, increasing access to urban gardens is just the first step to improving healthy food consumption for people. Access needs to be coupled with education efforts about the health value of fruits and vegetables grown in the gardens, as well as promotion of the gardens themselves to encourage participation by area residents. The pricing of any products sold should also be as such, that they are affordable to folks in a wide-variety of income strata. Recipes can also be provided that would educate purchasers of products about the preparation of fruits and vegetables to improve health outcomes. As rapid urbanization continues globally so too are issues of food access and vacant land likely to become more prevalent. To combat these related issues, more sophisticated planning strategies are needed to improve food access for residents. Although enhancing access is just the first step in improving healthy food consumption, urban gardens represent an inexpensive way to provide food to nearby residents. As demonstrated in this paper, spatial optimization models are an analytical tool that can be used to strategically locate these food sources on unused urban land, thereby mitigating two problems evident in rapidly expanding cities around the world. Note this definition of healthy food outlets is more comprehensive than that of the USDA, which bases its definition of food deserts on access to supermarkets [39]. Hotspots are defined as tracts corresponding to the high–high and high-low output of the local Moran. Census tracts are drawn to include roughly 4000 people [81]; thus, mapping a density measure or per capita number of food outlets in Fig. 1 would be redundant. ACGA: American Community Garden Association ACS: ANOVA: GIS: ESRI: Environmental Systems Research Institute MAG: Maricopa Association of Governments MCCE: Maricopa County Cooperative Extension NHGIS: National Historic Geographic Information System RUCA: Rural–Urban Commuting Area Bank W. 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Accessed 21 June 2017. Acheson D, Barker D. Independent inquiry into inequalities in health: report. 1998. http://journals.sagepub.com/doi/pdf/10.1177/14664240081280030701. Accessed 21 June 2017. Shaw HJ. Food deserts: towards the development of a classification. Geography. 2006;88:231–47. Whelan A, Wrigley N, Warm D, Cannings E. Life in a 'food desert'. Urban Stud. 2002. http://journals.sagepub.com/doi/abs/10.1080/0042098022000011371. Accessed 21 June 2017. EM collected and analyzed the garden and related secondary data for the neighborhood context analysis, and was a major contributor in the writing of the manuscript. DT conducted the spatial optimization analysis and wrote the related methods and results for this portion of the paper. KC helped compile and analyze the garden and related secondary data for the neighborhood context analysis, and was a contributor in the writing of the manuscript. EM, DT, and KC all contributed to revisions to the manuscript. All authors read and approved the final manuscript. Thank you to Matei Georgescu at the School of Geographical Sciences and Urban Planning, Arizona State University for support of this work. The garden data used in this analysis is included in this published article as a supplementary information file with the name Additional file 1. The proposed garden data generated during this study is included in this published article as a supplementary information file with the name Additional file 3. The food desert dataset analyzed for this study is available from the United States Department of Agriculture (USDA) Food Access Research Atlas: https://www.ers.usda.gov/data-products/food-access-research-atlas/download-the-data/. The demographic and socio-economic data analyzed for this study is available from the National Historic Geographic Information System (NHGIS): https://www.nhgis.org/. The land use data analyzed for this study is available upon request from the Maricopa Association of Governments (MAG): http://www.azmag.gov/Information_Services/default.asp. The Rural–Urban Commuting Area (RUCA) codes used in this study may be downloaded from the United States Department of Agriculture (USDA) Economic Research Service (ERS) at: https://www.ers.usda.gov/data-products/rural–urban-commuting-area-codes/. Work for this project was funded by National Science Foundation Grant No. 1419593 and USDA Grant No. 2015-67003-23508. Department of Geography, Environment and Spatial Sciences, Michigan State University, Geography Building, 673 Auditorium Rd, Room 202, East Lansing, MI, 48824, USA Elizabeth A. Mack & Kevin Credit School of Geographical Sciences and Urban Planning, Arizona State University, Tempe, AZ, 85281, USA Daoqin Tong Elizabeth A. Mack Kevin Credit Correspondence to Elizabeth A. Mack. 12942_2017_110_MOESM1_ESM.zip Additional file 1. Past and Present Phoenix Garden Locations. Point shapefile of the garden data used in this analysis. Additional file 2. Results of ANOVA tests for no garden, garden-adjacent, and garden-containing tracts. Three tables showing results of ANOVA analysis for each of the garden types and each of the variables of interest. Table includes the mean, standard deviation, and statistical significance for each variable/tract-type combination. Additional file 3. Proposed Phoenix garden locations. Point shapefile of garden data generated from the spatial optimization analysis. Mack, E.A., Tong, D. & Credit, K. Gardening in the desert: a spatial optimization approach to locating gardens in rapidly expanding urban environments. Int J Health Geogr 16, 37 (2017). https://doi.org/10.1186/s12942-017-0110-z Received: 26 June 2017 Spatial optimization Food access Food deserts Submission enquiries: mildred.antonio@springer.com	CommonCrawl
Symmetry in electricity and magnetism due to magnetic monopoles I was wondering about the differences between electricity and magnetism in the context of Maxwell's equations. When I thought over it, I came to the conclusion that the only difference between the two is that magnetic monopoles do not exist. Is this right? Next one. Now I searched for the equations with magnetic monopoles and found them at Wikipedia. They seem quite symmetrical (except the constants of course), except two major differences: It is $\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t} - \mu_0\mathbf{j}_{\mathrm m}$, but $\nabla \times \mathbf{B} = \mu_0 \epsilon_0 \frac{\partial \mathbf{E}} {\partial t} + \mu_0 \mathbf{j}_{\mathrm e}$. This means that the induced "magnetic emf" (if I may call it that) is produced by changing electric fields and currents in the exact opposite sense (I mean direction) to the counterpart phenomenon of Electromagnetic Induction. Why so?? Is there a lenz law for "magnetic emf" induction also?? Also, the lorentz force on magnetic charges $\mathbf {F}={}q_\mathrm m (\mathbf {B} - {\mathbf v} \times \frac {\mathbf {E}} {c^2})$. Why this minus sign in the force on magnetic charges that does not appear in the lorentz force on electric charges. electromagnetism classical-electrodynamics maxwell-equations magnetic-monopoles duality PhyEnthusiastPhyEnthusiast Both of these follow from desirable properties of this hypothetical magnetic charge, namely: Magnetic charge is conserved. Magnetic field lines radiate outwards from positive magnetic charges. The net force between two magnetic charges moving at constant speed along parallel tracks is less than that between two stationary charges. All three of these properties hold for electric charges. The last one may not be as familiar, but it basically works as follows: if we have a positive electric charge moving at constant velocity, it generates a magnetic field in addition to its electric field. A second positive electric charge moving parallel to the first one will therefore experience a magnetic force, and if you work out the directions, this force works out to be attractive. Thus, the net force between the two charges (electric and magnetic together) is less than the magnitude of the force they would exert on each other if they were at rest. [ASIDE: This can also be thought of in terms of the transformation properties of forces between different reference frames in special relativity, if you prefer to think of it that way.] Now, the conservation of electric charge can be written in terms of the continuity equation: $$ \vec{\nabla} \cdot \vec{j}_e + \frac{ \partial \rho_e}{\partial t} = 0 $$ Note that this can be derived from Ampère's Law and Gauss's Law ($\epsilon_0 \vec{\nabla} \cdot \vec{E} = \rho_e$), using the fact that the divergence of a curl is always zero: $$ 0 = \vec{\nabla} \cdot (\vec{\nabla} \times \vec{B}) = \mu_0 \vec{\nabla} \cdot \vec{j}_e + \mu_0 \frac{\partial ( \epsilon_0 \vec{\nabla} \cdot \vec{E})}{\partial t} = \mu_0 \left( \vec{\nabla} \cdot \vec{j}_e + \frac{\partial \rho_e}{\partial t} \right) $$ If we want to extend Maxwell's equations to magnetic charges, we need to have a magnetic version of Gauss's Law and add in a magnetic current term to Faraday's Law: $$ \vec{\nabla} \cdot \vec{B} = \alpha \rho_m \qquad \vec{\nabla} \times \vec{E} = \beta \vec{j}_m - \frac{\partial \vec{B}}{\partial t} , $$ where $\alpha$ and $\beta$ are arbitrary proportionality factors. But if we try to derive a continuity equation for magnetic charge from these two facts (as we did above for electric charge), we get $$ \beta \vec{\nabla} \cdot \vec{j}_m - \alpha \frac{\partial \rho_m}{\partial t} = 0, $$ and this is equivalent to the continuity equation if and only if $\alpha = - \beta$. Beyond this, the choice of $\alpha$ is to some degree arbitrary; different values correspond to different choices of which type of magnetic charge we call "positive", and what units we use to measure it. If we want to have magnetic field lines radiating away from "positive" magnetic charges, then we will want $\alpha > 0$; the usual choice in MKS units is to pick $\alpha = \mu_0$ (and $\beta = -\mu_0$), as you have in your equations above. This negative sign in the magnetic current term Faraday's Law then implies that the electric field lines created by a moving magnetic charge will obey a "left-hand rule" instead of a "right-hand rule". In other words, the direction of $\vec{E}$ created by a moving magnetic charge would be opposite the direction of $\vec{B}$ created by a moving electric charge. If we still want two magnetic charges moving along parallel tracks to exhibit a lesser force than what they feel when at rest, then we must also flip the sign of the $\vec{v} \times \vec{E}$ term in the Lorentz force law to compensate for this flip. Michael SeifertMichael Seifert You actually noticed something that is called electromagnetic duality. A duality correspond to two different theories which give the same physical results as long as we make specific mappings among their degrees of freedom. In the case of electromagnetism, what behaves as an electric field in one theory behaves as a combination of electric and magnetic fields in the dual one and vice-versa. Indeed you noticed just a particular duality transformation, namely, $\vec E$ and $\vec B$ in the original theory behave as $-\vec B$ and $\vec E$, respectively, in the dual theory. To see the general transformation we proceed as follows. The covariant formulation of Maxwell equations with sources, including magnetic monopoles, is $$\partial_\mu F^{\mu\nu}=j^\nu_e,\quad \partial_\mu \tilde F^{\mu\nu}=j^\nu_m,$$ where $F_{\mu\nu}$, $\tilde F_{\mu\nu}=\frac 12\epsilon_{\mu\nu\sigma\rho}F^{\sigma\rho}$, $j_e^\nu$ and $j_m^\nu$ are the electromagnetic tensor, the dual electromagnetic tensor, the electric four-current and the magnetic four-current, respectively. Those equations can be written in a single complex tensorial equation, $$\partial_\mu\mathcal F^{\mu\nu}=\mathcal J^\nu,\tag1$$ where $\mathcal F^{\mu\nu}=F^{\mu\nu}+i\tilde F^{\mu\nu}$ and $\mathcal J^\nu=j^\nu_e+ij^\nu_m$. Eq. $(1)$ is invariant under the whole group of transformations $$\mathcal F^{\mu\nu}\rightarrow e^{i\varphi}\mathcal F^{\mu\nu},\quad \mathcal J^\mu\rightarrow e^{i\varphi}\mathcal J^\mu,\tag2$$ where $e^{i\varphi}$ is a complex phase, which implies $$E_i+iB_i\rightarrow e^{i\varphi}(E_i+iB_i),$$ or $$ \begin{align} E_i&\rightarrow E_i\cos\varphi - B_i\sin\varphi ,\\ B_i&\rightarrow E_i\sin\varphi + B_i\cos\varphi , \end{align},$$ and similar relations for the currents. In particular, if we choose $\varphi=\pi/2$ then we get $$\vec E\rightarrow -\vec B,\quad \vec B\rightarrow \vec E.$$ Thus as long as the theory admits magnetic monopoles, there is a large freedom in what you call electric and magnetic fields. Note that in vacuum, this electromagnetic duality holds despite the existence or not of magnetic monopoles. DiracologyDiracology Is there a lenz law for "magnetic emf" induction also? A transformer is an electrical device that transfers electrical energy between two or more circuits through electromagnetic induction (Wikipedia). In detail a changing electric current induces a changing magnetic field (through the primary coil) which induces an electric current (in the secondary coil). For me the dependencies "changing electric field induces changing magnetic field induces changing electric field ..." is a modern interpretation of Lenz's law. And really that is what happens in a coil after one switch off the current: An attenuated current oscillates with changing sign until the energy stored in the coils magnetic field gets dissipated. But is the induced magnetic field a current. Somehow yes and somehow no. Yes because the magnetic field builds like a wave. The magnetic dipole moments of the involved electrons get aligned in a chain reaction, first in the coil and then in the transformers core and after in the secondary coil, which induces an electric current. So yes there is a flow of changing magnetic fields, but no there isn't a flow of particles. ...due to Magnetic Monopoles Is there a carrier for monopoles? Charged particles electron, proton and their antiparticles have the intrinsic properties of electric charge and magnetic dipole moment. In our surrounding (under our natural conditions) there are no other sources for this properties. Charges could be separated - for example by a potential difference - forming an electric dipole field. Charges could be aligned - for example by an external magnetic field - forming a magnetic dipole field. A magnetic dipole is of theoretical interest in high energy physics. So in short, there isn't a carrier for magnetic monopoles and this means that there aren't magnetic monopoles which we can use. One remark about the interchangeable interactions of magnetic and electric varying fields. In the near field of an antenna radiation the described by you induction processes really takes place: HolgerFiedlerHolgerFiedler Not the answer you're looking for? Browse other questions tagged electromagnetism classical-electrodynamics maxwell-equations magnetic-monopoles duality or ask your own question. EM duality transformation Maxwell equations and symmetry What would be the force constant for magnetic monopoles? Why aren't Faraday's law of induction and Maxwell-Ampere's law (without sources) symmetric? What's the Lagrangian of Electromagnetic field with magnetic and electronic charge? Is current density (J) in Ampere's law derivable? A question on the unification of electricity and magnetism What are the details behind causality and Maxwell's equations? Do the Maxwell equations definitively rule out the existence of magnetic monopoles? Maxwell theory : How to justify the potential gauge fields if there are magnetic monopoles? What is the formula for electromagnetic force on magnetic charge in condensed matter?	CommonCrawl
Search SpringerLink The value of winning: endorsement returns in individual sports Dirk F. Gerritsen1 & Saskia van Rheenen2 Marketing Letters volume 28, pages 371–384 (2017)Cite this article Using the results of 1068 different golf, tennis, and track and field (in particular: running) events, this paper examines the relation between athlete performance and stock returns of firms endorsed by athletes. We find that a tournament victory is associated with significant and positive market-adjusted stock returns for the endorsed clothing brand. Regression analysis reveals that winning is associated with a more positive price reaction than finishing as runner-up. In addition, we find that returns after a victory are significantly higher for endorsed clothing brands than for equipment brands. We did not detect return differences between superstars and regular athletes, nor between frequently endorsed brands and less commonly endorsed brands. In this paper, we study the relationship between athlete performance and the stock returns of firms endorsed by these athletes. Athlete endorsements constitute one form of celebrity endorsements (Agrawal and Kamakura 1995). Celebrity endorsement is "an agreement between an individual who enjoys public recognition (a celebrity) and an entity (e.g., a brand) to use the celebrity for the purpose of promoting the entity" (Bergkvist and Zhou, 2016: 3). Amis et al. (1999) argued that athlete endorsement is a valuable resource that can create a competitive advantage for the endorsed firm. Consequently, considerable amounts are invested in endorsements. Nike, for example, spends on average one tenth of its revenues on so-called demand creation costs (Stock 2014), which consist of advertising expenses and endorsement deals.Footnote 1 The effectiveness of endorsements is usually studied by using the endorsed firm's share price performance, both around the athlete's sign date and the athlete's performance. The rationale is that exposure through endorsements leads to increased brand associations. These can trigger sales, which in turn leads to a higher profitability and ditto firm value, which should be reflected in higher share prices shortly after the athlete performance. Evidence is mixed for stock returns in the trading days after an endorser is enlisted. While Agrawal and Kamakura (1995), Clark et al. (2005), and Elberse and Verleun (2012) found significant share price gains, Fizel et al. (2008) and Ding et al. (2011) did not find a statistically significant impact on share prices. Ding et al. (2011) attributed their findings to the shortfall of endorsement benefits as compared to their costs. In other words, a potential reason why the effect of the announcement of endorsement deals is not clear-cut, could be the fact that brand awareness and brand associations only increase after the signed athlete lives up to the expectations, e.g., wins events. The aspect of increased sales due to an athlete's performance is often stressed in the popular press. Kim (2014) reported on "big marketing victories for sponsors" following Kei Nishikori's wins during the US Open tennis tournament in 2014. While sales at the endorsed clothing brand Fast Retailing indeed increased, Nissin Food Holdings saw little immediate impact on its sales (Kim 2014). Elberse and Verleun (2012) were among the first to study the impact of endorsement on corporate sales directly. They found an increase in sales following an enlisted athlete's major achievement. More often, though, firm performance is studied by inspecting share price behavior surrounding victories. Nicolau (2011) studied the relationship between the performance of Real Madrid and the stock returns of the club's CEO's firm and found a significant impact of performance on returns. Farrell et al. (2000) focused on golf and analyzed the relationship between the performance of Tiger Woods and the stock returns of the firms he endorsed (i.e., Nike, American Express, and Fortune Brands). Farrell et al. (2000) found significant positive abnormal returns for Nike only, which was attributed to the visibility of the brand during golf tournaments. Nicolau and Santa-María (2013) focused on tennis. They studied the performance of Rafael Nadal alongside the stock returns of the endorsed firms. They found that victories by Rafael Nadal have significantly positive effects on the returns of the firms he endorsed. In addition, they found evidence for a diminishing sensitivity of returns to consecutive wins. To conclude, Elberse and Verleun (2012) analyzed the impact on stock returns of many different athletes winning major events. They concluded that the market value of the endorsed firms increased as a result of athletes winning an event. Although rigorously executed, previous research on the share price effects of victories by endorsing players could be biased due to a number of reasons. Farrell et al. (2000) and Nicolau and Santa-María (2013), for example, studied only one athlete in relation to the brands endorsed. Results of these studies can thus not per se be generalized. In addition, although Elberse and Verleun (2012) collected a large dataset and included many endorsed brands and events from many different sports, it remains unclear which factors determined their findings. Are they driven by a specific sports type (team versus individual) or a specific endorsement deal (clothing, equipment, or other)? Team sports events often take place during a league weekend, meaning many matches coincide. Attention for winning teams (and endorsed brands) is likely to be lower than for individual sports, for which there are usually just a couple of simultaneous events. Furthermore, highly visible brands (i.e., on clothing) may encounter different stock returns than less visible brands (e.g., Farrel et al. 2000). In response to these identified issues, we focused on popular individual sports, namely golf, tennis, and track and field (in particular: running).Footnote 2 These sports were selected as they employ high-paid athlete endorsers.Footnote 3 Rather than focusing on just top athletes, we gathered a unique dataset containing tennis, golf, and track and field tournaments during the period January 2001–July 2014, for which we hand-collected endorsed clothing and equipment brands for tournament winners and runners-up. For all endorsed firms, we studied the stock returns in the 5-day period after the end of a tournament. Using this methodology, we aimed to answer the following research questions: Is a tournament victory associated with positive stock returns for the endorsed clothing brand? Previous research indicated that there is a positive effect, but these studies considered just one athlete (e.g., Farrell et al. 2000; Nicolau and Santa-María 2013) or they grouped different categories of endorsed brands (Elberse and Verleun 2012). In addition, we investigate which factors drive stock returns of brands endorsed by winners. By making a distinction between superstars and non-superstars, and between frequently endorsed brands and non-frequently endorsed brands, we attempt to shed light on the generalizability of our findings. To what extent does a tournament victory affect the stock returns of endorsed equipment brands (i.e., brands of golf clubs and tennis rackets)? This question on a second endorsed brand is related to Farrell et al. (2000) and Nicolau and Santa-María (2013). However, they focused on just one player and on non-equipment endorsements. By using a large-scale event study, we contribute to this relatively untouched phenomenon. What is the effect on stock returns for brands endorsed by runners-up? Nicolau and Santa-María (2013) found for Rafael Nadal's sponsors that a loss did not have an effect on their share price, which they attributed to the fact that, although undesirable, losing is "part of the game" (Nicolau and Santa-María, 2013: 147). By studying a large sample of runners-up across different sports, we show whether "being in the tournament" for a long time conveys any positive brand effects. Hence, we contribute to the scarce evidence on how coming in second affects an endorsed firm's share price. This paper proceeds as follows. Section 2 describes the data and methodology. Our results are discussed in Sect. 3. Section 4 concludes this study. Events, players, and endorsed brands Our sample considered the time period January 2001 to July 2014. We focused on three different sports. First, we selected all tennis events from the Association of Tennis Professionals [ATP] tour (i.e., the male department of professional tennis) and we searched for both winners and runners-up of tournaments. Contrary to Nicolau and Santa-María (2013), we did not limit our research to Grand Slam tournaments, but we include ATP-500, ATP-1000, the Olympic Games, and the year-end World Tour Finals as well.Footnote 4 Second, we used the results of golf tournaments. As the PGA tour is characterized by the highest prize money and usually the better players, we focused on the events on this tour. Although there are usually no head-to-head finals at the end of a tournament (unless there is a playoff), players high on the leaderboard get more attention during play; hence, their endorsed brands are likely to get more exposure. We therefore collected both winners and runners-up for each PGA event. Third, we selected running events from major track and field events. To allow for diversity, we collected winners and runners-up from 100 and 10,000 m at the Olympic Games, World Championships (indoor and outdoor), and Diamond League meetings (previously known as Golden League). We hand-searched Web sources such as Getty Images for both clothing and equipment images. For golf, tennis, and track and field, we defined the endorsed clothing (equipment) brand as the clothing (equipment) brand the player is wearing (using) during the tournament. Note that we could collect equipment brands for golf and tennis only. We required that the endorsed firm, or its parent company, was stock market listed. In total, we could identify endorsed brands for 1068 events.Footnote 5 For all event winners, we additionally hand-collected their world ranking in the week prior to a tournament.Footnote 6 Table 1 describes the endorsed brands in our sample. In brackets, we displayed the number of observations we have for each subsample. For example, we have identified 236 cases where a tennis winner endorsed a stock market listed clothing brand. For brevity, we omitted (only in this table, not in our empirical analysis) the golf brands which occurred less than ten times. Among clothing brands, Nike and Adidas dominated the landscape across all three sports. In terms of equipment, Head and Wilson were most used in tennis, while Nike, TaylorMade, and Cleveland Golf provided the most widely used equipment for golf players. Table 1 Endorsed brands in our sample Share prices and returns We used Thomson Reuters Datastream to download share prices including reinvested dividends (i.e., total returns) for all endorsed firms. While companies as Nike and Adidas are publicly listed themselves, some other brands are part of a larger entity. For example, Uniqlo is part of Fast Retailing, Oakley is part of Luxottica, and Topper is owned by Alpargatas. In these instances, we used the share price of the parent company. In addition, we retrieved the index values (also on a so-called total return basis) for the main stock market index of the country on which the endorsed firm is listed (e.g., S&P 500 for US-listed stocks, FTSE 100 for UK-listed stocks, DAX 30 for German-listed stocks, etc.). In total, firms in our sample originated from 15 different countries. Lastly, we downloaded the 1-year risk-free rates availing in these countries. For each firm i and stock market M, we computed daily excess returns by comparing the price on day t with the price on the previous trading day t − 1, after which we subtracted the risk-free rate of return; see Eqs. 1 and 2, respectively. $$ {R}_{i, t}=\frac{P_{i, t}-{P}_{i, t-1}}{P_{i, t-1}}-{r}_{f, t} $$ $$ {R}_{M_i, t}=\frac{P_{M_i, t}-{P}_{M_i, t-1}}{P_{M_i, t-1}}-{r}_{f, t} $$ We computed two different types of abnormal returns (AR). First, we calculated the market-adjusted return (MAR) for each firm i and day t. We subtracted the excess return on the relevant market index from the firm's excess return, see Eq. 3. $$ { M AR}_{i, t}={R}_{i, t}-{R}_{M_i, t} $$ Second, we computed risk-adjusted returns (RAR) for which we applied the capital asset pricing model (Sharpe 1964; Lintner 1965; Black 1972) see Eq. 4. As estimation period for our alpha and beta coefficients, we used the period [−270, −10] prior to the event day, where the event day is seen as the first trading day following the tournament's final. To arrive at the risk-adjusted return, we subtracted the expected excess return from the observed excess return, see Eq. 5. $$ E\left({R}_{i, t}\right)={\alpha}_{i, t}+{\beta}_{i, t}{R}_{M, t} $$ $$ { R AR}_{i, t}={R}_{i, t}- E\left({R}_{i, t}\right) $$ For both our measures of abnormal return (e.g., market-adjusted return and risk-adjusted return), we computed cumulative returns for different event windows, see Eq. 6. Both the AR and the CAR were computed based on market-adjusted returns (MAR i , t and CMAR i , respectively), and on risk-adjusted returns (RAR i , t and CRAR i , respectively). $$ {CAR}_i=\sum_t^T{AR}_{i, t} $$ The cumulative market-adjusted return and the cumulative risk-adjusted return are summations of the respective daily returns over a time period of 2 to 5 days after the conclusion of a tournament. In our results, we refer to the simple-weighted averages of returns over the sample. The significance of ARs is computed by dividing the relevant return by its standard error (Brown and Warner 1985). Regression models Using regression analysis, we studied the determinants of the cumulative abnormal returns. We conducted a cross-sectional analysis in which we treated the cumulative 5-day abnormal return as the dependent variable. As we would like to test whether returns following a tournament win are different than those following a loss, we included "Winner" as our first independent variable. This variable is a dummy variable which is coded "1" in case the observation constitutes a tournament victory and "0" if not. In addition, we included dummy variables "Golf" and "Tennis" as control variables, given that we have included golf, tennis and track and field events in our dataset. As a result, we first estimated the following general OLS regression equation for each observation i: $$ {CAR}_i={\beta}_0+{\beta}_1{\mathrm{Winner}}_i+{\beta}_2{\mathrm{Golf}}_i+{\beta}_3{\mathrm{Tennis}}_i+{\varepsilon}_i $$ In a second model, we studied the returns for firms endorsed by winners in more detail. We make a distinction between returns for endorsed clothing brands and equipment brands. Compared to previous research (e.g., Farrell et al. 2000; Nicolau and Santa-María 2013), one of our contributions is the inclusion of non-superstars. We defined a superstar based on the world ranking in the week previous to the start of the tournament. For tennis and track and field, superstars comprise players who were ranked either first or second on the world ranking, while for golf superstars comprised top-10 ranked players. Although this method is relatively arbitrary, following it leads to roughly 30–40% of events being won by superstars across all sports. Superstars were captured by a dummy "Superstar" which is coded "1" if a player is categorized as a superstar, and "0" otherwise. Lastly, we considered a potential difference across endorsed firms. As Nike and Adidas dominate clothing endorsements (as is illustrated in Table 1), tournament victories for these brands might be more expected and may, hence, be associated with smaller stock market gains. As a result, we included an additional dummy variable "EndorsedMost" which is coded "1" for clothing firms if the endorsed firm is Nike or Adidas, and "1" for equipment firms if the endorsed firm equals Head or Wilson in tennis, or Nike, TaylorMade, or Cleveland Golf in golf. Other observations are coded "0" for this dummy. Consequently, we estimated the following general OLS regression equation, Eq. 8. $$ {CAR}_i={\beta}_0+{\beta}_1{\mathrm{Clothing}}_i+{\beta}_2{\mathrm{Golf}}_i+{\beta}_3{\mathrm{Tennis}}_i+{\beta}_4{\mathrm{EndorsedMost}}_i+{\beta}_5{\mathrm{Superstar}}_i+{\varepsilon}_i $$ In both regressions, we controlled for possible seasonal fixed effects by including year-dummies. In addition, all regressions were run with heteroskedasticity-consistent estimators of variance. Empirical results For ease of interpretation, we start by discussing the market-adjusted returns surrounding the end of a tournament. We consider both winners and runners-up, and both endorsed clothing and equipment brands. Figure 1 displays these returns in a cumulative fashion for the period ranging from five trading days prior to the conclusion of an event to five trading days after the conclusion of the event. No specific return pattern could be detected prior to the end of the tournament. Interestingly, the clothing brands endorsed by tournament winners outperformed the market as of day 0 (i.e., the first trading day after the conclusion of the event). Unreported statistics revealed that this pattern holds for all sports. The cumulative return after tennis, golf, and track and field equaled 0.33, 0.70, and 0.45%, respectively. The returns for the other categories were more opaque: although they all showed positive cumulative market-adjusted returns, these returns are of a considerably smaller magnitude. Cumulative market-adjusted returns surrounding the conclusion of a tournament. This figure illustrates the average cumulative market-adjusted returns for the endorsed firms during the event period (−5, 5) surrounding the date of a tournament's final. Endorsed clothing brands are collected for golf, tennis, and track and field (more specifically: running), while endorsed equipment brands concern golf and tennis only. "Clothing–Winner" and "Clothing–Runner-up" depict average returns for the endorsed clothing brands by winners and runners-up, respectively. "Equipment–Winner" and "Equipment–Runner-up" show returns for endorsed equipment brands by winners and runners-up, respectively Empirical analysis We start this section by discussing the results for clothing brands endorsed by winners, followed by a discussion of returns for clothing brands endorsed by runners-up, after which we turn to endorsed equipment brands for winners and runners-up, respectively. All results are given in Table 2. Table 2 Returns after conclusion of events Table 2 (A) depicts the returns for endorsed clothing brands by winners. Interestingly, the positive market-adjusted return on the trading day following the victory is followed by positive returns in the subsequent 4 days. Three of these individual days' returns exhibit statistical significance, and on top of that, they are statistically significant in a cumulative fashion, with a cumulative market-adjusted return (CMAR) of 0.53% after five trading days.Footnote 7 Although the risk-adjusted cumulative returns are positive as well, they lack statistical significance. It should be noted that the cumulative risk-adjusted return at t = 4 is positive and statistically significant at the 10% level. The findings—particularly those based on market-adjusted returns—support findings documented in previous literature. Table 2 (B) illustrates the average returns for clothing brands endorsed by runners-up. Despite some likely exposure for runners-up during the event, as well as some media coverage ex post, the endorsed firm's shares did not exhibit significant returns, neither on a market-adjusted basis nor on a risk-adjusted basis. These findings are in line with those of Nicolau and Santa-María (2013). Ngan et al. (2011) experimentally studied purchase intentions for endorsed brands for sports teams and found that winning (as opposed to losing) an event leads to the strongest purchase intentions. This effect can explain the different returns we found for winners and runners-up. Table 2 (C) considers the effects on the winners' endorsed equipment brands. The individual days' returns do not show a clear positive or negative pattern and this is reflected in non-significant cumulative returns, both on a market-adjusted basis and on a risk-adjusted basis. These findings loosely confirm the conclusions by Farrell et al. (2000) who used a case study approach of Tiger Woods' results. In their study, endorsed non-clothing brands did not experience statistically significant returns either. Apparently, through the eyes of stock market participants, non-clothing brands do not attract the awareness needed to significantly influence a firm's sales and earnings, due to which the share price remains relatively unaffected shortly after the event. It should be noted that we focus on equipment, while Farrell et al. (2000) focused on other non-clothing brands. Finally, Table 2 (D) shows the returns for the equipment brands endorsed by runners-up. Surprisingly, the cumulative returns are somewhat higher than for the endorsed firms by winners. However, these returns are not statistically significant, except for the 5-day cumulative market-adjusted returns which is, however, only significant at the 10% level. In general, we found evidence for positive cumulative returns for clothing brands endorsed by winners only. We explore the return differences between winners and runners-up, and between clothing and equipment brands more formally in the next section. Determinants of returns for endorsed brands So far, we established that winners' clothing sponsoring companies achieved significant and positive 5-day market-adjusted returns following a tournament victory. Since these 5-day returns were higher and more significant than both 1-day market-adjusted returns and 5-day risk-adjusted returns, we consider this estimate as measure for cumulative abnormal returns in our empirical analysis.Footnote 8 In this section, we use different regression models to quantify reported return differences between endorsements categories. First, we focused on determinants of stock returns of endorsed clothing brands. The sample consists of 1277 observations. Table 3 shows the regression results. We estimated four different models as to show the robustness of our findings to changes in explanatory variables. Table 3 Determinants of the 5-day CAR for endorsed clothing brands Model 1 shows that Winner positively affects the post-event CARs. Its coefficient equals 0.405, indicating that the CAR for brands is 0.405% higher when endorsed by winners instead of by runners-up. This finding is significant at the 10% level. Golf is positive and statistically significant as well, indicating higher post-event returns for golf clothing brands endorsed by either the winner or the runner-up. The model's F-statistic is significant, indicating that the coefficients are jointly unequal to zero. The R 2 is relatively low with a value 0.01. However, as our main focus is finding relationships rather than formulating predictions, we feel that the low R 2 is not an issue of concern.Footnote 9 The endorsed clothing firms originate from 10 different countries. To acknowledge potential differences between countries, model 2 includes country dummies in addition to the variables from model 1. Not only the economic significance of Winner increased (from 0.405 to 0.470) but also the statistical significance increased (from p < 0.10 to p < 0.05). Our results from models 1 and 2 might be partially driven by confounding effects during our event window. In model 3, we control for the announcement of earnings per share during either the event window or the preceding 5-day period to take into account the possibility of so-called post-earnings-announcement-drifts (see Kothari (2001) for an overview of the literature on this topic). This dummy variable EPS (coded "1" when earnings were published and "0" otherwise) is insignificant and does not qualitatively affect the coefficient of Winner. In an unreported test, we excluded all observations where EPS equaled 1. This did not alter our findings. In our last model, model 4, we ran a regression for US firms only rather than including country dummies, given the importance of US capital markets in general. As a result of this additional selection criterion, the number of observations dropped to 700. While the coefficient of Winner rises to 0.672, its t-value decreases to 1.96 which translates to a p value of 0.05.Footnote 10 We conclude from Table 3 that CARs for clothing brands endorsed by winners were significantly higher than for runners-up. This finding holds for a subsample of only US firms as well. We conducted a similar analysis for endorsed equipment firms (unreported). These tests did not reveal any statistically significant differences between brands endorsed by winners or runners-up. Now that we have established that a tournament victory leads to a different return than a defeat, we study the determinants of endorsement returns after an athlete's victory. Table 4 displays our results. Table 4 Determinants of 5-day CARs for firms endorsed by winners We estimated three different models. In model 1, we found that "Clothing" is statistically significant with a coefficient of 0.609, indicating that endorsed clothing firms experience a 0.609% higher CAR after a victory than endorsed equipment firms, after controlling for the sports type. Athlete achievements thus seem to have a higher impact on endorsed clothing brands than on equipment brands. A possible reason that brand awareness and associations could be higher for clothing brands is that these brands more prominently feature on television broadcasts as well as on official winner's photographs distributed after events. As a result, exposure for clothing brands is higher than for equipment brands. Model 2 additionally includes EndorsedMost and Superstar. Both variables have relatively low coefficients which are statistically insignificant. We conclude that we could not detect a dependence of the CAR on whether a superstar has won the tournament, or whether the player endorsed the Big-2 (in clothing for all sports, and tennis equipment) or the Big-3 (in golf equipment). Including these variables slightly increases the coefficient for Clothing. Finally, we estimated a model similar to model 1, but for US firms only. Model 3 shows that the number of observations drops to 618 as a result of this. While the magnitude of the coefficient of Clothing only slightly changes relative to our other models, the coefficient loses its statistical significance on the predefined levels for this subset.Footnote 11 A possible explanation for the reduced significance might be the large decrease of the sample size.Footnote 12 Concluding remarks For tennis, golf, and track and field (more specifically: running), players' performances were linked to stock returns of the firms they endorsed. We conclude that endorsed clothing brands exhibited statistically significant returns, as cumulative 5-day market-adjusted returns were positive after the enlisted athlete recorded a tournament victory. The fact that 5-day returns for the three different sports were individually positive as well, suggests the possibility for extrapolation of our results to other individual sports where athletes compete in multiple events throughout the year; however, future research in this area is needed. In contrast, we were unable to find significant returns for endorsed equipment brands after the end of a tournament. This discrepancy is possibly caused by a higher exposure to live coverage, press photographs, etc. for clothing brands relative to equipment brands. As such, brand associations seem to be strengthened for clothing brands only. For brands endorsed by runners-up, we failed to find evidence for significant abnormal returns. Hence, our findings can be attributed to a "winner-takes-all" effect (e.g., Ngan et al. 2011; Elberse and Verleun 2012). We could not find a return difference when an event was won by a superstar (such as Federer in tennis), or when the brand was commonly endorsed (such as Nike). Our results hold for a large dataset of events involving individual sports. With respect to future research, we encourage researchers to collect data for popular team sports as to conclude whether our findings can be generalized to team sports as well. As a further illustration, Nike pays Tiger Woods, Roger Federer, and Rafael Nadal on an annual basis about $20 million, $12 million, and $10 million, respectively (Totalsportek 2016). Although beyond the scope of our research, an interesting alternative approach would be to focus on team sports. We touch upon this issue in our concluding remarks. According to Opendorse (http://opendorse.com/blog/top-100-highest-paid-athlete-endorsers-of-2013/), the top ten of the highest-paid athlete endorsers consisted of three tennis players (Roger Federer, Rafael Nadal, and Maria Sharapova), two golf players (Tiger Woods and Phil Mickelson), and one track and field athlete (Usain Bolt). The remaining athletes in this top ten all played team sports. We exclude lower tier tournaments (ATP-250, Challengers and Futures), as they do not attract as much attention. This could be caused by many things, among which (i) the ATP website often lacks a television schedule for lower tiered tournaments, and (ii) there are often several of these lower tier tournaments in the same week. To prevent our runner-up sample from confounding effects, we only considered endorsed brands by runners-up in our analyses when the brand could not celebrate a victory at the same event. For tennis and golf, we relied on the official world rankings as published by ATP and PGA, respectively. For track and field, we consulted the rankings as published by All-Athletics (http://www.all-athletics.com) given the absence of official world rankings. All-Athletics rankings start in 2001. In addition, we considered the proportion of positive returns. On day 0, 51.7% of the market-adjusted returns were positive; 55.2% of the 5-day cumulative market-adjusted returns were greater than 0. This value is significant at the 1% level when judged by a Sign test. We stick to 5-day—simply put: weekly—market-adjusted returns in the main discussions of our results. In follow-up footnotes, we will devote attention to the robustness of our results with respect to (i) other event windows, and (ii) using cumulative risk-adjusted returns. Other studies on endorsements and abnormal returns also report relatively low levels of explained variance, see for example Farrell et al. (2000). Our results are robust to using an event window of 4 days. In fact, using a 4-day window would increase the statistical significance of "Winner." Shorter event windows are not associated with statistically significant results. With regard to cumulative risk-adjusted returns: "Winner" is significant at the 10% level in all models when applying a 5-day event window. Shortening the event window to 4 days increases the significance to the 5% level. CRARs for shorter windows are not statistically significant. Also for shorter event windows of up to 2 days, "Clothing" remains statistically significant at least the 5% level (significance even increases to the 1% level when using a 4-day event window). Based on cumulative risk-adjusted returns, "Clothing" is statistically significant at the 10% level for both 2- and 5-day event windows, at the 5% level for a 3-day event window, and at the 1% level for a 4-day event window. 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Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Gerritsen, D.F., van Rheenen, S. The value of winning: endorsement returns in individual sports. Mark Lett 28, 371–384 (2017). https://doi.org/10.1007/s11002-017-9422-9 Issue Date: September 2017 Celebrity endorsement Firm value Over 10 million scientific documents at your fingertips Switch Edition Academic Edition Not affiliated © 2022 Springer Nature Switzerland AG. Part of Springer Nature.	CommonCrawl
Mapping the complexity of political ideology using emergent networks: the Chilean case María P. Raveau ORCID: orcid.org/0000-0002-0769-28421,2, Juan P. Couyoumdjian2,3 & Claudio Fuentes-Bravo4 We propose a method to characterize political ideology using network theory. Our analysis is based on the 2015–2016 Chilean constituent process, where self-convened meetings were held throughout the country to discuss which Values, Rights, Duties, and Institutions should be included in the new constitution. Using this unique dataset, co-occurrence networks were constructed by considering the concepts selected in different meetings. The nodes are the concepts, and a link between two nodes represents the association between them. Political ideology is thus analyzed as an emergent network, and we can identify the main ideological communities in Chile and describe their characteristics. Beyond the local results, the proposed methodology enables representing the diversity of a community's political orientations in a realistic ecological context. The study of networks is increasingly influential in political science; topics of interest in the literature range from political participation, the study of electoral campaigns and the organization of public protests to the processes of political coalition formation, the relationships among Congressmen, and the cosponsorship of bills in Congress (for some general reviews in this area, see Brito et al. 2020; Faustino et al. 2019; Huckfeldt 2009; Siegel 2011; Ward et al. 2011). Nevertheless, these methods still offer new possibilities. In this paper, we are interested in the study of political ideology based on network analysis methodologies. While most network-based political analyses are based on survey data, where the nodes correspond to individuals or political parties, that is not the only way to examine these issues. The Chilean constituent process of 2015–2016 offers an extraordinary source of information for examining the political positioning of citizens in four dimensions: Values, Rights, Duties, and Institutions (MINSEGPRES 2018). This process had different levels of citizen participation, including an individual consultation and different levels of group participation. The first group stage consisted of self-convened local meetings (ELAs, for its Spanish acronym), and this is the level we will focus on here. Focusing on the concepts chosen by citizens/voters in each of the aforementioned dimensions, we can build a network based on the links between concepts, which allows us to detect specific communities and examine the centrality of some concepts and the associations between them. In this way, we can offer an illuminating overview of the structure of ideology in the country, where we view ideology as the mental models that allow agents to interpret the world around them; the preferences agents have over values, rights and duties clearly fit into this framework. Our work complements the literature on political ideology in Chile in two respects: from the point of view of the methodology used and in terms of the data considered. In the Chilean (and Latin American comparative) literature, we find different types of studies, mainly based on surveys or public opinion research. They include descriptive analyses focused on political parties (Alcántara and Rivas 2007; Colomer and Escatel 2005), studies with a focus on sociodemographic differences among voters (Maureira 2008), and works based on latent preference models (Bonilla and Silva 2008; Lindh et al. 2019).Footnote 1 These studies allow us to delve into different attributes of political ideology in Chile, but without exploring its fundamental organization and, when they do, impose a specific structure on the data. The method we propose does not impose such structure and instead lets the ideological communities emerge from the association of concepts. Given the complexity of the study of political ideology, the possibility of studying (and visualizing) an emergent network is an important result. Another advantage of the methodology we use is that our networks do not directly consider the popularity of the concepts but the relative frequency of co-occurrence between them. This enables the identification of underrepresented groups that are organized to participate. That said, the structure of the network will depend on the specific characteristics of the constituent process we consider. The way in which preference revelation processes are framed plays an important role in the result that emerges from them (see, for example, Riker 1982; Shepsle 2018). Regarding the data, although previous works on political ideology in Chile allow us to examine trends over time, they do not have the level of information available in the data collected from the constituent process, particularly in terms of the dimensions considered (MINSEGPRES 2018). At this point, it is important to recall the context of citizen participation in the Chilean constituent process—to gather material for drafting a new constitution—and the potential participation bias in this process, which has been examined by Raveau et al. (2020). The constituent process was marked by an important degree of ambiguity regarding the ultimate purpose of the work being carried out (Fuentes 2016), but to the extent that there were incentives for a truthful revelation of preferences, a network methodology allows us to identify the main ideological communities existing in Chile. Moreover, our analysis allows us to identify some groups that organized themselves to participate in this process, which is a topic that has been examined in previous studies (Fuentes 2016). Uncovering the "structural complexity" of political ideology is not a simple task, and it is important to make the analysis manageable. In this sense, we study the networks for Values, Rights, and Duties separately. Regarding the dimension of Institutions, political ideology is mixed with other factors, including citizens' knowledge of different public institutions; we have therefore decided to leave this issue aside. In any case, and before continuing, it is important to explain that this is not a work on political psychology, nor do we analyze the determinants of ideology. We leave the exploration of the psychological characteristics of the communities we identify as an open question for further research. Estimating ideology Inquiring into the structure of political ideology in Chile presupposes accepting that such ideology can be "structured" or that it presents a certain organization. The methods used in political science since the middle of the last century have sought to unveil this structure and thus far have done so either by assuming that there is a single predominant dimension (e.g., a left–right or liberal–conservative axis) or by suggesting a two-dimensional structure. The first known work to propose a two-dimensional system for political ideology is that of Eysenck (2018), in his 1954 book, The Psychology of Politics. In it, he seeks to extend the work by Adorno et al. (1950) on the factors behind fascism by proposing a two-dimensional structure for the existence of authoritarian and democratic systems on the right and left, respectively. In this way, social attitudes are organized along two axes, one in terms of left/right (radical/conservative) and the other of authoritarianism/democracy (tough-mindedness/tender-mindedness). Along the same lines as Eysenck, Rokeach (1973) proposed a model that explained the four major ideologies of the 20th century—socialism, communism, fascism, and capitalism—in the two dimensions of freedom and equality. Although the previous works may no longer be relevant today, it is important to note that they propose a system of two independent (orthogonal) dimensions based on an explanatory theory. After estimating these models, one can evaluate whether the dimensions found are independent and whether they explain the observed variability in ideology. Later, along with the emergence of the spatial theory of voting (Enelow and Hinich 1984), which is widely used in analytical political science, dimensional reduction methods appeared. These techniques seek to express the joint variability of multiple variables in a smaller number of unobserved variables. The best-known methods in this line include the work by Poole (1998) on the basic space method and the Cahoon–Hinich methodology (Cahoon et al. 1978). In the Cahoon–Hinich model, voter-candidate closeness is represented as a Euclidean distance between the ideal points of voters and candidates in a multidimensional space. This method assumes that the latent variables being searched are uncorrelated, which ultimately leads to the fact that the variance–covariance matrix of the utility can be decomposed using the singular value decomposition.Footnote 2 In contrast, Poole's basic space method directly analyzes any data matrix with missing values to estimate latent variables from observed variables. Although it is inspired by positive political theory, it is a technique that can be used in any setting, as long as the matrix contains real numbers.Footnote 3 In this sense, although both methods use the same type of data, they represent two different approaches to ideology estimation. On the other hand, even though both methods ensure orthogonal latent variables (unlike Eysenck and Rokeach), in the Cahoon–Hinich and Poole methods, the reduced variables do not have a direct meaning or interpretation; thus, these must be searched for later. Bonilla and Silva (2008) used the Cahoon–Hinich methodology with data from the 2003 Chilean presidential candidates. In this case, the first two dimensions explained 90% of the variance, where the first dimension corresponded to the left/right axis while the second was interpreted as the candidate's ability to change the status quo. In an analogous study of candidates in 2008, the first dimension explained 82% of the variance; the second dimension was unintelligible (Bonilla et al. 2011). Methods based on the spatial theory of voting also have been used for the ideological positioning of members of Congress through their votes in legislative projects ("roll call"). Perhaps the best-known work in this field is that of Poole and Rosenthal (1985), with the NOMINATE method (for nominal three-step estimation) and its subsequent variations D-NOMINATE, W-NOMINATE, and DW-NOMINATE. Other relevant works are those of Heckman and Snyder (1997), Clinton et al. (2004) and Londregan (1999). Even though they share a similar methodology, nominal voting models are not our main interest in this study, and therefore, we will not delve into this topic. The aforementioned methods have been the standard in multidimensional political ideology estimation, mainly because of their ability to explain much of the variance in a few dimensions. However, they impose strong requirements by requiring, by construction, the orthogonality of the latent variables. On the other hand, the evaluation of political figures may not adequately represent the diversity of political ideology at a given time, especially if such diversity is not sufficiently represented in Congress or in political actors. As we will see, the method we use in this study differs in several respects from previous methods for estimating ideology. We use the prioritization of concepts in the ELAs as an indicator of ideological positioning. Unlike factor analysis, we do not impose a restriction on the orthogonality of the dimensions but organize ideology into ideological communities that emerge from the concept association network. Like the factorial methods, these communities must be interpreted, but this is something we do directly from the texts accompanying the selected concepts. Additionally, using concepts instead of political actors allows for the greater diversity of ideas needed to map the political spectrum. In general, studies of political positioning and political psychology work under at least two problematic assumptions. The first is that of the perfection or transparency of the subjects' cognitive processes in the identification of their preferred alternative or even when answering a question in a given survey. In the tradition of bounded rationality, we find enough literature to question the operational assumptions with which many studies of political positioning work (Elster 1989; Gigerenzer and Selten 2002; Kahneman 2003; Simon 1990).Footnote 4 This limitation is inherent in any human exercise. However, extracting knowledge from statements in a realistic ecological context—such as spontaneous deliberative dialogues—avoids the framing effect, whereby the person's decision is affected by the way the question is asked or the options are presented. The second problematic assumption is whether the operational categories of political identification effectively represent what the subjects think of them. Studies that base political positioning on a right–left scale or on the evaluation of political figures work with a concept of political ideology that constitutes, in itself, a multiplicity of political attitudes related to democracy, social change, and trust in institutions, among other topics. In the ELAs, participants had a broad set of concepts to choose from, so we can expect less variation in the mental representations of these concepts. When working with a broad set of diverse and limited concepts, as in our case, there are more possibilities for combining these concepts, and this combination is what represents ideological positioning.Footnote 5 Furthermore, studies based on ideological scales may show a high level of centrist respondents (Visconti 2021). Context and data On October 13, 2015, the president of Chile, Michelle Bachelet, started a constituent process that incorporated public discussion on constitutional issues (MINSEGPRES 2018). The first stage of the process was the participatory stage, which took place between April 23 and August 6, 2016. In it, "citizens, social organizations, political movements and parties, academia, business and culture were invited to deliberate on constitutional issues" (Jordán et al. 2016). This stage considered four levels of participation: an individual online consultation and three instances of group participation (local, provincial, and regional). In this work, we have focused on the local group level, the self-convoked encounters (ELAs).Footnote 6 This methodological definition involves a trade-off between the quantity of data available and the information we have. While the number of ELAs is much lower than the number of participants in the individual consultations, in the case of the ELAs, the participants had to write down a short argument to explain their concept choices, which helped us interpret the meaning of certain concepts.Footnote 7 The self-convoked encounters (ELAs) were composed of between 10 and 30 citizens, Chileans or foreign residents, over the age of 14. The purpose of the ELAs was to deliberate on four dimensions: Values, Rights, Duties, and Institutions. To answer the questions that motivated the meetings, the organization of the ELAs prepared a reference list of constitutional concepts that was made available to each participant. This list was based on a comparative review of 16 international constitutions elaborated by the government. Individually, each participant had to choose the most relevant concepts for each of the four questions or propose other concepts. The discussion then began, and a record was made of the seven most mentioned concepts for each question. Finally, the group classified each of the seven concepts of the four questions into the categories of agreement, partial agreement, or disagreement, also adding a brief rationale text in each case (MINSEGPRES 2016). A total of 8113 ELAs were conducted throughout the country, with more than 100,000 participants. While there may have been a participation bias, this process was described as successful by the OECD (2017).Footnote 8 Here, we have, then, a valuable source of information on the dimensions of Chilean political ideology that has not been sufficiently explored (Raveau et al. 2020). Before continuing, let us note that the database we are working with was processed by Fuentes-Bravo and Martinez (2022). Among other things, these authors classified the new concepts that appeared in the encounters, which they called open concept arguments. Of the 22,015 such arguments, 10,263 were classified into one of the 114 original concepts, 3001 were considered "unclassifiable", and the remaining 8751 were grouped into 47 new concepts. Given our interest in the structure of the ideology itself, here we focus on only three of the four dimensions of the discussion: Values, Rights, and Duties. Let us note that there was a different list of concepts for each of the four dimensions, and that the selection of concepts was conducted on each dimension separately. Consistently, the corresponding datasets were analysed separately. Tables 1, 2 and 3, show the ELA instructions and the original list of concepts, together with the concepts added by the participants (after their classification), for each dimension. As seen, the proportion of new concepts is stable, although it grows as the number of original concepts is lower. In particular, there are 37 original concepts and 15 new ones in Values, 44 original concepts and 14 new ones in Rights, and 12 original concepts and 7 new ones in Duties. The low number of concepts proposed and classified in the dimension of Duties will limit in some ways the network analysis that we propose, and therefore the analysis regarding this point will necessarily be shorter. Table 1 What should be the main VALUES and PRINCIPLES that inspire and support the Constitution? Choose up to seven topics among the list below or suggest others Table 2 What should be the fundamental and universal RIGHTS contained in the Constitution? Choose up to seven topics among the list below or suggest others Table 3 What universal DUTIES and RESPONSIBILITIES should be established in the Constitution? Choose up to seven topics among the list below or suggest others As we previously explained, each ELA resulted in a set of 7 concepts (at most) for each dimension, with a short argument or rationale text (and an agreement category) associated with each concept. The dataset we used to build the networks consists only of the selected concepts, and the texts have been used only for interpretation purposes. Since the concepts were chosen from a larger pool, the process of selection in effect reflects a prioritization of values, rights or duties. Networks creation For each of the four dimensions, we represent the concept map using a co-occurrence network. Each concept is a node of the network, and the links between pairs of nodes symbolize the association between the respective concepts. This association is estimated by first calculating the coefficient $\phi$, a variation of Pearson's correlation coefficient for binary variables. This coefficient was designed to compare dichotomous distributions, which in this case respond to the choice or not of a concept in the ELAs. For example, for the pair of values Democracy and Justice, the $\phi$ coefficient is obtained from the following table (Read and Vidakovic 2006): Yes a b No c d where a, b, c, d are the frequencies of observation; that is, a is the number of ELAs that chose both concepts, b is the number of ELAs that chose Justice but not Democracy, and so on. Then, for a pair of concepts i and j, the $\phi _{ij}$ coefficient is calculated as: $$\begin{aligned} \phi _{ij} = \frac{ad-bc}{\sqrt{(a+b)(c+d)(a+c)(b+d)}} \end{aligned}$$ Once the $\phi _{ij}$ coefficient has been calculated, its significance can be tested with a $\chi ^2$ test: $$\begin{aligned} \chi _{ij}^2 = N \phi _{ij}^2 \end{aligned}$$ where $N=a+b+c+d$. Finally, the weight of the link between the nodes (concepts) is obtained by calculating the distance $d_{ij}=\sqrt{1-\phi _{ij}}$. If $\phi _{ij}$ is positive and significant at the 95% confidence level, a link between concepts i and j is constructed, with weight $1-d_{ij}$. The coefficient $\phi _{ij}$ is a metric that adjusts for the relative abundance of concepts. That is, two concepts may have been chosen infrequently, but if they were chosen together, they will present a high and significant coefficient $\phi _{ij}$. This is particularly important for us, as we do not seek to quantify the popularity of the concepts but rather the strength of the association between them. First, it is convenient to clarify that we will work with weighted networks, where each link takes a continuous value between 0 and 1, which represents the strength of the association between pairs of concepts. This association arises from the co-occurrence of concepts in the same ELA. On the other hand, they are undirected networks, that is, the association between a pair of concepts is not directional. Finally, for the following analyses, the giant component of the network will be used; that is, isolated nodes (concepts that have no link to any other concept) are excluded from the network. Distance and diameter Let us consider a pair of nodes, the shortest path between them is referred to as a geodesic. The length of a geodesic is called geodesic distance or simply distance. The diameter of the network is the maximum distance found between all possible pairs of nodes (Wasserman and Faust 1994); it quantifies how far apart the farthest nodes in the network are. In social networks, the interpretation of the distance between nodes and the network diameter is straightforward. For example, in a weightless communication network, the geodesic distance will represent the number of intermediaries a message has to go through to get from one actor in the network to another. In our network, the interpretation is not as straightforward. Each link represents the association between two concepts that arises from the co-occurrence of those concepts in the preferences of a group of people (the participants in the ELAs). Thus, nodes that are farther apart represent concepts that are less likely to be found in the set of people's preferences; at the extreme end, we have the diameter of the network, which would represent opposite ideological poles. In this work we analyse not the diameter's value itself, but rather the nodes that make up the shortest path between the farthest nodes in the network. Community detection A community (or cluster) is a group of nodes in which the probability of being connected to each other is greater than the probability of being connected to nodes outside the community. Community detection is a widely discussed problem in network theory, and there are no universal definitions of what constitutes a community or when one method is better than another (Fortunato and Hric 2016). One of the most popular techniques for community detection is based on the concept of modularity. This metric was designed to quantify the strength of the division of a network into modules and measures the density of links within the community with respect to the links between communities. Thus, algorithms based on this concept seek to maximize the modularity of the partition. Among these, one of the most widely used is Louvain's method, named after the university where it was developed. Louvain's method consists of a hierarchical algorithm in which each node is initially its own community. At each iteration, each node moves to the community where it contributes most to the modularity of the partition. This process is repeated until the modularity no longer increases, and then the first phase ends (Blondel et al. 2008). In the second phase, a new network is constructed in which the nodes are the communities found during this phase, and the links are calculated by summing the link weights of the nodes of the corresponding community. Then, the first phase is applied to this new network, and the process continues until maximum modularity is reached. As a robustness check, we compared our results using the Louvain algorithm with other standard methods, such as Fast Greedy and Leading Eigenvector (Clauset et al. 2004; Newman 2006). Centrality measures Centrality measures in networks were originally intended to study how small groups communicate and organize themselves to solve problems. Many centrality measures have been proposed, but among the most common ones are (Freeman 1978): (1) node i's degree centrality (degree) is the number of nodes that are in direct contact with i; (2) the betweenness centrality of node i represents the frequency with which node i is on the shortest path between pairs of nodes; (3) the closeness centrality of node i measures the number of steps required (i.e., the number of nodes to go through) to go from i to any other node in the network. These centrality measures were used in their igraph implementation for R (Csardi and Nepusz 2006). The specific algorithms for each metric also can be found at https://igraph.org/r/. These measures of centrality provide different information, and it is convenient to review their interpretation in the context of our concept networks. In this case, the degree tells how connected or associated a concept is with the other concepts in the network. Thus, a concept will have a high degree if it was frequently chosen together with other concepts, that is, it has links to many other concepts. On the other hand, the centrality of intermediation shows how key concepts connect different communities within the network. Next, a concept will have high betweenness centrality if it was frequently chosen by one ideological group as well as by another. Finally, closeness centrality tells us how central a given concept is within the network. A particularly interesting result that emerges from our analysis concerns the distinct ideological clusters within the networks. To reiterate, these clusters represent communities of concepts in the sense that they significantly co-occur across the ELAs. Starting with the dimension of Rights, an issue of great popularity in Chile today, Table 4 shows the three clusters identified by the Louvain algorithm. In Cluster D, we see first-generation rights, that is, negative rights that emphasize political and civil liberties.Footnote 9 Among them, we find the right to Life and Security/nonviolence, Equality before the law, the Right of association, the right to Suffrage/vote, and the freedoms of movement, expression, worship, work, education, entrepreneurship, conscience, and personal liberty. Therefore, we associate Cluster D with a right-wing ideology. In Cluster C, we have mainly second-generation rights, which are positive rights that promote equality and advocate the state's active participation to this end. Here, we find social and economic rights, such as the right to Education, Health care, Decent housing, and Social security. Additionally, but to a lesser extent, we find some third-generation rights, such as the rights of Indigenous people. This is why we associate Cluster C with the traditional left. Finally, in Cluster A, we find second-generation rights, such as Social rights, Equality, Standard of living, and Right to quality public health care, but also most of the third-generation rights, such as Conservation of cultural and historical heritage, Environmental respect/protection, and Animal rights. For this reason, we associate Cluster A with an orientation that is also left-wing but progressive. These labels—i.e. the political interpretation of the clusters, were proposed and discussed by the authors, by looking at the concepts within each cluster. Table 4 Communities by dimension First-generation rights have been catalogued as negative and individual, while second-generation rights also are individual but positive, and third-generation rights are collective and positive (Vasak 1977). In this framework, we see that the difference between Clusters D and C is given in the negative/positive nature of rights, that is, in the action of the state. While Cluster D emphasizes freedom and the role of the state in ensuring noninterference in the use of these freedoms, Cluster C demands that the state play an active role as the guarantor of social rights. On the other hand, the difference between Clusters A and C does not have to do with the role of the state, as both are inclined to positive rights but with the individual/collective character. This classification is consistent with what we see in the dimension of Values, where we also can identify the same Clusters A, C, and D. The concepts that allow us to classify Cluster D as right-wing have to do with the importance assigned to Autonomy/freedom, Private property, Rule of law, Development, Subsidiarity, Sovereignty, Family, Patriotism, Solidarity, and Dignity. Regarding Cluster A, the concepts of Freedom, Participation, Cultural identity, Gender equity, Environmental protection, Participatory democracy, Equity, and Human rights allow us to identify it as a progressive cluster. Finally, in Cluster C, we see the leftist concepts that relate to the ideas of Tolerance, Justice, and Equality. The distinction between Clusters A and C also can be related to their age differences. According to Inglehart and Abramson (1994), societies shift from materialistic concerns—such as physical and economic security—to postmaterialistic values—such as freedom of expression and standard of living—once the material needs are taken care of. To test this idea, we performed mean difference tests to compare the average age of/in different clusters. For both Values and Rights, Cluster A is younger than Cluster C (age difference = 6.5 years), which in turn is younger than Cluster D (age difference = 8.03 years).Footnote 10 Cluster B, which appears only in the Values dimension, is a special case. Let us note that the concepts within this cluster promote a very clear vision of society: the idea of Heterosexual marriage families is eloquent in this sense. Since these concepts are mostly added by participants and with almost identical text across different ELAs, this suggests a special level of organization. The references to Freedom of worship and Freedom of conscience are consistent with anecdotal evidence about the organization of the evangelical protestant community's participation in the constituent process; thus, we have identified this cluster as "evangelical".Footnote 11 The fact that this cluster appears only in the Values dimension suggests that its selection of concepts does not differ much from those of other clusters in the other dimensions. For example, in the dimension of Rights, in Cluster D (political right), we find a blend of concepts that could be called "conservative" (such as Life and Respecting life from conception) with others of a nationalist nature (Nationality) and those of a "liberal" type (those that promote individual liberty, such as Freedom of work, Property, and Free economic initiative/free enterprise). Therefore, we can assume that when Cluster B is not differentiated, it is Cluster D that absorbs its share. In the dimension of Duties, the network does not show the same disposition as in Values and Rights, perhaps because, as there were fewer concepts to choose from, each concept had a greater probability of being chosen by different people. Nevertheless, we can identify a progressive Cluster A and a cluster that seems to be right-wing (D). The remaining cluster (called N in Table 4) does not have a clear sociopolitical interpretation.Footnote 12 As community detection is a key part of this analysis, we compared the Louvain partition with other clustering methods as a robustness check. The purpose of this analysis is to test the stability of the partitions, i.e., modularity variations, how many cluster resulted and how many nodes changed membership community. For the Value network, the Fast Greedy algorithm yields the same clusters (and modularity) as Louvain. However, with Leading Eigenvector, modularity falls (from 0.56 with Louvain to 0.48), and some nodes change community membership. Compared to the Louvain partition, the concepts Private property and Integral development move from Cluster D to Cluster B, while Freedom moves from Cluster A to Cluster D and Citizenship moves from B to C. An additional small cluster appears, which contains Democracy, Equity and Secular state. In addition, Cluster A—the progressive cluster—splits into two clusters, plus an additional cluster with only one element (Social security). The presence of small clusters and the lower modularity make the Leading Eigenvector a less desirable option. Even so, the main clusters preserve their meaning. Regarding the Rights network, the three algorithms—Louvain, Fast Greedy and Leading Eigenvector—tie in modularity (0.44), identify three clusters, and overall, five nodes change community membership. With Fast Greedy, and compared to Louvain, Access to culture and Environmental respect/protection move from Cluster A to Cluster C, while Equality in relation to public burdens and Access to justice/due process move from Cluster D to Cluster A. Also compared to Louvain, the Leading Eigenvector algorithm makes Access to culture move from Cluster A to Cluster C, and Suffrage/vote move from D to C. Finally, we tested the Duties networks, where Louvain reaches the highest modularity (0.43). With Leading Eigenvector (modularity 0.39), three nodes change community membership: Fulfill public charges (from N to A), Responsibility (from D to N) and Community service (from A to D). With Fast Greedy (modularity 0.42), Cluster N remains the same, while Clusters A and D are combined in a large cluster, leaving three nodes apart (Protection of private property, Responsibility, Community service). But, as we said, communities in the Duties network are not so well defined because of the smaller pool of concepts. Overall, the Louvain algorithm reaches the highest modularity, and the changes in community membership do not significantly alter our main interpretations and conclusions. Throughout this work, we have used a 95% confidence level for link creation. At the 99% level, the communities remain the same for the Duties network, and only one node changes community membership in the Rights network. The largest change is shown in the Values network, where the progressive cluster splits into two groups, one with original concepts and the other composed almost exclusively of open concepts. However, both subgraphs consist of progressive concepts. On the other hand, another community appears, formed by Citizenship, Civic friendship and Integration, the first two previously belonging to the evangelical clusters and on the network periphery. Even when both concepts are now in a different cluster, they are still connected to conservative concepts such as Freedom of worship and Patriotism. Overall, cluster splitting is to be expected, given the fewer number of links in the network. One way to study the "ideological" closeness between communities is through the intercluster distance, which we estimate by calculating the average geodesic distance between all pairs of nodes belonging to two different clusters. Doing this for Values, we find that Cluster B (evangelical) is closest to D (right), then to C (left), and then to A (progressive). This result is quite intuitive. However, the shortest intercluster distance is between Clusters C and D. This indicates that for the Values dimension, the traditional left is ideologically closer to the political right than to the progressive left.Footnote 13 While this may seem counterintuitive, we see that for the Rights network, this relationship is reversed, and Cluster C is closer to Cluster A than to Cluster D. All of the above indicates that the traditional left's closeness to the political right is mediated by values and to the progressive left by rights. One explanation for this is that most of the traditional left and right tend to be conservative in this dimension. However, in regard to rights, the political right promotes freedom, while the left and progressivism share the vision regarding the positive role of the state as the guarantor of social rights. To assess the consistency between clusters and political conglomerates, we tested the cluster distribution between certain municipalities and the rest of the country. To narrow down the task, we focused on the Metropolitan Region, the one with the highest population in Chile. For Cluster A, we chose the top 3 municipalities where participation in the progressive Frente Amplio coalition 2017 primary election was maximum. These municipalities belong to District 10, and they are Providencia, Ñuñoa and La Reina.Footnote 14 Thus, we compared the number of observations belonging to Clusters A, C and D within these three municipalities and in the rest of the region. For both Values and Rights, the two distributions were significantly different at a significance level of 0.001. The proportion of observations in Cluster A increased from 0.40 to 0.49 for Values and from 0.20 to 0.28 for Rights. For Cluster D, we followed the same procedure and chose the top 3 municipalities where participation in the right-wing Chile Vamos coalition 2017 primary election was the highest. These municipalities belong to District 11, and they are Vitacura, Las Condes and Lo Barnechea.Footnote 15 Again, we compared the cluster distribution among these three municipalities and the rest of the region, and they were significantly different, at a significance level of 0.001, for Values and Rights. The proportion of observations in Cluster A increased from 0.22 to 0.31 for Values and from 0.26 to 0.49 for Rights. There were no presidential primaries of the traditional left-wing conglomerate for the 2017 presidential election. Therefore, to test Cluster C, we used the first-round results. Since District 13 has traditionally supported left-wing candidates, we chose the top 3 municipalities where the voting difference between the Nueva Mayoría (traditional left-wing coalition) and Frente Amplio was maximum: El Bosque, Pedro Aguirre Cerda and San Ramón.Footnote 16 The cluster distributions among these three municipalities and the rest of the region were significantly different at a significance level of 0.001. The proportion of observations in Cluster C increased from 0.34 to 0.42 for Values and from 0.49 to 0.60 for Rights. Here we show the results of our network analysis for each dimension: Values, Rights and Duties. The graphs are depicted in Figs. 1, 2 and 3. Network descriptors can be found in Table 5. Co-occurrence network for Values. The node size is proportional to the node degree. Nodes with empty circles and dashed line links are part of the network diameter: Civic friendship, Citizenship, Patriotism, Republic, Secular state, Gender equity, Cultural identity. Cluster A: progressive left; Cluster B: evangelical community; Cluster C: traditional left; Cluster D: right-wing Co-occurrence network for Rights. The node size is proportional to the node degree. Nodes with empty circles and dashed line links are part of the network diameter: Human rights, Freedom, Life, Peaceful assembly. Cluster A: progressive left; Cluster C: traditional left; Cluster D: right-wing Co-occurrence network for Duties. The node size is proportional to the node degree. Nodes with empty circles and dashed line links are part of the network diameter: Citizen participation, National unity, Lawful exercise of rights, Protection and conservation of cultural and historical heritage, Community service. Cluster A: progressive left; Cluster N: No sociopolitical interpretation; Cluster D: right-wing Table 5 Network descriptors Values Starting at the top left of the network (Figure 1), we can see one extreme of the diameter made up of the progressive concepts Cultural identity and Gender equity. Then, we see Secular state and Republic, both referring to the separation of powers, with the former serving as a link between progressive concepts and more centrist concepts that are less ideologically charged. We then move on to Patriotism, with a nationalist slant, to finish with Citizenship and Civic friendship. In the previous section, both concepts were identified as part of the evangelical cluster. In the case of Civic friendship, this concept absorbed many of the concepts added by the participants during the ELAs, work that was done by the data systematization team. On the other hand, it is interesting to note that Citizenship is connected both to Patriotism—by virtue of belonging to a nation—and to Integration, alluding to the integration of Chileans, migrants, and native peoples. In sum, we have progressivism on one side of the diameter and concepts that fall into the evangelical community on the other side. If we visually divide the network based on this axis, on one hand, we have the political right, where the concepts of an economic nature are farther away on the network, and on the other hand, we have the left, where concepts such as Social security and Social justice also tend to lie on the network periphery. Regarding the network's centrality measures, the three concepts with the highest betweenness centrality are Secular state, Freedom, and Family (see the second panel of Table 5). As we already have noted, the first serves as a link between progressivism and what can be labeled the political center. On the other hand, Family is connected to several concepts within the right-wing cluster (that is why it has high degree centrality) and serves as a link with the evangelical cluster through its connection with Freedom of worship and Freedom of conscience. Finally, Freedom does not exhibit a great degree centrality, but it does show a high betweenness centrality, since it connects diverse lines of thought. Thus, while progressives think about the freedom to decide about their own body, the right is thinking about the freedom to undertake and personal autonomy. The fact that Freedom does not have such high degree centrality may be because there are other concepts that are more specific with respect to freedom, such as Freedom of expression, Freedom of worship, and Free entrepreneurship, which "compete" when they are used. Since values are deeply embedded in culture, we would expect a stronger effect of participant age on concept selection in this dimension. The concept associated with the oldest average age is Sovereign (46.2 years), followed by Solidarity and Rule of law, all three from Cluster D, the right-wing cluster. As we would expect, the "youngest" concepts belong to Cluster A, the progressive cluster, with Equity as the concept with the youngest average age. Finally, within Cluster A, Human rights (43 years) and Social security (42.5 years) are the "oldest" concepts, suggesting that there is an older segment within progressivism that adheres to the discourse of the traditional left. Rights Fig. 2 shows the concepts within the network's diameter. These are: Human rights, which is embedded in the progressive cluster; then comes Freedom, which, as we saw earlier, refers to various objects of freedom and is in turn connected to Life. This concept plays the role that Family played in the Values network; that is, it has great centrality in the network, particularly among the right-wing and evangelical concepts. It precisely makes the link with the other end of the diameter, which is Peaceful assembly. This concept is strongly connected to other evangelical nodes, such as Freedom of worship, Freedom of conscience, and Respect life from conception, and it was probably added by the evangelical group thinking about congregating freely in public spaces, as seen in this phrase: "there should be the right to gather in public places, Plaza de Armas, without previous authorization for preaching, authorized artistic-musical activities". As happened in the Values dimension, the diameter of the network shows a progressive-religious axis, while the traditional right and left move away in other and opposite directions. Thus, on one side of the axis diameter, we have the Right to strike, Health care, and Decent housing, and on the other side, we have Property and Freedom to work. Continuing with the centrality measures (Table 5), the three most central nodes are Social rights, Education, and Life. The first two far surpass the third in betweenness centrality, which suggests that the provision of education and social rights are more widely held among the participants; not so for the right to Life, which has high degree centrality because it is very present in the right and evangelicals but lower betweenness centrality because it is not as connected with the concepts of the other groups. Regarding Social rights, note that this concept was not in the original set of rights that the ELA organization proposed, so it is likely that different things were grouped under the label of "social rights". If we look at the texts, we see many phrases that refer to constitutional guarantees already established in the current constitution, such as the right to vote, organize, and be elected to public office, and other phrases that postulate that article 19 should not be altered,Footnote 17 thus keeping the provision of rights constant. Other phrases seek to expand the current provision of rights, such as the right to housing and transportation. It is also worth noting that Human rights is deeply embodied in the progressive cluster, although in Chile this concept has usually been associated with the traditional left. There are two factors that may explain this. The first is that Human rights was not in the original set proposed for this dimension, probably because it was not a specific constitutional guarantee. Therefore, it was a concept added by the participants, and in general, these do not appear in the traditional left's cluster. It should be noted, however, that Human rights did appear in the original list of Duties, as the duty of Protection, promotion and respect of human and fundamental rights. On the other hand, if we look at the age ranges associated with each concept in the progressive cluster, we see that Human rights is one of the least chosen by young people. This suggests that within progressivism, there could be an older age group, perhaps serving as a bridge between progressivism and the traditional left. Duties As previously mentioned, the initial set of proposed concepts here is smaller; there are only 12, which become 19 after the open concepts systematization. As seen in the second panel of Table 5, in general, these concepts have low centralities. Regarding the diameter of the network (see Fig. 3), we have the concepts Citizen participation, National unity, Lawful exercise of rights, Protection and conservation of cultural and historical heritage, and Community service. The first of these, Citizen participation, is far from other progressive concepts. Continuing with the diameter, we then have National unity, a nationalist concept, and Lawful exercise of rights to finally arrive at progressive concepts such as Protection and conservation of cultural and historical heritage and Community service, which, although not exclusively progressive, is connected to the progressive triad of Conservation and natural-protection duties, Protection, promotion and respect of human and fundamental rights, and Protection and conservation of cultural and historical heritage. The progressive religious axis is not seen in this network. To test the robustness of our method, a null model was created by assuming a random selection of concepts. We use the final set of concepts by dimension, i.e., the original concepts plus those added by the participants. Then, for each ELA, we simulated a random selection of the same number of concepts they originally chose and applied the aforesaid network creation procedure. Over 100 randomized networks, the average number of links was 0.33 for Values, 1.01 for Rights and 0 for Duties. At the 90% confidence level for the chi-square test, these figures increase up to 0.65 for Values, 1.62 for Rights and 0 for Duties. This result shows that a random selection of concepts does not generate a meaningful network. This study has shown how political ideology can be analyzed as an emergent network. This way of examining ideology is a relevant methodological contribution that, applied to Chilean data, enlightens us about the characteristics of different ideological communities. Beyond the theoretical advantages that the network methodology offers, its performance does depend on the initial pool of concepts considered. Given a sufficiently broad set of concepts and a process of concept selection, the resulting network should adequately map the ideology of a group of participants. Our network methodology has allowed us to capture the differences between the traditional left and the progressive left in Chile, both for Values and Rights. Within the right-wing cluster, even when the networks contain liberal, nationalist and conservative concepts, they do not seem to form separate clusters, besides the organized evangelical one in the network for Values. On the other hand, although our analysis of the network of Duties is less conclusive, we believe that it is important to consider this dimension to offer a more complete picture of political ideology. Regarding the community detection, the Louvain algorithm consistently reached the highest modularity score. In general, the partitions remain stable, although some nodes change community membership. These changes do not significantly alter our main interpretations and conclusions. Our political maps also have showed that it is possible to recognize the evolution of the concept of rights in Chile. Along with the intercluster distances, the emergence of new rights allows us to be more specific to the right/left distinction. Thus, Clusters A and C (progressive and traditional left, respectively) are the closest in the Rights dimension and prioritize the selection of second-generation rights, i.e., they advocate for an active role of state. However, in Values, the traditional left is closer to the right than to the progressive left. This may be linked to what the first and second generations of rights have in common: their individual nature. In addition, the right-wing cluster and the traditional left-wing cluster are older than the progressive cluster. The evolution of political ideology has a generational component, examined by Putnam (2000), which may be interesting to explore further in the Chilean context. Leaving aside the communities, through the network diameter, we have identified a progressive/right-wing pole in the ideology map. The network visualization also displays the economic aspects of ideology in a different direction. These directions are not "axes", strictly speaking, because they are not orthogonal, nor do they represent coordinates. However, since the network visualizationFootnote 18 is designed to avoid crossing edges and make edge lengths uniform, the "directions" displayed in the resulting graph still hold their meaning. On the other hand, centrality measures can inform us about the relative importance of certain nodes. In this way, we have identified concepts that link different groups, such as Secular state, which is highly connected to progressive concepts but also to Republic and Democracy. Concepts with high closeness and a high degree—such as the right to Education—can be understood as widely held concerns in contemporary Chile because they are closer to all other nodes and frequently mentioned. The results we have presented, based on data prior to the social outburst of October 2019, show results consistent with the characteristics of different emerging groups in Chile and their priorities and "agendas" in terms of Values, Rights, and Duties. Since 2016, new conservative voices have arisen, and we also have seen the consolidation of new progressive movements in the country. The dataset supporting the conclusions of this article is available at http://constitucionabierta.cl/ or https://datos.gob.cl/dataset/proceso-constituyente-abierto-a-la-ciudadania. Studies based on political manifestos and programs, such as those of Gamboa et al. (2013) and Madariaga and Kaltwasser Rovira (2020), are somewhat different but also could be relevant here. For elaborations of this model, see Hinich and Munger (1996). In its political application, this method assumes that people have a set of beliefs that explain their political opinions and that respondents evaluate a political actor/issue based on how close they feel to them. Thus, a respondent's evaluation of a political actor/issue is a linear combination of their ideology and stochastic error. We can point out the following cognitive principles (Rosati 2000): (1) mental representations organized in a cognitive structure of beliefs, (2) selective memory focused on the big picture and not on details, (3) selective attention and perception, (4) causal inferences based on one's beliefs, and (5) cognitive stability or having a stable set of beliefs over time, once formed. An example of how this can affect political positioning is the "projection hypothesis". According to this hypothesis, when an individual is exposed to new information about a candidate, selective attention leads the person to pay attention to those aspects that reinforce their favorite view of the candidate. Another way of approaching this issue is with the distinction between the "symbolic" and "operational" aspects of political ideology (Jost et al. 2009). In this terminology, self-identification on a right–left scale is part of the symbolic aspect, since "right" and "left" are abstract and general categories. The operational aspect refers to more specific and concrete issues. Evidence suggests that the two forms of ideology do not always coincide (Stimson 2015). The data are publicly available and can be found at http://constitucionabierta.cl/. From a preference aggregation perspective, the individual consultation dataset should yield more consistent results. However, given the self-convoked nature of the encounters, it is to be expected that these groups (the ELAs) were relatively homogeneous, which makes the structure of the network emerge as we see it. However, it has been criticized for its limited impact in the country; see, for example, Heiss (2018). We owe the classification of rights into three generations to Vasak (1977). Although the first- and second-generation rights are included in the Declaration of Human Rights of 1948, it is in the International Covenant on Civil and Political Rights (ICCPR) and the International Covenant on Economic, Social and Cultural Rights (ICESCR) of the United Nations (1996) where they are instantiated (Domaradzki et al. 2019). The main difference between these two types of rights deals with the action of the state. In first-generation rights, the state "undertakes to respect and to ensure" those rights, while in second-generation rights, it "undertakes to take steps ... to the maximum of its available resources" to achieve them. Finally, third-generation rights are more recent and have been called collective (Domaradzki et al. 2019) or solidarity rights (Vasak 1977). They are mentioned in the declarations of Stockholm (1972) and Rio (1992) at the United Nations General Assembly. They include the (positive) rights to self-determination, development, a clean environment, and participation in cultural heritage. The average cluster age was estimated by selecting all concepts belonging to the cluster, identifying the ELAs that select those concepts, and taking the average age of their participants. These differences are significant at a 0.01 significance level. As noted, this may not have been the only group that organized to participate in the constituent process. During that time, there were several groups—political, economic, and social—that declared an interest in organizing to confront this process. The idea was, presumably, to put on the agenda issues that otherwise would have been absent. However, since the work of Olson (1965), we know that the existence of benefits associated with organizing collectively are not a sufficient reason to explain a capacity to organize. In the case of evangelical churches, that capacity to organize can be explained in the already existing organization at the local level, in each church with its pastor, and in the churches among themselves. Here, the motivation to organize seems to respond to a need to establish protection of life from conception and of the family as fundamental values of society. This cluster is composed almost exclusively of open concepts, except for Satisfying public burdens, which serves as a link to the progressive cluster. 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Finally, we are grateful to the anonymous referees of this journal for their very constructive suggestions. Of course, all errors are ours alone. Centro de Investigación en Complejidad Social, Universidad del Desarrollo, Santiago, Chile María P. Raveau Facultad de Gobierno, Universidad del Desarrollo, Santiago, Chile María P. Raveau & Juan P. Couyoumdjian Facultad de Economía y Negocios, Universidad del Desarrollo, Santiago, Chile Juan P. Couyoumdjian Facultad de Derecho, Universidad de Chile, Santiago, Chile Claudio Fuentes-Bravo Conceptualization, MPR and JPC; methodology, MPR; formal analysis, MPR, JPC and CF; data curation, CF; writing—original draft preparation, MPR and JPC; writing—review and editing, CF. All authors have read and agreed to the published version of the manuscript. All authors read and approved the final manuscript. Correspondence to María P. Raveau. Raveau, M.P., Couyoumdjian, J.P. & Fuentes-Bravo, C. Mapping the complexity of political ideology using emergent networks: the Chilean case. Appl Netw Sci 7, 22 (2022). https://doi.org/10.1007/s41109-022-00459-x Political ideology Latin american politics	CommonCrawl
Domain and Range of a Function Algebra Expressions, Equations, and Functions Domain and Range of a Function How do you determine the domain and range of a function? I will assume #{f(x),x} in RR# Then, the domain of #f(x)# is the set of all real values of #x# for which #f(x)# is defined. We can think of this as the valid inputs. Let's now call this set #D# Then the range of #f(x)# is the set of values of #f(x)# over #D#. We can think of this as the valid outputs. To determine the domain and range of a function, first determine the set of values for which the function is defined and then determine the set of values which result from these. E.g. #f(x) = sqrtx# #f(x)# is defined #forall x>=0: f(x) in RR# Hence, the domain of #f(x)# is #[0,+oo)# Also, #f(0) = 0# and #f(x)# has no finite upper bound. Hence, the range of #f(x)# is also #[0,+oo)# We can deduce these results from the graph of #sqrtx# below. graph{sqrtx [-4.18, 21.13, -6.51, 6.15]} Alan N. · 1 · May 25 2018 Is domain the independent or dependent variable? None of the two, actually. However, the domain is related to the independent variable, as it is the set of all the "permitted" values for the independent variable to assume. In particular, given a function, you must be sure that: If there is a fraction, the denominator can't be zero; If there is an even root, its argument must be positive or zero; If there is a logarithm, its argument must be strictly positive. These requests can of course be combined, as for example in #\sqrt{\log(\frac{x}{x+1})}#. Once you find out which values of #x# are permitted for the expression to have sense, you take the set of all those values, and obtain the domain of the function. KillerBunny · 1 · Feb 2 2015 How do you find the domain and range of a function in interval notation? There are so many different kinds of functions, but domain and range are important parts of your study of functions. Let me give you some examples of polynomial functions: y = 3x + 1, y = #x^2+3x + 2#, and y = #x^3#. Do you notice that each one of those functions has powers of x that are Whole numbers? Stick with those, and you will have a polynomial. All polynomials have a domain of "All Real Numbers". In interval notation, we write: #(-\infty,\infty)#. On the horizontal number line, that covers all numbers from left to right (your x-axis). Polynomials with ODD degree (highest power of x) stretch their way from low to high through all real numbers in the vertical direction. This means that their Range is "All Real Numbers" again: #(-\infty,\infty)#. Once these functions get going in those directions, you will never see the end of them! We call this their "End behavior". Polynomials with EVEN degree must have either a maximum or minimum value. If the graph has a minimum value, then its y-values (Range) stretch from that number, up to #\infty#. We write that Range as #[min, \infty)#. Look at the graph shown below, it has a minimum (vertex) at (2,-4). Its Range would be #[-4,\infty)#. Notice that whenever we use the #\infty# symbols, we use a round ( or ). That means that we can not include a numeric value for the infinities. When we use the square [ or ], it refers to an actual value that is included in the function. Your study of domain and range has just begun, and will include a wide variety of functions besides polynomials. When you discover a new function that behaves differently, carefully analyze its input and output values. You are on the way to great things! MrsRudolph221 · 2 · Nov 18 2014 What is Domain and Range of a Function? First, let's define a function: A function is a relationship between the #x# and #y# values, where each #x#-value or input has only one #y#-value or output . Domain: all x-values or inputs that have an output of real #y#-values. Range: the y-values or outputs of a function For more information, feel free to go to these following links/resources: https://www.intmath.com/functions-and-graphs/2a-domain-and-range.php Shantelle · 1 · Apr 7 2018 How do you determine if (-1, 4), (2, 8), (-1, 5) is a function? What is the domain for #f(x)=2x-4#? What is the domain and range for (3,1), (1,-4), and (2, 8)? What is the domain and range of a linear function? How do you find domain and range of a rational function? How do you find domain and range of a quadratic function? What is the domain of the function #f(x)=sqrt(6 - 2x)#? How do you find the domain of #g(x)=4sqrt(-3x+7.5)#? What is the domain and range of #2x-4y=-8#? How do you find the domain and range of #f(x)=3x^4-10#? How do you know whether a relation is a function and what the domain and range is for #(1,-3), (6,-2), (9,-1), (1,3)#? What is the range of the function #f(x) = x^2 + 3# if the domain is {-3, 0, 3}? How do you determine the domain and range of a function when given a graph? How do you determine the domain and range of a graph inequalities? How do you find the domain and range of a circle? How do you find the domain and range of a function without graphing? How do you find the domain and range of linear graphs? What is the domain and range of a sine graph? What is the domain and range of the graph #f(x)=1/x#? How would you find the domain and range of a circle on a graph whose points on the y axis are 5 and -5, and whose x axis coordinates are 8 and -8? What is the domain and range of the function #y = x^2- x + 5#? When do you use the brackets [ x, y ] and when do you use the parenthesis ( x, y) when writing the domain and range of a function in interval notation? How do you find the domain and range of #y = x^2 + 4x − 21#? What is the domain and range of the coordinates (-2,-1), (-2,2), (1,1), (2,2), (3, 2), and (3, -2)? What is the domain and range of the function #g(x)=sqrt(x-1)#? How do you know when to use brackets or parenthesis in finding domain or range? How do you find the domain and range of the function #y = −2x^2 − 6x + 1# without graphing? What is the domain and range of #y=x^2#? How do you find the range of the function #y=f(x)=x^2−25# on the domain −2≤x≤3? What is the range of the function #y=3x-2# when the domain is {-3, 1, 4}? What is the domain and range of #f(x)=abs(x)# written in interval notation? How do you find the domain and range of #y = −3x^2 − 3x + 4#? How do you find the domain and the range of an absolute value functions? How do you find the domain and range of #f(x)=(1/2)abs(x-2)#? What is the domain and Range of #1/(x+1)#? What is the domain and range of (-1, -1), (0, 0), (1, 1), (2, 2)? What is the domain and range of #e^x#? What is the domain and range of #f(x) = abs(x^2- 1)#? What is the domain and range of #f(x) = sqrt(x - 8)#? If #f(x) = x² - 5x + 8# and #g(x) = x² - 4# what is #f(x) + g(x)# and its domain? How do you find the domain of the function #f(x)=-6x+1#? How do you find the domain of the function #f(x) = 5/(x-9)#? How do you find the domain of #(3x-6)/ (sqrt(2x+1) - 3)?# How do you find the domain of the function: #f(x)= 1/(x+18)#? How do you find the domain of the function #F(x)= -4/(3x^2-5x-2)#? How do you find the domain of the function: #f(x) = x/(x-7)#? How do you find the Domain of the function #f(x) = 1/(2-e^x)#? How do you find the domain of the function in interval notation for #g(x)= sqrtx/(x^2+x-90)#? How do you find the domain of the rational function #g(x)=(x+4)/(x^2+4)#? How do you find the domain of the function: #g(x)=3/(10-3x)#? How do you find the domain of the function #f(x) = -2x + 4#? How do you find the domain of the function #f(x)= x/(x^2+2x-3)#? How do you find the domain of #g(x) = sqrt(x^2 - 9)#? How do you find the domain of #f(x) = sqrt{(x - 1)/x + 4)#? How do you find the domain of the function #f(x)= 1/(xsqrt [(x-3)/(4-x)])#? How do you find the domain of the function #f(x) = sqrt(4 - x^2)#? How do you find the domain of the functions #root(4)( -4-7x)# and #root(5)( -4-7x)#? How do you find the Domain of #f(x) = 7x^5 - 3x^2 - 2#? How do you find the domain of the function #f(x)=3/(x+2)#? How do you find the domain of the function {(3,1), (5,6), (8,-3), (7,-3)}? How do you find the domain of the function: #f(x) = sqrt(5-3x)#? How do you find the domain of this rational function: #G(x) = (x-3)/(x^4+1)#? How do you find the domain of the function #4/ (x^2-4)#? What is the domain of the function #f(x) = sqrt{x^3 - 3x^2}#? What is the domain of #3/(5-7x)#? How do you find the domain of the function #F(x) = (x^2+3x+4)/(x^2+1)^(1/2)#? How do you find the domain of #f(x) =sqrt(9 - x)#? How do you find the domain of the function #p(x) = x^2- 2x + 10#? How do you find the domain of this function #y = sqrt( (12/x) + 9) #? How do you find the domain of the function #f(x)=log(x-8)#? How do you find the domain of the function #f(x)= -x^2 + 2x +3#? How do you find the domain of functions using "set builder notation" and interval notation for #g(x) = (x-4)/(x-3)#? How do you find Domain of the function #F (X) = 4x^2 - 5x + 10#? How do you find the domain and the range of the function #f(x)= x^2 - 2x -3#? How do you find the domain of the function #f(x) = (4x^3 − 1) / (x^2 + 4x − 12)#? How do you find the domain of the function #f(x)=3ln(5x-2)#? How do you find the domain of the function #f(x)= (2x+3)/(x^2+9x+20)#? How do you find the domain of the function #p (x) = x^2 -2x + 6#? How do you find the domain and range of this function #f(x) = log_2(x-1) +3#? How do you find a domain of a function #f(x) =x^2- 2x - 15#? How do you find the domain of the function: #g(x)=(x+5)/(x^2-16)#? How do you find the domain of the function #g(x)=7/(10-3x)#? How do you find the domain of #g(t)= sqrt(1-2^t)#? How do you find the domain of this function #f(x)=1/(3x-6)#? How do you find the domain of #f(x)= sqrt(x+6)/(x-5)#? How do you find the domain and range of the inverse of the given function #f(x) = x^3 + 5#? What is the domain of #f(x) = {(x - 1)/(x + 4)}#? How do you find the range of the given function with domain D where #g: x → 1 - x^2#, D = {-1 , 0, 1}? How do you find the domain of the function #f(x) = (2x + 5)/(2 - x)#? How do you find the domain for #h(x)=(x+2)/sqrt(x^2 - 7)#? How do you find the domain of #f(x) = (sqrt[x - 5](x - 6))/(x^2 - 7x + 6)#? How do you find the domain for #g(x)=sqrt(40-8x)#? How do you find the domain for #h(x)=x^2+2#? How do you find the domain for #f(x) = sqrt(4 - x^5)#? Hw do you find the domain for #f(x)= (2x+7)/(x^2-13x-30)#? How do you find the domain for #f(x)=7#? How do you find the domain of #a(x)=64-2x^2#? How do you find the range of #f(x)=3x+2# given the domain D={-2, 0, 2}? How do you find the domain of #F(x)=x+7# if #x<=4# and #x^2# if x > 4? How do you find the range of #f(x)=-x^2+4x-3#? How do you find the domain and range of #y = x^2 - x + 5#? How do you find the range of #f(x)=abs(x^2-8x+7)# for the domain #3 <= x <= 8#? How do you find the range of the quadratic function #f(x) = -7(x - 2)^2 - 9#? What is the domain and range of #f(x) = sqrt(4-3x) + 2#? How do you find the domain and range of #y =sqrt(x-2) / (6+x)#? How do you find the range of a quadratic equation #f(x) = -x^2 + 14x - 48#? How do you find the range for #y = 1 / (x+5)#? How to find the Range of a function #f(x)= (x^3+1)^-1#? How do you find the domain and range of #y=-2^(x)+3#? How do I find the range of these functions without using a graph #y=-2+sqrt(16-x^2)#? How do you find the range of a rational function algebraically #y=(-4x-3)/(x-2)#? How would I algebraically find the range of #-x^2 + 4x -10#? How do you find the domain and range for #y=4x+2#? How do you find the range of #y = ln(x+3)#? How do you find the range of #y = -2 cos 3x#? How do you find the domain and range of the inverse of the given function #f(x) = x^3#? How do you find the domain and range of #f(x)= (x+7)/(2x-8)#? How do you find the domain and range of piecewise function #y={sqrt(-x)# for #-4<=x<=0# and #sqrtx# for #0<=x<=4#? How do you find the range of a function #f(x)=abs(x+1)#? How do you find the range of #f(x)=5cos(x + pi) + 3#? What is the domain and range of this function and its inverse #f(x) = sqrt(x + 7)#? How do you find the range of #f(x)=3 - ln(x+2)#? How do you find the range of the function: #f(t) = 1 + 0.9 e ^(-0.02t)#? How do you find the Domain and Range of #f(x)=(5x-3)/(2x+1)#? How do you find the range of a function algebraically #y=(x+5)/(x-2)#? What is the range of the function #r(x) = sqrt(x - 10)#? What is the domain and range of #f(x)=sqrt(x^2 +4)#? How do you find the range of the function #y=f(x)=x/(x^2-5x+9)#? What is the range of this function #x^2/(x-5)#? What is the range of #f(x) = -3^x + 4#? What is the range of #36, 64, 37, 45, 53, 60#? What is the range of # f(x) = -3x-1#? What is the range of # 2,1,7,3,5,2,9,7,10,4,2,10#? What is the range of # y=3x^2+2x+1#? What is the range of #y = 2^x-1#? What is the range of #y = 5x -2# if the domain is {-3, -1, 0, 1, 3}? What is the range of #y=[(1-x)^(1/2)]/(2x^2+3x+1)#? What is the range of #(-3,7) (1,-1) (6,34) (8,62)#? What is the range of # y=ln(x)#? What is the range of #f(x) = abs(-2x-1)#? What is the range of #-abs(x-1)+2#? What is the domain and range of #f(x)=x^4-4x^3+4x^2+1#? How do you find the domain of #f(x) = (x - 3)^(1/2)#? How do you find the domain of #f(x) = 2 / (1 - x^2)#? How do you find the domain of #f(x) = - sqrt(2 / (x^2 - 16))#? How do you find the domain of #y = 3/ (x + 6) #? How do you find the domain of #F(x) = -2(x + 3)^2 - 5#? How do you find the domain of #f(x)=x/(3x-1)#? How do you find the domain of #f(x) = {(x - 1)/(x + 4)}#? How do you find the domain of #f(x) = ( 9x+8)/(-9-8x)#? How do you find the domain of #f(x) = (x-4)/(x+3)#? How do you find the domain of #g(x) = x/((x-1)(x+3))#? How do you find the domain of #h(x) = 3x+9#? How do you find the domain of #p(x) = (x-2)/3 - 1/(3x)#? How do you find the domain of #p(x) =(4)/(x-3)#? How do you find the domain of #p(x) =sqrt(x-3) #? How do you find the domain of #p(x) =-(x-1)^2-1#? How do you find the domain of #y = (3x^2)/(x^2+1)#? How do you find the domain of #f(x)=(x^3+x^2-22x-40)/(x^4-x^3-7x^2+x+6)#? How do you find the domain of #(x^2-x-12)^-4#? How do you find the domain of #(x^2-x-12)^-(1/4)#? How do you find the domain of #p(x)=x^2-2x+8#? How do you find the domain of #g(x)=10/(4-5x)#? How do you find the domain of #y=-4/sqrt(x+1)#? How do you find the domain of #y=sqrt(9+x)#? What is the domain and range for #y = sqrt(x-3)#? What is the domain and range for #h(x)= x^2 - 5#? What is the domain and range for #y=-2sqrt(9-3x) +1#? What is the domain and range for #g(x)= x^2 - 3x#? What is the domain and range for #f(x)=7x+1#? What is the domain and range for # y = x^2 + 86#? What is the domain and range for # y = 2x^3 + 8#? What is the domain and range for # y = -9x + 11#? What is the domain and range for #y = 40 - 8x^2#? How do you find the range of the function #y=2x^2+1# when the domain is {9, 3, 99}? How do you find the domain and range for #y =sqrt(4x-1)#? How do you find the domain and range for #y =sqrt(x-1)#? How do you find the domain and range for #f(x)=2x+4#? How do you find the domain and range for #y= sqrt(x^3)#? How do you find the domain and range for #y = (3(x-2))/x#? How do you find the domain and range for #y = sqrt(x^2 + 2x + 3)#? How do you find the domain and range for #{(1, 3), (2, 3), (3, 3), (4, 3)}#? How do you find the domain and range for #x^2 + 5x + 6#? How do you find the domain and range for #F(x) = x^2 - 3#? How do you find the domain and range for #F(x) = 5/(x-2)#? How do you find the domain and range for #F(x) = 6x^2 - 2x +7#? How do you find the domain and range for #y=x^2=9#? How do you find the domain and range for #y=x^3-x#? How do you find the domain and range for #(2/3)^x – 9#? How do you find the domain and range for #y = 3x - 5#? How do you find the domain and range for #y = -.566021616 (x - 6) ^2 + 3.7#? How do you find the domain and range for #y= -2x+3, x>0#? How do you find the domain and range for #f(x) = 1/(1+x^2)#? How do you find the domain of #f(x) = sqrt ( x- (3x^2))#? How do you find the domain of #f(x) = sqrt (x^2 - 2x + 5)#? How do you find the domain in interval notation for #f(x)=x^2-4x+7 #? How do you find the domain in interval notation for #f(x)=(x-2)/(x+4) #? How do you find the domain in interval notation for #f(x)=(x^2+2x)/(x+1) #? How do you find the domain in interval notation for #f(x)=(x+4)/(x^2-4) #? How do you find the domain in interval notation for #f(x)=(x+6)/(x^2+5) #? How do you find the domain in interval notation for #f(x)=x/(x^3+8) #? How do you find the domain in interval notation for #f(x)=sqrt(x+7)/(x^2+7)#? What is the domain and range for #h(x)=6 - 4^x#? What is the domain and range for #f(x) = 2 - e ^ (x / 2)#? How do you find the domain of square root of 25-x^2? How do you find the domain of square root of 1-x^2? How do you find the domain of square root of x-2? How do you find the domain of #h(x)= sqrt( 4-x^2)/( x-3)#? How do you find the domain of #h(x)= sqrt(x-1)#? What is the domain and range if the function #f(x)= sqrt(4-x^2)#? What is the range of the quadratic function #f(x) = 5x^2 + 20x + 4#? What is the domain and range of #f(x) = (4x^2 - 4x - 8) / (2x + 2)#? How do you write #y=-2(x+1)^2 +3# in standard form? What is the domain of #(-3x^2)/(x^2+4x-45)#? Where is the hole in this rational function #f(x) = (x^2 + 2x - 8) / (x^2 - x - 2)#? What is the domain of #f(t) = (t+1)/(t^2+3t+2)?#? What is the domain of #f(x)= (2x^2+7x-15) / (x+5)#? What is the range of #8/(x^2+2)#? What is the range of #y=(-4x-3)/(x-2)#? How do you find the domain and range of #Y = g(x) = (x-3)/(x+1)#? How do you find the domain of #f(x)= (x^2-16) / (2x^2+13x+6)#? How do you find the domain of #f(x)=-6x+1 #? How do you find the domain of #f(x)=(x-2)/(x+4) #? How do you find the domain and range of #F(x) = -2(x + 3)² - 5#? How do you find the domain and range of #y=1/(x-4)#? How do you find the domain and range of #y=x/5#? How do you find the domain and range of#y = 3/ (x + 6) #? How do you find the domain and range of #g(x)= (3x)/(2x-5)#? How do you find the domain and range of #h(x)= 10/(x^2-2x)#? How do you find the domain and range of #f(x)= sqrt(x+6)/(x-5)#? How do you find the domain and range of #f(x) = sqrt(4 - x²)#? How do you find the domain and range of #f(x) = (x - 3)^(1/2)#? How do you find the domain and range of #f(x) = 2 / (1 - x²)#? How do you find the domain and range of #y = (x - 3)/( x^2 - 4)#? How do you find the domain and range of #f(x) = 1/(2-e^x)#? How do you find the domain and range of #h(x)= x^2 - 5#? How do you find the domain and range of #y = 3 sqrt (x-2) #? How do you find the domain and range of #F (X) = (4)/(x-3)#? How do you find the domain and range of #F (X) = sqrt(x-3) #? How do you find the domain and range of #F (X) = (x-2)/(x+4)#? What is the domain and range for {(-3,2), (0,3), (1, 4), (1, -6), (6, 4)}? Given the set of ordered pairs {(2,5), (5,2),(-2,2)}, how do you determine the domain and range? How do you find the range of #f(x)= 2/(3x-1)#? How do you find the range of #f(x)=x^2-x-2#? How do you find the range of #f(x) = x^3 - 3x + 2#? How do you find the range of #f(x) = 3/x^2#? How do you find the range of #f(x)=(2x^2 -1) / ( x^2 +1)#? How do you find the range of #f(x)=5x^2+2x-1#? What is the domain for #p(x) = x^2 - 2x + 9#? How do you find the domain of the function #g(x) = 2/3-5x#? What is the domain of R: {(6, −2), (1, 2), (−3, −4), (−3, 2)} ? What is the range of {-2,1}{-2,-1}{1,1}{1,2}{1,-1}? What is the range of R: {(3, −2), (1, 2), (−1, −4), (−1, 2)}? What is the domain and range of # y=3x^2#? What is the domain and range of # y=sqrt(x^2-1)#? What is the domain and range of #y=-sqrt(x^2-3x-10)#? What is the domain and range of #g(x)= 2/ (x-1)#? What is the domain and range of # y=-2^(x)+3 #? What is the domain and range of #f(x) = x^3 + 5#? What is the domain and range of #f(x) = x^3 - 3x + 2#? What is the domain and range of #y = sqrt(x-10) + 5#? What is the domain and range of #f(x) = (10x)/(x(x^2-7))#? What is the domain and range of #f(x) = 1/(1+x^2)#? What is the domain and range of #y=4x+2#? What is the domain and range of #y= x^2-2#? What is the domain and range of #y= sqrt(x- 2)#? What is the domain and range of #f(x)=1/(x+3)#? What is the domain and range of #(x-1)/(x-4)#? What is the domain and range of #y = - sqrt(9-x^2)#? What is the domain and range of #y = 1/(x^2 - 2)#? What is the domain and range of #g(x) = 1/(7-x)^2#? What is the domain and range of #x=(y+2)^2#? What is the domain and range of #y=x^2 - 5#? What is the domain and range of #y=4-x^2#? What is the domain and range of #y=(3/2)x+1#? What is the domain and range of #f(x) = -1 sqrt (1-x^2)#? What is the domain and range of #f(x)= x^2 - 6x + 8#? What is the domain and range of #f(x)=1/2(x-2)#? What is the domain and range of #f(x) = 1/(x-2) #? What is the domain and range of #f(x)= 1/(x+1)#? What is the domain and range of #g(x) = sqrt(x-2)#? What is the domain and range of #f(x)=3/x#? What is the domain and range of #y=4x-8#? What is the domain and range of #y=x^3-x#? What is the domain and range of #y=x^2-3#? What is the domain and range of #y=3x^2+5#? What is the domain and range of {(3,7),(3,8),(3,-2),(3,4),(3,1)}? What is the domain and range of #d(s)= 0.009s^2#? What is the domain and range of #d(s)= 0.04s^2#? What is the domain and range of #y= (4x) / (x^2 + x - 12) #? What is the domain and range of {(3,2),(1,4)(5,2)(7,6)}? What is the domain and range of #y = -7 /(x-5)#? What is the domain and range of #y = (x – 5)^2 + 10#? What is the domain and range of #F(x) = x^2 - 3#? What is the domain and range of #F(x) = 5/(x-2)#? What is the domain and range of #x=7#? What is the domain and range of #-(3/25)(x-26)^2#? What is the domain and range of {( -1, -9), ( -5, -10), ( -4, 1), ( 10, -6), ( 5, -2)}? What is the domain and range of #r(x)= -3sqrt(x-4) +3#? What is the domain and range of #y = 3x - 5#? What is the domain and range of {(-1, -2), (1, -2), (3,1)} ? What is the domain and range of #y= abs(x-1)+2 #? What is the domain and range of #x= -sqrty #? What is the domain and range of #y = 2(x-1)^2 - 6#? What is the domain and range of #f(x) = 1/(2x+4)#? What is the domain and range of #F (x)= -1/2 x^4+8x-1#? What is the domain and range of #f(x)= 4#? What is the domain and range of #f(x)= 1/x#? What is the domain and range of #y=x^2+3#? What is the domain and range of #F(x) = 7/(6x-5)#? How do you find the domain and range of #y=4-x^2#? How do you find the domain and range of #y=sqrt(x-3)#? How do you find the domain and range of #f(x)= 2x^2-1#? How do you find the domain and range of #f(x)= sqrt(x^2-1)#? How do you find the domain and range of #y=3x^2+4x+3#? How do you find the domain and range of #y=3x-2#? How do you find the domain and range of #1/(x+1)#? How do you find the domain and range of #f(x)=x^2-12x+36#? How do you find the domain and range of #f(x)=x^2 - 6x - 10#? How do you find the domain and range of #y = 1/x^2#? How do you find the domain and range of #y = 3(x-2)/x#? How do you find the domain and range of #f(x)=x^2+5#? How do you find the domain and range of #f(x)=5x^2+2x-1#? How do you find the domain and range of #y = x^2 - 4#? How do you find the domain and range of #y = 2x - 1#? How do you find the domain and range of #y = sqrt(x+8)#? How do you find the domain and range of #y = (3x+2)/(x-3)#? How do you find the domain and range of #f(x) = -sqrt(x+3)#? How do you find the domain and range of #f(x) = 3sinx#? How do you find the domain and range of #f(x) = 2/(x-1)#? What is the domain of #h = (x+1)sqrt(2x-6)#? What is the domain of #h(x)= x / (x ^2 - x - 6)#? What is the domain of #y= 5x^2 - 5x^(1/3)#? What is the domain of #f(x) = sqrt(x + 7)#? What is the domain of #f(x)= (8x)/((x-1)(x-2))#? What is the domain of #f(x) = (x^2) - 2x - 15#? What is the domain of #h(x) = (2x^2 + 5 )/ (sqrt(x-2))#? What is the domain of #f(x) = 5/(x-9)#? What is the domain of #( 6 + 3x^(3) -4x^(2) -17x ) / ( x^(3) -3x^(2) -10x )#? What is the domain of #f(x) = (4x/3)((x^2 - 1)^(-1/3))#? What is the domain of #f(x) = sqrt(x^2(x-3)(x-4))#? What is the domain of #f(x)= (x^2+18x+18 ) / ( x^2+9x+20)#? What is the domain of #f(x)=2x+4#? What is the domain of #f(x)=sqrt(x-1)#? What is the domain of #h(x)=x^2+2#? What is the domain of #h(x)=sqrt(( x- (3x^2)))#? What is the domain of #h(x)=sqrt(x^2 - 2x + 5)#? What is the domain of #h(x)=sqrt(x-2)#? What is the domain of #g(x) = 3 / (9 - 4x)#? What is the domain of #f(x)=2x+ 6#? What is the domain of #f(x) =(10x-4) / (x-1)#? What is the domain of #f(x)=-16x^2 +2#? What is the domain of #{(1,2),(2,6),(3,5),(4,6),(5,2)}#? What is the domain of #f(x)=7 #? What is the domain of #f(x) = sqrt(x^2-144)#? What is the domain of #f(x)=.5x-1/3#? What is the domain of #f(x)=x/(x^2-5x)#? What is the domain of #f(x) = (3x-1) / (x^2-x) #? What is the domain of #f(x)=x^2-4x+7 #? What is the domain of #f(x)=(x-2)/(x+4)#? What is the domain of #f(x)=(x^2+2x)/(x+1) #? What is the domain of #f(x)=(x+4)/(x^2-4) #? What is the domain of #f(x)=(x+6)/(x^2+5) #? What is the domain of #f(x)=x/(x^3+8) #? What is the domain of #f(x)=(x+3)/sqrt(x^2-9) #? What is the domain of #(2x^2+x-1)/(x^3-9x)#? What is the domain and range for #y= -abs(x-5)#? What is the domain and range for #y=4absx-1#? What is the domain and range for #f(x)= x/(x^2-5x)#? What is the domain and range for #f(x)=sqrt(x-1)#? What is the domain and range for #f(x)=sqrt(2x-8)#? What is the domain and range for #y=4x^2+2#? What is the domain and range for {(2,3), (3,7), (5,-1), (0,0)}? What is the domain and range for {(1,2), (2,3), (2,5), (1,6)}? What is the domain and range for {(1,4), (2,8), (3,12), (-1,-4), (1,4)}? What is the domain and range for #h(x)=-sqrt(x+3)#? What is the domain and range for (2,4), (3,9), (4,16) and (5,25)? What is the range if f(x) =2x + 5 and domain: -1,0,3,7,10 ? What is the range if f(x) =1/2x - 2 and domain: -1/2,0,3,5,9 ? What is the range if f(x) = 3x - 9 and domain: -4,-3,0,1,8? What is the domain and range of #g(x) = x^2 + 7x -18 #? What is the domain and range of ( (7.6, -0.2), (8.8, -0.2), (2.3, -4.6) )? What is the domain and range of #y= 4 / (x^2-1)#? What is the domain and range of {(-6,5),(-3,-4),(-2,-7),(2,-1)}? What is the domain and range for #f(x) = (4-2x) /5#? What is the domain and range for # f(x) = 3x - absx#? What is the domain and range for #F(x) = -2(x + 3)² - 5#? What is the domain and range for #f(x) = (2 - x) /( 3 + x)#? What is the domain and range for #f(x) = - ( 1 / ( x + 1) )#? How do you find the range of # f(x) = -x^2 + 3#? How do you find the range of # f(x)=1/(x-3)#? How do you find the range of #f(x)= x/absx#? How do you find the range of #f(x)=x+7#? How do you find the range of #y = 3x + 10#? How do you find the range of #x + sqrt( x-1 )#? How do you find the range of #y=4x²-5x+2#? How do you find the range of s(z) = 5 - 4z given D={-2,0,2}? How do you find the domain and range of #f(x)=sqrt(9-x^2)#? How do you find the domain and range of #f(x)= -sqrt(x-3)#? How do you find the range of #f(x)=x^2 + 3#? How do you find the range of #f(x)= 1/(x^2 + 9)#? How do you find the range of #x^2/(x-5)#? How do you find the domain and range of #f(x)= sqrt( x^2+4)#? How do you find the domain and range of #h(x)= 5/(x-3)#? How do you find the domain and range of #f(x)= (3x-1)/((x+3)(x-1))#? How do you find the domain and range of #f(x)= 1/x + 5/(x-3)#? How do you find the domain and range of #f(x)= sqrt(4-x^2) /( x-3)#? How do you find the domain and range of #f(x)= sqrt(4-x)/( (x+1)(x^2+1))#? How do you find the domain and range of #f(x)= sqrt(x^4-16x^2)#? How do you find the range of #f(x)=10-x^2#? How do you find the range of #g(x)= 5+sqrt(4-x)#? How do you find the range of #f(x)= x^2/(1-x^2)#? How do you find the domain and range of #y = sqrt(x-10) + 5#? How do you find the domain and range of #f(x)=3x+2#? If f(x) = 1/(x+1) and g(x) = 2/(2x-1) how do you find g(f(x)) and its domain and range? What is the domain and range of #f(x) = (x+9)/(x-3)#? What is the domain and range of #f(x)=2x+4#? What is the domain of # f (x) = 1 / sqrt((2 - x)(6 + x))#? What is the domain of #f(x) = (x^2 - x - 6) /( x^2 + x - 12)#? What is the domain of #f(x)=3x+2# when the range is {-2, -1, 2}? What is the domain and range of #f(x)= (x+1)/(x^2+3x-4)#? What is the domain and range of #y = (x + 2) /( x + 5)#? What is the domain of the function: {(1, 2); (2, 4); (3, 6); (4, 8)}? What is the domain of the function: #f(x) = sqrt(4x+1) #? What is the domain of the function: #f(x) =sqrt(( x- (3x^2)))#? What is the domain of the function: #f(x) =sqrt(x^2 - 2x + 5)#? What is the domain of the function: #f(x) = 5/(2x^2 - x - 3)#? What is the domain of the function: #f(x) =sqrt(x^2(x-3)(x-4))#? What is the domain of the function: #f(x) =sqrt(x-9)#? What is the domain of the function: #(2x-1) / (x²+2)#? How do you find the range of #f(x)=x^2+4x+12 # with the domain of #0<=x<=5#? How do you find the domain and range of #y = (x+4 )/( x-4)#? How do you find the domain and range of #y = sqrt( x^2 +4) /( x^2 - 4)#? How do you find the domain and range of #y=-2x^2+3#? How do you find the domain and range of #x/(x^2+1)#? How do you find the domain and range of #y = -2x^2 - 8#? How do you find the domain and range of #y= -1/2 x ^2#? How to find domain, asymptotes, holes, intercepts for #f(x) = (x+6 )/ (2x+1)#? How to find domain, asymptotes, holes, intercepts for #f(x) = (x+3 )/( x^2 + 8x + 15)#? How to find domain, asymptotes, holes, intercepts for #f(x) = x / (3x(x-1))#? How to find domain for #f(x) = sqrt(25 - x^2)#? How to find domain for #f(x) = sqrt(x^2 - 5x)#? How to find domain for #f(x) = x^2+3#? How to find domain for #f(x)=sqrt(x+4)#? How do you find domain for #f(x)=(2x+1)/(x-3)#? How do you find domain for #y = sqrt((4+x) / (1-x) ) #? How do you find domain and range for #y= x^2-2#? How do you find domain and range for #y=sqrt(x- 2)#? How do you find domain and range for # f(x) = (x^2) - 2x - 15#? How do you find domain and range for #y=3x^2#? How do you find domain and range for #y=sqrt((4 - x²))#? How do you find domain and range for #f(x) = 2 / (1 - x²)#? How do you find domain and range for #f(x)=x^2-4x+7 #? How do you find domain and range for #f(x)=(x-2)/(x+4) #? How do you find domain and range for #f(x)=(x^2+2x)/(x+1) #? How do you find domain and range for #f(x)=(x+4)/(x^2-4) #? How do you find domain and range for #f(x)=(x+6)/(x^2+5) #? How do you find domain and range for #f(x)=x/(x^3+8) #? How do you find domain and range for #f(x) = (4x - 7) /( 6 - 5x)#? How do you find domain and range for #f(x) =sqrt( x- (3x^2))#? How do you find domain and range for #f(x) =sqrt (x^2 - 2x + 5)#? How do you find domain and range for #f(x) = (x-6)/(x+1)#? How do you find domain and range for #f(x) = abs(x-2)#? How do you find domain and range for # f(x)= x/(x-2)#? How do you find domain and range for #g(x)=3/x#? How do you find domain and range for #y=sqrt(x^2+4)#? How do you find domain and range for #f(x)=5/(x-3)#? How do you find domain and range for #y=2x+3#? How do you find domain and range for # f(x) = sqrt(7x + 2)#? How do you find domain and range for #f(x) = 2 / sqrt(3x-2)#? How do you find domain and range for # f(x) = (x^2 - 16) / (x^2 - 25)#? How do you find domain and range for # f(x) =abs(2x+1)#? How do you find domain and range for # f(x) =sqrt(4-3x) + 2#? How do you find the range of #f(x)= (x^3+1)^-1#? What is the domain of # f(x)=sqrt(17-x)#? What is the domain and range of #(x^2+2)/(x+4)#? What is the domain and range of #f(t) = sqrt(9-t)#? What is the domain and range of #f(t) = sqrt(9-t^2)#? What is the domain and range of #f(x) = sqrt(x^2-36)#? What is the domain and range of #ƒ(x)= (5x+15)/ ((x^2) +1)#? What is the domain and range of (5,0),(-7,8),(-7,3),(5,3)? What is the domain and range of #f(x) = (x-1)/(x^2+1)#? What is the domain and range of #1 / (x^2 + 5x + 6)#? What is the domain and range of #f(x) = (x+3)/(x^2+4)#? What is the domain and range of #f(x) = (x+5)/(x^2+36)#? How do you find the domain and range of #y = -2x +3#? How do you find the domain and range of #y = 1/x+4#? How do you find the domain and range of #y = sqrt(2-x)#? What is the domain and range of #f(x) = x^2 + 4x – 6#? What is the domain and range of #f(x)=(x+2)^2-3#? What is the domain and range of #y= -1/2 x ^2#? What is the domain and range of #f(x) =sqrt(8.5 − 3 x)#? What is the domain and range of {(1.3), (2,2), (3,1), (4,0), (5,-1)}? What is the domain and range of #f(x)= sqrt(x+2) - 3#?? What is the domain and range of #f(x) = (x-4) /( x+2)#?? What is the domain and range of #h(x)=3x^2+5x-3#?? What is the domain and range of #m(x) = 5/(x^2+9)#?? What is the domain and range of #g(x) = (7x+4)/(x+4)#? What is the domain and range of #l(x) = 5x-4#? What is the domain and range of #y = 8x + 8#? What is the domain and range of #y = 3x+6#? What is the domain and range of #F(x) = 1/ sqrt(4 - x^2)#? What is the domain and range of #G(x) = (x^2 +x - 6) ^ (1/2)#? How do you find the range of f(x) = -x + 4 for the domain {-3,-2,-1,1}? What is the domain and range of the function f(t)=7.2t models the average distance f(t) in kilometers that BOB rides his bike over time ,t, in hours? What is the domain of #(4/(a+1))-(5/a) = (20/(a^2+a))#? How do you identify the excluded value for the rational function: #y=5/(x +1)#? What is the domain of #g(x)=x^3=1#? What is the domain of #f(t)=10/(t²-2t-3)#? What is the domain of #h(x)=sqrt(2x+1)#? What is the range of #f(x) = -3^x - 1#? How to find domain and range of say: #y = 1/(x^2 - 2)#? How do you find the domain of #sqrt((x/(x-2)))#? How do you find the domain and range of #y = sqrt (1-x^2) / x#? How do you find the domain and range of #f(x) = - sqrt2 / (x² - 16)#? How do you find the domain and range of #f(x) = sqrt(4+x) / (1-x)#? How do you find the domain and range of #y = 3 sqrt (x-2)#? How do you find the domain and range of #y=(3x-2)/(4x+1)#? How do you find the domain and range of #f(x)=(x-2)/(x+4) #? How do you find the domain and range of # f(x)= 2- 1/(x+6)^2#? How do you find the domain and range of #f(x)=sqrt(x+4)#? How do you find the domain and range of #f(x)=1/(3x-6)#? How do you find the domain and range of #f(x) = x^3 - 3x + 2#? How do you find the domain and range of # f(x) = (x+6 )/ (2x+1 )#? How do you find the domain and range of #f(x) = (x+3 )/ (x^2 + 8x + 15)#? How do you find the domain and range of #f(x) = x / (3x(x-1))#? How do you find the domain and range of #f(x) = 1/x#? How do you find the domain and range of #f(x) =sqrt(x-2)#? What is the domain and range of #y= sqrt(x^3)#? What is the domain and range of # y = 3(x-2)/x#? Which is the domain and range of #f(x) = -3sqrt (x+2) - 6#? What is the domain and range of (4,3),(5,6),(7,9)? What is the domain and range of #y= 1/2x#? What is the domain and range of #Q(s)=1/(sqrt(2s))#? What is the domain and range of #y= (sqrt (x+4))/x#? What is the domain and range of #(2/3)^x – 9#? What is the domain and range of #ln(x - 3) + 2#? What is the domain and range of #g(x)=abs(2x-8)+1#? What is the domain and range of #f(x) = -7(x - 2)^2 - 9#? What is the domain and range of #f(x)= sqrt(x-4) + 2#? What is the domain and range of #g(x)=sqrt(16-x^2) + 1 #? What is the domain and range of #h(x)=-sqrt(x^2-16) -3#? What is the domain and range of # f (x) =10^x#? What is the domain and range of #f(x) = abs(x-3) - (5/2)#? What is the domain and range of #F(x) = -2(x + 3)² - 5#? What is the domain and range of #F(x) = sqrt(x-3)#? What is the domain and range of #f(x) =sqrt(( x- (3x^2)))#? What is the domain and range of #f(x) =sqrt (x^2 - 2x + 5)#? What is the domain and range of # F(X)=1-x^2#? What is the domain and range of #f(x)=sqrt(16-x^3)#? What is the domain and range of #f(x)=sqrt(x^2+4)#? What is the domain and range of #h(x) = (x^2 - 3x - 4) / (x - 4)#? What is the domain and range of #y=sqrt((x² - 8) )#? How do you find the domain of #f(x) = 6/( x-4)#? How do you find the domain of #f(x) = x² - 5x + 8#? How do you find the domain of #g(x) = x² - 4#? How do you find the domain of #f(x)=4+e^-x/3#? How do you find the domain of #f(x)=3/(x-6)#? How do you find the domain of #g(x)= 1/x#? How do you find the domain of #(sqrt(9-x^2)) / (x-1)#? How do you find the domain of #p(x)=2x-4#? How do you find the domain of #3log(5x-2)#? How do you find the domain of #f(x)= (4x)/ sqrt(x-4)#? How do you find the domain of #f(x)=3x+2#? How do you find the domain of #f(x)= 1/ (x+1)#? How do you find the domain of #h(x)=sqrt(4-x)+sqrt(x^2-1)#? How do you find the domain of #g(x)= root3x/(x^2+x-90)#? How do you find the domain of #y=(x-1) / (x-2)#? How do you find the domain of #f(x)=sqrt(x+4)#? How do you find the domain of #f(x)=(2x+1)/(x-3)#? How do you find the domain of # f(x)=-2^x+2#? How do you find the domain of # f(x)=sqrt(5x-10)#? How do you find the domain of #y=4x+2#? How do you find the domain of #y= x^2-2#? How do you find the domain of #y= sqrt( x- 2)#? How do you find the domain of #f(x)=(x+5)^(1/2)#? How do you find the domain of #f(x) =( x - 2) / (x^2- 16)#? How do you find the domain of #f(x) = (x+7)/(x^2-4)#? How do you find the domain of #f(x)=(3x-1)/(x^2+9)#? How do you find the domain of #f(x)=(x-3)/(x^2-x-2)#? How do you find the domain of #f(x)=5/(3x+4)#? How do you find the domain and the range of the relation, and state whether or not the relation is a function {(1, 3), (2, 3), (3, 3), (4, 3)}? How do you find the domain and the range of the relation, and state whether or not the relation is a function {(-3,2), (0,3), (1, 4), (1, -6), (6, 4)}? How do you find the domain and the range of the relation, and state whether or not the relation is a function (8,8), (9,9), (10,9), (10,10)? How do you find the domain and the range of the relation, and state whether or not the relation is a function (1,0), (2,0), (3,0), (4,0)? How do you find the domain and the range of the relation, and state whether or not the relation is a function (2,1) (3,1) (3,2) (4,1) (4,2) (4,3)? How do you find the domain and the range of the relation, and state whether or not the relation is a function [(-1,-2),(0,0),(1,2),(2,4)]? How do you find the domain and the range of the relation, and state whether or not the relation is a function [(-1,-1),(0,-1),(1,-1),(2,-1)]? What is the value of #x# in the equation #(x-2)/3 + 1/6 = 5/6#? How do you find the domain for #f(x)= 2sinx+7#? How do you find the domain and range for #y=2/(5(x-2))#? How do you find the domain and range for #y=1/(x+6)#? How do you find the domain and range for #y=sqrt(x-4)#? How do you find the domain and range for #y=sqrt(x+4)#? How do you find the domain and range for #f(x)=(2x+1)/(x-3)#? How do you find the domain and range for #f(x)=sqrt( 3-8x)#? How do you find the domain and range for #f(x)=sqrt(4-2x)#? How do you find the domain and range for #y = 2x + 3#? How do you find the domain and range for #y = -sqrt ( x + 3)#? How do you find the domain and range for #y = x^2-5#? How do you find the domain and range for #y = 1/x#? How do you find the domain and range for #y = 2/(x-1)#? How do you find the domain and range for #y = sqrt(x^2 -3x +2)#? How do you find the domain and range for #y = (x-5)^2#? How do you find the domain and range for #y =sqrt(9-x^2)#? How do you find the domain and range for #y= (x+3)^0.5#? How do you find the domain and range for #y=4x^2 - 2x#? How do you find the domain and range for #y=-2/3x - 5#? How do you find the domain and range for # y= -2x +3#? How do you find the domain and range for #y= x^2- 6x + 8#? How do you find the domain and range for #y=5/4(x+2)^2 -1 #? How do you find the domain and range for #f(x)= (x+2)/(x+7)#? How do you find the domain and range for #f(x)= (x-3)/( x^2- 9)#? How do you find the domain and range for #g(x)=sqrt( x-1)#? How do you find the domain and range for #h(x)=x^2+2#? If there is a graph with a line going through (-1, -1), (0, 0), (1, 1), (2, 2) What is the domain and range? If there is a graph of a ray, with the end point on (3,0). The line goes through (0, 2), and (-3, 4), What is the domain and range? If there is a horizontal line, going through ( 0, 2), (1 , 2), ( 2, 2), (3 , 2) what is the domain and range? What is the domain and range of #y+2 = (x-3)^2#? What is the domain and range of #y=3/(x-5)#? What is the domain and range of #y= 1/(x^2-25)#? What is the domain and range of # y= sqrt(x) -2#? What is the domain and range of # y= sqrt(x-1)#? What is the domain and range of # y=e^x#? What is the domain and range of {(1,4) (0,-2) (2,3) (-1,4) (-3,0)? What is the domain and range of # f(x) = 2x^2 - 1#? What is the domain and range of {(4,2),(1,3),(3,3),(6,4)}? What is the domain and range of {(4,2),(-3,2),(8,2),(8,9),(7,5)}? What is the domain and range of #h(x)=6 - 4^x#? What is the domain and range of {(2,-3),(4,6),(3,-1),(6,6), (2,3)} ? What is the domain and range of # y= -2x+3#? What is the domain and range of #F(x)=sqrtx #? What is the domain and range of #G(x) = x+5 #? What is the domain and range of #h(x)=(x-1)/(x^3-9x) #? What is the domain and range of #y = x ^2 - x + 5#? What is the domain and range of #y =sqrt(4x-1)#? What is the domain and range of #y =sqrt(x^2-1)#? What is the domain and range of #y = -sqrt(x ^2 - 3x - 10)#? What is the domain and range of #p(x)= root3(x-6)/sqrt(x^2 - x - 30)#? What is the domain and range of #y=ln(2x-12)#? What is the domain and range of #y=(4+x)/(1-4x)#? What is the domain and range of #g(x)=2x^2-x+1#? What is the domain and range of #f(x) = -x/2#? What is the domain and range of #f (x) = -2x + 6#? What is the domain and range of #f (x) = (x^2-2)/(x^2-4)#? What is the domain and range of {(1,8) (2,3) ( 3,5) (4,0) (5,9)}? What is the domain and range of #y=sqrt( x- (3x^2))#? What is the domain and range of (0,0),(-1,1),(1,1),(-2,4)(2,4)? What is the domain and range of (-6,3)(-8,3)(-7,-5)? What is the domain and range of #y=absx -2#? What is the domain and range of #y=ln(x-3)+1#? What is the domain and range of #g(t)= sqrt(1-2^t)#? What is the domain and range of #x = y^2 -9#? What is the domain and range of #y = x^2 + 4#? What is the domain and range of #g(x)=2/(x+5)#? What is the domain and range of #f(x) = (x+6 )/ (2x+1) #? What is the domain and range of # f(x) = (x+3) /( x^2 + 8x + 15)#? What is the domain and range of # f(x) = x / (3x(x-1))#? What is the domain and range of # f(x) = 5/ \|x\|-3 #? What is the domain and range of #f(x) =sqrt(28.5 − 3 x)#? What is the domain and range of #f(x) =x/(x^2-1)#? What is the domain and range of #f(x) =(x-3)/(7x+4)#? Using the domain values {-1, 0, 4}, how do you find the range values for relation y=2x-7? Using the domain values {-1, 0, 4}, how do you find the range values for relation y=2x-10? Using the domain values {-1, 0, 4}, how do you find the range values for relation f(x)=3x-8? What is the domain and range of #y= 1 / (x-3)#? What is the domain and range of # f(x)= (3x) /(x^2-1)#? What is the domain and range of # f(t) = root3(3) sqrt (6t − 2)#? What is the domain and range of # f(x) = sqrt(x^2-36)#? What is the domain and range of #x=y^2#? What is the domain and range of #y= -x/(x^2-1)#? What is the domain and range of #y=x#? What is the domain and range of #y= 1/2 x- 2#? What is the domain and range of #-3x + 2y = -6#? What is the domain and range of #x= 3#? What is the domain and range of #y= -1#? What is the domain and range of #y = \| x + 3\|#? What is the domain and range of #y =sqrt(17x+8)#? What is the domain and range of #y =1/sqrt(17x+8)#? What is the domain and range of #f(x)=3^x#? What is the domain and range if pizzas are sold at $2.50 a slice and the initial cost for it is $350.00? What is the domain and range of #f(x) = (3 - x)^(1/2)#? What is the domain and range of #g(x)= (x^2 - 16)^(1/2)#? What is the domain and range of #f(x) = sqrt( x+3)#? What is the domain and range of #g(x) = x/2#? What is the domain and range of #5/(4(x+2)^2) -1#? What is the domain and range of # y=7#? What is the domain and range of #(x^3-8)/(x^2-5x+6)#? What is the domain and range of #F(x)=ln(x^2)#? What is the domain and range of #f(x)=(x^2+1)/(x+1)#? What is the domain and range of #f(x)=(x-2)/(x^2-6x+9)#? What is the domain and range of #h(t)=4/t #? What is the domain and range of #f(x)=7#? What is the domain and range of #f(x)= sqrt (3+x-2)#? What is the domain and range of #f(x) = 4 / (x+2)#? What is the domain and range of {(7,2) (8,2), (9,2), (10,2)? What is the domain and range of #f (x) = 2x + 3#? What is the domain and range of #f (x) =0#? What is the domain and range of #K(t) = 6cos (90t) - 10#? What is the domain and range of #f(x)=1-x^2#? What is the domain and range of #f(x) = (x-2) / (x+2)#? What is the domain and range of ln(x-1)? What is the domain and range of #y=(x^2-x-1) / (x+3)#? What is the domain and range of #y= ((x+1)(x-5)) /( x(x-5)(x+3))#? What is the domain and range of #y= (4x^2 - 9) / ((2x+3)(x+1))#? What is the domain and range of #y=(-4x-3)/(x-2)#? What is the domain and range of #f(x) = ln (10-x)#? What is the domain and range of #g(x) =(5x)/(x^2-36)#? What is the domain and range of #y= \| x - 3 \| + 8#? What is the domain and range of #y= - \| x + 3 \| - 8#? What is the domain and range of #f(x) = 1/(1 + sqrtx)#? What is the domain and range of #h(x)= 10/(x^2-2x)#? What is the domain and range of {(-2, 1), (-1, -2), (0, -3), (1, -2), (3, 6)}? How do you find the domain of #f(x) = (4x^2 - 9) /(x^2 + 5x + 6)#? How do you find the domain for #R(x) = (x^2 + x - 12)/(x^2 - 4)#? How do you find the domain for #H(x) = [(x - 1) (x + 2) (x - 3)]/(x(x - 4)^2)#? How do you solve #\|(x+1)/x\| > 2#, and represent the answer in interval notation? What is the domain and range of the quadratic equation #y = –x^2 – 14x – 52#? What is the domain and range of the quadratic equation #y = (x – 5)^2 + 10#? What is the domain and range of #y= -x/( x^2-1)#? What is the domain and range of #f(x)=(x^2-9)/(x^2-25)#? What is the domain and range of #y^2 = x#? What is the domain and range of #(x+5)/(x+1)#? What is the domain and range of #f(x,y)=2/(x-y^2)#? What is the domain and range of # y = (-4) / ( sqrt (x +1))#? What is the domain and range of # y = sqrt(9 + x)#? What is the domain and range of #y = x^x#? What is the domain and range of #y=5^x#? What is the domain and range of #f(x) = (x-1)/ (x^2 -x-6)#? What is the domain and range of #f(x) =e^x#? What is the domain and range of #f(x) =sqrt(-2x+5)#? What is the domain and range of #f(x) =x^2/ (x^2-6)#? What is the domain and range of #f(x)=sqrtx /( x-10)#? What is the domain and range of #y=2^(x-1)+1#? What is the domain and range of #y = ln((2x-1)/(x+1))#? What is the domain and range of #y =2^x#? What is the domain and range of #f(x)= (x+7)/(2x-8)#? What is the domain and range of #y= 1/(x-10)#? What is the domain and range of #f(x,y) = 3 + sin(sqrt y-e^x)#? What is the domain and range of #y=\|x-5\|#? What is the domain and range of #f(x,y) = sqrt(9-x^2-y^2)#? What is the domain and range of #y = -(sqrt(-x))#? What is the domain and range of #y = 1/(x - 2)#? What is the domain and range of #y = 1 (1/x)#? What is the domain and range of #f(x)= (2-x)/(x^2+7x+12)#? What is the domain and range of # f(x) = x^2 - 2x - 3#? What is the domain and range of #f(x) = 3x + 1#? What is the domain and range of #f(x) = \|x - 2\|#? What is the domain and range of #y = (x-3)/(x+11)#? What is the domain and range of #(x+3)/(x^2+9)#? What is the domain and range of #y=5sqrtx#? What is the domain and range of #y=sqrt(5x+2)#? What is the domain and range of #y=abs(x+4)#? What is the domain and range of #y=abs(x-5)#? What is the domain and range of #y=abs(x)-4 #? What is the domain and range of #y=-abs(x-5)#? What is the domain and range of #y=-absx-4#? What is the domain and range of #y= (x+1)/(x^2-1)#? What is the domain and range of #1/(x-7)#? What is the domain and range of #y= (2x^2-1)/(2x-1)#? What is the domain and range of #y=3x-11#? What is the domain and range of # y=5^x#? What is the domain and range of #y= 1/(x-7) -3#? What is the domain and range of #f(x) = sqrt (9 - x^2)#? What is the domain and range of #y= sqrt (x^2 + 1)#? What is the domain and range of #y=-x^2+4x-1#? What is the domain and range of #y = log2^x#? What is the domain and range of #y = 3/x#? What is the domain and range of #y = tan(2x)#? What is the domain and range of #f(x) = x^2 - 12#? What is the domain and range of #f(x) = sqrt(x + 5)#? What is the domain and range of #y= abs(x) - x#? What is the domain and range of #y = x^3#? What is the domain and range of #y = (x+1)/(x^2-7x+10)#? What is the domain and range of #y = x + 3 #? What is the domain and range of # f(x) = 4/(9-x) #? What is the domain and range of #y = 3 sqrt (x-2)#? What is the domain and range of # y=3/(x+4)#? What is the domain and range of #y = log(2x -12)#? What is the domain and range of #y =sqrt((x^2-5x-14))#? What is the domain and range of #y =sqrt(tanx)#? What is the domain and range of #y =sqrt(x-3) - sqrt(x+3)#? What is the domain and range of #f(x) = sqrt((x^2) - 3)#? What is the domain and range of #y=3/(x+5)#? What is the domain and range of #f(x)=(x-1)/(x+2)#? What is the domain and range of #y= 1/2(2)^x#? What is the domain and range of #y=7#? What is the domain and range of # f(x) = 10/x#? What is the domain and range of #y=1/(3x-2)#? What is the domain and range of # f(x) = ln( x - 4)#? What is the domain and range of # y = { x/ (x + 5) }#? What is the domain and range of # y =sqrt(2x - 3)#? What is the domain and range of # y =sqrt (x^2 - 9)#? What is the domain and range of # y =abs(x+4)#? What is the domain and range of # y =1/(2x-4)#? What is the domain and range of #f(x)=(2x-1)/(3-x)#? What is the domain and range of #f(x)=sqrt(4-x)#? What is the domain and range of #y = (2x^2)/( x^2 - 1)#? What is the domain and range of #y = y = (x^2 - 1) / (x+1)#? What is the domain and range of #y =- sqrt(1 - x)#? What is the domain and range of # f(x) = 7/(x+3)#? What is the domain and range of #y= 1 / (x-3) #? What is the domain and range of #y=(x^2 -5x -6) / (x^2 -3x -18)#? What is the domain and range of #f(x) = -2 * sqrt(x-3) + 1#? What is the domain and range of #y=( sqrt x)#? What is the domain and range of #r(x)=sqrt(x+6)-1#? What is the domain and range of #h(x)= 1 /x^2#? What is the domain and range of # c(x) =1/( x^2 -1) #? What is the domain and range of #f(x)={ x^2 - 81 }/ {x^2 - 4x}#? What is the domain and range of #f(x) = abs((9-x^2)/(x+3))#? What is the domain and range of #y= 1/(x+1)#? What is the domain and range of # f(x) = ln (10-x)#? What is the domain and range of #y=csc x#? What is the domain and range of #y = 13x+1#? What is the domain and range of #3y - 1 = 7x +2#? What is the domain and range of #y(x)=ln(x+2)#? What is the domain and range of # g(x) = \|4x+3\|#? What is the domain and range of #y=sqrt(4-x^2) #? What is the domain and range of #y=-3/(4x+4)#? What is the domain and range of #y=-\|x\|-9#? What is the domain and range of #y=\|x+13\|#? What is the domain and range of #y=\|x-1\|-9#? What is the domain and range of #y=ln(x)#? What is the domain and range of #f(x) =( x^2 - x - 6) / (x^2 + x - 12)#? What is the domain and range of # y=2e^(-x)#? What is the domain and range of #f(x) = 1/(x + 3)#? What is the domain and range of #f(x)=4log(x+2)-3#? What is the domain and range of #f(x)=sqrt(4x+2)#? What is the domain and range of #y=-5+2x#? What is the domain and range of #y = (x + 3) / (x -5)#? What is the domain and range of # y = (3(x-2))/x#? What is the domain and range of #y = sqrt(x^2 + 2x + 3)#? What is the domain and range of #y = 5 - (sqrt(9-x^2))#? What is the domain and range of #f(x) = sqrt x /( x^2 + x - 2)#? What is the domain and range of #y= (-2^-x) - 4#? What is the domain and range of #y= ln(6-x) +2#? What is the domain and range of #f(x) = 2x²-3x-1 #? What is the domain and range of #f(x) =(3x^2-2x-8)/(2x^3+x^2-3x)#? What is the domain and range of #f(x) = x^2+2#? What is the domain and range of #y=x^2 - 4x + 1#? What is the domain and range of # y = 2sqrt(x - 3) - 3#? What is the domain and range of # y = 3 sqrt(x-4) + 2#? What is the domain and range of # y = x^2 / (x^2 - 1)#? What is the domain and range of #y=log_2x#? What is the domain and range of #y=-3x-3#? What is the domain and range of #y = 4 - 3x#? What is the domain and range of #y =sqrt(3x - 5)#? What is the domain and range of #y =x^2 - 3#? What is the domain and range of #y =9 - x^2#? What is the domain and range of #y =2x^2 - 5x#? What is the domain and range of #y =4x - x^2#? What is the domain and range of #y =2x^2 - x - 6#? What is the domain and range of #y=ln(x^2)#? What is the domain and range of # f(x)=(3x-1)/(x^2+9)#? What is the domain and range of # f(x)=sqrt(5x-10)#? What is the domain and range of #ln(x^2+1)#? What is the domain and range of #y = \|x\| + 5#? What is the domain and range of #y = sqrt(x-4)#? What is the domain and range of #y=1/(x-1)^2#? What is the domain and range of # y=-3(x-10)^2+5#? What is the domain and range of #g(x)=-sqrt(x^2-4)#? What is the domain and range of #y = x^4 + 1 #? What is the domain and range of #y = x^4 #? What is the domain and range of #y=x^4+x^2-2 #? What is the domain and range of #t^3-t^2+t-1#? What is the domain and range of #f(x)= sqrt(4x-x^2)#? What is the domain and range of #y= 3 tan x#? What is the domain and range of #y= x^2 / (x^2-16) #? What is the domain and range of #y= \|x+1\|#? What is the domain and range of #Y(x)= -2 sqrt(-x) + 20#? What is the domain and range of #f(x) = 3+2sinx#? What is the domain and range of #g(x) =ln( 4 - x )#? What is the domain and range of #f(x)= x^2 - 2x -3#? What is the domain and range of # y = x^2 - 7#? What is the domain and range of #y = (x^2 + 4x + 4)/( x^2 - x - 6)#? What is the domain and range of #3sqrt( x^2 - 9)#? What is the domain and range of #g(x)=(1-x^2)#? What is the domain and range of #(x^4 + x^2) /(1+x^2)#? What is the domain and range of #y = sin x#? What is the domain and range of #y=sin^-1(x)#? What is the domain and range of # y=-5x^2#? What is the domain and range of # y=sqrt( x-4)#? What is the domain and range of #y=-2x^2+1 #? What is the domain and range of #(x+5)/(x^2+36)#? What is the domain and range of #F(x)=(x+2) /( x-2)#? What is the domain and range of # y=secx#? What is the domain and range of #ln(1-x^2)#? What is the domain and range of # f(x) = x^2-4x-7#? What is the domain and range of #y=1/2(2)^x#? What is the domain and range of #x =(y+2)^2#? What is the domain and range of #f(x) = ln(-x + 5) + 8#? What is the domain and range of #f(x) = sqrt(2x-8)#? What is the domain and range of #y=sec^2x+1#? What is the domain and range of #y=sqrt((x+5) (x-5))#? What is the domain and range of #f(x)=x-11#? What is the domain and range of the given function #f(x)= (x-1)/(x+3)#? How do you find the domain and range of #sqrt(8-x)#? What is the domain of #x^(1/3)#? How do you find the domain and range of #f(x) = 3x + 1#? How do you find the domain and range of #f(x) = \|x - 2\|#? How do you find the domain and range of #f(x) = x^2 + 1#? What is the domain of #y=log_(2)x#? How do you find the domain of #f(m)=-7/(m+14)# and write the domain in interval notation? How do you find the domain and range of # y=x^2+2#? How do you find the domain for #x/(3x-1)#? How do you find the domain for #1/(x+3)#? How do you find the domain for #1/(x-3)#? How do you find the domain for #f(x) = 1/(sqrt(3-2x))#? How do you find the domain for #f(x)=(1+3x)/(5-2x)#? How do you find the domain for #f(x)=1/(3x+2)#? What is the range of the graph of #y = 5(x – 2)^2 + 7#? How do you find the domain of #x^2 + 4#? How do you find the domain of #f(x)=(3x+1)/(sqrt (x^2+x-2))#? How do you find the domain of #x^2+3 #? What is the domain of the expression #sqrt(7x+35)#? How do you find the domain and range for #y=x#? How do you find the domain and range for #y=2x-10#? How do you find the domain and range for #y=-1/2x+3#? How do you find the domain and range for #y=x^2#? How do you find the domain and range for #y=absx#? How do you find the domain and range for #y=sqrtx#? How do you find the domain and range for #y=x^2+3#? What is the Domain for: h(x)=ln(x+1)? Question #f6a1b Question #a877a How do you find the domain of the equation #y = -x^2 – 6x – 13#? How do you find the range of the equation #y = -x^2 – 6x – 13#? What is the domain and range of 3x-2/5x+1 and the domain and range of inverse of the function? How do you find the domain of #y = 2(x-3)² - 1 #? How do you find the domain of #f(x) = sqr(25 - x^2)#? How do you find the domain of #f(x) = sqrt(x^2 - 5x)#? How do you find the domain of #f(x) = sqrt((3 - x) / (x + 2))#? How do you find the domain and range of # sqrt(x^2 - 8x +15)#? How do you find the domain and range of #y = log(2x -12)#? How do you find the domain and range of #sqrt(x^2-5x-14)#? How do you find the domain and range of #sqrt(x-3) - sqrt(x+3)#? How do you find the domain and range of #sqrt( x- (3x^2))#? How do you find the domain and range of #f(x)= 2/(x-5)#? How do you find the domain and range of #g(x)=1/(x+1)#? How do you find the domain and range of #log(x-9)#? How do you find the domain and range of #f(x) = x^2+3#? How do you find the domain and range of #y=3x^2#? How do you find the domain and range of #f(x)=-3x^(1/3)+4x^(1/2)#? How do you find the domain and range of #g(x)=8/(8-3x)#? How do you find the domain and range of #sqrt(6x-30)#? How do you find the domain and range of # arctan(x^2)#? How do you find the domain and range of #g(x)=3 sqrt(x+4)#? How do you find the domain and range of #g(x)=-x^2-3x-1#? How do you find the domain and range of #g(x)=sqrt((x+3)/(x-2))#? How do you find the domain and range of #f(x)=8x^2-5x+2#? How do you find the domain and range of #f(x)=(12x)/(x^2-36)#? How do you find the domain and range of #h(x) = e^(-x^2)#? How do you find the domain and range of #f(x) = 7/(x+3)#? How do you find the domain and range of #f(x) = (3x + 1)/ (sqrt(x^2 + x - 2) ) #? How do you find the domain and range of #f(x) = 7 #? How do you find the domain and range of #sqrt (4-5x)#? How do you find the domain and range of #f(x)=6x-3#? How do you find the domain and range of #f(x) = (2x)/(sqrt(16-8x))#? How do you find the domain and range of #f(x)= (3x-1)/(sqrt(x^2+x-2))#? How do you find the domain and range of #g(x)=sqrtx+7#? How do you find the domain and range of # f(x)=sqrt(1-x)#? How do you find the domain and range of #sqrt(x-4)#? How do you find the domain and range of #sqrt(x^2- 4)#? How do you find the domain and range of #sqrt(x+5)#? How do you find the domain and range of #root3( (x^2-x-12))#? How do you find the domain and range of #(x^2-x-12)^-4#? How do you find the domain and range of #(x^2-x-12)^-(1/4)#? How do you find the domain and range of #sqrt{1 - x}#? How do you find the domain and range of #sqrt{-x - 2}#? How do you find the domain and range of #p(x)=-x^3 - x^2 + x -10#? How do you find the domain and range of #g(x) = -11/(4 + x)#? How do you find the domain and range of #g(x) = (2x – 3)/( 6x - 12)#? How do you find the domain and range of #f(x) = 1/(1+x^2)#? How do you find the domain and range of #f(x)=(x^2-x)/(x+1)#? How do you find the domain and range of #10-x^2#? How do you find the domain and range of #f(x)= x^2/(1-x^2)#? How do you find the domain and range of #g(x)= (3+x^2)/(4-x^2)#? How do you find the domain and range of #f(x) = (x)/(sqrt{x - 4})#? How do you find the domain and range of #p(x) = sqrt{3/(x - 2)}#? How do you find the domain and range of #h(x) = log_3[x/(x - 1)]#? How do you find the domain and range of #g(x) = 1/(In x)#? How do you find the domain and range of #f(x) = sqrt{Inx}#? How do you find the domain and range of # f(a)=3sqrt(4a)#? How do you find the domain and range of #y=2x^2 - 4x - 5#? How do you find the domain and range of #(x-3) (3x-2)#? How do you find the domain and range of #y=\|x-3\|#? How do you find the domain and range of #y = -3x+1#? How do you find the domain and range of #h(x)=x^2+2#? How do you find the domain and range of #f(x) =sqrt( x - 1) - 1/sqrt( 2-x)#? How do you find the domain and range of #(x+2)/(x^2-1)#? How do you find the domain and range of #f(x)= 1/(x+1)#? How do you find the domain and range of #g(x)=sqrt(x^2-4)#? How do you find the domain and range of #f(x)=x/(x^2 - 2x -3) #? How do you find the domain and range of #M(x)= -2/14x^2-11x-15#? How do you find the domain and range of #log(x+7)#? How do you find the domain and range of #log_(6) (49-x^2)#? How do you find the domain and range of #f(x) = 2x - 8#? How do you find the domain and range of #g(x) = 9x + 5#? How do you find the domain and range of #(8x-48)/(x^2-13x+42)#? How do you find the domain and range of #(x^2-64)/(x-8)#? How do you find the domain and range of #x^5-2x^3+1#? How do you find the domain and range of #f(x)=(x^2+2x)/(x+1) #? How do you find the domain and range of #f(x)=(x+4)/(x^2-4) #? How do you find the domain and range of #f(x)=(x+6)/(x^2+5) #? How do you find the domain and range of #f(x)=x/(x^3+8) #? How do you find the domain and range of #f(x)=sqrt (x+7)/(x^2+7)#? How do you find the domain and range of #f(t)=-11/sqrtt#? How do you find the domain and range of #root4(9-x^2)#? How do you find the domain and range of #x^3#? How do you find the domain and range of #f(x)=x^2+2x+2#? How do you find the domain and range of #f(x)=sqrt(5x+1)#? How do you find the domain and range of #2 / x^2#? How do you find the domain and range of #f(x) =(x+4)/(x+2)#? How do you find the domain and range of #y=2/5{{x-2}}#? How do you find the domain and range of #y = 2x + 4#? How do you find the domain and range of #f(x)= (2x^2+7x-15) / (x+5)#? How do you find the domain and range of #f(x)= sqrt(x^2-x-6)#? How do you find the domain and range of #f(x)= sqrt(x² - 8) #? How do you find the domain and range of #f(x)=2^-x#? How do you find the domain and range of #y = sqrt(9 + x)#? How do you find the domain and range of # f(x)= x-7#? How do you find the domain and range of # 2(x-3)#? How do you find the domain and range of #y = x + 3 #? How do you find the domain and range of #y = sqrt(x - 1)#? How do you find the domain and range of #f(x)= ln(3x-2)#? How do you find the domain and range of #f (x) = 1 / ( x - 1)#? How do you find the domain and range of #f(x) = 1/(x + 3)#? How do you find the domain and range of # f(x)=1/(x-3)^2+5#? How do you find the domain and range of # f(x)=e^(5x)#? How do you find the domain and range of #f(x)= log(x-2)#? How do you find the domain and range of #f(x)= lne^(2x)#? How do you find the domain and range of #g(t)= sin(e^-t)#? How do you find the domain and range of #f(x)=1/2(x-2)#? How do you find the domain and range of #f(x)= sqrt(6x-10)#? How do you find the domain and range of #f(x)=2/(3/(x-6))-7#? How do you find the domain and range of #sqrt(1-sinx) #? How do you find the domain and range of #s=3t+12#? How do you find the domain and range of # 1/(3t+12)#? How do you find the domain and range of #sqrt(3t+12)#? How do you find the domain and range of #f(x)=-6x+1#? How do you find the domain and range of #g(x) = 1-2x^2#? How do you find the domain and range of #s(y) = (3y)/( y+5)#? How do you find the domain and range of #f(t) = 3sqrt(t + 4)#? How do you find the domain and range of #f(x) = sqrt(x+6) /( 6+x)#? How do you find the domain and range of #f(x)=(x+7)/(x^2-49)#? How do you find the domain and range of #(x-1) / (x-2)#? How do you find the domain and range of #1 /( x^3-9x)#? How do you find the domain and range of #sqrt1-sqrtx+7 #? How do you find the domain and range of #sqrt(25-x^2) #? How do you find the domain and range of #e^(-4t)#? How do you find the domain and range of #t/sqrt(t^2-25) #? How do you find the domain and range of #t^(1/3) #? How do you find the domain and range of #g(x) = sqrt x / (2x^2+x+1)#? How do you find the domain and range of # 1/(x-7)#? How do you find the domain and range of #f(x) = (x+2) / (x-1)#? How do you find the domain and range of #g(x) = sqrt(x-4) #? How do you find the domain and range of #y=-2(x+1)^2-3 #? How do you find the domain and range of #f(x)=1/x+3 #? How do you find the domain and range of #y=2^(-x)#? How do you find the domain and range of #f(x)=cosx+1#? How do you find the domain and range of #x^2+y^2=9#? How do you find the domain and range of #f(x) =2sinx#? How do you find the domain and range of #g(x) = 2(1/2)^(2x) +3#? How do you find the domain and range of #y=log(2x-3)/(x-5) #? How do you find the domain and range of #5 /( 7-3x) #? How do you find the domain and range of # p(x)=x^2-2x+7#? How do you find the domain and range of #p(x)=x^2-2x+10#? How do you find the domain and range of #f(x) = x+2#? How do you find the domain and range of #f(x) = sqrt(x-1)#? How do you find the domain and range of #y = { 1/ (x - 1) }#? How do you find the domain and range of # y = { x/ (x + 5) }#? How do you find the domain and range of #sqrt(2x - 3)#? How do you find the domain and range of #sqrt(x^2 - 9)#? How do you find the domain and range of #y = x^2 + 86#? How do you find the domain and range of #g(t) = sqrt(3-t) - sqrt(2+t)#? How do you find the domain and range of #ln(14t)#? How do you find the domain and range of # sqrt(t+7)#? How do you find the domain and range of #1/sqrt(8-t)#? How do you find the domain and range of # f(x)=x^2+x#? How do you find the domain and range of #root4(-4-7x)#? How do you find the domain and range of #2x+8=y#? How do you find the domain and range of #g(x)=5^x#?	CommonCrawl
A hydrotrope pretreatment for stabilized lignin extraction and high titer ethanol production Hairui Ji1, Le Wang1, Furong Tao2, Zhipeng Yao1, Xuezhi Li3, Cuihua Dong1 & Zhiqiang Pang1 The biomass pretreatment strategies using organic acids facilitate lignin removal and enhance the enzymatic digestion of cellulose. However, lignin always suffers a severe and irreversible condensation. The newly generated C–C bonds dramatically affect its further upgrading. In this study, we used a recyclable hydrotrope (p-Toluenessulfonic acid, p-TsOH) to dissolve lignin under mild condition and stabilized lignin with a quenching agent (formaldehyde, FA) during extraction, achieving both value-added lignin extraction and efficient enzymatic saccharification of cellulose. Approximately 63.7% of lignin was dissolved by 80% (wt. %) p-TsOH with 1.5% FA addition at 80 °C, 30 min. The obtained lignin was characterized by FTIR spectroscopy, TGA, 2D HSQC NMR spectroscopy, and GPC. The results indicated that the extracted lignin exhibited excellent properties, such as light color, a low molecular weight (Mw, 5371 g/mol), and a narrow polydispersity (Mw/Mn, 1.63). The pretreated substrate was converted to ethanol via a quasi-simultaneous saccharification and fermentation process (Q-SSF). After fermentation of 60 h, the ethanol concentration reached 38.7 ± 3.3 g/L which was equivalent to a theoretical ethanol yield of 82.9 ± 2.2% based on the glucan content, while the residual glucose concentration was only 4.69 ± 1.4 g/L. In short, this pretreatment strategy protected lignin to form new C–C linkages and improved the enzymatic saccharification of glucan for high-titer ethanol production. The non-renewability and limited reserves of fossil resource have stimulated a worldwide initiative to find a sustainable resource for production of fuel and chemicals (Khan et al. 2011). Lignocellulosic biomass, the most abundant renewable feedstock on the earth, has received considerable attention as a potential alternative of petroleum in recent years. Lignocellulose is mainly composed of cellulose, hemicellulose, and lignin along with small amounts of pectin, protein, extractives, and ash. The enzymatic hydrolysis of cellulose and hemicellulose can release various monosaccharides, good precursors for the production of fuels and value-added chemicals. However, the three polymers (cellulose, hemicellulose, and lignin) linked into a complex matrix forming a protective barrier against enzyme and microbial degradation (Yi et al. 2014). Therefore, a pretreatment process is essentially required to facilitate the enzymatic accessibility of carbohydrate components (cellulose and hemicellulose) and promote the conversion efficiency of lignocellulosic biomass. Current pretreatment techniques involved physical, physical–chemical, chemical, biological or combined methods (Kumar et al. 2009; Lynd et al. 2022). Physical pretreatments include grinding, extrusion (Zheng and Rehmann 2014), and irradiation (ultrasound and microwave) (Gao et al. 2021). Physical–chemical pretreatments typically conclude hydrothermolysis (liquid hot water) (Negro et al. 2003; Zhou et al. 2016), steam explosion (Singh et al. 2015), ammonia fiber explosion (AFEX) (Murnen et al. 2007), and CO2 explosion (Kim and Hong 2001). Chemical pretreatments refer to using dilute acids (Jung et al. 2013), alkalis (NaOH, Ca(OH)2, KOH, and NH3.H2O), organosolv (Zhao et al. 2009), and ionic liquids (Tadesse and Luque 2011; Zhang et al. 2021) to alter the physical and chemical structure of lignocellulosic biomass. Although these pretreatment methods can effectively break down the structural barrier from lignin, most of them require special reaction equipment and huge energy consumption. Compared with physical and chemical methods, biological pretreatments have many advantages, such as low energy consumption, no chemicals addition, and mild reaction condition (Yi et al. 2014). However, long pretreatment time has limited its utilization on commercial scale (Taherzadeh and Karimi 2008). In addition, the effect of pretreatment methods on the changes in lignin molecular structure is generally ignored. Lignin, the second most abundant biopolymer on the earth comprising up to 20–35% of cell wall, is composed of three kinds of phenylpropane structural units, namely, guaiacyl (G), syringyl (S), and p-hydroxyphenyl (H) structures. These units are connected by carbon–carbon bonds and ether bonds (Costa et al. 2016). The aromatic and functional groups, such as methoxy, phenolic, alcoholic, carbonyl, and aldehyde groups, in lignin structure enable great potential applications in the preparation of biofuels, high-value chemicals, and composites. However, high pretreatment severity caused the skeleton rearrangement and condensation of lignin resulting in difficulties of depolymerize and further upgrading (Udeh and Erkurt 2016). Therefore, it is necessary to explore a pretreatment method that not only can improve enzymatic digestibility of glucan but also hinder the formation of C–C bonds in lignin molecules. In previous studies, a recyclable acid hydrotrope (p-TsOH) has been mentioned for its unparalleled performance of delignification at mild temperatures below water boiling point. It is worth noting that 90% of lignin and hemicellulose were removed from poplar wood (Ni et al. 2017). By commercial crystallization technology, p-TsOH was recycled and reused for many times to achieve environmental sustainability (Ji et al. 2016). However, acid or high temperature conditions during lignin extraction caused malignant and irreversible condensation. The lignin condensation mechanism is shown in Fig. 1A. When lignin ether bonds are cleaved, the carbon cations in the alpha active sites of lignin side chain attack the negatively charged lignin aromatic rings to form stable carbon–carbon bonds (icon red key). A previous study has reported that using a protecting agent (FA) to stabilize lignin during extraction. FA molecule can quickly react with the α- and γ-hydroxyl groups of the side chain of lignin to form a stable 1, 3-dioxane structures through acetal reaction, thereby blocking the formation of benzylic carbocations. At the same time, FA can also react with the negatively charged benzene ring active sites to generate hydroxymethyl groups and deactivate the active sites preventing these positions from undergoing undesirable condensation reactions. Condensation mechanism of lignin (A) and mechanism of formaldehyde preventing polymerization (B) In this study, we used the hydrotrope p-TsOH to dissolve lignin and FA as quenching agent to stabilize lignin under mild conditions. An optimum pretreatment severity was determined according to the enzymatic hydrolysis of glucan and the lignin characterization results from FT-IR spectroscopy, TGA, 2D HSQC NMR spectroscopy, and GPC. Finally, the obtained pretreated substrate was converted into high-titer ethanol with a Q-SSF process. The novelty of the present study is to demonstrate a combination of high-efficiency dissolution of lignin by hydrotrope p-TsOH under mild conditions and avoidance of lignin molecules condensation using FA as quenching agent, achieving both value-added lignin extraction and efficient enzymatic saccharification of cellulose. Therefore, this study is important to the valorization of lignocellulosic biomass. Poplar wood chips were provided by Shan Dong Sun Paper Industry Joint Stock Co., Ltd. (Shandong, China), they were milled into particles with a size range of 40–60 mesh; p-TsOH and some chromatographic grade organic solvents were supplied by Macklin biochemical Co., Ltd. (Shanghai, China); FA solution (37–40%, wt.%) and H2SO4 (95–98%, wt.%) were purchased from Yantai Far Eastern Fine Chemical CO., Ltd. (Shandong, China); 1,4-dioxane was obtained from Kemiou Chemical Reagent CO., Ltd. (Tianjin, China); DMSO-d6 was provided by Cambridge Isotope Laboratories, Inc. (MA, United States). Cellulase (Cellic® CTec2) was supplied by Novozymes (Beijing, China). Pretreatment and lignin isolation 4 g wood powder with 40–60 mesh was added in 50 mL p-TsOH solution (60%, 70% and 80%). Reactions were conducted at temperatures of 70 °C and 80 °C with a reaction time range of 15 min, 30 min, and 60 min. Each pretreatment had 3 replications. At the end of each reaction, solid and spent liquor were separated using filter papers (15 cm, medium speed, Hangzhou Fuyang North Pulp paper CO., Ltd., Hangzhou, China). The solid was washed with pure water to neutral pH and freeze-dried for component analysis and enzymatic hydrolysis. The extracted lignin (EL) in filtrate was precipitated by adding water. After dialysis and freeze-drying, the purity of the obtained EL sample reached to 95.06% (wt.%). Besides, a control experiment with addition of 3% FA was performed to analyze the effects of FA molecule on blocking the formation of new C–C linkages. The EL and the cellulolytic enzyme lignin (CEL) (extracted from biomass by means of ball-milling and repeated enzymatic steps) were isolated and characterized for a comparison. For the CEL extraction, the dried pretreated substrate was milled by a planetary ball mill for 4 h (400 rpm). The obtained powder was subjected to enzymatic hydrolysis (180 rpm, 50 °C, and 24 h) to decompose cellulose and hemicellulose. Subsequently, the lignin-rich solid was centrifuged (5000 rpm, 5 min), washed for three times, and freeze-dried. Finally, the lignin was extracted by dioxane/water (94:6, v/v), and the concentrated solution obtained by rotary evaporation was dropped into 20 ml of water to precipitate CEL with a purity of 92.58%. The determination of specific surface area of raw material and pretreated substrate was performed on a mercury porosimeter (Autopore IV 9500, Micrometrics, USA) with stepwise pressure increment in the range from 0.0036 to 413 MPa. Before measurements, the pretreated wood chips were dried at 105 °C and subsequently degassed in a vacuum degree of 6.67 Pa at temperature of 20 °C. The surface morphological features were measured by a SEM apparatus (Hitachi S-3400 N, Japan) with an accelerating voltage of 5–10 kV. Enzymatic saccharification of cellulose The enzymatic hydrolysis of cellulose was performed in a 250 mL conical flask with 50 mL citrate buffer (PH 4.8) at 50 °C with a rotate speed of 180 rpm. Cellulose-rich solid and cellulase (Cellic® CTec2) loadings were 2% and 15 FPU/g glucan, respectively. Samples were withdrawn (400 μL) at 3 h, 6 h, 12 h, 24 h, 36 h, 48 h, 60 h, and 72 h and centrifuged at 8000 rpm for 5 min. Glucose concentrations were determined by a biosensor analyzer (SBA-40E, Biological institute of Shandong academy sciences, Jinan, China). The calculation of the enzymatic saccharification of glucan was based on the following equation: $$\mathrm{Yield} \left(\%\right)=\frac{{m}_{\mathrm{glucose}}}{{m}_{\mathrm{Raw}}\times {C}_{\mathrm{glucan}}/0.90}\times 100\%$$ where ${m}_{\mathrm{glucose}}$ is the total weight of produced glucose after enzymatic hydrolysis; ${m}_{\mathrm{Raw}}$ and ${C}_{\mathrm{glucan}}$ are the weight of used raw material (the pretreated substrate) and the content of glucan in raw material; 0.90 is a conversion coefficient of xylan to glucose. Lignin characterization FT-IR spectra of lignin was recorded on a spectrophotometer (ALPHA, BRUKER, Germany) in a range from 500 to 4000 cm−1 at a scanning resolution of 4 cm−1. Thermogravimetric analysis was performed on a thermogravimetric analyzer (TGAQ50, TA Instruments CO., Ltd., USA) according to a previous publication (Wen et al. 2013). The lignin samples were heated from 35 °C to 800 °C at an increment of 10 °C/min in nitrogen. 2D-HSQC NMR spectra were recorded on a Bruker 400 MHz spectrometer (AVANCEII, BRUKER, Germany) at 25 °C. Before measurement, 40 mg of lignin was dissolved in 0.6 mL of DMSO-d6. Weight average molecular weight (Mw), number average molecular weight (Mn), and polydispersity index (Mw/Mn) were determined by a gel permeation chromatography (GPC) system (Waters CO., USA) with an ultraviolet detector. For lignin acetylation, 50 mg of dry lignin was dissolved in 4 mL solution of pyridine: acetic anhydride (1:1, v/v) and stirred in dark at 25 °C for 24 h. 20 mL acid water (pH 2) was dropped slowly into the concentrated solution to precipitate acetylated lignin. 20 μL acetylated lignin solution of 1 mg/mL was injected into a GPC system equipped a chromatography column (Styragel® HR 4 THF, 7.80 × 300 mm, Ireland). The operation was run at 35 °C using THF as eluent with at a flow rate of 0.6 mL/min. The GPC system was calibrated using standard polystyrene samples. Fermentation for ethanol production The Q-SSF of cellulose was carried out in 150 mL erlrnmeyer flask with a solid loading of 15% and cellulose (Cellic® CTec2) addition of 15 FPU/g glucan. Enzymatic hydrolysis was carried out for 6 h at 50 °C and 180 rpm. Subsequently, the sample was inoculated with 2‰ active dry yeast (Angel Yeast Company, Hubei province, China) and incubated for 60 h. Then, the samples were withdrawn at 12 h intervals and detected the concentrations of sugar and ethanol on a HPLC system equipped with a refractive index detector (RID-20A) and a separated column (Aminex HPX-87H, Bio-Rad, CA, United States). All experiments were performed in triplicates. Pretreatment and enzymatic saccharification Figure 2 reveals the effect of different pretreatment conditions on the changes of components in biomass. Obviously, some of hemicellulose and lignin were removed after pretreatment leaving about 60% of original total content. The increased pretreatment severity significantly improved the dissolution of hemicellulose and lignin while caused negligible degradation of cellulose. The structural destruction will facilitate the contact between enzyme and cellulose, and can effectively promote the enzymatic digestibility of the substrate. Hence, an appropriate pretreatment intensity is necessary for biomass conversion. However, a high pretreatment severity inevitably caused chemical structure changes of lignin and reduced its potential application value. Therefore, a suitable pretreatment condition is essential to remove hemicellulose and lignin and maintain high-value utilization of lignin. a Content of three components in the pretreated substrates (Cx stands for the acid concentration; Tx stands for the temperature; tx stands for the time), b Enzymatic saccharification of the pretreated substrates. c SEM images of raw material, the pretreated substrates obtained from C70T70t60 and C80T80t30 The enzymatic saccharification of the pretreated substrates with different conditions is shown in Fig. 2b. Increasing pretreatment severity from C60T70t60 to C80T80t30, enzymatic saccharification yield increased from 34.7 ± 2.6% to 94.8 ± 1.9% after 72 h. At C80T80t15, only 4.91 ± 0.35% hemicellulose and 8.98 ± 0.58% lignin were found in the pretreated solid. The enzymatic hydrolysis efficiency of cellulose reached to 84.6 ± 0.8% after 72 h. After the partial removal of lignin and hemicellulose, pores and gaps were formed on the cell wall (Fig. 2c). The surface area was also increased from 8.81 m2/g (raw material) to 13.25 m2/g (the pretreated substrate obtained from C80T80t30). Therefore, the chemical accessibility of glucan significantly improved resulting in high enzymatic saccharification of the pretreated substrates. Although high pretreatment severity enhanced the enzyme digestibility of glucan, the native chemical structure of lignin was destroyed as revealed by a dark color (Fig. 3). We tried to use FA as a protecting agent to stabilize lignin during pretreatment. When adding FA in p-TsOH solution, the extracted lignin exhibited a lighter color than that of the obtained lignin without FA addition, as shown in Fig. 3. It may be the reason that the formed C–C bonds from the condensation reaction of lignin during pretreatment process cause the color to be darker under acid or high temperature conditions. Adding FA during pretreatment blocked the condensation reaction between lignin molecules resulting in not only a light apparent morphology but also the improvement of enzymatic hydrolysis of glucan. Lignin condensation causes non-productive binding with enzyme. Except for lignin backbone disruption and fractionation, the condensation/re-polymerization usually occurred during pretreatment. Aliphatic OHs elimination and condensation of lignin segments raised hydrophobicity accompanying with p-hydroxyphenyl re-polymerization onto lignin skeleton. More condensation involved more branched lignin sections with hydrophobic moieties and this meant that more free enzyme was trapped in complex lignin net structures. Moreover, cellulase usually contains tryptophane, phenylalanine and tyrosine which belong to hydrophobic residues. These aromatic amino acids are responsible for driving cellulase to align with pyranose rings on glucose chains through stacking and hydrophobic interactions. Unfortunately, this type of hydrophobic interaction also occurs in non-productive adsorption of cellulase onto condensed lignin. (Song et al. 2020). Meanwhile, we also investigated the effect of FA on the enzymatic saccharification of glucan. When adding 3% FA in p-TsOH solution, the enzymatic hydrolysis efficiency of the obtained cellulose-rich substrate was significantly reduced, as shown in Fig. 4. FA not only reacted with lignin to block new C–C bonds formation during pretreatment, but also reacted with monosaccharides and polysaccharides. In addition, it is likely that the formed 1, 3-dioxane structures from the reaction between FA and hydroxyl on cellulose surface lead to a much lower enzyme digestibility of the pretreated substrates. It has been reported that the changes in the chemical properties of cellulose surface can severely affect enzyme binding and complexation to the surface resulting in decrease of enzymatic digestibility of cellulose (Pan et al. 2006; Shuai et al. 2016). Therefore, a low concentration of FA was suggested to be used during pretreatment. When the FA addition decreased to 1.5%, the enzymatic hydrolysis of glucan reached to 85.5 ± 3.0% at 72 h. Therefore, an optimal condition (C80T80t30 with 1.5% FA) was selected for the pretreatment. Morphology comparison of the extracted lignin with and without FA addition after 12 h storing Enzymatic saccharification of substrates with different FA additions Subsequently, FT-IR spectroscopy, TGA, 2D HSQC NMR spectroscopy, and GPC were used to investigate the effects of adding FA on the structures and properties of the EL and CEL. Figure 5 shows the FT-IR spectra of the obtained lignin samples with and without FA addition, and the signals were assigned according to a previous literature (Chong et al. 2018). The spectrum of these four lignin samples showed a wide absorption band at about 3432 cm−1, which is related to the stretching vibration of phenolic or aliphatic OH groups. The bands at about 2935 cm−1 and 2857 cm−1 are attributed to the C–H asymmetric and symmetrical vibrations of the methyl and methylene groups, separately. The signals at 1717 cm−1 are assigned to the C=O stretching vibrations in conjugated carboxylic acid and ketone groups, which is more pronounced after adding FA than that without FA, suggesting that the FA stabilized lignin obtained contained more conjugated C=O group. In addition, the signals at 1599 cm−1 and 1570 cm−1 are corresponded to aromatic skeletal vibrations and the C–H deformation vibrations, respectively. The bands at 1460 cm−1 and 1420 cm−1 originated from the C–H deformations asymmetric in –CH3 of methoxy groups. The typical peaks of GS type lignin at 1328 cm−1, 1273 cm−1, and 1122 cm−1 are corresponded to the breathing vibration of syringyl (S), condensed guaiacyl (G), and guaiacyl ring breathing with C=O stretching vibration. Furthermore, the signal at 1226 cm−1 is ascribed to the C–C, C–O and C=O stretching. In addition, the peaks at 1032 cm−1 and 838 cm−1 are attributed to the aromatic C–H in plane deformation vibrations and the C–H out of plane stretching vibrations. In Fig. 5, similar signal profile indicated that these lignin samples obtained from different pretreatment conditions maintained their core chemical structures as that of native lignin. For the pretreatment with FA addition, new signals appeared at 1032–1122 cm−1 and 1122–1226 cm−1 in the infrared spectrum of the extracted lignin. The peak at 1032–1122 cm−1 represents a characteristic absorption of acetal, which is generated from the reaction between FA and lignin. FT-IR spectra of the obtained lignin The TGA curves of lignin samples obtained from the pretreatment with and without FA addition are shown in Fig. 6. Four samples showed different DTG profile below 100 °C, which was mainly caused by the removal of free water on the surface of lignin. In the range of 100–180 °C, the molecular structure of lignin was relatively stable as revealed by the horizontal TG curve. As the temperature increased to 200 °C above, the increased weight loss rate indicated that thermal decomposition reaction of lignin occurred resulting in cleavage of arylalkyl ether bonds. When temperature reached to 300–400 °C, the maximum weight loss rate was observed, which was mainly caused by oxidation or carbonylation of aliphatic hydroxyl groups and the cleavage of benzene ring and C–C bonds. When temperature risen above 500 °C, the curve was gentle, and the weight loss rate was gradually reduced, which was the finishing stage of pyrolysis. By comparison, CEL has a higher content of β-O-4 bonds, so the thermal decomposition rate is higher than that of EL. Compared with the sample without FA stabilization, the FA stabilized lignin has more residual mass at 800 °C, indicating that the lignin after acetalization has better thermal stability. TGA curves of lignin with and without FA We analyzed the chemical properties of CEL and EL obtained from pretreatment with and without FA addition using 2D HSQC NMR spectroscopy. Figure 7 shows the NMR spectrum concluding a side-chain region (δC/δH 50.0–90.0/2.90–5.70) and an aromatic region (δC/δH 100.0–135.0/6.20–7.90) along with the identified chemical structures. The assignments of main cross-signals in the spectra of lignin were assigned according to a previous publication (He et al. 2017; Ji et al. 2017; Li et al. 2019). The formation of the six-membered 1,3-dioxane structures in the presence of FA was confirmed by the 2D HSQC NMR. Typically, the signals of methoxy groups and major linkages, such as β-aryl-ether (β-O-4′, A unit), resinol (β–β′, B unit), and phenylcoumaran (β-5′, C unit) substructures, were found in the side-chain region (Fig. 7). The methoxy groups (-OCH3) were identified according to the cross signals at δC/δH 55.60–3.71. The cross signals at δC/δH 71.90/4.85, δC/δH 84.40/4.40, δC/δH 85.60/4.20, and δC/δH 59.40/3.70 were attributed to Cα–Hα, Cβ–Hβ and Cγ–Hγ correlation in β-O-4′ substructure (A unit), respectively. Moreover, the β–β' resinol substructures (B unit) were observed by the cross signals at δC/δH 87.70/5.50 (Cα–Hα) and δC/δH 63.40/3.60 (Cγ–Hγ). Furthermore, the β-5' phenylcoumaran substructures (C unit) were also discovered based on the signals of Cα–Hα (δC/δH 85.50/4.60) and Cγ–Hγ (δC/δH 71.20/4.20 and 3.80). Meanwhile, the formation of the six-membered 1, 3-dioxane structures in lignin also confirmed by the signal at δC/δH 92.50/4.80–5.10 in the side chain region, which indicated that FA reacted with lignin during pretreatment with p-TsOH hydrotrope. The disappearance of some structural signals (A, B unit) and the appearance of 1, 3-dioxane structure proved that FA addition during the pretreatment process block the reactive benzylic positions and effectively prevented the irreversible condensation during lignin extraction. Side-chain (left) and aromatic regions (right) in the 2D HSQC NMR spectra of CEL and EL obtained from different pretreatment conditions and their main structure In the aromatic regions, the typical cross signals from syringyl (S) and guaiacyl (G) units were easily discovered in Fig. 7. The S unit was observed with correlation of C2,6–H2,6 at δC/δH 103.80/6.69. Besides, the G units were found according to the signals at δC/δH 111.10/6.98 (C2–H2), δC/δH 114.70/6.71 (C5–H5), and δC/δH 118.90/6.80 (C6–H6). In addition, the p-Coumarate acid was also identified with C2,6–H2,6 correlations at δC/δH 129.80/7.50. The p-benzoate (PB unit) was discovered according the cross signals at C2,6–H2,6 (δC/δH 131.60/7.70). In short, these signals indicated that the CEL and EL contained typical lignin structural features. Overall, adding FA in p-TsOH hydrotrope can block the active reaction sites of aromatic rings and hinder the formation of C–C linkages, thereby reducing the lignin condensation. To explore the influence of FA on the molecular weight of lignin, the weight average molecular weight (Mw), number average molecular weight (Mn) and polydispersity index (PDI, Mw/Mn) were determined by GPC and the results are shown in Table 1. The FA stabilized lignin showed a higher molecular weight (5371 g/mol) and lower polydispersity index (PDI 1.63) than that of extracted lignin without FA reaction. The addition of FA promoted the acetal reaction between FA and lignin resulting in a high molecular weight. The low polydispersity index (PDI < 2) indicates that the obtained lignin is a uniform lignin fragment with relatively stable properties and high industrial value. Table 1 Weight-average molecular weight, number-average molecular weight (Mn) and polydispersity index (PDI, Mw/Mn) of the lignin with FA and without FA High titer ethanol production via a Q-SSF process Because FA addition of 1.5% showed a negligible effect on enzymatic saccharification of glucan, the final glucan-rich solids obtained from C80T80t30 with 1.5% FA were converted into ethanol by a Q-SSF process. The changes of glucose and ethanol concentrations and ethanol conversion rate during Q-SSF are shown in Fig. 8. Within 12 h, the glucose concentration dropped rapidly and the ethanol concentration reached to 29.80 ± 2.3 g/L after 12 h of yeast inoculation. After 60 h of fermentation, the ethanol concentration reached a maximum value of 38.70 ± 3.3 g/L, which was equivalent to the theoretical ethanol yield of 82.90 ± 2.2%, while the concentration of residual glucose was only 4.69 ± 1.4 g/L. It can be seen that there was no obvious inhibitory effect during the process of converting glucose to ethanol, indicating that the pretreatment procedure, specifically, using a recyclable p-TsOH hydrotrope to dissolve lignin under mild condition and stabilized lignin with FA as a quenching agent during pretreatment, achieved both high-quality lignin extraction and efficient enzymatic saccharification of glucan for high-titer ethanol production. The mass balance of biomass is shown in Fig. 9. Therefore, this study is important to the valorization of lignocellulosic biomass. Concentrations of glucose and ethanol and the ethanol yield in the Q-SSF process Mass balance of biomass via hydrotrope pretreatment and Q-SSF In this study, we used a recyclable p-TsOH hydrotrope to pretreat biomass under mild condition and stabilized lignin with FA as a quenching agent during pretreatment. At C80T80t30, the removal of hemicellulose and lignin achieved 83.8 ± 0.7% and 67.1 ± 2.6%, respectively. Meanwhile, FA can effectively prevent the vicious condensation of lignin as revealed by a lighter color. The lignin samples were characterized by FTIR spectroscopy, TGA, 2D HSQC NMR spectroscopy, and GPC. The results indicated that the FA stabilized lignin showed a higher molecular weight (5371 g/mol) and polydispersity index (PDI 1.63). Subsequently, the pretreated solids obtained from C80T80t30 with 1.5% FA addition were converted into ethanol by a Q-SSF process. The maximum ethanol concentration reached 38.7 ± 3.3 g/L, which was equivalent to the theoretical ethanol yield of 82.9 ± 2.2%. In summary, the pretreatment strategy achieved both high-quality lignin extraction and efficient enzymatic saccharification of glucan for high-titer ethanol production. 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Curr Org Chem 20(26):2799–2809 The authors would like to express thanks for the supports from the Youth Program of National Natural Science Foundation of China (31901268), the International Cooperation Funding of Qilu University of Technology (QLUTGJHZ2018027), the Young Doctors Cooperation Foundation of Qilu University of Technology (2019BSHZ0023), the Innovation and Entrepreneurship Training Program for College Students in Shandong Province (S202010431058), the Project Supported by the Foundation (No. XWZR201902) of State Key Laboratory of Biobased Material and Green Papermaking, Qilu University of Technology, Shandong Academy of Sciences. State Key Laboratory of Biobased Material and Green Papermaking, Qilu University of Technology (Shandong Academy of Sciences), 3501 Daxue road, Jinan, 250353, China Hairui Ji, Le Wang, Zhipeng Yao, Cuihua Dong & Zhiqiang Pang School of Chemistry and Chemical Engineering, Qilu University of Technology (Shandong Academy of Sciences), 3501 Daxue road, Jinan, 250353, China Furong Tao State Key Laboratory of Microbial Technology, Shandong University, Jinan, China Xuezhi Li Hairui Ji Le Wang Zhipeng Yao Cuihua Dong Zhiqiang Pang HJ and LW conducted the experiments; HJ and CD conceived and designed the experiments; HJ analyzed the results and wrote the paper. FT, XL, and ZP provided guidance for experiment design. All authors read and approved the final manuscript. Correspondence to Xuezhi Li or Cuihua Dong. Ji, H., Wang, L., Tao, F. et al. A hydrotrope pretreatment for stabilized lignin extraction and high titer ethanol production. Bioresour. Bioprocess. 9, 40 (2022). https://doi.org/10.1186/s40643-022-00530-6 Recyclable hydrotrope, Lignin quenching agent Q-SSF Bioenergy: A Sustainable Solution for Carbon Neutrality	CommonCrawl
OSA Publishing > Applied Optics > Volume 59 > Issue 22 > Page G107 Towards cavity-free ground-state cooling of an acoustic-frequency silicon nitride membrane Christian M. Pluchar, Aman R. Agrawal, Edward Schenk, and Dalziel J. Wilson Christian M. Pluchar,1 Aman R. Agrawal,1 Edward Schenk,2 and Dalziel J. Wilson1,2,* 1College of Optical Sciences, University of Arizona, 1630 E. University Blvd., Tucson, Arizona 85721, USA 2Department of Physics, University of Arizona, 1118 E. Fourth St., Tucson, Arizona 85721, USA *Corresponding author: dalziel@optics.arizona.edu Dalziel J. Wilson https://orcid.org/0000-0002-0822-9892 C Pluchar A Agrawal E Schenk Issue 22, pp. G107-G111 •https://doi.org/10.1364/AO.394388 Christian M. Pluchar, Aman R. Agrawal, Edward Schenk, and Dalziel J. Wilson, "Towards cavity-free ground-state cooling of an acoustic-frequency silicon nitride membrane," Appl. Opt. 59, G107-G111 (2020) Spotlight Summary Spotlight Summary by Nils Johan Engelsen Slowing down a child on a swing is perhaps the most ubiquitous form of feedback cooling, but in recent years the technique has also been widely applied in the field of optomechanics. In well-engineered cavity optomechanical systems, laser light can be used to measure the position of a mechanical oscillator and apply an appropriate feedback force. These previous works relied on an optical cavity to enhance measurement precision and achieved cooling all the way to the quantum ground state. Pluchar et al. take the first step towards achieving cavity-free feedback cooling of a mechanical oscillator to its ground state: using a free-space interferometer they cool a Si3N4 membrane by five orders of magnitude, taking it from room temperature to 5 millikelvin (phonon occupation of 3000). The membrane position is measured using a balanced Michelson interferometer and feedback is applied by radiation pressure with a second, auxiliary light field. The authors project that ground state cooling could be achieved with improved mechanical resonators at moderate cryogenic temperatures (~5K). Article Reference Appl. Opt. 59(22) G107-G111 (2020) View: Abstract \| HTML \| PDF You must log in to add comments. Efficient ground state cooling of a mechanical resonator in a membrane-in-the-middle system by a single drive (JOSAB) Phonon counting thermometry of an ultracoherent membrane resonator near its motional ground state (OPTICA) Thermal intermodulation noise in cavity-based measurements (OPTICA) Atomic force microscopy Nanopositioning equipment Tunable diode lasers Original Manuscript: April 3, 2020 Revised Manuscript: May 10, 2020 Manuscript Accepted: May 10, 2020 August 7, 2020 Spotlight on Optics MEASUREMENT-BASED FEEDBACK COOLING TRAMPOLINE RESONATOR INTERFEROMETRIC READOUT RADIATION PRESSURE FEEDBACK COOLING SUMMARY AND OUTLOOK Equations (10) We demonstrate feedback cooling of a millimeter-scale, 40 kHz SiN membrane from room temperature to 5 mK (3000 phonons) using a Michelson interferometer, and discuss the challenges to ground-state cooling without an optical cavity. This advance appears within reach of current membrane technology, positioning it as a compelling alternative to levitated systems for quantum sensing and fundamental weak force measurements. Strained thin-film resonators (strings and membranes) with millimeter dimensions can support acoustic frequency modes with extremely high quality factors, leveraging the effect of dissipation dilution [1–4]. It has been speculated that they may enable room-temperature quantum optomechanics [3], ultraprecise force and acceleration sensing [5,6], quantum memories, and detection of fundamental weak signals such as spontaneous waveform collapse [7] and ultralight dark matter [8]. Here we discuss an additional potential of acoustic frequency thin-film resonators, which is to remove the need for a cavity in quantum optomechanics experiments. This possibility is due to the large zero-point fluctuations of an acoustic frequency nanomechanical resonator, as exploited in experiments with levitated nanoparticles [9]. In contrast to levitated nanoparticles, thin-film resonators can be read out with high efficiency by direct reflection or near-field sensing [10]. The main challenge to reaching the quantum regime is technical noise, such as laser relaxation oscillations, which can be far in excess of shot noise at acoustic frequencies. Optical absorption can 2also lead to large bolometric effects in tethered nanostructures, while in principle they can be decoupled from motion of a levitated particle [11]. To illustrate the potential for "cavity-free" quantum optomechanics, we describe an experiment in which the fundamental mode of a 2.5 mm, high-stress silicon nitride (${{\rm Si}_3}{{\rm N}_4}$) trampoline resonator [3,4] is subject to radiation pressure feedback cooling using a Michelson interferometer. The conditions for ground-state cooling are twofold [12]: (1) the oscillator's thermal decoherence rate ${\Gamma _{{\rm th}}}$ must not exceed its frequency ${\Omega _0}$, (1)$${\Gamma _{{\rm th}}} = \frac{{{k_{\rm B}}{T_0}}}{{\hbar {Q_0}}} \lt {\Omega _0},$$ and (2) the measurement imprecision $S_\textit{xx}^{{\rm imp}}$ (expressed as a single-sided power spectral density) must be low enough to resolve zero-point motion ${x_{{\rm zp}}}$ in the thermal decoherence time (2)$$S_\textit{xx}^{{\rm imp,gs}} = \frac{{4x_{{\rm zp}}^2}}{{{\Gamma _{{\rm th}}}}} = \frac{{2{\hbar ^2}}}{{{k_{\rm B}}{T_0}}}\frac{{{Q_0}}}{{m{\Omega _0}}},$$ where ${T_0}$ is the intrinsic device temperature. In our experiment, operated at room temperature, an optimized trampoline design [3,4] yields a fundamental frequency of ${\Omega _0} = 2\pi \cdot 40\;{\rm kHz} $, a quality factor ${Q_0} = 3 \times {10^7}$, and an effective mass of $m = 12 \;{\rm ng}$, corresponding to a thermal decoherence rate of ${\Gamma _{{\rm th}}} = 5{\Omega _0}$, a zero-point displacement of ${x_{{\rm zp}}} = 4\;{\rm fm}$, and a ground-state cooling requirement of [Eq. (2)] ${(S_\textit{xx}^{{\rm imp,gs}})^{1/2}} \approx {10^{- 17}}\;{\rm m}/\sqrt {{\rm Hz}}$. The latter is 3 orders of magnitude below the sensitivity of our interferometer; nevertheless, using an auxiliary laser field as a radiation pressure actuator, we realize feedback cooling to an effective temperature of ${T_{{\rm eff}}} = 5\;{\rm mK}$, corresponding to a mean phonon number of (3)$$\langle n\rangle = \frac{{{k_B}{T_{{\rm eff}}}}}{{\hbar {\Omega _0}}} \approx \sqrt {\frac{{S_\textit{xx}^{{\rm imp}}}}{{S_\textit{xx}^{{\rm imp,gs}}}}} \approx 3 \times {10^3}.$$ Below we discuss the design and limitations of this experiment and speculate that $\langle n\rangle \sim 1$ should be possible with simple modifications, including pre-cooling in a helium cryostat and using a common path interferometer topology. 1. MEASUREMENT-BASED FEEDBACK COOLING In feedback cooling protocols, a continuous position measurement is used to suppress the thermal motion of a mechanical oscillator by derivative feedback (velocity damping). The technique dates back to regulation of electrometers [13] and is commonly used in atomic force microscopes to increase their dynamic range [14]. More recently, feedback cooling has received attention in the cavity optomechanics community as a means to prepare a nanomechanical oscillator in its ground state [15,16]. Cooling to $\langle n\rangle \sim 4$ has been achieved with a free space optically levitated nanoparticle [17], while cavity-enhanced measurements have been used to cool a ${{\rm Si}_3}{{\rm N}_4}$ nanostring to $\langle n\rangle \sim 4$ [12] and, more recently, a ${{\rm Si}_3}{{\rm N}_4}$ membrane to $\langle n\rangle \sim 0.3$ [18]. An important feature of feedback cooling is that, unlike optomechanical sideband cooling [19,20], it does not require a "good" (sideband-resolved) cavity to reach the ground state [21,22]. It is only necessary to achieve sufficient measurement efficiency, which in fact requires a "bad" cavity and in principle requires no cavity at all (enabling use of nonresonant sensors such as single-electron transistors and superconducting quantum interference devices) [17,23–26]. To this end, agnostic to the measurement scheme, consider a real-time estimate $y$ of the oscillator displacement $x$ obscured by imprecision noise ${x_{{\rm imp}}}$: (4)$$y = x + {x_{{\rm imp}}}.$$ Feedback cooling can be understood by including a velocity-proportional feedback force in the Langevin equation [24] (5)$$m\ddot x + m{\Gamma _{0}}\dot x + m\Omega _{0}^2x = \sqrt {2{k_B}{T_0}m{\Gamma _0}} \xi (t) - gm{\Gamma _0}\dot y,$$ where $\xi (t)$ is a normalized Gaussian white noise process and ${\Gamma _0} = {\Omega _0}/{Q_0}$ is the intrinsic mechanical damping rate. Applying the Wiener–Khinchin theorem, the spectral density of physical $(x)$ and apparent $(y)$ displacement can be expressed as [12,18] (6a)$$\frac{{{S_\textit{xx}}[\Omega]}}{{2S_\textit{xx}^{{\rm zp}}}} = \|{\chi _g}[\Omega {]\|^2}\left({{n_{{\rm th}}} + {g^2}{n_{{\rm imp}}}} \right),$$ (6b)$$\frac{{{S_\textit{yy}}[\Omega]}}{{2S_\textit{xx}^{{\rm zp}}}} = \|{\chi _g}[\Omega {]\|^2}\left({{n_{{\rm th}}} + {{(1 + g)}^2}\|{\chi _0}[\Omega {{]\|}^{- 2}}{n_{{\rm imp}}}} \right),$$ where $S_\textit{xx}^{{\rm zp}} = 4x_{{\rm zp}}^2/{\Gamma _0}$ is the zero-point displacement spectral density, ${n_{{\rm th}}} = {k_{\rm B}}{T_0}/m{\Omega _0}$ is the thermal bath occupation, and $\chi _g^{- 1} \approx (1 + g) + 2i(\Omega - {\Omega _0})/{\Gamma _0}$ is the closed-loop mechanical susceptibility. Evidently feedback damping can be "cold" in the sense that ${n_{{\rm imp}}} = S_\textit{xx}^{{\rm imp}}/2S_\textit{xx}^{{\rm zp}} \lt {n_{{\rm th}}}$ when the measurement resolves the thermal motion. Increasing the feedback gain $g$ thus reduces the average displacement of the oscillator $\langle {x^2}\rangle = \int\! {S_\textit{xx}}[\Omega]/2\pi$, resulting in a mean phonon number of (7)$$\langle n\rangle + \frac{1}{2} = \frac{{\langle {x^2}\rangle}}{{2x_{{\rm zp}}^2}} = \frac{{{n_{{\rm th}}} + {g^2}{n_{{\rm imp}}}}}{{1 + g}} \ge 2\sqrt {{n_{{\rm th}}}{n_{{\rm imp}}}}.$$ Ground-state cooling requires accounting for measurement back-action ${n_{{\rm th}}} \to {n_{{\rm th}}} + {n_{{\rm ba}}} = {n_{{\rm th}}} + \eta /(16{n_{{\rm imp}}})$, where $\eta \in [0,1]$ is the measurement efficiency [12,18]. Equation (7) thus yields Eq. (2) for $\langle n\rangle \lt 1$ and Eq. (3) for $1 \ll \langle n\rangle \ll {n_{{\rm th}}}$ (noting that ${\Gamma _{{\rm th}}} = {\Gamma _0}{n_{{\rm th}}}$). In addition to high efficiency, we emphasize that reaching low occupancy is facilitated by having a high $Q/m{\Omega _0}$ factor, which is equivalent to a high force sensitivity $S_\textit{FF}^{{\rm th}} = 4{k_B}Tm{\Omega _0}/Q$. 2. TRAMPOLINE RESONATOR Our mechanical resonator is a modified version of the ${{\rm Si}_3}{{\rm N}_4}$ trampoline introduced by Reinhardt [4] and Norte et al. [3]. Trampoline resonators, like strings [27–29], exhibit quality factors scaling as $Q \propto {Q_{\text{mat}}}(h)\sqrt \sigma L/h$, where $Q_{{\rm mat}}^{- 1}$ is the material loss tangent, $L$ is the tether length, $h$ is the film thickness, and $\sigma$ is the tensile stress in the film. Since ${\Omega _0} \propto \sqrt \sigma /L$ and $m \propto hL$, the implication is that $Q/m{\Omega _0} \propto {Q_{{\rm mat}}}(h)L/{h^2}$. Counterintuitively, larger devices can have larger zero-point fluctuations. Fig. 1. ${{\rm Si}_3}{{\rm N}_4}$ trampoline resonator. (Top left) Camera image of a typical device. (Top right) Microscope image of the trampoline used in the experiment. (Bottom right) Finite element simulation of the fundamental 40 kHz vibrational mode. (Bottom left) Energy ringdown of the fundamental mode before (red) and after (blue) deposition of a dust particle onto a tether. Download Full Size \| PPT Slide \| PDF The trampoline used in our experiment is shown in Fig. 1. The device is suspended from a $h \approx 90\,{\rm nm}$ thick ${{\rm Si}_3}{{\rm N}_4}$ film on a $200\,\unicode{x00B5}{\rm m}$ thick Si wafer (WaferPro) using a standard two-sided photolithography and wet etching technique [3,4,29]. A $200\,\unicode{x00B5}{\rm m}$ pad and $L \approx 1.7$ mm long, $w = 4.2\,\,\unicode{x00B5}{\rm m}$ wide tethers were chosen, as well as an "optimal" [30] $50\,\,\unicode{x00B5}{\rm m}$ radius fillet for this window size (2.5 mm) and tether width. Mechanical ringdown measurements performed in high vacuum [${ \lt\! 10^{- 7}}\; {\rm mbar}$, Fig. 1(c)] reveal a fundamental frequency of ${\Omega _0} = 2\pi \times 39.9\;{\rm kHz} $ and a quality factor as high as $Q = 4.4 \times {10^7}$, which agrees with finite element simulations (COMSOL) assuming a film stress of $\sigma = 0.9 \; {\rm GPa}$ and internal quality factor of ${Q_{{\rm mat}}} = 6 \times {10^3}$. (The latter is consistent with the ${Q_{\text{mat}}} \propto h$ surface loss model of Villanueva et al. [28], suggesting that our device is not limited by clamping loss.) For the experiments described below, dust deposited on the tether resulted in a reduced quality factor of $Q = 2.6 \times {10^7}$. Together with a simulated effective mass of $m = 12 \; {\rm ng}$, this implies a force sensitivity of $S_\textit{FF}^{{\rm th}} = (43\;{\rm aN}/\sqrt {{\rm Hz}} {)^2}$, a zero-point displacement of $S_\textit{xx}^{{\rm zp}} = (86 \; {\rm fm}/\sqrt {{\rm Hz}} {)^2}$, and a ground-state cooling requirement $S_\textit{xx}^{{\rm imp,gs}} = S_\textit{xx}^{{\rm zp}}/{n_{{\rm th}}} \approx {(0.68 \times {10^{- 17}} \;{\rm m}/\sqrt {{\rm Hz}})^2}$. Fig. 2. Setup for probing the trampoline, consisting of a confocal microscope embedded in a balanced Michelson interferometer. Electronics for stabilizing the interferometer path length (PI = proportional integral controller, Newport LB1005) and for radiation pressure feedback cooling (see main text for details) are indicated in black. An image of the focused optical beam on the trampoline pad is shown at bottom left. 3. INTERFEROMETRIC READOUT Displacement of the trampoline was read out using a confocal microscope integrated into a Michelson interferometer [10]. Details are shown in Fig. 2. To minimize gas damping, the device chip is mounted in a high vacuum chamber operating at ${ \lt\! 10^{- 7}}\; {\rm mbar}$. This is enabled by a long-working-distance microscope objective (Mitutoyo M Plan APO 10X) with a spot diameter of ${\lt}5\,\,\unicode{x00B5}{\rm m}$. The light source used for the experiment was an 850 nm external cavity diode laser (Newport TLB-6716). To mitigate laser frequency and intensity noise, both the arm length and power of the interferometer were carefully balanced. Fig. 3. Characterization of interferometer sensitivity. Upper plot: imprecision in noise quanta units versus power, compared to Eq. (8) (blue line). Lower plot: apparent displacement spectrum of the trampoline versus frequency for different optical powers. The dashed line is a model for ${S_\textit{xx}}$. The blue line is obtained by blocking the signal arm of the interferometer at highest power. (Inset: broadband spectrum for highest power). Ideally, the interferometer sensitivity is limited by shot noise (8)$$S_\textit{xx}^{{\rm imp,shot}} = \frac{{\hbar c\lambda}}{{16\pi\! \eta}}\frac{{{R_{\rm m}}}}{P},$$ where $P$ is the power incident on the membrane, $\lambda$ is the laser wavelength, ${R_{\rm m}}$ is the membrane reflectance, and $\eta \in [0,1]$ is the detection efficiency. We investigated this limit by recording apparent displacement spectra ${S_\textit{yy}}$ at different optical powers, where $y$ is proportional to the voltage signal produced by the balanced photoreceiver (Newport 1807). Results are shown in Fig. 3. To calibrate each measurement, a piezo underneath the device chip was used to drive the trampoline near its fundamental resonance with a coherent amplitude of ${x_{{\rm cal}}} = 0.8$ pm (inferred by bootstrapping to the area beneath the thermal noise peak, $\langle {x^2}\rangle \approx 2x_{{\rm zp}}^2{n_{{\rm th}}}$, after an averaging time ${\gt}{Q_0}/{\Omega _0}$). At low powers ($P \lt 100\; \unicode{x00B5}{\rm W}$), $S_\textit{xx}^{{\rm imp}}$ scales inversely with power, as expected for shot noise, with an apparent efficiency of $\eta \approx 10\%$ (using ${R_{\rm m}} = 0.3$ [31]). This value is consistent with the return loss of our microscope objective (which employs a free-space-to-fiber coupler), and in principle allows cooling to $\langle n\rangle \approx 1.1$. In practice, the interferometer is limited by extraneous noise at sufficiently high power. This is seen in Fig. 3 for powers above 1 mW, where the noise floor saturates to $S_\textit{xx}^{{\rm imp,ext}} \approx 10 \;{\rm fm}/\sqrt {{\rm Hz}}$. Broadband measurements (Fig. 3, inset) suggest that $S_\textit{xx}^{{\rm imp,ext}}$ is related to differential polarization or path-length fluctuations, possibly exacerbated by peaking of the homodyne phase lock. (We note that extraneous laser frequency noise was ruled out by introducing a path length imbalance of several millimeters, to no apparent effect.) Although an impressive 2 orders of magnitude below the intrinsic zero-point motion $({n_{{\rm imp,ext}}} \approx 0.01)$, this extraneous noise practically limits feedback cooling of the fundamental trampoline mode to $\langle n\rangle \approx 2.5 \times {10^3}$ starting at room temperature (${n_{{\rm th}}} = 1.6 \times {10^8}$), according to Eq. (7). Heating from optical absorption is another important consideration at high powers. To investigate this effect, we consider the off-resonant thermal noise in Fig. 3, which in the presence of heating should increase linearly with power (${S_\textit{xx}}[\Omega - {\Omega _0} \gg \;g{\Gamma _0}] \propto {n_{{\rm th}}}{\Gamma _0}/(\Omega - {\Omega _0}{)^2}$). The variation observed is within the ${\sim}10\%$ statistical error of the spectral density estimate, suggesting that heating is less than $10 \; {\rm K}/{\rm mW}$. This value is consistent with a simple heat conduction model $dT/dP \approx \alpha L/4wh\kappa$, assuming a thermal conductivity of $\kappa = 3 \; {\rm W}/{\rm m} {\rm K}$ and a conservative optical absorption coefficient of $\alpha = 10\;{\rm ppm} $ [31]. 4. RADIATION PRESSURE FEEDBACK COOLING Feedback cooling was carried out using radiation pressure actuation. The main advantage of this approach is its high bandwidth; however, we note that other methods such as piezoelectric [32] and dielectric [33] actuation are in principle equally viable and may be simpler to interface with feedback electronics. To implement radiation pressure feedback, we introduce a second laser beam into the microscope, which is intensity modulated by an amplified copy of the photosignal. Specifically, we use a 670 nm laser diode (Hitachi HL6712) modulated by dithering its drive current about the threshold value. To approximate derivate feedback while suppressing feedback to higher-order modes, the photosignal is passed through a 10–50 kHz bandpass filter and a delay line, resulting in an approximately $\phi = 90^ \circ$ phase shift for frequencies near mechanical resonance. The feedback force can in this case be approximated as (9)$$\delta\! {F_{{\rm fb}}} \approx - g\!m{\Gamma _0}(\dot y + {\Omega _0}\cot (\phi)y),$$ corresponding to a normalized susceptibility ${\chi _g}{[\Omega]^{- 1}} \approx (1 + g) + 2i(\Omega - {\Omega _0})/{\Gamma _0} + ig\cot (\phi)$, where $ig\cot (\phi)$ is a residual feedback stiffening term that contributes negligibly to cooling. The results of feedback cooling with a 3 mW read out beam and a 60 µW feedback beam are shown in Fig. 4. The feedback gain is tuned electronically using a voltage preamplifier (Stanford Research Systems SR560). To estimate $\langle n\rangle$, thermal noise spectra are fit to Eq. (6a) with $g$ as a free parameter, assuming ${n_{{\rm th}}} = 1.56 \times {10^8}$, ${n_{{\rm imp}}} = 0.013$, ${\Gamma _0} = 2\pi \cdot 1.5\; {\rm mHz}$, and $\phi = - 0.15$ [Eq. (9)]. To facilitate fitting, in Fig. 4, we focus on high gain settings for which the loaded damping rate $(1 + g){\Gamma _0} \gt 1\; {\rm Hz}$. The model accurately reproduces the noise spectra until the damped peak coincides with the noise floor, for which the inferred gain is $g = 1.4 \times {10^5}$, corresponding to $\langle n\rangle = 3.0 \times {10^3}$. At higher gain, the noise floor exhibits typical "squashing" behavior [12,34], and the inferred $\langle n\rangle$ begins to increase. Fig. 4. Radiation pressure feedback cooling. Upper plot: feedback cooling curve for parameters described in the main text. Colored points correspond to models overlaying experimental data. Lower plot: experimental measurements (colored) overlaid with models (dashed curves) using Eq. (9). The solid black curve is a model for $g = 0$ (no feedback). 5. SUMMARY AND OUTLOOK We have demonstrated measurement-based feedback cooling of a 40 kHz ${{\rm Si}_3}{{\rm N}_4}$ trampoline resonator from room temperature ($1.6 \times {10^8}$ phonons) to an effective temperature of 5 mK ($3 \times {10^3}$ phonons) using a simple two-path interferometer. The main limitation of our experiment is technical noise at the level of $10 \; {\rm fm}/\sqrt {{\rm Hz}}$. Absent this noise, the apparent 10% efficiency of our interferometer would in principle enable cooling to $\langle n\rangle \sim 100$ with a probe power of several megawatts. Operating at 4 K, assuming no increase in mechanical Q and no photothermal heating, would enable cooling to $\langle n\rangle \sim 10$, for which motional sideband asymmetry could be readily measured. We speculate that a combination of monolithic interferometer design and moderate cryogenics could give access to $\langle n\rangle \sim 1$ without an optical cavity for state-of-the-art ${{\rm Si}_3}{{\rm N}_4}$ thin-film resonators. Particularly compelling are "soft-clamped" nanobeams [2], which have demonstrated megahertz modes with quality factors approaching ${10^9}$ and zero-point spectral densities exceeding $1 \;{\rm pm}/\sqrt {{\rm Hz}}$, and can be read out with high efficiency by evanescent coupling to optical waveguide. For soft-clamped resonators, an important challenge is the large density of states and low thermal conductance of the phononic crystal shield, which reduces power handling capacity and can introduce extraneous thermal noise. Clamp-optimized trampolines [3,4,30] might offer a simpler route, since the fundamental mode is well isolated and can also have ${Q_0}{ \gt 10^8}$ at millimeter dimensions [2]. In the future, resonators made of strained crystalline thin films promise ${Q_0}{ \gt 10^9}$ and increased thermal conductivity at 4 K [35]. A recent proposal for soft-clamping fundamental modes using a "fractal clamp" might push this performance even further [36]. National Science Foundation (ECCS-1725571). C.M.P. gratefully acknowledges support from an Amherst College Fellowship. The reactive ion etcher used in this study was acquired by an NSF MRI grant ECCS-1725571. REFERENCES AND NOTE 1. Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, "Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution," Nat. Nanotechnol. 12, 776–783 (2017). [CrossRef] 2. A. H. Ghadimi, S. A. Fedorov, N. J. Engelsen, M. J. Bereyhi, R. Schilling, D. J. Wilson, and T. J. Kippenberg, "Elastic strain engineering for ultralow mechanical dissipation," Science 360, 764–768 (2018). [CrossRef] 3. R. A. Norte, J. P. Moura, and S. Gröblacher, "Mechanical resonators for quantum optomechanics experiments at room temperature," Phys. Rev. Lett. 116, 147202 (2016). [CrossRef] 4. C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, "Ultralow-noise sin trampoline resonators for sensing and optomechanics," Phys. Rev. X 6, 021001 (2016). [CrossRef] 5. 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Ribichini, and P. Tombesi, "Macroscopic mechanical oscillators at the quantum limit through optomechanical cooling," J. Opt. Soc. Am. B 20, 1054–1065 (2003). [CrossRef] 17. F. Tebbenjohanns, M. Frimmer, V. Jain, D. Windey, and L. Novotny, "Motional sideband asymmetry of a nanoparticle optically levitated in free space," Phys. Rev. Lett. 124, 013603 (2020). [CrossRef] 18. M. Rossi, D. Mason, J. Chen, Y. Tsaturyan, and A. Schliesser, "Measurement-based quantum control of mechanical motion," Nature 563, 53–58 (2018). [CrossRef] 19. I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, "Theory of ground state cooling of a mechanical oscillator using dynamical backaction," Phys. Rev. Lett. 99, 093901 (2007). [CrossRef] 20. F. Marquardt, J. P. Chen, A. A. Clerk, and S. Girvin, "Quantum theory of cavity-assisted sideband cooling of mechanical motion," Phys. Rev. Lett. 99, 093902 (2007). [CrossRef] 21. C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, "Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes," Phys. Rev. A 77, 033804 (2008). [CrossRef] 22. K. Jacobs, H. I. Nurdin, F. W. Strauch, and M. James, "Comparing resolved-sideband cooling and measurement-based feedback cooling on an equal footing: analytical results in the regime of ground-state cooling," Phys. Rev. A 91, 043812 (2015). [CrossRef] 23. P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, "Feedback cooling of a single trapped ion," Phys. Rev. Lett. 96, 043003 (2006). [CrossRef] 24. M. Poggio, C. Degen, H. Mamin, and D. Rugar, "Feedback cooling of a cantilever's fundamental mode below 5 mK," Phys. Rev. Lett. 99, 017201 (2007). [CrossRef] 25. A. Hopkins, K. Jacobs, S. Habib, and K. Schwab, "Feedback cooling of a nanomechanical resonator," Phys. Rev. B 68, 235328 (2003). [CrossRef] 26. A. Vinante, A. Kirste, A. Den Haan, O. Usenko, G. Wijts, E. Jeffrey, P. Sonin, D. Bouwmeester, and T. Oosterkamp, "High sensitivity squid-detection and feedback-cooling of an ultrasoft microcantilever," App. Phys. Lett. 101, 123101 (2012). [CrossRef] 27. A. H. Ghadimi, D. J. Wilson, and T. J. Kippenberg, "Radiation and internal loss engineering of high-stress silicon nitride nanobeams," Nano Lett. 17, 3501–3505 (2017). [CrossRef] 28. L. G. Villanueva and S. Schmid, "Evidence of surface loss as ubiquitous limiting damping mechanism in sin micro- and nanomechanical resonators," Phys. Rev. Lett. 113, 227201 (2014). [CrossRef] 29. We follow the method of Reinhardt et al. [4] using a simplified Teflon sample holder for wet etching. Fabrication begins with standard two-sided photolithography followed by dry etch of ${{\rm Si}_3}{{\rm N}_4}$, using plasma Ar+SF$_{6}$, to define the trampoline on one side and a square window on the other. The chip is then wet etched from both sides using a 45% percent KOH solution at 65 C for 21 hours. After the trampoline is released, the gradual dilution method described in [4] is used in lieu of a critical point dryer, in order to suspend the trampoline. 30. P. Sadeghi, M. Tanzer, S. L. Christensen, and S. Schmid, "Influence of clamp-widening on the quality factor of nanomechanical silicon nitride resonators," J. Appl. Phys. 126, 165108 (2019). [CrossRef] 31. D. Wilson, C. Regal, S. Papp, and H. Kimble, "Cavity optomechanics with stoichiometric sin films," Phys. Rev. Lett. 103, 207204 (2009). [CrossRef] 32. S. Sridaran and S. A. Bhave, "Electrostatic actuation of silicon optomechanical resonators," Opt. Express 19, 9020–9026 (2011). [CrossRef] 33. Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, "Universal transduction scheme for nanomechanical systems based on dielectric forces," Nature 458, 1001–1004 (2009). [CrossRef] 35. E. Romero, V. M. Valenzuela, A. R. Kermany, F. Iacopi, and W. P. Bowen, "Engineering the dissipation of crystalline micromechanical resonators," Phys. Rev. Applied 13, 04407 (2020). [CrossRef] 36. S. A. Fedorov, A. Beccari, N. J. Engelsen, and T. J. Kippenberg, "Fractal-like mechanical resonators with a soft-clamped fundamental mode," Phys. Rev. Lett. 124, 025502 (2020). [CrossRef] Article Order Y. Tsaturyan, A. Barg, E. S. Polzik, and A. Schliesser, "Ultracoherent nanomechanical resonators via soft clamping and dissipation dilution," Nat. Nanotechnol. 12, 776–783 (2017). [Crossref] A. H. Ghadimi, S. A. Fedorov, N. J. Engelsen, M. J. Bereyhi, R. Schilling, D. J. Wilson, and T. J. Kippenberg, "Elastic strain engineering for ultralow mechanical dissipation," Science 360, 764–768 (2018). R. A. Norte, J. P. Moura, and S. Gröblacher, "Mechanical resonators for quantum optomechanics experiments at room temperature," Phys. Rev. Lett. 116, 147202 (2016). C. Reinhardt, T. Müller, A. Bourassa, and J. C. Sankey, "Ultralow-noise sin trampoline resonators for sensing and optomechanics," Phys. Rev. X 6, 021001 (2016). R. Fischer, D. P. McNally, C. Reetz, G. G. Assumpcao, T. Knief, Y. Lin, and C. A. Regal, "Spin detection with a micromechanical trampoline: towards magnetic resonance microscopy harnessing cavity optomechanics," New J. Phys. 21, 043049 (2019). A. G. Krause, M. Winger, T. D. Blasius, Q. Lin, and O. Painter, "A high-resolution microchip optomechanical accelerometer," Nat. Photonics 6, 768–772 (2012). S. Nimmrichter, K. Hornberger, and K. Hammerer, "Optomechanical sensing of spontaneous wave-function collapse," Phys. Rev. Lett. 113, 020405 (2014). D. Carney, A. Hook, Z. Liu, J. M. Taylor, and Y. Zhao, "Ultralight dark matter detection with mechanical quantum sensors," arXiv preprint arXiv:1908.04797 (2019). Z.-Q. Yin, A. A. Geraci, and T. Li, "Optomechanics of levitated dielectric particles," Int. J. Mod. Phys. B 27, 1330018 (2013). A. Barg, Y. Tsaturyan, E. Belhage, W. H. Nielsen, C. B. Møller, and A. Schliesser, "Measuring and imaging nanomechanical motion with laser light," Appl. Phys. B 123, 8 (2017). E. Hebestreit, R. Reimann, M. Frimmer, and L. Novotny, "Measuring the internal temperature of a levitated nanoparticle in high vacuum," Phys. Rev. A 97, 043803 (2018). D. Wilson, V. Sudhir, N. Piro, R. Schilling, A. Ghadimi, and T. Kippenberg, "Measurement-based control of a mechanical oscillator at its thermal decoherence rate," Nature 524, 325–329 (2015). J. Milatz, J. Van Zolingen, and B. Van Iperen, "The reduction in the Brownian motion of electrometers," Physica 19, 195–202 (1953). J. Mertz, O. Marti, and J. Mlynek, "Regulation of a microcantilever response by force feedback," App. Phys. Lett. 62, 2344–2346 (1993). J.-M. Courty, A. Heidmann, and M. Pinard, "Quantum limits of cold damping with optomechanical coupling," Eur. Phys. J. D 17, 399–408 (2001). D. Vitali, S. Mancini, L. Ribichini, and P. Tombesi, "Macroscopic mechanical oscillators at the quantum limit through optomechanical cooling," J. Opt. Soc. Am. B 20, 1054–1065 (2003). F. Tebbenjohanns, M. Frimmer, V. Jain, D. Windey, and L. Novotny, "Motional sideband asymmetry of a nanoparticle optically levitated in free space," Phys. Rev. Lett. 124, 013603 (2020). M. Rossi, D. Mason, J. Chen, Y. Tsaturyan, and A. Schliesser, "Measurement-based quantum control of mechanical motion," Nature 563, 53–58 (2018). I. Wilson-Rae, N. Nooshi, W. Zwerger, and T. J. Kippenberg, "Theory of ground state cooling of a mechanical oscillator using dynamical backaction," Phys. Rev. Lett. 99, 093901 (2007). F. Marquardt, J. P. Chen, A. A. Clerk, and S. Girvin, "Quantum theory of cavity-assisted sideband cooling of mechanical motion," Phys. Rev. Lett. 99, 093902 (2007). C. Genes, D. Vitali, P. Tombesi, S. Gigan, and M. Aspelmeyer, "Ground-state cooling of a micromechanical oscillator: Comparing cold damping and cavity-assisted cooling schemes," Phys. Rev. A 77, 033804 (2008). K. Jacobs, H. I. Nurdin, F. W. Strauch, and M. James, "Comparing resolved-sideband cooling and measurement-based feedback cooling on an equal footing: analytical results in the regime of ground-state cooling," Phys. Rev. A 91, 043812 (2015). P. Bushev, D. Rotter, A. Wilson, F. Dubin, C. Becher, J. Eschner, R. Blatt, V. Steixner, P. Rabl, and P. Zoller, "Feedback cooling of a single trapped ion," Phys. Rev. Lett. 96, 043003 (2006). M. Poggio, C. Degen, H. Mamin, and D. Rugar, "Feedback cooling of a cantilever's fundamental mode below 5 mK," Phys. Rev. Lett. 99, 017201 (2007). A. Hopkins, K. Jacobs, S. Habib, and K. Schwab, "Feedback cooling of a nanomechanical resonator," Phys. Rev. B 68, 235328 (2003). A. Vinante, A. Kirste, A. Den Haan, O. Usenko, G. Wijts, E. Jeffrey, P. Sonin, D. Bouwmeester, and T. Oosterkamp, "High sensitivity squid-detection and feedback-cooling of an ultrasoft microcantilever," App. Phys. Lett. 101, 123101 (2012). A. H. Ghadimi, D. J. Wilson, and T. J. Kippenberg, "Radiation and internal loss engineering of high-stress silicon nitride nanobeams," Nano Lett. 17, 3501–3505 (2017). L. G. Villanueva and S. Schmid, "Evidence of surface loss as ubiquitous limiting damping mechanism in sin micro- and nanomechanical resonators," Phys. Rev. Lett. 113, 227201 (2014). We follow the method of Reinhardt et al. [4] using a simplified Teflon sample holder for wet etching. Fabrication begins with standard two-sided photolithography followed by dry etch of ${{\rm Si}_3}{{\rm N}_4}$Si3N4, using plasma Ar+SF$_{6}$6, to define the trampoline on one side and a square window on the other. The chip is then wet etched from both sides using a 45% percent KOH solution at 65 C for 21 hours. After the trampoline is released, the gradual dilution method described in [4] is used in lieu of a critical point dryer, in order to suspend the trampoline. P. Sadeghi, M. Tanzer, S. L. Christensen, and S. Schmid, "Influence of clamp-widening on the quality factor of nanomechanical silicon nitride resonators," J. Appl. Phys. 126, 165108 (2019). D. Wilson, C. Regal, S. Papp, and H. Kimble, "Cavity optomechanics with stoichiometric sin films," Phys. Rev. Lett. 103, 207204 (2009). S. Sridaran and S. A. Bhave, "Electrostatic actuation of silicon optomechanical resonators," Opt. Express 19, 9020–9026 (2011). Q. P. Unterreithmeier, E. M. Weig, and J. P. Kotthaus, "Universal transduction scheme for nanomechanical systems based on dielectric forces," Nature 458, 1001–1004 (2009). E. Romero, V. M. Valenzuela, A. R. Kermany, F. Iacopi, and W. P. Bowen, "Engineering the dissipation of crystalline micromechanical resonators," Phys. Rev. Applied 13, 04407 (2020). S. A. Fedorov, A. Beccari, N. J. Engelsen, and T. J. Kippenberg, "Fractal-like mechanical resonators with a soft-clamped fundamental mode," Phys. Rev. Lett. 124, 025502 (2020). Aspelmeyer, M. Assumpcao, G. G. Barg, A. Beccari, A. Becher, C. Belhage, E. Bereyhi, M. J. Bhave, S. A. Blasius, T. D. Blatt, R. Bourassa, A. Bouwmeester, D. Bowen, W. P. Bushev, P. Carney, D. Chen, J. P. Christensen, S. L. Clerk, A. A. Courty, J.-M. Degen, C. Den Haan, A. Dubin, F. Engelsen, N. J. Eschner, J. Fedorov, S. A. Fischer, R. Frimmer, M. Genes, C. Geraci, A. A. Ghadimi, A. Ghadimi, A. H. Gigan, S. Girvin, S. Gröblacher, S. Habib, S. Hammerer, K. Hebestreit, E. Heidmann, A. Hook, A. Hopkins, A. Hornberger, K. Iacopi, F. Jacobs, K. Jain, V. James, M. Jeffrey, E. Kermany, A. R. Kimble, H. Kippenberg, T. Kippenberg, T. J. Kirste, A. Knief, T. Kotthaus, J. P. Krause, A. G. Li, T. Lin, Q. Lin, Y. Mamin, H. Mancini, S. Marquardt, F. Marti, O. Mason, D. McNally, D. P. Mertz, J. Milatz, J. Mlynek, J. Møller, C. B. Moura, J. P. Müller, T. Nielsen, W. H. Nimmrichter, S. Nooshi, N. Norte, R. A. Novotny, L. Nurdin, H. I. Oosterkamp, T. Painter, O. Papp, S. Pinard, M. Piro, N. Poggio, M. Polzik, E. S. Rabl, P. Reetz, C. Regal, C. Regal, C. A. Reimann, R. Reinhardt, C. Ribichini, L. Romero, E. Rossi, M. Rotter, D. Rugar, D. Sadeghi, P. Sankey, J. C. Schilling, R. Schliesser, A. Schmid, S. Schwab, K. Sonin, P. Sridaran, S. Steixner, V. Strauch, F. W. Sudhir, V. Tanzer, M. Taylor, J. M. Tebbenjohanns, F. Tombesi, P. Tsaturyan, Y. Unterreithmeier, Q. P. Usenko, O. Valenzuela, V. M. Van Iperen, B. Van Zolingen, J. Villanueva, L. G. Vinante, A. Vitali, D. Weig, E. M. Wijts, G. Wilson, A. Wilson, D. Wilson, D. J. Wilson-Rae, I. Windey, D. Winger, M. Yin, Z.-Q. Zhao, Y. Zoller, P. Zwerger, W. App. Phys. Lett. (2) Appl. Phys. B (1) Eur. Phys. J. D (1) Int. J. Mod. Phys. B (1) J. Appl. Phys. (1) J. Opt. Soc. Am. B (1) Nano Lett. (1) Nat. Nanotechnol. (1) Nat. Photonics (1) New J. Phys. (1) Opt. Express (1) Phys. Rev. A (3) Phys. Rev. Applied (1) Phys. Rev. B (1) Phys. Rev. Lett. (11) Phys. Rev. X (1) Physica (1) OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here. Alert me when this article is cited. Click here to see a list of articles that cite this paper View in Article \| Download Full Size \| PPT Slide \| PDF Equations on this page are rendered with MathJax. Learn more. (1) Γ t h = k B T 0 ℏ Q 0 < Ω 0 , (2) S xx i m p , g s = 4 x z p 2 Γ t h = 2 ℏ 2 k B T 0 Q 0 m Ω 0 , (3) ⟨ n ⟩ = k B T e f f ℏ Ω 0 ≈ S xx i m p S xx i m p , g s ≈ 3 × 10 3 . (4) y = x + x i m p . (5) m x ¨ + m Γ 0 x ˙ + m Ω 0 2 x = 2 k B T 0 m Γ 0 ξ ( t ) − g m Γ 0 y ˙ , (6a) S xx [ Ω ] 2 S xx z p = \| χ g [ Ω ] \| 2 ( n t h + g 2 n i m p ) , (6b) S yy [ Ω ] 2 S xx z p = \| χ g [ Ω ] \| 2 ( n t h + ( 1 + g ) 2 \| χ 0 [ Ω ] \| − 2 n i m p ) , (7) ⟨ n ⟩ + 1 2 = ⟨ x 2 ⟩ 2 x z p 2 = n t h + g 2 n i m p 1 + g ≥ 2 n t h n i m p . (8) S xx i m p , s h o t = ℏ c λ 16 π η R m P , (9) δ F f b ≈ − g m Γ 0 ( y ˙ + Ω 0 cot ⁡ ( ϕ ) y ) ,	CommonCrawl
A square wave is a periodic function that takes only two values – a minimum and a maximum – and alternates between these two values in equal intervals. In discrete time, for example, if N is the period of the function, then the function $$x(k)=\begin{cases} -1, \,\, k \mod \, N \lt\frac{N}{2} \\ 1, \,\, k \mod N \ge \frac{N}{2} \end{cases}$$ is a square wave. It alternates between -1 and 1. Its period is N samples. It takes each value for an interval equal to N/2 samples before switching to the other value. Alternatively, $$x(k)=\mathrm{sgn}(\sin(\frac{2 \pi\,k\,f}{f_s}))$$ since the sign function "sgn" is equal to 1 when its argument is positive and to -1 when its argument is negative. However, care must be taken where the argument is zero, as, as usually defined, sgn(0) = 0. Here, f is the desired square wave frequency and fs is the sampling frequency. If, for example, N = 60, then the first function above will be as follows. The following is a square wave with the frequency of middle C. Click Play to hear a square wave. Using square waves Analysis of the frequency content of square waves show that they can be thought of as the combination of many harmonics. Below, for example, is the discrete Fourier transform of 500 components of the example square wave above. The harmonics in the square wave are all integer multiples of the frequency of the square wave. Note the evenly occurring notches in the magnitudes of frequencies present in the square wave. Because of these harmonics, square waves are often used in synthesizers. Square waves with the desired harmonics can be combined and the result filtered (e.g., through a low pass filter) to synthesize a sound resembling the sound of a specific instrument. Harmonics of the square wave The peaks in the Fourier transform of a square wave with frequency f occur at all odd harmonics of f, which are (2k – 1) f, k = 1, 2, …. For example, since the frequency of the square wave in the graph above is 33.3 Hz, the peaks occur at 33.3 Hz, 100 Hz, 166.7 Hz, 233.3 Hz, and so on. In other words, the Fourier series expansion of the square wave is an infinite series of the odd harmonics of the square wave frequency. Fourier series expansion of the square wave The Fourier series expansion at sample k of the square wave is as follows. $$\frac{4}{\pi} \sum_{n=1}^\infty \frac{\sin(\frac{2\,\pi\,k\,(2n-1)\,f}{f_s})}{2\,n -1}$$ where f is the frequency of the square wave and fs is the sampling rate. The following four graphs show the first term of the series sum, the sum of the first two terms, the sum of the first three terms, and the sum of the first eight terms for f = 33.3 Hz, fs = 16000 Hz and for the first 500 or so samples k on the horizontal axis. The ripples at the points where the square wave changes value are the result of the Gibbs phenomenon – approximating a discontinuous function with a continuous function.	CommonCrawl
Instrument Calibration of the Interface Region Imaging Spectrograph (IRIS) Mission J.-P. Wülser ORCID: orcid.org/0000-0002-9332-73301, S. Jaeggli2 nAff7, B. De Pontieu1,5, T. Tarbell1, P. Boerner1 nAff8, S. Freeland1, W. Liu1,6, R. Timmons1, S. Brannon2, C. Kankelborg2, C. Madsen3, S. McKillop3, J. Prchlik3, S. Saar3, N. Schanche3 nAff9, P. Testa3, P. Bryans4 & M. Wiesmann5 Solar Physics volume 293, Article number: 149 (2018) Cite this article The Interface Region Imaging Spectrograph (IRIS) is a NASA small explorer mission that provides high-resolution spectra and images of the Sun in the 133 – 141 nm and 278 – 283 nm wavelength bands. The IRIS data are archived in calibrated form and made available to the public within seven days of observing. The calibrations applied to the data include dark correction, scattered light and background correction, flat fielding, geometric distortion correction, and wavelength calibration. In addition, the IRIS team has calibrated the IRIS absolute throughput as a function of wavelength and has been tracking throughput changes over the course of the mission. As a resource for the IRIS data user, this article describes the details of these calibrations as they have evolved over the first few years of the mission. References to online documentation provide access to additional information and future updates. The Interface Region Imaging Spectrograph (IRIS) is a NASA small explorer mission launched on 27 June 2013. Its primary objective is to understand how the solar atmosphere is energized. IRIS observes high-resolution spectra and images in the 133 – 141 nm and 278 – 283 nm wavelength bands focused on the chromosphere and transition region of the Sun. The IRIS instrument consists of a Cassegrain telescope that feeds a dual-range spectrograph and a slit-jaw imager. The telescope secondary mirror is actuated to compensate for spacecraft jitter and to scan the spectrograph slit across a field of view of up to 130 arcsec. The far-ultraviolet (FUV) and near-ultraviolet (NUV) spectrographs share a single, 175 arcsec tall slit. The FUV spectrograph has two detectors; the FUV-S and the FUV-L CCDs cover the 133.17 – 135.84 and 138.9 – 140.7 nm ranges, respectively. The NUV spectrograph has a single CCD that covers the 278.27 – 283.51 nm range. The slit-jaw imager is fed by light reflected off the spectrograph slit jaws. It has separate FUV and NUV branches that feed different halves of the same CCD detector. Both paths use the same filter wheel for passband selection. The NUV path includes a birefringent Šolc filter that reduces the bassband to about 0.4 nm. The IRIS mission and instrument are described in more detail in De Pontieu et al. (2014) and Wülser et al. (2012). The goal of this article is to describe the various calibrations that are either routinely applied to the IRIS data or that are otherwise important to the users of IRIS science data. Some of the calibrations have evolved substantially since the mission article (De Pontieu et al., 2014) was published. All calibrations have specific characteristics and limitations that may affect the proper interpretation of the IRIS data and therefore warrant a more detailed discussion. The article may also provide lessons learned for the calibration procedures of future missions. Recent solar physics science missions have typically chosen one of two different approaches to the distribution of the science data and their calibration: (1) Distribute raw data (or nearly raw data) and provide the user with the software necessary to calibrate that raw data. (2) Distribute data that are already calibrated. Both approaches have their advantages and disadvantages. The former approach puts the burden on the data user, requiring possibly resource-intensive calibration steps to be performed by the end user. However, it allows the user to apply the most up-to-date calibrations to a given dataset. The second approach does not burden the user with the calibration and requires less insight into the calibration steps by the user. On the other hand, the calibration of some of the mission archive may be outdated at the time the data are being used. Substantial improvements in the calibration procedures require reprocessing of the whole mission archive, which can become a major burden to the mission team. The IRIS project has chosen the second approach, partly because of the complexity and memory requirements of the calibrations necessary for the proper interpretation of the IRIS science data and partly to take advantage of the existing Solar Dynamics Observatory (SDO) / Atmospheric Imaging Assembly (AIA) data calibration pipeline. The primary science data product for the scientist is the calibrated Level 2 data. The IRIS Level 2 mission archive has been reprocessed several times since launch and in 2017 with the updated calibrations described in this article. This article is organized into sections for each of the main calibration steps: dark calibration (Section 2), scattered light correction (Section 3), flat fielding (Section 4), geometric correction (Section 5), wavelength calibration (Section 6), and image alignment (Section 7). Most of the described calibrations are applied during the creation of the Level 2 data. The descriptions include a few calibration issues that have been identified but are not currently being corrected, for example, spectral burn-in in the vicinity of the C ii lines (Section 4.3). These sections are followed by a discussion of the IRIS absolute throughput calibration and the sensitivity change of IRIS with time (Section 8). The spectral response and absolute throughput calibrations are not applied to the Level 2 data, but there are software tools that provide the user with mission time dependent spectral response and absolute throughput calibrations. Later sections briefly discuss other miscellaneous calibrations that are of interest to the data user (Section 9), outline the Level 2 data processing pipeline (Section 10), and comment on remaining calibration issues and known data peculiarities (Section 11). The article concludes with a brief summary. Dark Calibration IRIS dark frames (integrations with the shutter closed) show a residual signal coming from two sources: an electronic pedestal introduced as a base level and the dark current. Both of these contributions are sensitive to their thermal environment. The latter is also sensitive to integration time and summing level. IRIS has many observation modes and summing schemes, and so to avoid the need for extensive daily dark calibrations, a model dark frame is used. Prelaunch and subsequent (approximately monthly) dark observations of varying dark integration times and summing schemes were taken to measure the contributions to the dark level. A model for the shape and level of the dark frame has been developed from these observations over the course of the mission and continues to be modified and improved regularly. This dark model is then used instead of actual dark frames. The dark model and how it was developed and calibrated is described below. Observations, Processing, and Calibration To gather the data needed for calibrating the dark model, regular (approximately monthly) dark images are taken in two observing sequences. One focuses on unsummed ($1\times 1$) darks, taken with four dark integration times, $t_{\mathrm{int}}$, from 0.09 s to 30 s, over at least one spacecraft orbit. The shortest integration images (≈ 0 s) are used to track the thermal dependence of the pedestal level over the orbit. They are also used to construct an averaged "basal" dark, free of particle hits and hot pixels. The basal dark essentially represents the pixel-to-pixel variation component of the dark correction. The second observing sequence concentrates on summed data, taking darks at three integration times over all summing modes. These data are useful to establish summing dependencies and also to establish how the shape of the dark current surface varies with summing and $t_{\mathrm{int}}$. In practice, the active area of the CCDs are extracted for each read port, the image median smoothed, and all pixels $>4\sigma $ above local background replaced by that background average. The average level is then taken as a fiducial to match. Initial calibration of the dark frame levels was discussed in De Pontieu et al. (2014), where they gave the model for the total dark level, $D$, in read port $j$ as $$ D_{j} = P_{j}\bigl[T_{\mathrm{CEB}j}(t-\delta t_{j})\bigr] + \mathrm{e}^{(a_{j} + b_{j} T_{\mathrm{CCD}j})} n_{x} n_{y} t_{\mathrm{int}} + \Delta D _{j}(x, n_{x}, n_{y}, t_{\mathrm{int}}). $$ Here, $P_{j}$ is the pedestal level in read port $j$, which is a function of the camera electronics box (CEB) temperature, $T_{ \mathrm{CEB}j}$, time lagged by $\delta t_{j}$. The second term gives the average dark-current rate, which is the product of an exponential dependence on the CCD temperature, $T_{\mathrm{CCD}j}$, the amount of on-chip summing, $n_{x} n_{y}$, and the time between CCD reads (i.e. $t_{\mathrm{int}}$). The final term, $\Delta D$, models the change in the shape of the dark in the wavelength (i.e. $x$) direction as $t_{\mathrm{int}}$ and summing are increased, from flat for $t_{\mathrm{int}} \approx 0$ s and 1×1 summing, to roughly bilinear in $x$, rising first quickly and then more gradually away from the read-out point. The full amplitude of the pattern is $\Delta D \approx 10$ data numbers (DN) for the FUV ports with $n_{x} n_{y} = 32$. In practice, $D_{j}$ is computed for each port and added to the appropriate port of a basal dark. This basal dark was constructed by averaging 30 $t_{\mathrm{int}} \approx 0$ s images, after the pedestal $P_{j}$, particle hits, and hot pixels were removed. After more on-orbit data had been accumulated, it became clear that the model above was incomplete. There were small differences in the predicted and observed dark levels for certain summing schemes. The latter was found to be due to an additional noise source dependent on $n_{x}$ alone. There were also small differences, differing from port to port and varying quasi-periodically in time, when the average model dark level was compared with actual darks. A long-term trend function, $L_{j}$, was developed to attempt to model and predict these long-timescale variations. The revised dark model, $D'_{j}$, can thus be written as $$ D'_{j} = D_{j} + c_{j}(n_{x}) + L_{j}(t), $$ where $c_{j} = 0$ for $n_{x}=1$. The exact nature and cause of the long-term trend is uncertain, and thus the exact form of the trend has evolved over time, as more data become available to characterize it. It is currently modeled by the sum of two sinusoids with periods $p_{Lj}$ and $p_{Lj}$/2, plus a weakly quadratic background. The variations on a timescale of $p_{Lj}$ are typically $\leq \pm 1$ DN (except for FUV port 3, where it is ±2 DN), on a background that has risen $\approx 4.5$ DN (FUV) or 0.5 DN (NUV). Hints about the origin of the trend may be found in the facts that it is independent of summing and $t_{\mathrm{int}}$, and that all the $p_{Lj} \approx $ 1 year; hence some yearly and biennial orbital variations (possibly due to seasonal temperature changes) may be playing a role. The full form of the long-term trend model $L_{j}$ is currently $$ L_{j} = d_{j} \sin \bigl(2 \pi (t/p_{Lj} + \phi _{1j})\bigr) + e_{j} \sin \bigl(2 \pi (2 t/ p_{Lj} + \phi _{2j})\bigr) + f_{j} + g_{j} t + h_{j} t^{2} , $$ where $d_{j}$, $e_{j}$, $f_{j}$, $g_{j}$, $h_{j}$, $p_{Lj}$, $\phi _{1j}$, and $\phi _{2j}$ are constants, fit for each port using the offsets, over time, between the predicted and the actual average (cleaned) dark levels. The $h_{j}$ are considerably smaller for the NUV/slit-jaw imager (SJI) ports and are set to zero before a fixed time (which is different for the FUV and NUV/SJI CCDs) and return to zero at a second fixed time (identical for FUV and NUV/SJI). In the time interval early in the mission lacking darks (October–December 2013), we used measurements of the overscan lines (virtual lines created by extra CCD clock cycles) to guide the fitting. Empirically, the average 0 s dark level tends to track at or just above the average overscan values. The set of modeled $L_{j}$ compared with monthly dark data (as of June 2017) is shown in Figure 1. The root-mean-squares (RMS) of the trend fits with the data are satisfyingly small: the standard deviation of the model fit to the data for $1\times 1$ summing and $t_{\mathrm{int}} = 0$ s is $\sigma \approx $ 0.12 DN for the FUV ports (except for FUV port 3, where $\sigma \approx 0.28$ DN). The corresponding levels for the NUV/SJI ports show an average $\langle \sigma \rangle \approx 0.09$ DN. Average data number (DN or ADU) of the FUV and NUV long-term trends – the residuals between mean 0 s $1\times1$ summed dark levels in each read port and the dark model (as defined at launch) – are plotted versus time as symbols. The current long-term trend models are overplotted as lines; they fit the data well and reduce the errors. Based on 4595 $t_{\mathrm{int}}$ = 0 s images from January 2014 through November 2015, the median offset error of the model for the lower binning modes ($n_{x} n_{y} \leq 4$) is < 0.3 DN for all FUV ports and < 0.1 DN for all NUV/SJI ports. The difference between the FUV and NUV/SJI ports is consistent with the factor 3 higher gain of the FUV CCD camera amplifier (Section 8.3). Considering all binning modes, the average offset error for a binning mode is always $<3$ DN, with RMS scatter $\sigma <$ 4 DN (FUV errors are slightly larger on average than NUV/SJI errors). Errors for longer integrations are discussed in De Pontieu et al. (2014). The dark model is generated by iris_make_dark.pro, which in turn calls iris_dark_trend_fix.pro to generate the $L_{j}$. The model requires an hour of temperature data, which is generated externally. When housekeeping data are unavailable due to data loss, we search for an hour of valid temperature data $\pm nP_{ \mathrm{orb}}$ in time, where $n$ is an integer, and $P_{\mathrm{orb}}$ is the satellite orbital period. As long as $n$ is small, this retains the orbital phasing of the temperatures, and closely approximates the actual (missing) $T_{\mathrm{CCD}}$ and $T_{\mathrm{CEB}}$. All the above described improvements to the dark correction were applied during the reprocessing of the IRIS Level 2 data archive between May and August 2017. Nevertheless, the calibration of IRIS data is an ongoing effort with gradual improvements introduced with time. Users are encouraged to always use the latest version of the Level 2 data. Hot Pixels In addition to helping develop and refine the dark model, the dark observations provide a good dataset to observe the change in hot pixels. Hot pixels are defined as pixels whose values are above the local background average (typically $5\sigma $) for an extended period, and therefore falsely report an inflated value. We use this information to determine which pixels are hot, and track the change in the number of hot pixels over time. Each month, the short ($\approx 0$ s) and long ($\approx 30$ s) $1\times1$ summed integrations are separately grouped; each port is considered separately throughout. A first pass through the data is made, pixels $>5\sigma $ removed, and the median determined. Hot pixels are now redetermined using the "cleaned" median as a base level. We monitor the pixels that are "hot" in at least 10%, 50%, and 90% of the images during a month (typically covering a time span of two orbits); only the 50% and 90% pixels persist enough to be truly be considered hot. Examples of the number of hot pixels, $n_{\mathrm{hot}}$, over time for the FUV are shown in Figure 2. These plots are kept up to date at http://iris.lmsal.com/health-safety/longtermtrending/in_other.html . Plots showing the trend in the number of FUV hot pixels over time at the $>90$% threshold (NUV/SJI trends are similar, with 100 – 200 fewer $n_{\mathrm{hot}}$). The vertical dashed lines indicate the times of CCD bakeouts. The ports are shown separately, but follow a similar trend. The plot shows that $n_{\mathrm{hot}}$ is similar in all ports, with FUV ports showing 100-200 more hot pixels than NUV/SJI. There is considerable time variation, with a small average increase until the long CCD bakeout in April 2016, which appears to have reset $\approx 2/3$ of them. Shorter CCD bakeouts show weaker ($\approx 20$%), though still noticeable, reductions in $n_{ \mathrm{hot}}$. The variation in $n_{\mathrm{hot}}$ correlates with seasonal variations in $T_{\mathrm{CCD}}$, as the elevated dark current of hot pixels is highly temperature sensitive. Investigation of the longer term behavior of individual hot pixels shows that they typically do not stay hot for long – most return to normal in a month or less. This is reflected already in the significant differences in $n_{\mathrm{hot}}$ at the 50% and 90% thresholds within a month; on average, $n_{\mathrm{hot}}(50\%)/n_{\mathrm{hot}}(90\%) \approx 1.6$. Typically only 7 – 8% (FUV) and 8 – 10% (NUV/SJI) of the pixels that were hot at the >50% short-term threshold were also hot for $>50$% of the mission months. There also appears to be a local maximum in hot-pixel number in December–January, coinciding with eclipse season. Future Improvements In addition to regular recalibrations of the long-term trend, we are exploring methods for correcting hot pixels. At least a few of them, including some of the more prominent hot pixels, are persistent and show a good correlation with $T_{\mathrm{CCD}}$. Specifically, these potentially correctible hot pixels, $k$, show a dark current rate $\propto \exp(a_{j} + b_{j} (T_{\mathrm{CCD}j} + \delta T_{ \mathrm{CCD}k} ))$, where $\delta T_{\mathrm{CCD}k}$ reflects the incrementally enhanced temperature sensitivity of that pixel. As noted above, however, it is likely that only a few ($<10$%) will be correctable; furthermore, since for most hot pixels, $\delta T_{ \mathrm{CCD}k}$ eventually decays in time, the corrections would be imprecise for exposures that are temporally distant from the monthly dark datasets. Scattered Light and FUV Background The IRIS FUV spectrograph (SG) experiences a modest level of infrared (IR) and visible (V) parasitic light. This was discovered during the course of in-flight calibration and commissioning. This parasitic light manifests as a fairly uniform background level that is present in the FUV short- and long-wavelength channels. Although the level is fairly uniform and lower than the intensity in the lines, this background interferes with flat-field determination and correction and must be removed. In this section, we outline the properties of the background, and methods for its characterization and removal. The NUV SG and NUV slit-jaw channels may also have a background contribution, but it is not as significant relative to the solar signal in these channels. This is no longer the case for the FUV slit-jaw channels. The decrease in FUV sensitivity, combined with an unchanged level of parasitic light, has recently led to noticeable ghosts in off-limb FUV images. While this ghosting is mostly cosmetic in nature, the removal of the FUV slit-jaw background may nevertheless be a topic of future work. The following paragraphs focus on the FUV SG background, since it potentially affects the quantitative analysis of spectra. Background Properties Although the IRIS telescope rejects most of the incoming solar IR–V, a small portion is passed to the entrance of the spectrograph and slit-jaw imager. Imperfections in the light trap around the slit prism allow some residual light to scatter into the spectrograph. A second contributor is light that is first reflected off the slit-jaws toward the slit-jaw imager and then back to the slit-prism by one of the NUV filters in the filter wheel. Most of this light is reflected back out through the telescope, but a residual fraction enters the spectrograph again through imperfections in the light trap around the slit. The second component is only present if the filter wheel is configured for NUV slit-jaw imaging; the FUV background is reduced when the filter wheel is configured for FUV imaging. The background component is most evident in the FUV channels because there is little continuum intensity at these wavelengths. The background does seem to be present in the NUV channel as well, but it is more difficult to separate from the bright and highly structured spectrum around the Mg ii lines. It is also less prominent because of the lower gain setting of the NUV camera amplifier. A full-frame, long-exposure image from the two FUV CCDs is shown in Figure 3. The background in the FUV channels is fairly uniform across the spectrum, with the exception of the edge on the blue side of the FUV-L spectrum and a corner that overlaps the brighter Si iv line near the top. The slit in the FUV-S channel does not extend over the full CCD area, and the region at the top of the detector contains background, but not spectrum. This fortunate alignment offset can be used to determine the background level accurately for on-disk pointings. Typical long exposure from the FUV-S CCD on the left and the FUV-L CCD on the right showing the scattered light background. The dark area on the short-wavelength side of the FUV-L detector is not illuminated by the spectrograph optics. While the spatial pattern of the background on the CCD changes relatively little with pointing, the total intensity of the background changes with the IRIS pointing by a factor of about five from the solar center to the limb. The peak intensity is slightly offset south and west from Sun center, and the intensity as a function of radius from this center has the appearance of a smoothed or defocused limb-darkening function. The orientation of the pointing dependence of the stray-light pattern is fixed with respect to the telescope orientation, and has the same orientation with respect to the telescope during rolled observations. Figure 4 shows the intensity pattern interpolated from observations at the plotted positions for $\text{roll} = 0^{\circ }$. In Figure 5 it is clear that the background intensity is offset from disk center, but that the pattern shows a regular behavior as a function of radius from this offset center. Color-coded pointing positions on a coarsely interpolated map of the background intensity. Background intensity as a function of solar radius with the same color-coding as used in Figure 4. For the reasons stated above, the background intensity is higher when an NUV filter is in place in the SJI at the time of the observation. The background pattern, however, remains largely the same. Figure 5 shows the average intensity of the background as a function of radius. The different filters are indicated by triangles (1330 Å), plus signs (2796 Å), stars (1400 Å), and diamonds (2832 Å). Observations for characterization of the FUV background are taken on a monthly basis outside of eclipse season. They consist of 30 s exposures with the FUV CCDs at each science filter position (1330 Å, 1400 Å, 2796 Å, and 2832 Å) along eight radial spokes covering the solar disk and limb (see Figure 4). Dark frames of the same exposure length are also taken at every position. The observations are processed to remove cosmic ray spikes, and the darks are subtracted from the light frames. The median of the FUV background is taken from the region above the edge of the slit at the top of the FUV-S image. Each image is normalized to this median, and the average is taken across all filters for all of the off-limb pointings to create the average background frame. The frame should contain only the background and should have no spectral lines. Further analysis is done for the set of background intensity values from each filter to determine the center of the intensity distribution and its behavior as a function of radius from this center. The solar $X$-coordinate of the slit and solar $Y$-coordinate at the center of the slit are paired with the background intensity values and fitted with a smoothed limb darkening function. We adopt a limb darkening function of the form $$ I(\theta )/I(\theta =0) = 1 - u - v + u \cos {\theta } + v \cos {^{2} \theta }, $$ where $u=0.97$ and $v=-0.22$ are the tabulated values for the limb-darkening function at 5000 Å from Section 14.7 of Allen's Astrophysical Quantities (Cox, 2002). The free parameters in the fit of the limb darkening are $X_{0}$ and $Y_{0}$, the middle of the background distribution in solar coordinates, $dw$, the width of a Gaussian profile used to smooth the limb-darkening function, $a_{0}$, the offset of the base of the limb-darkening function, and $a_{1}$, the amplitude of the limb-darkening function from the base. Figure 6 shows the results of fitting the limb-darkening function for all four filters from the same set of observations. The NUV 2796 Å filter generates the highest background level, while the 2832 Å filter is slightly decreased, and the centers of the distribution are significantly different. The FUV 1330 and 1400 Å filters show almost identical background properties with the lowest level. Median level of the FUV background as a function of radius from position $X_{0}$, $Y_{0}$ for each filter wheel position used for science observations. The fit in red is a broad-band limb-darkening function smoothed with a Gaussian. The IR–V background is removed from the FUV SG frames of science observations during reduction from a Level 1 to Level 2 data product. The background calibration results nearest in time are used to apply the correction. Based on the filter and pointing of the observation relative to the orientation of IRIS, the median background level is calculated using the empirical, smoothed limb-darkening function and applied to the median background frame produced during the calibration. This scaled image is then subtracted from the science image. The implemented background correction uses pointing information to adjust the intensity of the background, but not its shape. In reality, however, the shape of the background in the FUV-L channel changes slightly with pointing, especially in the vicinity of the Si iv 1394 Å line. Even though these changes are small compared to the typical Si iv line intensity, it is unwise to use the region close to, and longward of, the Si iv 1394 Å line to determine the FUV continuum level. The FUV spectrum shortward (blueward) of 1394 Å is less affected and better suited for continuum level measurements. The properties of the FUV background have changed slightly over the lifetime of the IRIS mission. The center of the limb-darkening function has drifted slightly with time, while the smoothing width that determines the shape of the limb-darkening function is fairly constant for each filter. The greatest changes are in the intensity amplitude and pedestal for the limb-darkening function, which show consistent annual variations as well as significant long-term drifts. The pedestal level has steadily decreased, while the amplitude of the limb darkening function has slightly increased. All filters show nearly the same pedestal level. This may indicate that the pedestal level is caused by general scattering of light off optical surfaces inside the instrument. Flat Field Raw images from IRIS contain a variety of undesirable features that need to be removed before data analysis. These include the pattern of gain variation on the CCD, dust on various optical surfaces near focal planes in the spectrograph and imagers, and possible vignetting. Spectrograph images also contain a fixed intensity variation pattern along the spatial dimension that is due to slight imperfections in the slit. In this section we describe the techniques used to construct flat fields from in-flight data. Slit-Jaw Imager Flat Fields The flat-field method put forth by Chae (2004) can be used to build a flat field from a set of non-uniform images where the illumination pattern has been shifted relative to the detector in each image. The technique extracts the illumination pattern (or object) from the flat-field pattern using a least-squares method, keeping the object shifts and illumination level as free parameters. This technique has been proven more robust than other similar methods (e.g. Kuhn, Lin, and Loranz, 1991). In-flight Observations Flat-field observations for the SJI are taken on a monthly basis using observations of quiet-Sun or network regions, which are less likely to change during the eight-minute observing sequence. The field of view must not include the solar limb; regions close to disk center are preferable because they will not include large systematic gradients that are due to limb darkening or brightening. Prior to April 2016, three sets of observations from different regions of the Sun were taken for all filters and combined in processing to reduce the effect of noise and residual solar structure in the individual flat fields. The number of sets was increased from three to six in April 2016 for the FUV filters to compensate for sensitivity loss at those wavelengths. The images for each filter wheel position are taken in rapid sequence to minimize the amount of change in the solar scene. During the sequence, the pointing is dithered about the center of the field in a Reuleaux triangle, as suggested by Chae (2004). This is a commonly used dither pattern in optical and radio astronomy, which is formed from the intersection of three circles of equal radius. The dither pattern used for the IRIS SJI NUV flat field observations is shown in Figure 7. A pattern size of 70 arcsec was adopted for the NUV channels to properly sample the large shadow from the Šolc filter mask (Berger et al., 2012) that appears in the upper right quadrant of the images. The sequences for the 1330, 1400, and 2796 Å filters are taken with the telescope out of focus to decrease the contrast of dynamic features and spread intensity more evenly over the detector. The sequences for the 2832 Å filter remain in focus as the solar granulation seen at 2832 Å is sufficiently stable over the duration of the flat-field sequence. Example of a Reuleaux dither pattern, as used for the SJI NUV flat-field observations, with 30 pointings and a pattern size of 70 arcsec. Calibration Processing and Products The software to produce the flats for the SJI read the data, despike, construct, and subtract dark images, and provide a wrapper for the Chae code. After flat fields for the FUV and NUV sequences have been produced, the slit is removed and the images are averaged together. Removing the slit from the flats allows the slit to remain visible in science images after flat-fielding. The slit removal treats the pixels around the slit as missing data and smoothes the large-scale pattern over the slit. That region is then multiplied by a pre-flight flat (created from UV lamp exposures) to re-establish the small-scale pattern. The flats are normalized to the average signal level in the observations. The flat fields are provided as FITS files to the data-processing pipeline. We provide images for each filter both with and without the slit. Files from each month are monitored for quality. In iris_prep, the nearest flat available at the time of processing is applied. Figure 8 shows an NUV flat, the object image, and a quiet-Sun image before and after flat-fielding. Flat-fielding clearly improves the quality of the image. The characteristic small-scale anneal pattern of the e2v CCD, visible in both the flat and the raw image, is no longer present in the corrected image. The vignetting from the Šolc filter mask in the upper right corner is also much reduced. Nevertheless, the NUV object image still shows a significant residual from the Šolc filter mask, which indicates that the correction is not perfect. Chae's technique assigns about half of the darkening to the object frame, and the flat field only corrects for part of the drop in intensity due to the mask. A larger dither pattern might help the technique to distinguish this pattern, but the duration of the flat-field sequence would become excessively long. The flat-field correction away from the upper right corner is quite good, and the other corners do not seem to show vignetting at all. Example of the resulting flat field and object frame from Chae's method applied to the 2832 Å channel of the SJI. The two bottom frames show an original image from the observed sequence and its correction by the flat field. Flat-fielding is also successful with FUV images, even though it has its own challenges. Because the contrast in the FUV object is high and slightly changes with time, the flat fields from Chae's method contain some residual structure (Figure 9). To correct for this, multiple sequences are processed using Chae's method, which are then averaged together to even out the structure in the final flat field. Finally, small dust specks on the slit-jaws may introduce subtle artifacts. Residual filter wheel position variations and orbital temperature changes may cause the detector image of these dust specks to shift by up to a few pixels (mostly in the $x$ dimension). If the shift between the flats and the science images is different, artifacts result that look like bipoles in the processed data. The position of the dust specks is well known so they can easily be distinguished from real solar features. An example of these flat-field residuals in the NUV channel is shown in Figure 10. Level 2 data from the 2796 Å channel of the SJI. The slit prism is shifted in the science observation with respect to the flat field so that dust specks on the surface of the slit prism show bipolar signatures that are indicated by the arrows. The removal of the slit in the vicinity of a dark dust speck on the detector produces a streak across the slit (circled). Dosage Burn-in Dosage burn-in has been contributing to a loss of sensitivity in the FUV channels of the slit-jaw imager. The burn-in preferentially affects the middle of the detector more than the edges, so there has been a gradual deepening of the burn-in pattern, which is fairly smooth and Gaussian. Very little change is apparent in the NUV channels. Figure 11 shows the characterization of that depression with time. Dosage burn-in in the slit-jaw images is mostly corrected by the flat field, although there remains a residual component similar to the one caused by the Šolc filter mask in the NUV images. Depth of the 2D Gaussian fitted in the flat field of each month. This is the depth relative to the "continuum" fit for the Gaussian, which translates into a measure of the steepening of the profile. The horizontal bars at the bottom of the plot indicate the eclipse seasons. The vertical dashed lines indicate detector bakeouts. Slit Brightening The apparent intensity of the slit as seen in the 1330 and 1400 Å slit-jaw images has been increasing with time since launch. The effect is largest and most noticeable in the 1330 Å channel, where the slit at the middle of the detector became brighter than the region surrounding the slit in the Fall of 2015. Figure 12 illustrates the bright slit in a raw flat field, but it is equally seen in regular SJI images. The slit brightening makes automated detection of the fiducial marks in the slit less reliable, which has an impact on some spatial calibration tasks. Lower half of the 1330 Å flat from January 2016. This is a raw flat, i.e. the slit was left untouched. In some places, the slit has become brighter than the surrounding areas. Dark dust specks on the slit remain dark. Dosage burn-in is visible as a large-scale pattern. The cause of the slit brightening is not understood. We know that it is not an artifact of dosage burn-in on the detector, otherwise it would prominently appear in exposures with the onboard calibration LED. Instead, the root cause must be at the location of the slit, which receives a considerable dose of FUV radiation on orbit. The slit-jaw images were created by deposition of chromium and aluminum on the $\mathrm{MgF _{2}}$ slit prism. The metal layers and the slit then received a $\mathrm{MgF_{2}}$ overcoat to maximize the FUV reflectivity. We speculate that either deterioration of the slit-jaw coating reflectivity (relative to the residual reflectivity of the uncoated $\mathrm{MgF _{2}}$ surface in the slit), effects of deposited contaminants, or a combination of both may have caused the observed slit brightening. Spectrograph Flat Fields There are several artifacts in IRIS raw spectra that can in principle be removed with a flat-field process. These artifacts include dust particles in the spectrograph slit, spectrograph vignetting, the CCD anneal pattern (see, e.g., the lower right panel of Figure 13), and detector burn-in from high doses of UV exposure. We have conducted several types of flat-field-related calibrations prior to launch. In particular, we acquired CCD flat-field images at several UV wavelengths, although not at all of our observing wavelengths. However, we found that the CCD anneal pattern is very similar over a range of wavelengths, except for the amplitude. We have recreated fairly accurate CCD flats by appropriately scaling the amplitude of the anneal pattern from flats at different UV wavelengths. We also confirmed that vignetting in the spectral direction is negligible; response variations are dominated by the spectral response of the optical components and coatings. The spectrograph spectral response is discussed in Section 8. NUV spectrograph flat fields. See text for details. The two prominent horizontal lines in the top panels are caused by the fiducial marks in the slit. The spatial flat (bottom left panel) has the fiducial marks removed; the remaining dark horizontal line near the bottom is caused by a small dust particle on the slit. On-orbit spectrograph flat fields are more difficult to produce than SJI flat fields, because IRIS neither has a UV calibration source, nor can it move the solar spectrum across the detector. The general approach for IRIS is as follows: i) Create a raw flat field by averaging a large number of frames taken at many different quiet-Sun locations. ii) Produce a spatially smoothed "spectral flat". iii) Produce a spectrally averaged "spatial flat". iv) Derive a detector flat by dividing the raw flat by the spectral flat. This essentially removes the solar spectrum. v) Divide the detector flat by the spatial flat. This separates variations along the slit from the detector flat and allows them to be applied separately. The final detector flat field contains the CCD anneal pattern, but is blind to detector burn-in and vignetting in the spectral direction. We are successfully applying the above approach to NUV SG data. However, the approach was not successful in the FUV. By their nature, FUV spectra show extreme spectral and spatial variations that lead to high levels of noise in the flat fields. Instead, we flat-field our FUV SG data only with a pre-launch detector flat. The following paragraphs discuss the NUV flat-field process in more detail. The spectrograph flat-field observations are conducted on a monthly basis. Both NUV and FUV flat-field data are acquired, even though only the NUV data are currently used for flat-fielding. The observations should ideally be confined to quiet-Sun regions near disk center, but the quiet Sun does not provide enough counts in the FUV channels, so network or a quiescent active region plage is used. Thirty-second exposures are taken with the telescope out of focus, while the pointing is semi-randomly slewed about the center of the field to further average over the solar structure. In addition, the slit is rastered. 150 images are taken, and darks are taken every 10 images so that the dark correction will be accurate for the flat field. Images from a flat-field sequence are dark subtracted using the darks taken with the observation if they are available and using the iris_prep dark correction if they are not. The data are despiked. Then all the images are averaged together to produce the intermediate flat field. The intermediate flat is further processed into a detector flat and a spatial flat as described earlier in this section. The fiducial marks are removed from the spatial flat through interpolation. This has the effect that the fiducial marks remain in the data processed by the flat field. The spatial flat is retained separately, so that it can be shifted and applied to compensate for thermal drifts between slit and detector. This compensation is not currently implemented, partly because the drift is quite small and partly because the prerequisite detection of the fiducial mark location is not sufficiently reliable. For the NUV flat field applied in the processing pipeline, the detector flats from several months are averaged together and the nearest spatial flat is used. For the FUV we use only the pre-flight lamp flat, but the FUV flat data are retained for the record. NUV Results Figure 13 shows the results of this technique applied to the NUV data. The top left panel shows the intermediate flat field, which is an average of a sequence of 150 images. The top right shows the final spectral flat field, and the bottom left shows the final spatial flat field without the fiducial marks. The bottom right panel shows the result of removing all the spatial and spectral features from the intermediate flat field. The master flat field is similar to the NUV lamp flat field, but it has a slightly different contrast and contains some very subtle residuals of solar features. Spectrograph Detector Burn-in Changes in sensitivity of the CCD, or charge burn-in, is mainly a concern for the bright C ii and Si iv lines in the FUV. For the SJI, burn-in is not an issue, and can easily be measured and removed using the flat-fielding technique. For the spectrographs, burn-in might occur isotropically along the spatial dimension of a line, causing an apparent deepening in the emission line core with respect to the dimmer wings, but more likely, the damage will show some spatial variation, with most of the burn-in occurring at the middle of the slit, where bright interesting targets tend to be centered. Because spectral filtering is applied during the spectrograph flat field processing, the final flat field cannot properly account for burn-in. However, there are indications for detector burn-in in the FUV SG. IRIS occasionally acquires exposures with an onboard blue LED. IRIS carries LEDs primarily for verifying that the instrument is functional, so these LEDs have not been designed to fully illuminate all detectors. The FUV LED covers the locations of the two C ii lines and the 1403 Å Si iv line, but not the Si iv line at 1394 Å. The top panel of Figure 14 shows an LED exposure taken on 17 July 2013, just before IRIS first light, and the exposure in the bottom panel was taken on 4 October 2014. The latter clearly shows the location of the two C ii lines as bands with slightly lower sensitivity. The location of the Si iv line does not show a significant signature because the Si iv line is at least four times weaker and likely to cause much less burn-in. Blue LED images taken shortly after launch (top) and in October 2014 (bottom). The second image shows the burn-in pattern from the two C ii lines on the left. The LEDs have not been designed to fully cover the CCDs, hence the large non-illuminated area in the middle. If the burn-in in the LED images were similar to the burn-in in the FUV, then we could use the LED data as a proxy for the FUV burn-in. Figure 15 shows the C ii burn-in profile in selected LED images taken over the course of the mission. Each profile is an average along the slit. We find that the burn-in amplitude at the blue LED wavelength increased to about 2.8% in mid-2015 and decreased thereafter. Some of the decrease correlates with detector bake-outs, e.g. between April and May 2016, but most of it does not. Burn-in profile from the C ii lines in selected blue LED images. The amplitude of the burn-in at the actual FUV wavelengths is about six times larger than it is at the blue wavelengths shown here. Measuring the burn-in with FUV light is more difficult since we cannot scan the solar spectrum across the detector. However, we found that we can move the spectrum by up to ten pixels over the course of an hour if we apply a thermal gradient across the spectrograph with the IRIS instrument heaters. If we assume that the average C ii line profile of a quiet-Sun region does not change over an hour, then we can use this spectral scan to probe the approximate depth of the burn-in at the nominal location of C ii. We have performed this calibration in March 2015 and again in June 2017. We found typical burn-in depths of about 16% in 2015 and about 5% in 2017. The results are accurate to only about 30%, probably because of the slowness and small range of the scan combined with residual small variations of the solar C ii profile. Nevertheless, the measurements indicate that the burn-in has decreased in the FUV as well, not only in the blue light of the LED. The relative decrease was comparable within the accuracy of the FUV measurements: a factor of about 3.2 in the FUV versus 2.5 in the blue over the same period. The test also suggests that the burn-in is about five to six times deeper in the FUV than in the blue. These results indicate that the burn-in pattern in the blue LED images may be a good proxy for the FUV burn-in, if scaled by about a factor of five to six. As a sanity check, we compare the depth of burn-in in the FUV and in the blue with the depth of the CCD anneal pattern at those two wavelengths. We indeed find that the anneal pattern is very similar and the amplitude of the pattern is 6.0 times larger in the FUV. This is fully consistent with the ratios we found for the burn-in. It is important to note that we are not correcting for any burn-in in the spectrographs at this time, although we may implement a correction in the future. Nevertheless, the burn-in should be taken into account if the C ii lines are being analyzed for subtle deviations from a Gaussian profile and for detailed line width work. In contrast to the FUV SG at C ii, the detector of the NUV SG does not show a significant burn-in at the location of the Mg ii line cores in images taken with the blue LED. The lower energy NUV photons do not appear to have the damaging effect of the higher energy FUV photons. Geometric Correction In order to facilitate scientific analysis, it is desirable to have spatial and dispersion directions in a spectrum aligned with the pixel dimensions in the observations. However, distortions from rectilinear dimensions are present in any spectrograph. In addition, the IRIS spectrograph design produces spectral lines that are inherently curved. The top panels in Figure 13 show an NUV spectrum before distortion correction. Calibration Approach A spectrum from IRIS contains bright emission lines (for the FUV) or a combination of absorption and emission features (for the NUV) crossed by two dark fiducial marks, which are sections of the slit that have been intentionally coated as a spatial reference. The geometric calibration is determined by measuring the very features that should be rectilinear, the bright or dark spectral lines, and the dark slit fiducials crossing the spectrum. We assume that the warping is a smoothly varying field that can be characterized by a 2D second-order polynomial function. The transformation from warped to unwrapped coordinates can be expressed by $$ x' = \sum_{ij} k_{x_{ij}} x^{j} y^{i}, \qquad y' = \sum _{ij} k_{y_{ij}} x^{j} y^{i},\quad 0 \leq i,j \leq 2, $$ where $k_{x_{ij}}$ and $k_{y_{ij}}$ are the to-be-determined coefficients of the warping function, the original image coordinates are $(x,y)$, and the transformed coordinates are $(x',y')$. For arbitrary features in the image, such as the crossings between spectral lines and fiducials, we need to know the location in terms of the original image coordinates, and where we wish all crossings of a particular line and all the crossings of a particular fiducial to be in the transformed image. Given many such $(x,y)$ and $(x',y')$ coordinate pairs, we can fit the coefficients $k_{x_{ij}}$ and $k_{y_{ij}}$ using a least-squares technique. Once we have the function, the task of determining the transformed coordinates of all of the pixels in the original image is trivial. We call the 2D table of $x$ and $y$ coordinate transforms a "distortion map." The distortion map is an array the size of the transformed image where each element contains the $x$ or $y$ coordinate of that pixel in terms of the original coordinate frame. Given a distortion map for both $x$ and $y$ coordinates, the intensity values of an image can be transformed from one coordinate frame to the other using a standard interpolation technique. In the above process, we allow the spectral and fiducial lines to have arbitrary positions assuming only that they have a fixed separation, so it still remains to make the wavelength a linear function of pixel position. Combining a wavelength solution with the above process would require a higher-order polynomial function, which leads to greater uncertainty, and non-unique solutions, when the $(x,y)$ pairs are too sparsely sampled. Therefore we determine a wavelength solution after the distortion map is determined (and the spectral lines are aligned with the vertical columns in the image) and combine the result of the wavelength solution with just the distortion map for the $x$ coordinate, to linearize the wavelength. It is not the goal of this calibration to provide a definitive wavelength reference. That is discussed further in Section 6. Acquisition and Processing The same data taken for flat fields are used to determine the in-flight geometric correction for the NUV SG. The NUV has many narrow absorption lines of neutral atomic species, which have higher contrast than the continuum, and they show small velocity perturbations, which can be averaged over in time-series observations of the flat field. Good in-flight characterization is not possible for the FUV SG. The bright lines of the transition region are broad, often have high velocities with respect to the average central position of the line, and large systematic Doppler shifts. Some neutral lines appear in emission in the FUV channels, but they are often too dim to see across the entire field of view, even in heavily averaged spectra. There are also far fewer lines in a typical spectrum. All of these effects cause the geometric solution and the wavelength solution to be poorly constrained from in-orbit FUV data. Instead, we use pre-launch data to determine the FUV geometric and wavelength corrections. During integration and testing, the FUV SG was illuminated with a deuterium lamp source, which has many narrow emission lines that are due to excitation of electronic transitions in molecular deuterium. An example of the deuterium spectrum seen with the FUV-S channel is shown in Figure 16. A quadratic fit was performed on the spectral lines with respect to the $y$ dimension of the image, and a linear fit was performed on the fiducial lines with respect to the $x$ direction. We found that the line and fiducial marks wander to different positions during tests at different temperatures, but the slope, shape, and position of the lines with respect to other lines in the spectrum change very little and amount to changes of 0.1 pixel over the full area of the detector. We concluded that the high-order terms in the distortion in the spectrograph images are stable to thermal variation and that only the offsets (discussed in Sections 6 and 7) change with temperature. Portion of the deuterium lamp spectrum observed with the FUV-S spectrograph channel during ground testing. Fitted line positions and fiducial positions are shown in red, while the desired rectilinear coordinates are shown in blue. The fiducial/spectral line crossings are indicated by the diamonds, while the line centroids are plotted as small points. The 2D fitting of the red and blue points yields the geometric transformation. The image is upside down with respect to typical IRIS Level 1 data and is displayed in inverted grayscale to show emission lines as dark features. This robustness has led us to adopt static corrections for the geometric distortions for the FUV and NUV spectrographs. The averaged series of dark- and flat-corrected data from the NUV flat-field observation of 6 March 2014 was used to produce the NUV geometric correction. The deuterium spectrum from a pre-launch test on 28 June 2012 was used to produce the FUV geometric distortion correction. The wavelength non-linearity component of this correction, however, is based on flare spectra observed on 11 October 2013, which show fluorescence-enhanced neutral atomic and molecular lines (Jaeggli, Judge, and Daw, 2018). Level 1 data are dewarped during iris_prep. During this step, a static distortion map for each channel is used to resample the data from the original detector pixels using a cubic interpolation with the IDL interpolate function. The positional error in dewarping should produce positional errors smaller than 0.1 pixels over the entire detector area, but systematic intensity errors are introduced by resampling, and they may become noticeable for high-precision observations. In the standard data pipeline invoked by iris_prep, despiking is not performed prior to dewarping, primarily because automated despiking has the potential of removing real solar features. On the other hand, the resampling technique used to apply the distortion map broadens spikes caused by energetic particles, making them less discrete and more difficult to identify and remove from processed data. Nevertheless, spikes in spectra are typically still identifiable as such on closer inspection. Wavelength Calibration The wavelength associated with a given pixel location on the IRIS spectrograph CCDs varies with time as a result of thermal effects. This is a source of velocity error if not properly calibrated. The goal of the calibration is to provide the data analysis software with accurate wavelength information through the header of the Level 2 FITS files. The IRIS pipeline software (i.e., iris_prep) is currently using two different wavelength calibration methods, depending on the characteristics of the observations. The primary calibration method is a three-step process that runs automatically in the science data pipeline. This process is carried out separately for each observing sequence (OBS). In the first step of the process, the software measures the pixel location of a chosen spectral line in the spatially averaged spectrum of each SG frame of the given OBS. In the second step, it fits a sine function with a one-orbit period to all the line location measurements from the first step. The one-orbit period accommodates orbital Doppler velocity variations as well as orbit-induced thermal variations in the spectrograph alignment. The purpose of the fitting process is to reduce the noise inherent in the individual measurements from each frame. The third step applies the best-fit sine function to spectrally calibrate all frames of the given OBS. Figure 17 shows an example of wavelength measurements and the best-fit sine function used for the calibration. Example of wavelength measurements and best-fit calibration function. The lines chosen for the primary wavelength calibration are a Ni i line at 2799.474 Å and an O i line at 1355.598 Å. In addition, an Fe ii line at 1392.817 Å is measured, but is not used for the calibration of the data because it is weak. Instead, the wavelength calibration assumes that the FUV-L (1389 – 1407 Å) CCD detector has a fixed wavelength offset from the FUV-S (1332 – 1358 Å) detector. However, we use Fe ii line measurements to track and verify this assumption. Figure 18 shows that there is no systematic drift between the two detectors. Most of the scatter is due to the uncertainty of the measurements. The 90-day running average (solid line) stays within a small fraction of a pixel, or about $\pm 0.5$ km s−1 over the first three years of the mission. The pipeline does not correct for these minute variations. Offset measurements between the FUV-S and FUV-L detectors. The solid line is a 90-day running average. There is no systematic drift over the course of the mission. In about 90% of the NUV observations and 80% of the FUV observations, the primary wavelength calibration method is successful and leads to a velocity calibration accuracy of about 1 km s−1. For the remaining observations, an alternate, parameterized wavelength calibration model is used. It is based on instrument temperatures, pointing, roll orientation of IRIS at the time of the observations, and elapsed mission time. The alternate calibration method is always available, but it is typically less accurate and subject to slow secular drifts over the course of the mission. Figure 19 shows a scatterplot of the difference between the two wavelength calibration methods in the FUV. It reflects the calibration update that was the basis for the Level 2 data reprocessing effort in mid-2017. Earlier versions of the alternate calibration method showed a substantially larger error. Reprocessing in 2017 also fixed an issue where the wavelength calibration of the FUV-L range was redshifted by about 11 km s−1 relative to the (correctly calibrated) FUV-S range. It is therefore important to always use the latest version of Level 2 data. SolarSoft routines reading IRIS Level 2 data now alert the user if not the latest version of a data file is being ingested. Difference between the primary and alternate wavelength calibration methods for the FUV SG over the first several years of the mission. Pointing, Fiducials, and Coalignment Slit Location and Alignment Thermal variations in the instrument not only affect the wavelength calibration, but also the CCD pixel location of any spatial point on the slit. This motion of the slit image on the CCD affects i) the correction of any features on the slit during the flat-field process and ii) the accurate pointing of the CCD pixels relative to Sun center. To aid in the correction of these variations, the slit has two small gaps, or fiducial marks along its length, which can be detected in both the spectra and the slit-jaw images. The pipeline process that tracks the wavelength calibration also tracks the location of the slit in the SJI frames, as well as the location of the fiducial marks in the SJI and the SG frames. Similar to the wavelength correction, there is also an alternate parameterized model for this calibration. Both calibration methods work sufficiently well to obtain accurate pointing information. However, when this calibration was applied to the spatial component of the flat field (Section 4), the residual jitter introduced undesired noise to the flat-fielded data. Consequently, the calibration is not being used in the flat-field process. Absolute Pointing Thermal variations on-orbit also affect the alignment between the guide telescope (GT) and the main telescope. Since the solar pointing is defined through the GT boresight, these variations affect the absolute pointing accuracy. Relative variations with an orbital period are corrected in the instrument in real time using the tip-tilt secondary mirror and an onboard wobble calibration table (Section 9.1). The absolute pointing, however, may still be off by some arcseconds. To reduce this error post facto, the calibration pipeline automatically correlates IRIS FUV SJI images with SDO/AIA 1700 Å images. The same pipeline process that determines the wavelength and slit position corrections also tracks the IRIS-AIA cross-calibration and creates a sinusoidal best-fit model for the absolute pointing of IRIS. The resulting pointing is tied to AIA, but the absolute accuracy is typically better than 1 arcsecond. This improved pointing information will be incorporated into the Level 2 data FITS header later in 2018, but has not yet been completed at the time of this writing. Absolute Throughput Calibration The purpose of an absolute throughput calibration is to provide the data user with a means to convert observed intensities into absolute fluxes at the Sun. This knowledge may be an important factor in the interpretation of the observations in terms of physical processes. IRIS observations are not routinely converted into absolute units. Instead, the IRIS team provides the community with instrument-effective areas as a function of wavelength for each channel. As the instrument is aging, the effective areas have been changing, so the effective area values must be provided as a function of time. In addition to the effective area, the user must also know the gain of the CCD camera amplifiers in terms of data numbers (DN) per photon. The current best-estimate of the IRIS effective area for any given time is available in SolarSoft via the function iris_get_response.pro. The output of the routine also includes values of the CCD camera gain for each channel. In the past, various methods have been used to radiometrically calibrate UV instruments. Suborbital rocket experiments are often calibrated in the laboratory shortly before launch, using calibrated standard detectors or sources (e.g. Kohl and Parkinson, 1976). On high-altitude balloon experiments where uncertain atmospheric attenuation is a concern, observed photospheric emissions may be compared with measurements from well-calibrated rocket payloads (e.g. Samain and Lemaire, 1985). The Solar Ultraviolet Measurements of Emitted Radiation (SUMER) instrument on the Solar and Heliospheric Observatory (SOHO) was primarily calibrated on the ground. However, the calibration was subsequently refined on-orbit i) by using solar line pairs at different wavelengths but with known intensity ratios and ii) by observing spectra of previously well-observed reference stars (Wilhelm et al., 1997). The IRIS spectral response and absolute throughput was initially derived from measured efficiency curves for each individual optical element of the IRIS instrument. These curves were then folded together and combined with the geometric telescope aperture to create effective area curves for each channel of the IRIS instrument (Figure 20). Estimates of the pre-launch effective area. The spectral windows of the spectrograph detector are indicated by vertical dotted lines. The two curves in each of the bottom panels indicate the response of each of the two FUV and NUV slit-jaw imager channels. Post launch, we are using two methods to measure and track the instrument throughput: i) by observing B-type stars and comparing the results with historic International Ultraviolet Explorer (IUE) or Hubble Space Telescope (HST) measurements, and ii) by carrying out a full-disk mosaic of the Sun and comparing the results with cotemporal Solar Radiation and Climate Experiment (SORCE)/Solar Stellar Irradiance Comparison Experiment (SOLSTICE) or Thermosphere Ionosphere Mesosphere Energetics and Dynamics (TIMED)/Solar EUV Experiment (SEE) measurements. B stars are bright enough only in the FUV, while SOLSTICE allows calibrations in both the FUV and NUV. We further found that the SOLSTICE cross-calibrations are more accurate and reliable than the stellar calibrations and chose them as the main method to calibrate IRIS. Nevertheless, the stellar calibrations are still useful as an independent verification method. The following subsections first outline the cross-calibration process with SOLSTICE and how the results are implemented in iris_get_response, the second subsection briefly discusses the stellar calibrations, and the third describes the CCD camera gain calibration. Cross-Calibration with SORCE/SOLSTICE The SOLSTICE instrument on SORCE regularly measures the solar UV spectrum integrated over the solar disk with a spectral resolution of 1 Å (McClintock, Rottman, and Woods, 2005). The observed spectral range includes all IRIS spectral channels. During orbital night, SOLSTICE observes calibration stars to track and maintain the SOLSTICE absolute calibration. Unfortunately, the SORCE spacecraft experienced a battery failure just two days before IRIS first light, so SOLSTICE measurements simultaneous with IRIS were initially not available. The SORCE team later established a new observing mode that reinstated the SOLSTICE solar observations starting on 24 February 2014, although without the capability of measuring reference stars. The absolute accuracy of the SOLSTICE measurements after over a decade on orbit is estimated to be 5% (Snow et al., 2005). Spectral Cross-Calibration Figure 21 shows the disk-integrated solar FUV spectrum on 20 October 2014 observed by IRIS (top panel) and SOLSTICE (middle panel). The two spectra are not strictly simultaneous as the IRIS full-disk mosaic was acquired over a 14-hour time period. The IRIS spectrum is smoothed, while the SOLSTICE spectrum is shown at full resolution. SOLSTICE partly resolves the two C ii lines around 1350 Å and mostly separates the O iv line near 1401 Å from the Si iv line near 1403 Å. For cross-calibration purposes, we find that we can use the total of the two C ii lines, each of the two Si iv lines (at 1394 and 1403 Å), and the total of the Cl i, the O i, and the C i lines (between 1351 and 1356 Å). This provides us with four calibration wavelengths where we can determine the ratio of observed IRIS flux and observed SOLSTICE flux. The SOLSTICE flux has been calibrated in terms of photons Å−1 s−1 cm−2, so this ratio provides the IRIS effective area. It is indicated by stars in the bottom panel of Figure 21. Since there are two calibration wavelengths in each of the two IRIS FUV spectral windows, one could use a linear fit through each pair of data points to obtain the best-estimate effective area curves. However, we found that the measurements near 1354 Å show a substantial amount of scatter, probably because the lines used for the calibration are relatively weak. We also see some random measurement-to-measurement variability of the slope between 1394 and 1403 Å that is unlikely to be real. It is more likely that the true slope near 1400 Å does not change with time and is, in contrast to the pre-launch calibration, close to being flat. For the IRIS FUV calibrations, we therefore adopted the more robust model shown in Figure 22, in which: i) The spectral response of the long (1389 – 1407 Å) FUV range is flat and is determined by the weighted average response at the two Si iv lines. ii) The spectral response of the short (1332 – 1358 Å) FUV range is linear and the slope is determined by the C ii calibration at 1335 Å, and the Si iv calibration at 1394 Å. Full-Sun FUV spectra for 20 October 2014. Top panel: IRIS, middle panel: SOLSTICE, and bottom panel: derived IRIS effective area at four wavelengths (star symbols). Vertical dotted lines in the top and middle panels indicate the spectral regions used for the cross-calibration. Model used for the calibration of the FUV SG (shown here with values for 1 March 2015). See text for details. In the NUV, the solar spectrum shows substantial emission throughout most of the range of the IRIS spectrograph, and the cross-calibration with SOLSTICE is not limited to a few bright lines. Figure 23 shows the disk-integrated NUV spectrum from IRIS (top panel) and SOLSTICE (bottom panel) for 20 October 2014. The bottom panel indicates the derived IRIS effective area at six different wavelengths using stars. We found that the absolute effective area does vary with time, but the shape of the spectral response does not. For calibration purposes, the relative spectral response is derived from the average of the 2014 IRIS–SOLSTICE cross-calibrations, using a spline function to interpolate in wavelength between the six wavelength points shown in the bottom panel of Figure 23. Full-Sun NUV spectra for 20 October 2014. Top panel: IRIS, middle panel: SOLSTICE, and bottom panel: derived IRIS effective area. Vertical dotted lines in the top and middle panels indicate the spectral regions used for the cross-calibration. Spectrograph Trending In the previous paragraphs, we described our simplified spectral models for the FUV and NUV spectrograph calibrations. These models reduce the time-dependent variables to only two in the FUV and one in the NUV, or essentially the average IRIS response in the three spectral windows around 1335 Å, 1400 Å, and 2800 Å. The IRIS response for these wavelength windows over time is shown in the three panels of Figure 24. The colored symbols in each panel indicate the results of the IRIS–SOLSTICE cross-calibrations. Trending of the IRIS SG response over the course of the mission. Top panel: FUV near 1335 Å, middle panel: FUV near 1400 Å, and bottom panel: NUV. Colored diamonds and crosses indicate absolute cross-calibrations with SOLSTICE, black dots are scaled running averages of IRIS quiet-Sun observations, and colored solid lines are the final parametric fits. See text for details. Full-disk mosaics are very time consuming, and IRIS–SOLSTICE cross-calibrations are performed only a few times per year. To monitor the medium-term variability of its response, IRIS takes daily standardized observations of a quiet-Sun region near disk center that provide average quiet-Sun intensity values at the three calibration wavelengths. Because of solar variability, these values show substantial scatter, which can be smoothed by a running monthly average. These smoothed intensities are a useful means to track the IRIS response between SOLSTICE cross-calibrations, but in the long run, they do not accurately track the cross-calibration results, in particular in the FUV. This is presumably due to the fact that the typical quiet-Sun intensity in the UV depends on the solar cycle. However, we can capture both medium- and long-term trends by multiplying the smoothed quiet-Sun intensities with a function that varies only on solar cycle timescales. The function is chosen from a best fit to the SOLSTICE cross-calibrations. The resulting smoothed and adjusted quiet-Sun intensities are shown in all panels of Figure 24 as black dotted lines. In a final step, we fit parametric functions to these intensities (colored solid lines in Figure 24) that provide the time variability for our spectral response model in iris_get_response.pro. It is worth discussing a few features of the temporal evolutions in Figure 24. i) The FUV SG response declines by about a factor of two over the first nine months of the mission, but then starts leveling off. This initial decline may be related to residual outgassing of the observatory condensing, and possibly polymerizing on the optics. The FUV response changes in the very early portion of the mission are not very well understood as the first absolute calibration did not occur until 2.5 months after first light. In general, the post-launch effective area near 1335 Å appears to be somewhat lower than the pre-launch effective area value of 1.5 cm2, while near 1400 Å, the post-launch area appears to be slightly larger than the pre-launch value of 2.1 cm2. ii) Both FUV curves show a slight response gain toward the end of each year, around the time of the beginning of the eclipse season (i.e. the time of the year when the Sun is eclipsed by the Earth for several minutes every orbit). iii) The 1335 Å curve shows a sudden response increase in the Fall of 2014. This change was caused by the first IRIS detector bake-out. It appears that a good portion of the sensitivity decrease at that time was caused by a thin layer of contamination on the CCDs. Later bake-outs did not show nearly as much improvement. The material condensed on the CCD affected 1335 Å much more than 1400 Å, which is not surprising as molecular contaminants absorb more strongly at shorter wavelengths. iv) The NUV response does not show a long-term response decline. On shorter time scales it shows a nearly opposite behavior to the FUV response, with a sensitivity increase/decrease at times when the FUV shows the strongest decrease/increase. This phenomenon is not fully understood, but we hypothesize that it may be caused by a thin contamination layer on the CCD acting as an anti-reflection (AR) coating. When the layer thickness grows, as was the case early in the mission, the AR effect increases, while during the bake-out, the removal of the contamination layer from the CCD caused the AR effect to disappear. After three years on orbit, the NUV sensitivity appears to have returned to nearly the same value as at launch. Slit-Jaw Imager Post-launch spectral calibration of the slit-jaw imager (SJI) is more difficult and more prone to error than the SG calibration. A component-wise calibration of the spectral response was carried out pre-launch, but it is likely that the actual (post-launch) response is noticeably different and/or may have shifted since the pre-launch measurements. This uncertainty predominantly affects the relative contributions of the C ii versus the Si iv lines to the images in each of the two FUV channels. We attempted to carry out a best estimate of the relative spectral response changes in the FUV SJI by assuming that they are similar to the changes in the FUV SG. We implemented this by calculating the ratio of actual versus pre-launch response for the SG at 1335 and 1400 Å, and then applied a linear correction based on those two ratios to the SJI pre-launch response curves. However, it is not clear that the SJI changes are the same as the SG changes. In fact, the SJI has a transmission filter that may age differently than the reflective surfaces used in the SG. The latter were found to be quite stable in tests, while the aging of the FUV transmission filter has not been thoroughly studied. Nevertheless, we use the SJI pre-launch transmission curves, corrected by the measured SG changes (as discussed above), as the basis of the effective area calibration. To obtain an absolute calibration value, these effective area curves were then scaled as a whole so that the integrated SOLSTICE spectrum folded with these adjusted SJI curves matches the total measured photon fluxes from the IRIS full-disk observations. The results are shown using color symbols in Figure 25. Medium-term trending was derived from the daily IRIS quiet-Sun observations in the same way as the SG trending, and is shown as black dotted lines in Figure 25. The colored solid lines show the functional fit that is used for the response calibration in iris_get_response.pro. Trending of the response of the four IRIS SJI channels over the course of the mission. Diamonds indicate cross-calibrations with SOLSTICE, black dots are scaled running averages of IRIS quiet-Sun observations, and colored solid lines are the final parametric fits. See text for details. The most noteworthy findings from Figure 25 are as follows: i) The response change in the FUV SJI is more pronounced than in the FUV SG, with a decrease of about a factor of three over the first nine months of the mission. As in the FUV SG, the decline starts leveling off afterwards. ii) All channels show a pronounced change at the first detector bake-out. iii) The SJI 2832 Å (Mg ii wing) channel appears to vary more than the SJI 2796 Å (Mg ii line center) channel. This latter result is slightly puzzling. More analysis may be required to confirm this behavior. It is perceivable that the AR coating effect of a contamination layer on the CCD is more effective at the longer wavelength. Stellar Calibration IRIS can observe objects up to about 5 arcmin above the solar limb without its Guide Telescope losing fine-pointing control. Over the course of a year, about a dozen sufficiently bright B stars pass the Sun within that range and provide an alternate throughput calibration opportunity. In addition to their UV brightness, the target stars have been selected for minimum variability and the availability of good spectra from at least IUE and preferably also from HST. We routinely observe HD19374, HD91316, HD142096, HD144470, and HD210424 with the FUV SJI, although we have observed a few others early in the mission. Only HD91316 ($\rho \ \mathrm{Leo}$) and HD144470 were bright enough for IRIS to obtain spectra with the FUV spectrograph and only during the first year of the mission. None of these stars are bright enough for NUV observations. Our observing strategy (as suggested by John Raymond) is to place the IRIS slit a few arcseconds west of the star, let the star transit the slit, and then repeat the process. Up to about 20 such slit transits are possible over the course of several hours. At each transit we acquire a series of exposures in the FUV SG and the two FUV SJI channels. The images provide the calibration data for the SJI and allow us to locate the proper spectrograph exposure and location when the star passed the slit. The slit transit time is about 10 s. In August and November 2013, we observed 17 spectra of HD91316 and 3 spectra of HD144470, respectively. To derive an IRIS effective area, we first predict the total count rate for the star in the IRIS spectra by folding the calibrated IUE spectrum of the star with the pre-launch effective area of IRIS. We then divide the total observed counts in the IRIS spectrum by the slit transit time and compare this observed rate to the predicted rate. The IRIS spectra are too noisy to obtain the spectral shape of the FUV SG response, but sufficient to obtain effective areas separately for the FUV-L (1389 – 1407 Å) and FUV-S (1332 – 1358 Å) spectral ranges. The observed count rates were very similar to the predicted ones for the FUV-L range, and slightly lower for the FUV-S range. The derived effective areas were 2.2 cm2 for the FUV-L and 1.2 cm2 for the FUV-S. This compares very well with the effective areas derived from the SOLSTICE calibration of 2.3 and 1.1 $\mathrm{cm^{2}}$, respectively. The results from HD144470 were similar but noisier and therefore less accurate. Stellar observations with the slit-jaw imager have been possible throughout the mission thus far. These stellar calibrations qualitatively appear to track the results from the SOLSTICE calibration. However, the implied loss of sensitivity over the course of the mission is roughly a factor of two higher than the SOLSTICE calibration indicates. The discrepancy is not well understood, but we have much more confidence in the accuracy of the SOLSTICE cross-calibration. First, the SOLSTICE results are not hampered by low count rates and associated noise as the stellar results are. Second, the SOLSTICE calibration is carried out with the Sun and the same spectral lines that IRIS primarily observes. In contrast, the stellar calibration uses the spectra of B stars, which have a strong FUV continuum. This would not be an issue if we had accurate knowledge of the SJI filter response as a function of wavelength. Unfortunately, this is not the case. The spectral response of the SJI channels cannot be measured on orbit and has likely changed from pre-launch as a result of contaminants and the aging of coatings. As we are using the pre-launch response curves to predict the SJI count rates for the B star, we are introducing a considerable source of error, especially several years into the mission. For more details and the result of the stellar calibration, we refer to IRIS Technical Note (ITN) 24 at http://iris.lmsal.com/documents.html . Gain Calibration The calibration of solar observations in terms of absolute units requires knowledge of the instrument effective area, the instrument spatial and spectral plate scales, and finally the CCD camera gain. Most commonly, we use the inverse camera gain, $j$, for converting the number of detected photons, $P$, into data units, $S$: $$ S = P /j. $$ The (inverse) camera gain is typically measured via a photon transfer curve (PTC). The PTC takes advantage of the fact that the noise in a CCD camera is dominated by the shot noise at moderately high signal levels. This leads to the following relationship between shot-noise-induced signal variance, $\sigma ^{2}_{S}$, and signal level: $$ \sigma ^{2}_{S} = S/j. $$ A PTC can be generated by imaging a constant light source with multiple images at each of a range of exposure times. The average signal variance is plotted against signal for each signal level. The PTC curve will deviate from the idealized curve at short exposures because of the camera read noise and at long exposures because of camera non-linearities. Figure 26 shows a PTC curve for the SJI CCD illuminated by the onboard blue LED shortly before IRIS first light. The (inverse) CCD camera gain was close to 18 photons DN−1. We have repeated this measurement at various times over the mission and found no change. The NUV SG CCD uses the same camera gain, while the FUV SG camera uses an electronic gain that is three times higher for increased sensitivity at low count rates. Photon transfer curve for the SJI CCD measure with a blue LED. The CCD camera gain is essentially constant over a range of photon energies from the infrared to the near UV. At higher photon energies, however, a single photon can create more than one electron-hole pair, which causes the gain to increase (or the inverse gain to decrease). Figure 27 shows a PTC curve for the SJI 1330 Å channel illuminated by a deuterium lamp during ground testing. The resulting FUV (inverse) gain is 12 photons DN−1, i.e. about a factor 1.5 different from blue light. We have adopted this factor for all of our FUV calibrations. Photon transfer curve for the SJI CCD measured with a deuterium lamp at 1350 Å. On closer look, however, the factor 1.5 gain difference is less than expected, since the energy of the FUV photons is sufficient to create at least two electron-hole pairs. We suspect that charge spreading in the CCD substrate may occasionally allow one of the two simultaneously created photo-electrons to migrate into a neighboring pixel. This effect would artificially reduce the apparent shot noise and the resulting gain factor in the PTC measurement. We have recently analyzed PTC measurements with larger pixels to reduce the effect of charge spreading. The results suggest that the gain factor at 1350 Å may indeed be as high as 2. We have not measured a PTC at 2800 Å, but the NUV gain is expected to be very similar to the gain in the blue. Table 1 summarizes the adopted gains for the various IRIS channels. As the table shows, we are currently still using a factor of 1.5 for the gain in the FUV, not the potentially more accurate value of 2. It is important to note that an error in this factor does not affect the accuracy of the absolute cross-calibration results with SOLSTICE. Owing to the nature of the cross-calibration process, an error in the CCD camera gain is compensated for in the effective area results of the calibration. A gain factor of 2 instead of 1.5, for example, would result in 25% lower FUV effective area numbers. The gain factor does, however, affect estimates of the Poisson noise. Table 1 (Inverse) CCD camera gains for all IRIS channels in photons DN−1. Other calibrations Wobble Calibration The thermal conditions at IRIS vary over the course of an orbit as a result of the satellite orientation with respect to terrestrial albedo. These thermal variations induce bending in the mounting of the guide telescope, which in turn introduces a pointing wobble that is a function of the orbital position. The wobble varies annually, but is relatively stable on a weekly timescale. Over an orbit, typical magnitudes of the wobble are 2 – 4 arcsec in $x$ and 1 – 2 arcsec in $y$. The thermal conditions of the satellite vary more dramatically during the eclipse season, resulting in larger changes in the wobble over an orbital period (up to 8 arcsec in $x$ and 3 arcsec in $y$) as well as more significant changes to the magnitude of the wobble on a weekly to monthly timescale. The roll angle of the satellite also affects the wobble since the orientation of the guide telescope is altered when IRIS is rolled. As described below, the wobble under rolled conditions is phase shifted from that when not rolled. In contrast to the calibrations discussed earlier, the wobble calibration is not applied to the data post facto. Instead, a periodic, orbital-phase-dependent pointing correction is applied to the telescope secondary mirror in real time. The first stage of the calibration procedure to correct for the pointing wobble is to quantify its effect. We measure the on-orbit wobble by collecting SJI 2832 Å channel images over two successive orbits with 10 s exposure time and 20 s cadence. We quantify the wobble in the $x$- and $y$-directions independently by performing this observing routine at both the east limb and the north pole, such that the limb of the solar disk is in the field of view, and running a cross-correlation algorithm on the data. These results are used to create an orbital wobble table (OWT) that consists of corrections to the piezoelectric transducers (PZTs) of the secondary mirror to compensate for the wobble. The above analysis has been performed at roll angles of $0^{\circ }$, $\pm 45^{\circ }$, and $\pm 90^{\circ }$. Figure 28 shows the results of these analyses for October 2015. The magnitude of the wobble shown here is typical of that during non-eclipsed observations. When in eclipse season, the wobble is on the order of 10 arcsec. The magnitude of the wobble is similar across different roll angles, but shifted in phase. For a roll angle of $\alpha $, the wobble can be approximated by the wobble for $0^{\circ }$ roll angle, shifted in phase by $\alpha /360^{\circ }$. This is illustrated in the bottom panel of Figure 28. This property allows us to correct for the orbital wobble at an arbitrary roll angle without overburdening the IRIS science observations with calibration routines. When rolled to angle $\alpha $, we correct for the wobble by applying the $0^{\circ }$ OWT shifted in phase by $\alpha /360^{\circ }$. The exception to this is for $\alpha =\pm 90^{\circ }$. Because $\pm 90^{\circ }$ rolls are used more frequently than other angles and the phasing formula decreases in accuracy with the degree of roll, we perform the calibration routine separately for $\pm 90^{\circ }$ and generate separate OWTs for these angles. Orbital wobble correction. Top panel: IRIS orbital wobble in units of IRIS 0.16 arcsec pixels, for the $x$- (solid lines) and $y$- (dashed lines) directions, and three roll angle values: 0 (black), $+90$ (red), and −90 (dark blue). Bottom panel: Same curves as in the top panel, but with a phase shift of the wobble curves for $+90$ and −90 of $+0.25$ and −0.25, respectively. The shifted curves are very similar to the wobble curves for $0^{\circ }$ roll angle. The orbital phase is zero at the time when IRIS passes through its ascending node. Figure 29 shows how the magnitude of the wobble has varied over the mission. Shown here is the magnitude of the wobble over an orbit, i.e. the $\sqrt{x^{2}+y^{2}}$ drift within an orbital period. Wobble calibration data are sparse for 2014, but for the last three years, we see that the annual variation in the wobble has been consistent from year to year. The effect of eclipse season (November to February) on the magnitude of the wobble is also evident. Given the timescale of the wobble variation, calibration observations for roll angles of $0^{\circ }$ and $\pm 90^{\circ }$ are normally performed on a monthly basis. In addition, the wobble correction is checked weekly and more frequent calibrations are performed as needed, notably when entering and exiting the eclipse season. Variation of the wobble over the mission at a roll angle of $0^{\circ }$. Measurements for each year are shown in different colors. The wobble magnitude is defined as the absolute value (in Euclidean space) of the drift within an orbit. The asterisks indicate where orbital calibration data were taken with dashed lines to guide the eye on the annual variation. There were only three calibrations in 2014, so we have not connected these data points with lines. Although IRIS is not a spectropolarimeter, it was expected that the FUV and NUV gratings may both act as partial linear polarizers. There are phenomena on the Sun (i.e. strong magnetic fields in active regions, scattering, and atomic level polarization) that induce polarization in spectral lines and continua. The Mg ii lines in the NUV are expected to have a fairly strong linear polarization signal (as much as 10%) based on recent spectral synthesis (Belluzzi and Trujillo Bueno, 2012). To assess the potential amplitude of polarization-induced intensity changes in the Mg ii line measured with IRIS, we characterized the efficiency with which the NUV grating acts as a polarizer. The linear polarization response of the NUV spectrograph was measured during optical integration and testing prior to launch. A 2796.74 Å laser was used to provide light 100% polarized in one direction. A half-waveplate retarder optimized for 2660 Å was used to modulate the linear polarization direction from the laser, and was placed in the optical setup of the stimulus telescope (StimTel) that illuminated the IRIS instrument for ground testing. The StimTel was aligned with the IRIS telescope, and the laser spot was placed in the middle of the slit as verified by the NUV slit-jaw imager. The focus was adjusted to provide a larger and less intense laser spot so that the laser in the spectrograph images would not saturate. Four different series of measurements were taken. For each measurement, the waveplate was adjusted from $0^{\circ }-90^{\circ }$ in increments of $5^{\circ }$. The waveplate was mounted in a simple rotation mount, and adjustments were made by hand. Because the placement of the waveplate made the scale difficult to see, the adjustments may be imprecise at the $2^{\circ }$ level. The intensity of the laser was totaled, totals from an adjoining region of the same size with no signal were subtracted to account for the background signal. Figure 30 shows the results from the four series in different colors. It is immediately apparent that there is a great deal of noise in the intensity measurement. This is due to drift of the laser across the slit. During the first three sets of measurements (yellow, green, and blue), the optical table was floated, but during the final set of measurements (red), the table was settled on its supports. In the spectrograph images it appears that the laser spot was drifting across the slit, leading to a change in the illumination pattern and intensity level. Intensity of the laser spectrum as a function of the half-waveplate orientation for the four measurement series (colored points). The fit to the data is shown by the solid black line. We adopted the manufacturer's value for the retardance at the laser wavelength, and fit the observed intensity for the grating polarization efficiency, $e$, and an additional angle term to account for an offset error between the laser and the waveplate. The fit is shown by the black line in Figure 30. The resulting polarization efficiency for the grating for this fit is 13% perpendicular to the groove direction of the grating. When we combine this polarization sensitivity with a potential linear polarization signal of 10%, we find that the resulting polarization induced intensity change would be only about 1.3%. In addition to the calibrations discussed above, the IRIS team performs periodic calibrations of onboard system settings, such as the PZT actuator gains of the image stabilization and spectrograph raster scan system, and the focus setting of the IRIS telescope. These systems are very stable on short terms, but show slow drifts due to seasonal variations of the instrument thermal environment. As an example, Figure 31 shows the evolution of the setting for best focus of the IRIS telescope. Evolution of the setting for best focus (in focus motor steps) over the mission. The changes are primarily due to variations of the thermal environment. The annually recurring jumps are caused by the eclipse seasons. Other calibrations or corrections applicable to the IRIS data include the characterization of the instrument point spread function (PSF) and the dust particle removal process that may be applied to the raw slit-jaw images. The PSF of the IRIS spectrograph was first characterized pre-launch in the laboratory and recently in-flight using the 9 May 2016 Mercury transit. The results are documented in Courrier et al. (2018). Dust particles that migrated onto the SJI CCD pre-launch result in speckle-like dark features in the SJI images. They can be removed on the data-user end by calling an IDL routine iris_dustbuster.pro, which fills the dust pixels with good-pixel values of the same location on the Sun from neighboring frames adjacent in time. This thus works best on coarse or many-step dense/sparse rasters, where good-pixel data are readily available. For sit-and-stares or narrow rasters, the routine still works to some extent, but fills the dust specks with a spatially blurred interpolation of the surrounding area. Dust removal is not routinely applied in the science data pipeline, but is applied to the quick-look imagery on the IRIS website. Note that the current dust-buster does not always work perfectly, because it uses a set of dust masks at fixed positions and does not take into account thermal drifts of the fiducials. In practice, the actual image data are placed so that the fiducials always remain at the same locations in the FITS files. At times when thermal flexing of the instrument causes the fiducials and thus the images to drift, this correction could fail and miss the dust by a few pixels. This shortcoming could be improved by allowing the dust masks to move with time to compensate for the thermal drifts. For various calibration-related subjects not covered or only briefly mentioned in this article, we refer to the latest technical notes at http://iris.lmsal.com/documents.html , which are periodically updated. In this section, we describe the flow of IRIS data through the processing pipeline from raw telemetry to data products for distribution to the science community. As summarized in Figure 32, IRIS has four data levels that are processed sequentially as follows: Raw telemetry is captured and converted into Level 0 image files. Images are rotated and flipped to produce Level 1 data, for which all relevant spacecraft and instrument telemetry is incorporated into the FITS headers. This constitutes the lowest level of scientifically useful data. The next step is key in the data processing pipeline, where a series of calibration corrections are applied to produce Level 2 data, which is the product released to the public. The type of processing depends on whether the data come from the slit-jaw imager or the spectrograph. In general, darks and pedestal offsets and overscan rows are removed, flat-fielding corrections for telescope and CCD properties are applied, and the background in FUV spectral images is subtracted. In addition, geometric and wavelength corrections are applied, so that all images are mapped to a common spatial plate scale and an "ideal" CCD. Spectral images are also remapped to align with an equal-sized array where wavelength and spatial coordinates align with the grid. An array mapping the wavelength axis to physical wavelength is created in this process. We refer to relevant sections of this article for technical details of these calibrations. Finally, the data are rearranged and saved as Level 2 FITS files. The rearrangement is based on the spatial and spectral windows defined in the observing sequence (OBS) and depends on the type of data – SJIs or spectrograph rasters: Level 2 SJI-files are time series. That is, all SJIs of the same wavelength channel are put together in one file of a 3D cube by $(x, \, y, \, t)$. Here $x$ and $y$ are spatial dimensions in the direction of raster scan and along the slit, respectively, and $t$ is time. The SJI-images are padded in the $x$ dimension, so that the full field-of-view (FOV) is included. Each single SJI-image is then placed in its appropriate position within this padded area. Each spectral window is saved in its own cube, so that each raster file contains one cube per window. The axes of these cubes are $\lambda $ (wavelength), $y$, $x$. Each raster repetition is saved in a separate file. For sit-and-stare observations, there is only one raster repetition, i.e. all rasters are in one file. iv) On the data user end, Level 2 data can be reorganized by SolarSoft tools into Level 3 data for further analysis with the CRISPEX software package (see ITN 26 at http://iris.lmsal.com/itn26/itn26.pdf ). Level 3 datacubes are 3D in $(x, \, y, \, t)$ for SJI data and 4D in $(\lambda , y, \, x, \, \,t)$ for spectral data. Figure 33 shows a schematic of the spectral data layouts at various levels. Flow chart of various IRIS data levels and associated pipeline processing. IRIS spectral data layout for various data levels. Left: Levels 0 and 1 spectral data have up to eight windows appropriately placed within a pixel array matching the CCD detector. Middle: Level 2 data have extracts of the eight windows, assembled into rasters based on slit position $x$. Right: Level 3 data assemble the Level 2 rasters into time-series datacubes. Processing from Level 1 to 2 is carried out in the data processing pipeline through calls to the IDL routine iris_prep.pro in the SolarSoft IRIS package. iris_level1to2_driver2.pro is the top-level driver and takes two passes for each OBS: In the first pass, it invokes iris_prep with explicit keyword settings to generate a database for various calibrations. In the second pass, it invokes iris_level1to2.pro, which calls iris_prep with inherit and keyword pipeline=1 to apply the actual corrections using the database from the first pass. iris_level1to2 then rearranges the data and saves them in Level 2 FITS files. In terms of timing, fresh telemetry is processed in near real time (NRT) with data semi-calibrated. NRT data are a transitory, quicklook product, not released to the public, and are used to produce images and movies posted on the "IRIS Recent Observations" webpage. The full pipeline processing takes place within a few days to produce the final Level 2 data, and the online images and movies are then updated accordingly. When applying various time-dependent corrections, we use the results of the calibration runs that were carried out closest in time to the observations. IRIS data are occasionally reprocessed when problems with data quality are discovered or calibrations are improved. Data users are advised to download the latest data for their science analysis. We encourage the general science community to report IRIS data issues to iris_calib@lmsal.com. Note that, however, iris_prep is not intended to be used by individual end users because of the complexity involved in the Level 1 to 2 processing and various housekeeping data and because the huge, intermediate database is not being distributed. Idiosyncrasies and Known Problems Despite careful calibrations and data processing, there are still some minor problems in the final IRIS data product. Some of these problems have been corrected in the recent mission-long data reprocessing completed in August 2017, although some still persist and may not be solved soon. While the underlying causes vary from telemetry data dropouts to pipeline software bugs, the majority of these problems, especially those that are ongoing, have negligible to minor impact on science data in general. We describe below a few well-understood problems. A complete list of IRIS idiosyncrasies, together with examples and figures, is documented at http://iris.lmsal.com/documents.html . For a limited number of historic datasets, there were artificial jumps or steps in time in the spectral intensity. This occurred when there were missing housekeeping temperature data due to telemetry dropouts, which caused the temperature-dependent dark correction to fail. This issue has been corrected as of March 2017 by interpolating the temperature data from neighboring orbits. There are vertical stripes in spectroheliograms at a period equal to the number of SJI channels used times the cadence. The peak-to-peak amplitude is only at a negligible ≈ 0.2 DN level. It is usually noticeable in space–time plots of low-intensity continuum spectra, made from observing sequences with alternating FUV and NUV SJI images. This is a result of imperfect correction of the FUV spectrograph background, which depends on the filter-wheel position (see Section 3.1) and creates an intensity dip at the times of the 2796 SJI images. To remove this artifact, one can adopt empirical tools such as those under the SolarSoft package "mosic" at https://sohowww.nascom.nasa.gov/solarsoft/packages/mosic . There is an upside-down L-shaped feature in FUV-L spectra near the Si IV 1394 line (as shown in Figure 3), which results from the residual of imperfect background subtraction. There are features of regular geometric shape in off-limb SJI images that move together with the slit during rasters. The intensity of such features is low, usually no more than 2 – 4 DNs, and thus they only show up against a faint, off-limb background. They are due to scattered light in the SJI optical paths and are very difficult to remove. Examples of such features include i) a ghost of the solar limb (arc) on the left plus a vertical step on the right, appearing off the eastern limb; ii) a bright donut shape with a dark, central vertical bar running across it, appearing off the western limb; and iii) a circular arc of the North Pole. The SG detector burn-in at the C ii lines is currently not being corrected for (see Section 4.3). We have provided a detailed description of various important calibrations applied to IRIS data, including dark correction, scattered light and background correction, flat fielding, geometric distortion correction, wavelength calibration, throughput trending, and wobble corrections. Many aspects of the calibrations have improved substantially since launch, and recent reprocessing of the IRIS Level 2 data archive has made these improvements available to early IRIS data as well. Using the latest version of Level 2 data is therefore important, and SolarSoft routines reading IRIS Level 2 data now alert the user if an outdated version of a data file is being ingested. There remain a few minor calibration issues and idiosyncrasies, as described in this article. The IRIS team has been and will continue to constantly monitor the data quality and make improvements to the calibration procedures and data processing pipeline on a regular basis to accommodate the evolving instrument characteristics over the mission and to meet the ever-growing needs of the science community. New users should consult the Guide to IRIS Data Analysis, IRIS Technical Note (ITN) 26. It is found online under http://iris.lmsal.com/documents.html , together with other documents of interest. This article supersedes most of the calibration ITNs found there, but relevant ones will be updated as calibrations evolve. Belluzzi, L., Trujillo Bueno, J.: 2012, The polarization of the solar Mg II h and k lines. Astrophys. J. Lett. 750, L11. DOI . ADS . Berger, T.E., Mudge, J., Holmes, B., Searcy, P., Wuelser, J.P., Lemen, J., Title, A.: 2012, Design and fabrication of the near-ultraviolet birefringent Solc filter for the NASA IRIS solar physics mission. In: Proc. SPIE 8486. DOI . ADS . Chae, J.: 2004, Flat-fielding of solar H$\alpha $ observations using relatively shifted images. Solar Phys. 221, 1. DOI . ADS . Courrier, H., Kankelborg, C., De Pontieu, B., Wülser, J.-P.: 2018, An on orbit determination of point spread functions for the interface region imaging spectrograph. Solar Phys. 293, 125. DOI . Cox, A.N.: 2002, Allen's Astrophysical Quantities, Springer, New York. 978-1-4612-1186-0. DOI . Book Google Scholar De Pontieu, B., Title, A.M., Lemen, J.R., Kushner, G.D., Akin, D.J., Allard, B., Berger, T., Boerner, P., Cheung, M., Chou, C., Drake, J.F., Duncan, D.W., Freeland, S., Heyman, G.F., Hoffman, C., Hurlburt, N.E., et al.: 2014, The interface region imaging spectrograph (IRIS). Solar Phys. 289, 2733. DOI . ADS . Jaeggli, S.A., Judge, P.G., Daw, A.N.: 2018, Formation of the UV spectrum of molecular hydrogen in the Sun. Astrophys. J. 855, 134. DOI . ADS . Kohl, J.L., Parkinson, W.H.: 1976, The Mg II h and k lines. I. Absolute center and limb measurements of the solar profiles. Astrophys. J. 205, 599. DOI . ADS . Kuhn, J.R., Lin, H., Loranz, D.: 1991, Gain calibrating nonuniform image-array data using only the image data. Publ. Astron. Soc. Pac. 103, 1097. DOI . ADS . McClintock, W.E., Rottman, G.J., Woods, T.N.: 2005, Solar-stellar irradiance comparison experiment II (Solstice II): instrument concept and design. Solar Phys. 230, 225. DOI . ADS . Samain, D., Lemaire, P.: 1985, Balloon–Borne ultraviolet solar telescope and high resolution echelle spectrograph – instrumentation and first results. Astrophys. Space Sci. 115, 227. DOI . ADS . Snow, M., McClintock, W.E., Rottman, G., Woods, T.N.: 2005, Solar stellar irradiance comparison experiment II (Solstice II): examination of the solar stellar comparison technique. Solar Phys. 230, 295. DOI . ADS . Wilhelm, K., Lemaire, P., Feldman, U., Hollandt, J., Schühle, U., Curdt, W.: 1997, Radiometric calibration of SUMER: refinement of the laboratory results under operational conditions on SOHO. Appl. Opt. 36, 6416. DOI . ADS . Wülser, J.-P., Title, A.M., Lemen, J.R., De Pontieu, B., Kankelborg, C.C., Tarbell, T.D., Berger, T.E., Golub, L., Kushner, G.D., Chou, C.Y., Weingrod, I., Holmes, B., Mudge, J., Podgorski, W.A.: 2012, The interface region imaging spectrograph for the IRIS small explorer mission. In: Proc. SPIE 8443. DOI . ADS . We wish to thank Marty Snow and the SORCE/SOLSTICE team for providing the high-resolution spectra used in the IRIS absolute throughput calibration. We also wish to thank John Raymond for his help with the stellar calibrations and Reza Rezaei, Lucia Kleint, and Pradeep Chitta for reporting calibration issues and helping with troubleshooting efforts. This work is supported by NASA contract NNG09FA40C (IRIS). IRIS is a NASA small explorer mission developed and operated by LMSAL with mission operations executed at NASA Ames Research center and major contributions to downlink communications funded by ESA and the Norwegian Space Centre. NASA's Solar Radiation and Climate Experiment (SORCE) is managed by the Laboratory for Atmospheric and Space Physics (LASP) at the University of Colorado-Boulder. NCAR is supported by the National Science Foundation. S. Jaeggli Present address: National Solar Observatory, Pukalani, HI, USA P. Boerner Present address: Apple Inc., Cupertino, CA, USA N. Schanche Present address: University of St Andrews, St Andrews, Scotland, UK Lockheed Martin Solar & Astrophysics Laboratory, Lockheed Martin Advanced Technology Center, Org. A021S, Bldg. 252, 3251 Hanover St., Palo Alto, CA, 94304, USA J.-P. Wülser, B. De Pontieu, T. Tarbell, P. Boerner, S. Freeland, W. Liu & R. Timmons Department of Physics, Montana State University, Bozeman, P.O. Box 173840, Bozeman, MT, 59717, USA S. Jaeggli, S. Brannon & C. Kankelborg Harvard-Smithsonian Astrophysical Observatory, 60 Garden Street, Cambridge, MA, 02138, USA C. Madsen, S. McKillop, J. Prchlik, S. Saar, N. Schanche & P. Testa High Altitude Observatory, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO, 80307, USA P. Bryans Institute of Theoretical Astrophysics, University of Oslo, P.O. Box 1029, Blindern, Oslo, Norway B. De Pontieu & M. Wiesmann Bay Area Environmental Research Institute, NASA Research Park, Mailstop 18-4, Moffett Field, CA, 94035-0001, USA W. Liu J.-P. Wülser B. De Pontieu T. Tarbell S. Freeland R. Timmons S. Brannon C. Kankelborg C. Madsen S. McKillop J. Prchlik S. Saar P. Testa M. Wiesmann Correspondence to J.-P. Wülser. The authors declare that they have no conflict of interest. Wülser, JP., Jaeggli, S., De Pontieu, B. et al. Instrument Calibration of the Interface Region Imaging Spectrograph (IRIS) Mission. Sol Phys 293, 149 (2018). https://doi.org/10.1007/s11207-018-1364-8 Instrumentation: calibration	CommonCrawl
Earth Perspectives Transdisciplinarity Enabled The sensitivity of present-time electricity demand on past climate change: a case study for Italy Simone Scapin1,2,3, Francesco Apadula1, Michele Brunetti2 & Maurizio Maugeri2,3 Earth Perspectives volume 2, Article number: 4 (2015) Cite this article A methodology for estimating secular daily minimum, mean and maximum (Tn, Tm and Tx) temperature records for any urbanised point of a 30-arc-second-resolution grid covering Italy is presented. It is based on the superimposition of 1961–1990 climatologies and departures from them (anomalies). The anomalies are obtained by applying inverse distance weighting to 143 Italian high-quality records, whereas the climatologies are based on a larger dataset and on the application of local weighted linear regression of temperature versus elevation. The grid-point Tn, Tm and Tx records are then used to set up secular records (period 1801–2013) of temperature-derived variables that influence Italy present-time national electricity demand. They are national averages over Italian urbanised areas of cooling degree-days (CDD), heating degree-days (HDD) and solar radiation deficit with respect to a defined threshold (S), with solar radiation estimated using daily temperature range as a proxy. The monthly and yearly sums of the daily CDD, HDD and S records are then used, alongside with a model allowing to link these variables to present-time Italy electricity demand, in order to understand the impact of climate variability and change on present-time Italian electricity demand. We find that temperature changes as the ones observed in the last two centuries are capable of altering significantly the present-time monthly profile of the electricity demand, raising (lowering) summer (winter) months contributions. The impact is higher in summer months where it exceeds 5 % of present-time Italy average monthly electricity demand, whereas the decrease of the winter demand is rather low because of a very limited use of electricity for heating. The summer and winter opposite-sign changes result globally in an increase of the yearly demand of about 5 TWh, corresponding to about 1.5-2.0 % of present-time Italy yearly electricity demand. Spatial climate datasets in digital form are currently in great demand and gridded estimates of 30 years climatological normals are requested by a variety of models and decision support tools, such as those used in agriculture, engineering, hydrology, ecology, energy management and natural resource conservation (Daly et al. 2002; Daly 2006). These datasets have to be set up providing a realistic representation of the major forcing factors that affect spatial climate patterns, in order to give reasonable estimates also for areas with poor station coverage, such as high elevation sites in mountain areas (Daly et al. 2008). Beside the spatial distribution of the climatological normals, it is also important to describe the spatio-temporal behaviour of climate variability and change. It is therefore necessary to set up methodologies that allow for estimating both the climatological normals of any point of the territory and the corresponding long-term records. As the desired resolution turns often out to be rather high (e.g., 1 km2), such spatialisation methodologies present a number of non-trivial issues. In this context, this paper discusses the estimation of daily secular records of minimum, mean and maximum temperatures (Tn, Tm, and Tx) for any cell of a 30-arc-second resolution grid covering Italy classified, according to the EC JRC Global Land Cover 2000 (European Commission 2003), as "artificial surfaces and associated areas" (these grid-cells are hereinafter called "urbanized"). These records are then used to investigate past variability and change of temperature-derived variables that influence present-time national electricity demand and to estimate the impact of past variability and change on present-time Italy electricity demand. Such an estimation may be useful within the estimation of the costs of climate change. The basic assumption of the methodology we use to set up the grid-cell daily temperature records is that the spatio-temporal structure of the signal of a meteorological variable over a given area can be described by the superimposition of two fields: the climatological normals over a given reference period (i.e. the climatologies) and the departures from them (i.e. the anomalies) (New et al. 2000; Mitchell & Jones 2005; Brunetti et al. 2009; Brunetti et al. 2012). The climatologies, which we produce with the procedure described in Brunetti et al. (Brunetti et al. 2014), are basically linked to the geographical features of the territory, therefore they exhibit remarkable spatial gradients. On the contrary, the anomalies, which we produce by inverse distance weighting, are linked to climate variability and change and are characterized by higher spatial coherence. We reconstruct the two fields in a completely independent way from each other, using different datasets: for the anomalies the priorities are data quality and the availability of long records, whereas for the climatologies the most relevant aspect is the availability of a large number of stations. In this case, in fact, we consider the issue of record length as less relevant, as a 30 year period is enough to estimate climate normals. The technique we consider to capture the dependence of present-time Italy electricity demand on meteorological variables is that presented by Scapin et al. (Scapin et al. 2015). They model the demand of ordinary days by means of a linear regression model made up of i) a time-dependent term capturing long-term trends, ii) a term accounting for the differences among the different days of the week and iii) a set of terms depending on temperature-derived variables that can be obtained from high-resolution Tn, Tm, and Tx fields. The latter are national averages over Italian urbanised areas of cooling degree-days (CDD), heating degree-days (HDD) and solar radiation deficit with respect to a defined threshold (S), with solar radiation estimated using daily temperature range as a proxy. Applying this technique, Scapin et al. (Scapin et al. 2014) quantified the present-time dependence of the Italian electricity demand of an ordinary day on CDD, HDD and S in, respectively, 24.6 GWh degree-day−1, 6.6 GWh degree-day−1 and 2.9 GWh day−1 MJ−1 m2. These values give evidence of a relevant contribution of meteorological conditions on the electricity demand, especially in the summer period: in this season, the fraction of the electricity demand driven by meteorological conditions can exceed 20 %. Temperature is indeed the most important meteorological variable influencing the electricity demand: it regulates the request for conditioning in summer and for heating in winter (Pardo et al. 2002; Moral-Carcedo & Vicéns-Otero 2005; Hor et al. 2005; Bessec & Fouquau 2008; Hekkenberg et al. 2009; Apadula et al. 2012). The latter request is however rather low in Italy as the use of electricity for heating is limited. Variability and change of CDD, HDD and S from the beginning of the 19th century to present can be used, alongside with the model proposed by Scapin et al. (Scapin et al. 2015), to get a rough estimation of how the present-time electricity demand would be if the climate were still in the situation prior to global warming. To this purpose, we apply this model keeping, on the one hand, the time-dependent term and the term accounting for the differences among the different days of the week as they are at present-time and considering, on the other hand, the secular CDD, HDD and S records we get from the corresponding high-resolution Tn, Tm, and Tx fields over the 1801–2013 period. In other words, we investigate what would happen in present-time conditions if the meteorological variables changed as they did in the past. The shortcoming of this approach is that present-time meteorology-electricity demand relationships are not completely independent from past climate variability and change as global warming may, e.g., have caused a wider diffusion of air conditioning devices. We assume, however, that this dependence is weak and that meteorology-demand relationships are mainly influenced by socio-economic factors such as the time evolution of the Gross Domestic Product (GDP). The CDD, HDD and S secular records and the virtual electricity demand record we get using them in the model proposed by Scapin et al. (Scapin et al. 2015) allow therefore giving a rough assessment of the impact of past climate variability and change on Italy present-time electricity demand. As far as we know, this assessment was still missing for Italy. In fact, although some papers have discussed the relationships between meteorological variables and the national electricity demand (Bessec & Fouquau 2008; Apadula et al. 2012; Manera & Marzullo 2005; Lee & Chiu 2011), none of them studied how much of present-time demand can be ascribed to past temperature changes. Therefore this paper represents a first step toward the wider objective of assessing the impact of past temperature changes on present-time Italy energy demand, which has to be estimated considering, beside the electricity demand, also the use of natural gas, fuel oil and other fuels. They are particularly relevant for heating energy use. The paper is organised in six parts. After the introduction, we focus on the climatologies; then we present the anomaly records and the procedure we adopt in order to superimpose the climatologies and the anomalies. After these parts on the meteorological data, we discuss the method we use to set up national average records allowing to capture the dependence of present-time Italy electricity demand on meteorological variables; then we present past variability and change of these records and discuss the relevance of their changes on the light of the sensibility of Italy present-time electricity demand on CDD, HDD and S. In the end, we summarize the results of the paper and discus some open issues. High-resolution climatologies High-resolution monthly Tm climatologies for Italy have been presented by Brunetti et al. (Brunetti et al. 2014), who estimated monthly 1961–1990 normals on the 30-arc-second resolution GTOPO30 (USGS (United States Geological Survey): GTOPO30 Documentation 1996) Digital Elevation Model (DEM), whereas corresponding Tn and Tx climatologies are presented in this paper. The Brunetti et al. (Brunetti et al. 2014) Tm climatologies are based on a dense and quality-controlled observational dataset which includes 1484 stations and on three distinct approaches: multi-linear regression with local improvements (MLRLI), an enhanced version of the model used by Hiebl et al. (Hiebl et al. 2009) for the Greater Alpine Region, regression kriging (RK), widely used in the literature (see e.g. (Hengl 2009)), and local weighted linear regression (LWLR) of temperature versus elevation, based on the PRISM (parameter elevation regression on independent slopes model) conceptual framework (Daly et al. 2002; Daly 2006; Daly et al. 2008; Daly et al. 1994). The performances of these methods were evaluated by estimating, with a leave-one-out approach, the climatologies at the station locations and then comparing the predicted values with the corresponding observed station normals. All three approaches led to quite reasonable estimates of the station normals, with the lowest errors in spring and autumn and the highest errors in winter. However the LWLR approach showed slightly lower errors than the other two approaches (root mean square errors (RMSEs) range from 0.74 °C (April and May) to 1.03 °C (December)). The better performance of LWLR was even more evident when selected station clusters were considered, giving evidence of a greater reliability of a local approach in modelling the behaviour of the temperature-elevation relationship in Italy's complex territory. For the reasons discussed above, we use the same LWLR approach for Tn and Tx as well. For this purpose, we consider a dataset of 1109 stations distributed over the entire Italian territory (Fig. 1a) with monthly 1961–1990 Tn and Tx normals that have been subjected to the same quality-control procedure carried out for Tm in Brunetti et al. (Brunetti et al. 2014) and we apply LWLR as described in that paper. Station network for the construction of a) Italy monthly 1961–1990 Tn and Tx climatologies and b) Italy secular Tn, Tm and Tx anomaly fields. We also show the spatial distribution of the urbanised Italian grid-cells according to GLC2000 (European Commission 2003) Specifically, we use a weighted linear regression of the data from nearby stations to predict the monthly temperature normal at any GTOPO30 grid-cell as a function of its elevation. The weights of the stations involved in the regression depend on their geographic similarity with the grid-cell. They are obtained by the product of five Gaussian weights (w) of the form: $$ {w}_i^{var}\left({\lambda}_g,{\phi}_g\right)={e}^{-\left(\frac{\varDelta_i^{var}{\left({\lambda}_g,{\phi}_g\right)}^2}{c_{var}}\right)} $$ where (λ g , ϕ g ) is the position of the grid-cell, var is the specific geographical variable which is considered (position, elevation, distance from the sea, slope steepness and slope orientation), ∆ i var is the difference between the value of this variable at the grid-cell and that at the i-th station location and c var is a coefficient which regulates the decrease of the weight for increasing values of ∆ i var. The stations selected for the regression are the 35 with the highest weights among those within 200 km from the given grid-cell. Instead of progressively extending the search range until a sufficient number of stations is available, we consider a very large search range (200 km) and choose only the stations with the highest weights. This is because the radial distance from the grid-cell is not always the leading discriminant. As the position weight is the most important one for the performance of the procedure, we optimized its c var for each month by minimizing the average RMSEs over all stations, with errors estimated with a leave-one-out approach. This procedure was performed independently for Tn and Tx. For the other geographical variables, we simply used the c var values proposed by Brunetti et al. (Brunetti et al. 2014). After such optimization of the parameters, we estimated the errors of the climatologies at the station locations. They are reported in Table 1 in terms of mean error (BIAS), mean absolute error (MAE) and RMSE. Table 1 gives evidence of higher errors for Tn; moreover, we observe that summer and winter months have in general higher errors than spring and autumn months. Table 1 Errors of Tn, Tm and Tx climatologies at station locations. Tm errors are retrieved from Brunetti et al. (Brunetti et al. 2014). All errors have been estimated with the leave-one-out approach Once the monthly Tn, Tm, and Tx 1961–1990 climate normals are available, the next step of our procedure consists in obtaining corresponding daily values by fitting them by means of the first two harmonics of a Fourier series. We assume then that the error due to this step is negligible and that Table 1 represents the errors of daily climatologies too. Grid-cell anomaly and temperature records Beside the climatologies, our methodology requires the estimation of secular daily temperature anomaly fields that have to be superimposed to the grid-cell temperature normals. Station anomaly records A key issue for the application of our methodology is the availability of a high-quality database of long-term secular records. Here we use updated and improved versions of the datasets presented by Brunetti et al. (Brunetti et al. 2006a) and Simolo et al. (Simolo et al. 2010). Updating mainly concerns the last 10 years, whereas the activities for improving the records mainly concern data homogenisation. The Brunetti et al. (Brunetti et al. 2006a) dataset was used to assess Italian temperature trends up to 2003. It is mainly based on the data collected at observatories established in the 19th century: most of them ended their observations in about the last 30 years. The Simolo et al. (Simolo et al. 2010) dataset concerns the stations of the network of the Italian Air Force (Aeronautica Militare, hereinafter AM): a significant fraction of them are currently managed by the Italian Agency for Civil Aviation (ENAV). We update most of the stations of this network in near real time by means of the Global Surface Summary of the Day, (GSOD) managed by US National Climatic Data Center (NCDC). The dataset we use in this paper includes a significant fraction of composite records. In some cases it was just necessary to merge data from different sources for the same station (e.g. AM/ENAV and GSOD), in other cases the merging concerned also data from different stations, such as some of the oldest observations from the Brunetti et al. (Brunetti et al. 2006a) dataset merged in the last decades with the AM/ENAV records from the Simolo et al. (Simolo et al. 2010) dataset and updated for the last years with the GSOD records. A detailed homogenisation was therefore mandatory. We performed it subjecting all monthly temperature records to a relative homogeneity test based on the procedure described by Brunetti et al. (Brunetti et al. 2006a). In this procedure, each series is tested against 10 other series by means of a multiple application of the Craddock test (Craddock 1979). When a break is identified in the test series, some reference series are chosen among those series that prove to be homogeneous in a sufficiently large period centred on the break and that correlate well with the test series. Several series are used in order to better identify the break and to get more reliable adjustments. When a break is homogenised, the preceding portion of the series is corrected, leaving the most recent portion of the series unchanged. This allows for updating the records without considering any adjustment. Homogenisation is performed at daily resolution, with the adjustments obtained fitting the first two harmonics of a Fourier series to the adjustments we get for the monthly records. The dataset we use in this paper to get the grid-cell anomalies consists of 143 daily Tn, Tm and Tx records. Stations sites are shown in Fig. 1b, whereas Fig. 2 shows data availability versus time. Temporal evolution of the number of available records. A record is considered as available when in a year less than 20 % of the data are missing After the homogenisation of the station records, the next step of our methodology consists in filling the gaps in the monthly-homogenised records over the 1961–1990 period by means of the procedure described by Brunetti et al. (Brunetti et al. 2006a). The completed records are then used to calculate monthly 1961–1990 station normals from which corresponding daily normals are estimated by fitting them with the first two harmonics of a Fourier series. We prefer this approach with respect to directly calculating daily station normals because i) it is the same approach we use to get the daily grid-cell normals on the basis of monthly high-resolution climatologies, ii) the monthly records are easier to complete than the daily records and iii) direct calculation of the daily normals from the daily data would produce rather noisy values. The homogenised daily temperature records are finally transformed into anomaly records with respect to the 1961–1990 normals, by simply subtracting from each data the corresponding daily normal. Assessment of the anomaly record interpolation technique Once homogenised station anomaly records are available, the next step of our methodology consists in using them to evaluate, by means of a leave-one-out approach, the performance of the interpolation technique. Specifically, we predict the anomaly record A(t) at each station site (λ i , ϕ i ) by means of a weighted average of the anomaly records of the other stations and we compare it with the corresponding observed record. The basic assumption of this procedure is that the comparison of the predicted and the observed records at the station-sites, gives also a reasonable picture of the accuracy of the predicted records at the grid-cells. The predicted record at the i-th station is constructed by first building weighting terms accounting for distance and elevation difference from each of the other stations: $$ {w}_j^i(t)={e}^{-\frac{d_{j,i}^2}{{\scriptscriptstyle \raisebox{1ex}{${\left({\mathrm{T}}_{\mathrm{d}}\right)}^2$}\!\left/ \!\raisebox{-1ex}{$ \ln 2$}\right.}}}\cdot {e}^{-\frac{\varDelta {z}_{j,i}^2}{{\scriptscriptstyle \raisebox{1ex}{${\left({\mathrm{T}}_{\Delta \mathrm{z}}\right)}^2$}\!\left/ \!\raisebox{-1ex}{$ \ln 2$}\right.}}}\; if\ j\ \ne\ i\ and\ if\ station\ j\ data\ are\ available\ at\ time\ t,\ otherwise{w}_j^i(t)=0 $$ where d j,i and Δz j,i are, respectively, the distance and the elevation difference between the station under analysis and the j-th station and τ d and τ ∆z regulate the extent to which a station is weighted with respect to distance and elevation difference: exponentials decrease by half when distance reaches τ d and, in analogy, when elevation difference equals τ ∆z . For these parameters we use here the values proposed by Scapin et al. (Scapin et al. 2015). They are 80 km for τ d and 400 m for τ ∆z . We use then these weighting terms for the projection of the observed anomalies on the site of the i-th station: $$ A\left({\lambda}_i,{\varphi}_i,t\right)=\frac{{\displaystyle {\sum}_j{w}_j^i{A}_j(t)}}{{\displaystyle {\sum}_j{w}_j^i}} $$ With the data availability of our dataset - before about 1870 the distribution of the stations is so inhomogeneous that they can not be considered as representative of the grid-cells - this simple procedure can however not be applied to assess the accuracy of the grid-cell records. Moreover, as the urbanised grid-cells we consider in this paper are mainly located at low elevation (99.5 % of the urban grid-cells are below 750 m) we prefer restricting the comparison to the station-sites below 750 m. Therefore, we first divided the 1801–2010 interval in 42 consecutive 5 year periods. Then we looked for the stations with available data in each of these periods and we used only the records of these stations to estimate, by means of (1) and (2), the station-site anomalies in the 1974–2003 period (i.e. the period with the best data availability). In case a record used for the estimation was not available in the 1974–2003 period, it was simply substituted with a neighbouring one, in order to prevent missing data to bias the estimation process. Finally, we compared the estimated and the observed station anomalies in the 1974–2003 period. The comparison was therefore performed for a subset of stations (the 122 stations with available data in the 1974–2013 period) covering the entire Italian territory, whereas the estimation of the anomalies at the station sites was performed with a subset of stations defined on the basis of the data availability in each of the 5 year periods. The results of this comparison are shown in Fig. 3a by means of box-plots, which give evidence of the distributions of the RMSEs of the estimated station anomalies with respect to the observed ones. The upper whisker of each box extends from the upper hinge to the highest value that is within 1.5 time the inter-quartile range from it. The same for the lower whisker. Data beyond the end of the whiskers are outliers: they are plotted as points. The figure gives evidence that in the period of best data availability (i.e. from 1950) the results are rather similar for all 5 year periods, showing that the different station subsets we use for the estimation of the 1974–2003 anomalies give equivalent results. In this period the median of the RMSEs of the station Tm anomalies ranges between 0.97 °C (stations with available data in the 1956–1960 period) and 1.09 °C (stations with available data in the 1996–2000 period), whereas for Tn and Tx the values range, respectively in the intervals 1.33-1.40 °C and 1.35-1.51 °C. On the contrary, for the station subsets corresponding to data availability before 1950 the errors are larger, showing that the smaller is the subset of the stations used for the estimation of the anomalies, the larger is the error of the reconstructed anomalies. With the station subsets corresponding to data availability before 1880, and even more with those corresponding to data availability before 1870, there is an additional difficulty in the reconstruction of the station anomalies. In fact, in this period, almost all the stations are in northern Italy. Due to this problem, for a significant fraction of the stations the errors become so high that the RMSE of the estimated anomalies becomes higher than the standard deviations of the observed anomalies. Box-plots summarizing the RMSEs of the anomalies at the station-sites in the 1974–2003 period, with the anomalies obtained according to relations (1) and (2) and using as predictors the stations with available data in 42 5 year periods of the 1801–2010 interval. a RMSEs are calculated considering all the 122 station-sites below 750 m with data in the 1974–2003 period; b) RMSEs are calculated excluding station-sites of central and southern Italy (i.e. with latitude below 44 degrees) before 1880 In order to better highlight the influence of stations in central and southern Italy on the errors before 1880, we applied the previous procedure also evaluating for the station subsets concerning the years before 1880 only the errors of northern Italy stations (i.e. the stations with latitude above 44°). The results are shown in Fig. 3b. They give evidence of much lower errors than in Fig. 3a, with almost all Tm 1974–2003 RMSEs within 2 °C. Grid-cell temperature records Once the reliability of the technique for the projection of the anomalies has been verified, it has been applied to any urbanized grid-cell of the DEM. The construction of the grid-cell records was naturally limited to the areas and the periods for which the analyses performed for the station-sites highlighted reasonable errors. In particular, we did not reconstruct central and southern Italy anomalies before 1880. Once daily Tn, Tm, Tx anomaly records were estimated for all the relevant grid-cells, we obtained temperature records by simply superimposing the anomaly records to the corresponding grid-cell climate normals. The construction of such daily grid-cell records had not yet been performed for Italy, whereas corresponding monthly records had already been presented by Brunetti et al. (Brunetti et al. 2009; Brunetti et al. 2012). Local secular records and electricity demand A number of recent papers have shown that temperature has a strong impact on electricity demand in many areas of the world (see e.g. (Bessec & Fouquau 2008; Apadula et al. 2012; Feinberg & Genethliou 2005)). In this context, Scapin et al. (Scapin et al. 2015) have developed a linear model linking the Italian daily aggregate electricity demand in the 1990–2013 period to temperature-derived variables. The model is based on the superimposition of deterministic components related to the weekly cyclical demand pattern and to long-term demand changes and on weather sensitive components. It assumes that the Italian daily electricity demand (D(t)), can be described by means of the following relation: $$ D(t)={\displaystyle \sum_{i=0}^3{\alpha}_i}{t}^i+{\displaystyle \sum_{j=1}^4{\beta}_j}{I}_j(t)+{\displaystyle \sum_{k=1}^3{\gamma}_k{V}_k(t)}+\varepsilon (t) $$ The first term consists of a third order polynomial which aims to describe the temporal evolution of electricity demand caused by the economic conjuncture and by long-term changes in consumption habits. The second term consists of dummy variables I j (t), introduced in order to account for the strong weekly pattern of electricity demand. In particular I 1 (t) is set to 1 on Monday and 0 otherwise; in analogy, I 2 (t), I 3 (t) and I 4 (t) are used to model the behaviour of Friday, Saturday and Sunday. No dummy variables are used for central weekdays (Tuesday, Wednesday, Thursday) which can be grouped together since they exhibit similar behaviour. In this way, the dummy variable term accounts for the differences between central weekdays and the rest of the week. The third term consists of a summation over three exogenous variables (CDD, HDD and S), describing the influence of weather factors on the Italian electricity demand. The last term represents the error of the model (i.e. the difference between the actual and the estimated demand). The coefficients αi, βj and γk of relation (3) are obtained by means of least squares regression. The model was applied to the Italian aggregated National electricity demand of ordinary days (holidays and special events are excluded) considering twelve two-year periods, starting from 1990–1991 and ending in 2012–2013 (Scapin et al. 2015). The CDD, HDD and S records considered in relation (3) were obtained with a bottom-up approach: first, local CDD, HDD and S records were estimated for all Italian grid-cells of the GTOPO30 DEM that are classified as urbanised according to GLC2000 land cover (European Commission 2003), then an average was computed over them. The first step consisted in estimating Tn, Tm and Tx records for each Italian urbanised grid-cell. Then effective temperature (T), a delayed signal obtained through exponential smoothing of Tm series (it allows taking into account temporal inertia of buildings), was considered and cooling and heating degree-days were defined according to: $$ CDD(t)= max\left\{\left({T}^{}(t) - {T}_{S_1}\right)\right.\left.0\right\} $$ $$ HDD(t)= max\left\{\left({T}_{S_2} - {T}^{}(t)\right)\right.\left.0\right\} $$ where T is the grid-cell daily mean effective temperature, $ {T}_{S_1} $ is 20 °C and $ {T}_{S_2} $ is 15 °C (Scapin et al. 2015). Finally, the grid-cell daily Tn and Tx records were used to estimate grid-cell global solar radiation records (H) by means of the following formula (Hunt et al. 1998): $$ H(t)={a}_0{H}_0\varDelta T{(t)}^{0.5}+{a}_1 $$ where a 0 and a 1 are site-dependent empirical coefficients, ΔT is the daily temperature range (T x -T n ) and H 0 is the exo-atmospheric radiation on the horizontal plane, i.e. the daily integral of solar irradiance that would be observed on a horizontally oriented surface placed at the top of the atmosphere. H 0 can be easily determined by standard computation (see e.g. Iqbal (Iqbal 1983)), whereas a 0 and a 1 can be recovered from previous studies. Scapin et al. (Scapin et al. 2015) used for the entire Italian territory the values (a 0 = 0.190 K -0.5, a 1 = −2.041 MJ m −2) that Abraha and Savage (Abraha & Savage 2008) proposed for Padua (northern Italy). Term S, which was introduced to take into account the effect of lighting on electricity demand, was then defined from solar radiation as (Scapin et al. 2015): $$ S(t)= max\left\{\left({H}_s-H(t)\right)\right.\left.0\right\} $$ where H S was set to 17 MJ m −2. Relation (3) explains from 97.7 % (2008–2009) to 99.4 % (1996–1997) of the variance of the Italian daily demand record (ordinary days only), with a mean absolute percentage error (MAPE) of about 1 % (Scapin et al. 2015). The CDD term shows a strong positive trend in the 1990–2007 period, followed by a tendency toward stationarity in the following 6 year period. The data of the last 3 two year periods considered by Scapin et al. (Scapin et al. 2015) allow therefore for quantifying the present-time dependence of the Italian electricity demand of an ordinary day on CDD in 24.6 GWh degree-day−1 (Scapin et al. 2014). For HDD and S we prefer quantifying this dependence considering the average values over the latest 6 two-year-period coefficients. This because these terms show a tendency toward stationarity in the last 12 years. The values are, respectively, 6.6 GWh degree-day−1 and 2.9 GWh day−1 MJ−1 m2 (Scapin et al. 2014). This paper focuses on the impact of climate change on CDD, HDD and S and on the corresponding impact on present-time electricity demand. We are therefore much more interested on yearly, seasonal or, at least, monthly values, rather than on daily values. We sum then equation (3) over all days of each year, season or month (it is actually a virtual year, season or month as it is composed only of ordinary days), getting cumulated contributions obtained multiplying the γ k terms in equation (3) (i.e. 24.6 GWh degree-day−1, 6.6 GWh degree-day−1 and 2.9 GWh day−1 MJ−1 m2) by the yearly, seasonal or monthly sums of the daily CDD, HDD and S values. We consider therefore hereinafter only these cumulated CDD, HDD and S data. We know we are able to construct Italy CDD, HDD and S records covering the 1880–2013 period, whereas we are not able to construct them before 1880, as the estimation of grid-cell temperatures can be performed only for the northern part of Italy. We observe however that, even though northern and southern Italy temperature anomalies may have strong differences at daily resolution, the agreement increases when monthly, seasonal or yearly periods are considered (see e.g. (Brunetti et al. 2006a)). The same behaviour concerns naturally the temperature-derived variables we use in this paper. We used therefore the period 1880–2013 to check whether yearly sums of CDD, HDD and S obtained only from northern Italy urbanised grid-cells can be used to estimate the corresponding national CDD, HDD and S values. The results of this analysis are shown in Fig. 4. They give evidence that northern Italy CDD, HDD and S yearly records capture a large fraction of Italy corresponding records. The latter records can therefore be estimated from the former. Linear relationship between yearly sums of CDD, HDD and S for the entire national territory and corresponding values calculated only for northern Italy (i.e. latitude above 44°). The data cover the 1880–2013 period Based on these results, we extended the estimation of the yearly Italian CDD, HDD and S records also to the years before 1880. In order to further check the errors of the yearly CDD, HDD and S data in the first years of the 19th century, when only Milan, Padua and Turin were available, we first estimated northern Italy urbanised grid-cell temperatures of the 1974–2003 period using only these 3 stations. Then we used these temperatures to get northern Italy yearly CDD, HDD and S records from which we estimated corresponding national records by means of the linear regressions shown in Fig. 4. The comparison of these records with those estimated by means of the full dataset gives evidence of a bias of −1.7 % for CDD, of 0.4 % for HDD and of 0.5 % for S. We conclude therefore that the yearly CDD, HDD and S records we get by means of only Milan, Padua and Turin data have rather low bias. It is also interesting to check the RMSEs of the CDD, HDD and S yearly records we get by means of these 3 stations. They turn out to be 7.1 % for CDD, 2.5 % for HDD and 1.5 % for S, where the percentages are expressed in relation to the average values in the 1974–2003 period, obtained from the full dataset. Long-term evolution of CDD, HDD and S and corresponding impact on Italy present-time electricity demand The yearly Italian CDD, HDD and S records are shown in Fig. 5, together with a 10 year standard deviation Gaussian low-pass filter. Italian CDD, HDD and S yearly series (thin lines), plotted together with 10-y standard deviation Gaussian low-pass filters (thick lines) These curves give evidence of a strong rise of CDD across the last 2 centuries, showing a more pronounced slope in the last 30 years. Consequently, the low-pass filter curve increases from about 200 degree-days at the beginning of the 19th century to over 400 degree-days in the last years. Year 2003 has by far the highest CDD value of the whole series (699 degree-days): summer 2003 was indeed characterised by exceptionally hot weather, which was a matter of concern for many reasons (Grazzini et al. 2003; Schär et al. 2004). The minimum CDD value is found in year 1816 (88 degree-days), which is widely renowned as the year without a summer for its abnormally low summer temperatures (Stommel & Stommel 1979). On the contrary, heating degree-days have been decreasing in the examined period. The decrease, which starts at about 1865, is more regular than the increase of CDD. As for CDD, the trend has strengthened in the last 30 years. Solar radiation instead does not show a significant trend in the considered period. In order to investigate better the increasing and decreasing tendencies highlighted by Fig. 5, we subjected the records to running trend analysis (Brunetti et al. 2006b). Specifically, we estimated the slopes of the time series over all time windows with minimum length of 30 years. The slopes are computed using the Theil-Sen method (Sen 1968; Theil 1983), which estimates the slope as the median of the slopes of lines crossing all possible pairs of points: such methodology is particularly suitable in presence of outliers as it significantly reduces their influence on the results. The results are shown in Fig. 6, where window widths and the starting years of the windows that the trends refer to are represented on y and x axes, respectively. Slopes are represented by means of a color scale. Significances are evaluated by the Mann–Kendall non-parametric test (Sneyers 1990). This type of running trend analysis, first introduced by Brunetti et al. (Brunetti et al. 2006b), is an instrument to investigate trends in depth and to produce plots that allow for visualizing trends on a wide range of timescales. Therefore, Fig. 6 captures the whole spectrum of significant trends in the CDD, HDD and S records and provides quantitative description of the peculiarities observed in Fig. 5. Trends of CDD, HDD and S records over all possible time windows of at least 30 years of the 1801–2013 period. The results are reported in terms of both slopes and significances. The y axis represents window width, and the x axis represents starting year of the window used for the computation of the trend. The reported slope values are evaluated with the Theil-Sen method. The pixels size indicates the significance of the trend in terms of the p-value of the regression (large pixels: < 0.01; medium pixels: between 0.01 and 0.1; small pixels: >0.1) The results in Fig. 6 give evidence of the statistical significance of the positive (negative) trends of CDD (HDD): the trend is significant for all windows with length of at least 100 years. For shorter periods the picture is more complex. Specifically, for CDD the positive trend pixels reflect the increase in Fig. 5 between 1820 and 1870, 1920 and 1950 and from the beginning of the 1980s to present-time, whereas the negative trend pixels reflect the decrease in the last decades of the 19th century and in the 1960s. The strongest trends are those of the last decades, with the highest value corresponding to 7.0 degree-days/year in the 1976–2006 period. For HDD the variability is lower and only very few pixels correspond to positive trends. As well as for CDD the strongest trends are those of the last decades, with the strongest trend corresponding to −9.4 degree-days/year (1978–2008 period). Finally, for S the trends of the longest windows are very low. For shorter time windows the strongest trends are those starting in the first half of the 20th century: they are associated to the clear maximum in Fig. 5 between the beginning of the 1950s and the end of the 1970s. This maximum in solar radiation deficit seems to be associated to solar radiation dimming, probably caused by atmospheric aerosol linked to air pollutant emissions, even though in Italy the reduction of solar radiation in the global dimming period (Wild 2009) has been partially masked by a reduction of total cloud cover (Maugeri et al. 2001; Manara et al. 2015). Finally we investigated what would happen to Italy present-time electricity demand if CDD, HDD and S changed as they did in the past. Specifically, we first computed the virtual yearly series of the weather-related terms in relation (3), using for γ k values which are representative of present-time conditions. Then we constructed a summer contribution (driven by CDD) and a winter one (given by the sum of the HDD and S contributions), considering all days as ordinary. These contributions are shown in Fig. 7. This figure gives evidence that the winter contribution is much greater than the summer one with the temperatures we had at the beginning of the 19th century, whereas with present-time temperatures the winter and the summer contributions are rather similar. The net effect of these changes (total curve in Fig. 7) is a slight rise of the weather-related contribution to electricity demand, driven by the recent increase of CDD. In fact, with the temperatures corresponding to the beginning of the 19th century, the weather related contribution to present-time electricity demand would be nearly 20 TWh, whereas with nowadays temperatures it is around 25 TWh. We estimate therefore the contribution of past climate change on Italy present-time electricity demand in roughly 5 TWh, which corresponds to about 1.5 %-2.0 % of present-time Italy electricity demand. weather related terms of relation (3) with present-time meteorology-demand relationships and with weather variables driven by past temperatures. The summer curve concerns the CDD term, the winter curve concerns the sum of the HDD and S terms. As in Fig. 5, we show also a low-pass Gaussian filter As we did for the CDD, HDD and S yearly data, we subjected also the total curve we show in Fig. 7 to running trend analysis (Brunetti et al. 2006b). The results are shown in Fig. 8. They give evidence that the trends of this curve are much more influenced by CDD trends than by HDD trends. The net effect of the weather related terms in relation (3) reflects therefore very closely the evolution of the CDD record, with slightly lower positive trends due to the fact that the HDD decrease causes a lower electricity demand. Trends of the curve marked as "total" in Fig. 7 over all possible time windows of at least 30 years of the 1801–2013 period. The results are reported in terms of both slopes and significances. The y axis represents window width, and the x axis represents starting year of the window used for the computation of the trend. The reported slope values are evaluated with the Theil-Sen method. The pixels size indicates the significance of the trend in terms of the p-value of the regression (large pixels: < 0.01; medium pixels: between 0.01 and 0.1; small pixels: >0.1) Beside the analysis performed at yearly resolution, it is also interesting to study how climate change affects the present-time monthly profile of the electricity demand. For this reason, we plot the monthly average values of the CDD, HDD and S terms of relation (3) for 3 different 40 year periods and we add to the plot also the corresponding values for the 2001–2013 period (Fig. 9). As well as for the yearly analysis, all values were calculated with γ k values that are representative of present-time conditions. It is evident that, as expected, changes in air temperature, as those that occurred in the past, substantially modify the yearly profile of the demand, lowering winter month contributions and raising summer month contributions. The results also indicate that summer months are those with the highest impact of climate change on present-time energy demand, whereas in May and October present-time electricity demand seems to respond in a very limited way to temperature changes as those that occurred in the past. Monthly averages of weather-driven contributions to present-time Italy electricity demand evaluated using CDD, HDD and S of 3 consecutive 40 year (1881–1921, 1921–1960, 1961–2000). In addition, we also plot CDD, HDD and S contributions relative to the years 2001–2013 in order to highlight the impact on present-time demand of the recent temperature rise A methodology was developed for estimating secular daily temperature records (Tn, Tm and Tx) for any urbanised grid-point of a high-resolution DEM covering Italy. It is based on the superimposition of two fields: the 1961–1990 climatologies and the departures from them (anomalies). They were obtained in a completely independent way from each other and they are based on completely different data sets. The root mean square error of the climatologies turns out to be between 0.7 °C and 1.4 °C, with higher errors for Tn and lower errors for Tm. The error of the anomalies is generally higher, with values strongly depending on data availability of the considered period. In order to keep the root mean square error of the Tm anomalies within 2 °C, we decided to avoid reconstructing the anomalies for central and southern Italy before 1880, whereas for northern Italy we reconstructed them from 1801. It is also worth noticing that the anomalies of high-elevation points have rather high errors. This problem is not relevant for the application presented in this paper as a very high fraction of Italian urbanised areas is at low elevation. It has however to be addressed in case of study areas which include a significant fraction of high-elevation grid-points. A better representation at those grid-points is likely to be obtained by using both a higher density network of anomaly records and a methodology that allows to take into account the elevation-dependence of the temperature anomalies in a more sophisticated way than by means of the elevation weight used in equation (1) (see e.g. (Frei 2014)). The estimated daily temperature records allowed investigating past variability and change of temperature-derived variables that influence Italy present-time national electricity demand. They are national averages over Italian urbanised grid-points of cooling degree-days (CDD), heating degree-days (HDD) and solar radiation deficit with respect to a defined threshold (S). CDD and HDD yearly totals give evidence of strong and highly significant trends. Specifically, CDD increase across the last 2 centuries, with 30 year normal values increasing from about 200 degree-days at the beginning of the 19th century to over 400 degree-days in the last years. On the contrary, HDD 30 year normals decrease in the examined period from about 1500 degree-days to about 1100 degree-days. The strong trends of these variables makes it relevant to compare the present-time Italy electricity demand with the virtual demand Italy would have at present if the climate were still in the situation prior to global warming. Assuming that the present-time dependence of the electricity demand from meteorological variables is independent from climate change, this comparison can be used to assess the impact of climate variability and change on present-time Italian electricity demand. The results, which were obtained by means of an electricity demand model discussed in Scapin et al. (Scapin et al. 2015), give evidence, at a yearly scale, of an impact of global warming of about 5 TWh, which correspond to 1.5-2.0 % of Italy electricity demand. It results from the increase of CDD which is partially counterbalanced by the decrease of HDD. The impact is highest in summer months where it exceeds 5 % of Italy average monthly electricity demand, whereas the decrease of the winter demand is rather low because of a very limited use of electricity for heating. Even though the impact of climate change we found is rather small with respect to long-term electricity demand changes driven by socio-economic factors, assessing it may give an interesting contribution in the context of the evaluation of the impact of climate change on the energy sector. This assessment, together with a corresponding assessment based on future climate scenarios (see Scapin et al. (Scapin et al. 2014), may be considered within climate change costs estimation. In the future, it may be interesting to extend the methodology presented in this paper to investigate the impact of HDD variability and change on total energy requested for heating by considering, in addition to electricity, natural gas, fuel oil and other fuels. 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J Geophys Res 114:D00D16 We acknowledge all the institutions that provided the meteorological data used in this work. Specifically, we refer to those listed in Brunetti et al. (Brunetti et al. 2006a) and in Simolo et al. (Simolo et al. 2010), and we mention, for recent updates, US National Oceanic and Atmospheric Administration - National Climatic Data Center, NESDIS - Global Surface Summary of the Day, Asheville, NC (Available at https://data.noaa.gov/dataset/global-surface-summary-of-the-day-gsod). The present work was partly funded by the Research Fund for the Italian Electrical System under the Contract Agreement between RSE S.p.A. and the Ministry of Economic Development – General Directorate for Nuclear Energy, Renewable Energy and Energy Efficiency, stipulated on July 29, 2009 in compliance with the Decree of March 19, 2009 and partly by the EU FP7 project ECLISE (265240). Ricerca sul Sistema Energetico, RSE Spa. Via Rubattino, 54, 20134, Milan, Italy Simone Scapin & Francesco Apadula Istituto di Scienze dell'Atmosfera e del Clima (ISAC), Consiglio Nazionale delle Ricerche (CNR), Via P. Gobetti, 101, 40129, Bologna, Italy Simone Scapin, Michele Brunetti & Maurizio Maugeri Dipartimento di Fisica, Università degli Studi di Milano, Via Celoria, 16, 20133, Milan, Italy Simone Scapin & Maurizio Maugeri Simone Scapin Francesco Apadula Michele Brunetti Maurizio Maugeri Correspondence to Maurizio Maugeri. All authors participated in the conceptualization of the work, contributed in drafting parts of the manuscript and approved its final version. Scapin, S., Apadula, F., Brunetti, M. et al. The sensitivity of present-time electricity demand on past climate change: a case study for Italy. Earth Perspectives 2, 4 (2015). https://doi.org/10.1186/s40322-015-0030-7 Electricity demand Secular records	CommonCrawl
Spatio-temporal coexistence in the cross-diffusion competition system Numerical analysis of an ODE and a level set methods for evolving spirals by crystalline eikonal-curvature flow March 2021, 14(3): 909-918. doi: 10.3934/dcdss.2020391 Numerical and mathematical analysis of blow-up problems for a stochastic differential equation Tetsuya Ishiwata and Young Chol Yang , Shibaura Institute of Technology, 307 Fukasaku, Minuma, Saitama 337-8570, Japan * Corresponding author: Young Chol Yang Received January 2019 Revised March 2020 Published June 2020 Fund Project: The first author is partly supported by JSPS KAKENHI Grant number 15H03632 and 19H05599 Figure(8) / Table(3) We consider the blow-up problems of the power type of stochastic differential equation, $ dX = \alpha X^p(t)dt+X^q(t)dW(t) $. It has been known that there exists a critical exponent such that if $ p $ is greater than the critical exponent then the solution $ X(t) $ blows up almost surely in the finite time. In our research, focus on this critical exponent, we propose a numerical scheme by adaptive time step and analyze it mathematically. Finally we show the numerical result by using the proposed scheme. Keywords: SDE, blow-up, blow-up time, Euler-Maruyama scheme, adaptive time step control. Mathematics Subject Classification: Primary: 60H10, 65C20; Secondary: 34F05. Citation: Tetsuya Ishiwata, Young Chol Yang. Numerical and mathematical analysis of blow-up problems for a stochastic differential equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 909-918. doi: 10.3934/dcdss.2020391 J. A. D. Appleby, G. Berkolaiko and A. Rodkina, Non-exponential stability and decay rates in nonlinear stochastic differential equations with unbounded noise, Stochastics, 81 (2009), 99-127. doi: 10.1080/17442500802088541. Google Scholar J. A. D. Appleby, X. R. Mao and A. Rodkina, Stabilization and destabilization of nonlinear differential equations by noise, IEEE Trans. Automat. 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Platen, Numerical Solution of Stochastic Differential Equations, Applications of Mathematics (New York), 23. Springer-Verlag, Berlin, 1992. doi: 10.1007/978-3-662-12616-5. Google Scholar J. E. Macías-Díaz and J. Villa-Morales, Finite-difference modeling à la Mickens of the distribution of the stopping time in a stochastic differential equation, Journal of Difference Equations and Applications, 23 (2017), 799-820. doi: 10.1080/10236198.2017.1284828. Google Scholar J. M. Sanz-Serna and J. G. Verwer, A study of the recursion $y_{n+1}=y_n+\tau{y_n^m}$, J. Math. Anal. Appl., 116 (1986), 456-464. doi: 10.1016/S0022-247X(86)80010-5. Google Scholar Figure 1. Numerical solutions (4 samples) Figure 2. Numerical Brownian motion Figure 3. Histogram of $ T_\tau^L $ and exact distribution of blow-up time (green) Figure 6. Distribution of numerical blow-up time Figure 7. The number of non-blow-up solutions with fixed $ T_{\max} = 1000 $ Figure 8. The number of non-blow-up solutions with fixed $ L = 1000 $ Table 1. Numerical paramaters at numerical blow-up time Sample No. $ X_n $ $ T_\tau^L $ $ \|W_n-M\| $ 1 $ 1000.343314 $ $ 0.043027 $ $ 0.00076978 $ 2 $ 1000.154401 $ $ 0.39964 $ $ 0.0007528 $ 3 $ 1000.61063 $ $ 0.0209 $ $ 0.00040622 $ Table 2. The number of Blow-up solutions with fixed $ T_{max} = 1000 $ $ a $ 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 $ L=100 $ 977 941 888 791 665 486 369 226 118 $ L=1000 $ 995 988 968 880 756 566 377 223 122 Table 3. The number of non-blow-up solutions with fixed $ L = 1000 $ $ T_{\max}=100 $ 995 988 968 880 756 566 377 223 122 $ T_{\max}=1000 $ 996 989 940 848 668 401 234 105 44 Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216 Manuel del Pino, Monica Musso, Juncheng Wei, Yifu Zhou. Type Ⅱ finite time blow-up for the energy critical heat equation in $ \mathbb{R}^4 $. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3327-3355. doi: 10.3934/dcds.2020052 Juliana Fernandes, Liliane Maia. Blow-up and bounded solutions for a semilinear parabolic problem in a saturable medium. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1297-1318. doi: 10.3934/dcds.2020318 Takiko Sasaki. Convergence of a blow-up curve for a semilinear wave equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1133-1143. doi: 10.3934/dcdss.2020388 Justin Holmer, Chang Liu. Blow-up for the 1D nonlinear Schrödinger equation with point nonlinearity II: Supercritical blow-up profiles. Communications on Pure & Applied Analysis, 2021, 20 (1) : 215-242. doi: 10.3934/cpaa.2020264 Alex H. Ardila, Mykael Cardoso. Blow-up solutions and strong instability of ground states for the inhomogeneous nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2021, 20 (1) : 101-119. doi: 10.3934/cpaa.2020259 Daniele Bartolucci, Changfeng Gui, Yeyao Hu, Aleks Jevnikar, Wen Yang. Mean field equations on tori: Existence and uniqueness of evenly symmetric blow-up solutions. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3093-3116. doi: 10.3934/dcds.2020039 Sören Bartels, Jakob Keck. Adaptive time stepping in elastoplasticity. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 71-88. doi: 10.3934/dcdss.2020323 Qiwei Wu, Liping Luan. Large-time behavior of solutions to unipolar Euler-Poisson equations with time-dependent damping. Communications on Pure & Applied Analysis, , () : -. doi: 10.3934/cpaa.2021003 Xu Zhang, Chuang Zheng, Enrique Zuazua. Time discrete wave equations: Boundary observability and control. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 571-604. doi: 10.3934/dcds.2009.23.571 Lars Grüne, Matthias A. Müller, Christopher M. Kellett, Steven R. Weller. Strict dissipativity for discrete time discounted optimal control problems. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020046 Awais Younus, Zoubia Dastgeer, Nudrat Ishaq, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Devendra Kumar. On the observability of conformable linear time-invariant control systems. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020444 Chaman Kumar. On Milstein-type scheme for SDE driven by Lévy noise with super-linear coefficients. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1405-1446. doi: 10.3934/dcdsb.2020167 Lars Grüne, Roberto Guglielmi. On the relation between turnpike properties and dissipativity for continuous time linear quadratic optimal control problems. Mathematical Control & Related Fields, 2021, 11 (1) : 169-188. doi: 10.3934/mcrf.2020032 Guangjun Shen, Xueying Wu, Xiuwei Yin. 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Identification of novel and differentially expressed MicroRNAs in goat enzootic nasal adenocarcinoma Bin Wang1, Ni Ye1, San-jie Cao1, Xin-tian Wen1, Yong Huang1 & Qi-gui Yan1 MicroRNAs (miRNAs) post-transcriptionally regulate a variety of genes involved in eukaryotic cell growth, development, metabolism and other biological processes, and numerous miRNAs are implicated in the initiation and progression of cancer. Enzootic nasal adenocarcinoma (ENA), an epithelial tumor induced in goats and sheep by enzootic nasal tumor virus (ENTV), is a chronic, progressive, contact transmitted disease. In this work, small RNA Illumina high-throughput sequencing was used to construct a goat nasal miRNA library. This study aimed to identify novel and differentially expressed miRNAs in the tumor and para-carcinoma nasal tissues of Nanjiang yellow goats with ENA. Four hundred six known miRNAs and 29 novel miRNAs were identified. A total of 116 miRNAs were significantly differentially expressed in para-carcinoma nasal tissues and ENA (54 downregulated; 60 upregulated; two only expressed in control group); Target gene prediction and functional analysis revealed that 6176 non-redundancy target genes, 1792 significant GO and 97 significant KEGG pathway for 121 miRNAs (116 significant expression miRNAs and five star sequence) were predicted. GO and KEGG pathway analysis revealed the majority of target genes in ENA are involved in cell proliferation, signal transduction and other processes associated with cancer. This is the first large-scale identification of miRNAs in Capra hircus ENA and provides a theoretical basis for investigating the complicated miRNA-mediated regulatory networks involved in the pathogenesis and progression of ENA. MicroRNAs (miRNAs) are endogenous, 21–24 nucleotide-long, non-coding RNAs that regulate gene expression in eukaryotes; however, some viruses also express miRNAs in host cells [1–3]. MiRNAs are complementary to specific sequence motifs in the 3′ untranslated regions (UTRs) of their target mRNAs and negatively regulate gene expression at the post-transcriptional level by inhibiting translation or promoting mRNA degradation, based on the degree of complementary base pairing between the miRNA and mRNA. MiRNAs regulate approximately 30 % of genes in higher eukaryotic cells, including genes involved in development, metabolism, apoptosis, proliferation and viral defense [4–10]. The earliest evidence for an association between miRNAs and cancer came from the study of chronic lymphocytic leukemia (CLL) [11]. To date, more than 50 % of miRNAs have been shown to be encoded in chromosome fragile sites that are often absent, amplified or rearranged in malignant tumor cells leading to dysregulated expression of miRNAs, and numerous miRNAs have been shown to play important roles in tumorigenesis [12, 13]. MiRNAs can act in a similar manner to oncogenes or tumor suppressor genes and have emerged as a novel type of regulatory factor in the epigenetic modification of gene expression. According to predictions in vertebrates, a single miRNA can regulate more than 400 target genes, forming complicated regulatory networks [14–23]. Therefore, miRNAs have become a focus of cancer research in order to identify novel molecular methods for the diagnosis, prognostication and treatment of human cancer. Now researchers can directly obtain miRNA sequences and discover novel miRNAs through utilize Illumina high-throughput sequencing technology [24]. Enzootic nasal adenocarcinoma (ENA) is an epithelial tumor caused by enzootic nasal tumor virus (ENTV), and is a chronic, progressive, contact transmitted disease [25]. With the exception of Australia and New Zealand, this disease has spread throughout goats or sheep almost worldwide [26]. ENA originates from the ethmoid area of the nasal cavity either unilaterally or bilaterally, and the tumors are soft, whitish or pinkish-red in color and can partially or completely obscure the nasal cavity [27]. Metastases to the regional lymph nodes, brain or other organs does not occur [28]. So far, there are no effective methods for early diagnosis of ENA and the goats or sheep can only be culled after symptoms appear. More seriously, as it is difficult to distinguish between animals with a latent infection and healthy animals, the virus spreads within herds, and can infect a large number of goats or sheep and threaten the entire population. There are currently 2581 human mature miRNAs in the miRbase (v21) database; however, there is no public miRNA library of Capra hircus nasal tissues and there have been no reports of miRNAs in ENA. To further complicate matters, attempts to establish a system of cultivating ENTV in vitro have failed, which presents a significant obstacle to investigating the immunological characteristics of ENTV and the mechanisms by which it promotes tumorigenesis [29]. Therefore, taking advantage of knowledge of the roles of miRNAs in human cancer to research the miRNAs involved in ENA may not only avoid the problem of cultivating ENTV in vitro, but also shifts the focus to the cells targeted by ENTV - goat or sheep nasal epithelial cells - and may provide an alternative method for investigating the tumorigenic effects of ENTV. Using Illumina high-throughput sequencing technology to detect miRNAs expressed in the tumor and para-carcinoma nasal tissues of Nanjiang yellow goats with ENA, we constructed the first goat nasal tissue miRNA library. Furthermore, the target genes of the differentially expressed miRNAs in ENA were predicted and their corresponding biological functions were analyzed. This research may help to identify novel biomarkers for ENA, lays a foundation for investigating the mechanism by which ENTV promotes tumorigenesis, and provides further information on the role of miRNAs in cancer. Furthermore, as the sequences and roles of miRNAs are well conserved, the findings of this study may also be relevant to human cancers such as nasopharyngeal carcinoma. Animals and tissue samples Eight goats (3a-4a, Nanjiang Yellow Goat) infected by ENTV under natural conditions at a farm in Sichuan were quarantined and transported to Sichuan Agricultural University laboratory animal center, and grew up the center. After slaughter, tumor and para-carcinoma nasal tissues were collected, frozen rapidly in liquid nitrogen and stored at −80 °C. After pathological analysis, the samples from three Nanjiang yellow goats whose nasal passages were unilaterally blocked by tumors were selected for high-throughput sequencing. The nasal tumors in these animals were poorly differentiated (i.e., at the same state of differentiation) with no tumor cell infiltration in the matched para-carcinoma tissues. Preparation of samples for sequencing and qPCR Samples of cDNA from the tumor tissues (numbers S1, S3, S5) and matched para-carcinoma tissues (numbers S2, S4, S6) of the three animals described above were shipped on dry ice to Jing Neng Bio-Technology corporation (Shanghai, China) for high-throughput sequencing. Briefly, total RNA was extracted from the tissues using RNAzol RT RNA Isolation Reagent (GeneCopoela, Rockville, MD, USA) according to the manufacturer's protocol. The RNA concentrations were determined using a Smart Specplus Spectrophotometer (Bio-Rad, Hercules, CA, USA) and the integrity of the total RNA samples was verified by polyacrylamide gel electrophoresis (PAGE). The All-In-One miRNA qRT-PCR Detection Kit (GeneCopoela) was used to add poly(A) tails to the miRNAs in the total RNA samples and M-MLV reverse transcriptase was used to synthesize cDNA according to the manufacturer's instructions. Each reaction mixture contained 5 μL of 5x reaction buffer, 1 μL RTase Mix, 1 μL of 2.5 U/μL PolyA Polymerase, 2 μg total RNA and RNase-/DNase-free H2O to 25 μL, and was incubated at 37 °C for 1 h and then at 85 °C for 5 min to inactivate the enzyme. Analysis of sequence data and creation of miRNA library Single-read 50 bp sequencing was adopted for high-throughput sequencing. Illumina CASAVA software was used to convert the original data image files into sequence files, and FastQC statistical software was used to evaluate the quality of the data. Primer, adaptor and low quality sequences were excluded and 15–40 base sequences meeting the length and quality requirements were selected as clean reads of reliable quality for further analysis (Figs. 1, 2, 3, 4, 5 and 6). Total clean reads from each individual sample were aligned with the Capra hircus genome in NCBI (ftp://ftp.ncbi.nlm.nih.gov/genomes/Capra_hircus) using Bowtie software [30] (http://bowtie-bio.sourceforge.net/index.shtml), and then blasted against the Rfam (http://www.sanger.ac.uk/resources/databases/rfam.html), RepBase (http://www.girinst.org/repbase/), EST (http://www.ncbi.nlm.nih.gov/nucest/) and miRBase (http://www.mirbase.org/) databases. Sequence alignment was set to allow only a single base mismatch, and the results were sorted in the order of known miRNAs > rRNAs > tRNAs > snRNAs > snoRNAs > repeat, respectively, which enabled each small RNA to obtain a unique annotation. The remaining sequences were mapped to Denovo prediction data sets [31] and the Capra hircus genome to exclude known non-miRNA sequences (such as tRNAs, rRNAs, snRNAs and snoRNAs) and identify novel miRNAs. MiRDeep [32] and RNAfold [33] were used to predict miRNA precursor sequences, star miRNAs and mature miRNAs, and then the energetic stability, position and read frequencies for each potential miRNA precursor were computed using miRDeep according to the compatibility of energetic stability, positions, frequencies of reads. Ultimately, a Capra hircus nasal tissue miRNA library was created by combining the sequencing data from all six samples. Reads length distribution statistical of S1 Identification of differentially expressed miRNAs in ENA The sequences in each sample were compared with the miRNA library established in this study by assessing the numbers of transcripts per million (TPM). TPM was calculated as (numbers of each miRNA matched to total reads)/(number total reads) × 106. TPM is an indicator of the quantity of miRNA expression per million match paired sequences. The total numbers of matched pair reads were used in the normalized numerical expression algorithm to calculate miRNA expression. DESeq [34] software was used to identify differentially expressed miRNAs between the para-carcinoma tissues (S2, S4, S6) and ENA (S1, S3, S5) on the basis of a fold-change greater than or equal to two and P-value ≤ 0.05. Prediction and analysis of miRNA target genes The Miranda algorithm [35] was used to predict the target genes of the miRNAs that were differently expressed in ENA. The threshold parameters for predicting miRNA target genes were a total score ≥150, ΔG ≤ −30 kcal/mol, and strict 5′ seed pairing. The pathways these candidate target genes are involved in was analyzed by functional annotation utilizing the NCBI, KEGG (http://www.genome.jp/kegg/) [36] and GO (http://geneontology.org/) [37] databases. Additionally, high-throughput sequencing allowed the mRNA expression of all of the potential target genes to be analyzed in the same samples (data not shown); therefore, GO and KEGG analyses could be conducted on the differentially expressed target genes of the differentially expressed miRNAs. GO annotation and enrichment analysis was performed for three gene ontologies: molecular function, cellular components and biological processes. The following formula was used to calculate the P-values: $$ \mathrm{P}=1-{\displaystyle \sum_{i-0}^{m-1}\frac{\left(\begin{array}{c}\hfill M\hfill \\ {}\hfill i\hfill \end{array}\right)\left(\begin{array}{c}\hfill N-M\hfill \\ {}\hfill n-i\hfill \end{array}\right)}{\left(\begin{array}{c}\hfill N\hfill \\ {}\hfill n\hfill \end{array}\right)}} $$ where N is the number of genes with GO/KEGG annotations; n is the number of target gene candidates in N; M is the number of genes that annotated to a certain GO term/pathway, and m is the number of target gene candidates in M. GO terms and KEGG pathways with a corrected P-value ≤ 0.5 were regarded as significantly enriched. Validation of the expression of key differentially expressed miRNAs Key miRNAs that were identified in all of the analyses described above were quantified in ENA and para-carcinoma tissue samples from five goats with ENA whose nasal passages were unilaterally blocked by tumors. Total RNA was isolated and reverse transcribed as described above, then the cDNA products were diluted 5-fold with sterile H2O and subjected to quantitative real-time PCR (qPCR) using the All-In-One miRNA qRT-PCR Detection Kit (GeneCopoela) with U6 snRNA and GAPDH as internal references. Each reaction contained 10 μL of 2x All-in-One qPCR Mix, 2 μL All-in-One miRNA qPCR Primer (2 μM; prepared by Life Technologies, Shanghai, China), 2 μL Universal Adaptor qPCR Primer (2 μM), 2 μL first-strand cDNA and 4 μL double distilled water. The cycling conditions were 95 °C for 10 min, 40 cycles of 95 °C for 10 s, 60 °C for 20 s and 72 °C for 20 s, followed by melting curve analysis. Relative quantification was performed using the 2-△△Ct method [38], and t-tests were used to examine the significance of the differences in expression between the para-carcinoma tissues and ENA. Capra hircus nasal tissue miRNA library High-throughput sequencing generated hundreds of millions of reads for each tissue. The raw data (tag sequences and counts) have been submitted to Gene Expression Omnibus (GEO) under series GSE65305. To estimate sequencing quality, the quality scores were analyzed across all bases (Fig. 7). The lowest quality score was ≥30; therefore, the error rate was lower than 0.1 %. Reads including adaptor sequences, low quality sequences and sequences of unqualified length were removed, and the remaining clean reads were aligned with the Capra hircus genome in NCBI using Bowtie software to analyze the genomic distribution and expression of small RNAs. The vast majority of clean reads (at least 84.75 %) and unique reads (at least 57.56 %) mapped to the Capra hircus genome (Table 1). Base quality distribution in each cycle Table 1 The results of clean reads and unique reads maped to the Capra Hircus genome in cancer and control groups Unique reads were blasted against the Rfam, RepBase, EST and miRBase databases, in the order of known miRNAs > rRNAs > tRNAs > snRNAs > snoRNAs > repeat sequences, which enabled each small RNA obtain a unique annotation. To exclude other RNAs, such as tRNAs, rRNAs, snRNAs and snoRNAs, the remaining sequences were mapped to Denovo prediction data sets and the Capra hircus genome to identify novel miRNAs. miRDeep prediction [32] and RNAfold [33] software were used to analyze secondary structure. A total of 435 sequences (29 novel miRNAs) were included in the miRNA library. Additional file 1: Table S1 displays the sequencing generated codes and corresponding Capra hircus miRNAs or novel miRNA_id. As research into miRNAs in human cancer is widespread, we blasted all goat miRNAs against the human miRNAs in miRBase v21 to further understand their function. A total of 615 of the goat miRNAs had analogues in the human miRNA datasets (Additional file 2: Table S2). A total of 435 miRNAs were identified in the ENA and para-carcinoma tissues. The Additional file 3: Table S3 lists the expression of all miRNAs. The expression of 116 miRNAs was significantly different in para-carcinoma tissues and ENA, of which 54 were downregulated and 60 were upregulated in ENA. In addition, 2 miRNAs were only expressed in the para-carcinoma tissues (Additional file 4: Table S4). The majority of the fold change-log2 values ranged from 1 to 5.42; chi-miR-133a-3p had the highest fold-change-log2 of at least 5.4-fold, and 65 miRNAs had fold-change-log2 values of at least two-fold. Figure 8 indicates the differences in expression of all 435 miRNAs between ENA and the para-carcinoma tissues. Relative expression of miRNAs in ENA and para-cancerous tissues. The x- and y-axes indicate the mean TPM expression levels of the miRNAs in each tissue. The red circles represent miRNAs with a fold change ≥ 2; green circles represent miRNAs with a fold change ≤ 2; the points on the dotted line represent miRNAs with a fold change = 2. Fold changes were calculated as the mean miRNA TPM in ENA/mean miRNA TPM in para-cancerous tissues Functional analysis of differentially expressed target genes regulated by differentially expressed miRNAs The Miranda algorithm indicated thousands of potential target genes for the 435 miRNAs. According to the total scores and predicted energies, the 6176 non-redundancy target genes of these 121 miRNA (116 significant expression miRNAs and five star miRNAs) were selected, reflecting 15222 corresponding relationships between the differentially expressed miRNAs and their target genes. Additional file 5: Table S5 shows the total stores, total energy, and protein-id and genomic location of predicted target genes. The expression of these candidate target genes was assessed in the high throughput sequencing data obtained from the same ENA and para-cancerous tissue samples (data not shown; this data will be described in another article). A total of 175 mRNAs that were significantly differently expressed in ENA were selected for this analysis. Additional file 6: Table S6 lists the differentially expressed miRNAs and their corresponding differentially expressed target genes. Additional file 7: Table S7 summarizes the degree of regulation between the differentially expressed miRNAs and their differentially expressed target mRNAs. MiRNA-gene ontology network analysis of miRNA target genes Functional analysis was conducted on the mRNAs predicted as targets of the 435 differentially expressed miRNAs. A total of 9777 GO enrichments were identified, of which 1792 GO categories were significant (P ≤ 0.05). The mRNA sequencing identified a total of 90 target genes corresponding to miRNAs with significantly decreased expression and 84 target genes corresponding to miRNA with significantly increased expression in tumor group. Four hundred seventy-two significant GO enrichments exist in significant expression miRNA-mRNA network (Additional file 8: Table S8). The target genes of the differentially expressed miRNAs were mainly involved in cell differentiation, MAP kinase activity, cell adhesion and angiogenesis; each of these pathways may be implicated in the tumorigenic effect of ENTV. Figure 9 presents the ten most-enriched GO categories for the differentially expressed target genes of the differentially expressed miRNAs in ENA. The ten most-enriched GO categories of the differentially expressed target genes of the differentially expressed miRNAs Analysis of signaling pathways regulated by the miRNA target genes Signal transduction analysis was conducted on the mRNAs predicted as targets of the 435differentially expressed miRNAs, and 267 KEGG enrichments were identified of which 97 were significant (P ≤ 0.05). The target genes of the differentially expressed miRNAs participate in pathways related to the signal transduction, specific types of cancer and immune system. Among significantly differently expressed miRNA, miRNA with increased expression in tumor group were involved in 83 significant signal transduction pathways (Additional file 9: Table S9), miRNA with reduced expression in tumor group were involved in 89 significant signal transduction pathways (Additional file 10: Table S10). Figure 10 illustrates the ten most-enriched KEGG pathways for the differentially expressed target genes of the differentially expressed miRNAs in ENA. The ten most-enriched signaling pathways of the differentially expressed target genes of the differentially expressed miRNAs Quantitative RT-PCR validation of differentially expressed miRNAs We selected nine of the key miRNAs that were significantly differently expressed in ENA including five miRNAs that featured in both the GO and KEGG pathway analyses and two novel miRNAs (NW_005102245.1_1433,NC_022308.1_285). The main functions of target genes regulated by these miRNAs are involved in cancer pathogenesis, virus infection, cell apoptosis and proliferation. As shown in Fig. 11, qRT-PCR confirmed the expression of the nine miRNAs between ENA and the para-cancerous tissues with an increased sample size. The expression trend of eight miRNAs is in accordance with Illumina High-Throughput Sequencing, one miRNA (chi-miR-218) have shown a down-expression in tumor group in sequencing and qPCR verification, but the down-expression multiple is different. qRT-PCR validation of the identified miRNAs using Illumina sequencing technology. Real-time RT-PCR analysis of nine miRNAs in the tumour and para-carcinoma tissues from five goats with ENA. Relative quantification was assessed using the 2-△△Cq method and was normalized to U6 and GAPDH. 2-△△Ct Means ± SE relative expression levels are presented. * represents p < 0.05, ** represents p < 0.01 ENTV, a betaretrovirus that infects sheep (ENTV-1) and goats (ENTV-2), is associated with neoplastic transformation of ethmoid turbinate epithelial cells and leads to ENA. The clinical symptoms of goats are a loss of appetite, extreme weight loss, dyspnea, rhinorrhea, and unilateral or bilateral nasal puffiness. The incidence of ENTV infection ranges from 5 to 15 %, and once the clinical symptoms of ENA appear, almost all cases are fatal [39–41]. High-throughput sequencing technology is gradually being used in animal and has provided some knowledge of goat miRNAs. Ji et al. [42] discovered 290 known miRNAs and 38 novel miRNAs in dairy goat mammary gland tissue and reported that miRNA-mediated regulation of gene expression occurs during early lactation. Hao et al. [43] found that the expression of 64 miRNAs was reduced in the skin of a 70-day fetus relative to a lamb born at 2 weeks, with the expression of ten miRNAs decreasing more than 5-fold, which implies that miRNAs play an important role in maintaining normal skin function. Cancer is a leading cause of morbidity and death in humans. Significant research has been conducted on miRNAs in human cancer, and miRNAs have been demonstrated to be directly involved in human nasopharyngeal carcinoma (NPC). For example, miR-29c, the miR-34 family, miR-143, miR-145 and miR-9 are downregulated in NPC, leading to increased expression of their target genes which influence the function and synthesis of extracellular matrix proteins, which in turn affects tumor invasion and metastasis, and activates the TGF-Wnt, IP3 and VEGF signaling pathways [44, 45]. In contrast, miR-200, the miR-17-92 cluster and miR-155 are upregulated in NPC, and miR-200 inhibits the migration and invasion of NPC cells by inhibiting the expression of ZEB2 (zinc finger E-box binding homeobox 2) and CTNNB1 (catenin-β-like 1) [46]. By blasting the 435 miRNAs identified using high–throughput sequencing in this study against the human miRNA datasets in miRBase, we found that hsa-miR-9, hsa-miR-34 and hsa-miR-143 are significantly downregulated and hsa-miR-200 is significantly upregulated in ENA. GO and KEGG pathway analysis revealed these miRNAs are involved in intracellular signal transduction, the MAPK cascade and cell morphogenesis, among other processes. Our study found according to the percentage, the top five signaling pathways are MAPK signaling pathway、Pathways in cancer、PI3K-Akt signaling pathway、Ras signaling pathway and Viral carcinogenesis. Kano et al. [47] and Chiyomaru et al. [48] found that miR-133a was significantly inhibited human esophageal squamous cell cancer and the invasion of bladder cancer cell. Iorio [49] found that expression of miR-133a significantly reduced during the progression of breast cancer. Our results also reveal the expression of miR-133a-3p was at least 5-fold lower in ENA compared to para-carcinoma nasal tissues. These results suggest that miR-133a-3p may regulate the expression of oncogenes and inhibit tumorigenesis. KEGG analysis displayed that the target genes of miR-133a-3p are involved in tumor biology at multiple nodes, such as regulation of cell differentiation, apoptosis, signal transduction and cell adhesion, invasion and migration. In esophageal squamous cell carcinoma and bladder cancer, miR-133a targets fascin actin-bundling protein 1 (FSCN1) to regulate cancer cell invasion, migration and proliferation [47, 49]. However, in this study we identified that serine/threonine-protein kinase B-raf (BRAF) as chi- miR-133a-3p, chi-miR-145-5p, chi-miR-146a/200a and two novel miRNA (NC-022308.1-260、NC-022294.1-874) target gene which acts upstream regulatory factor in RAS-RAF-MEK-ERK. Sustained activation of BRAF will lead to cell deterioration and excessive proliferation [50]. In addition, the miR-133a-3p target genes: MDS1 and EVI1 complex (MECOM) may also play a significant role in pathways related to cancer. In chronic myeloid leukemia (CML), expression of the oncogene MECOM correlates with progression. The tyrosine kinase catalytic activity of the oncoprotein BCL-ABL1 regulates MECOM expression, and conversely MECOM partially mediates BCR-ABL1 activity [51]; BCR-ABL1 activates the PI3K, MAPK and JAK-STAT signal transduction pathways [52–54] to promote abnormal proliferation, differentiation, transformation and survival in myeloid cells [55]. However, forkhead box O (FoxO) as the intersection of PI3K and RAS signaling pathway can inhibit cell proliferation and induce cell cycle stop. The activation of the PI3K signaling pathway inhibits the activity of the FoxO transcription factor [56, 57], which increase the chances of tumor formation. Further study is required to determine if MECOM and BCR-ABL1 play a role in the pathogenesis of ENA. miR-148a is an oncogene that is upregulated in hepatocellular carcinoma cells (HCC) and enhances cell proliferation, migration, invasion and stimulates the epithelial to mesenchymal transition (EMT) by targeting tumor suppressor gene: phosphatase and tensin homolog (PTEN) [58]. However, PTEN was not identified as a target of miR-148a in this study. Its predicted targets were the transforming growth factor β receptor associated protein 1 (TGFβRAP1) which can specifically combine with the receptor of transforming growth factor β (TGFβ), and then help to realize the biological function of TGFβ [59]. TGFβ can inhibit cells growth in malignant tumor such as head and neck squamous cancer, colon cancer, breast cancer [60–62]. The present studies have pointed out that the expression of TGFβ in nasopharyngeal phosphorus tumor generally weakened or even disappear, but the adjacent epithelium have stronger expression [63]. The expression of miR-148a-3p was at least 2.5-fold higher in ENA compared to para-carcinoma nasal tissues. Influenced by miR-148-3p expression, TGFβRAP1 will drop, which will affect the signal pathway of TGFβ and make the cancer cell reduction or loss of ability to react to TGFβ, finally, the tumor cells escape from negative growth regulation of TGFβ. Although this is our speculation, but we believe there is a link between them. This study provides a solid basis for further research and highlights a number of miRNAs and genes that may be involved in the pathogenesis of ENA. This study of miRNAs in ENA may also provide useful information for basic research into human cancer. In future studies, we aim to confirm the function of the candidate miRNAs in nasal cells. 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Briskin KB, Fady C, Mickel RA, Wang M, Lichtenstein A. Inhibition of head and neck squamous cell carcinoma cell lines by transforming growth factor-β. Otolaryngol Head Neck Surg. 1995;112(6):728–34. Arteaga C, Coffey Jr R, Dugger T, McCutchen C, Moses H, Lyons R. Growth stimulation of human breast cancer cells with anti-transforming growth factor beta antibodies: evidence for negative autocrine regulation by transforming growth factor beta. Cell Growth Differ. 1990;1(8):367–74. Bin L, Hu C, Zhan F. [The expression in situ of transforming growth factor beta s, their receptors and TGF beta-receptor interacting protein-1 in nasopharygneal carcinoma]. Zhonghua Er Bi Yan Hou Ke Za Zhi. 1999;34(4):210–2. The skillful technical assistance of Shanghai Genergy Bio-Corporation is gratefully acknowledged. The raw data (tag sequences and counts) have been submitted to Gene Expression Omnibus (GEO) under series GSE65305. All authors have read and approved of the submission of the manuscript. Conceived and designed the experiments: YQG CSJ WXT. Performed the experiments: WB YE. Analyzed the data: WB YE HY. Contributed reagents/materials/analysis tools: YQG WB YE. Wrote the paper: WB YN. Competing interest This study was carried out in strict accordance with the Guidelines for Experimental Animals of the Ministry of Science and Technology (revised in 2004; Beijing, China) and was approved by the Institutional Animal Care and Use Ethics Committee of Sichuan Agricultural University, NO. SYXK (Chuan) 2014–187. College of Veterinary Medicine, Sichuan Agricultural University, Hui Min Road 211, Chengdu, Sichuan, 611130, People's Republic of China Bin Wang, Ni Ye, San-jie Cao, Xin-tian Wen, Yong Huang & Qi-gui Yan Bin Wang Ni Ye San-jie Cao Xin-tian Wen Yong Huang Qi-gui Yan Correspondence to Qi-gui Yan. Ni Ye as the joint first author. The miRNAs expressed in samples detected by Illumina sequencing. (XLSX 39 kb) Blast results of all miRNAs against human miRNAs in miRBase v21. (XLSX 152 kb) The expression of miRNAs in ENA and para-cancerous tissues. (XLSX 171 kb) Significantly differentially expressed miRNAs in ENA. Positive FoldChange_Log2 indicates upregulation in ENA relative to the para-cancerous tissues; a negative FoldChange_Log2 indicates downregulation in ENA relative to the para-cancerous tissues; inf indicates no expression in para-cancerous tissues; −inf indicates no expression in ENA. (XLSX 30 kb) Predicted target genes of the differently expressed miRNAs in ENA. (XLSX 2391 kb) Differentially expressed miRNAs and their differentially expressed target genes in ENA. (XLSX 30 kb) Node attributes of the differentially expressed miRNAs and their differentially expressed target genes in ENA. (XLSX 13 kb) Significantly enriched gene ontology categories the differentially expressed target genes of the differentially expressed miRNAs. (XLSX 85 kb) Significantly enriched signaling pathways (m = 83) of gene targets of the significantly increased miRNAs in ENA. (XLSX 34 kb) Additional file 10: Table S10. Significantly enriched signaling pathways (m = 89) of gene targets of the significantly reduced miRNAs in ENA. (XLSX 34 kb) Wang, B., Ye, N., Cao, Sj. et al. Identification of novel and differentially expressed MicroRNAs in goat enzootic nasal adenocarcinoma. BMC Genomics 17, 896 (2016). https://doi.org/10.1186/s12864-016-3238-5 Illumina high-throughput sequencing	CommonCrawl
Diversity and abundance of terrestrial gastropods in Skikda region (North-East Algeria): correlation with soil physicochemical factors Nedjoua Zaidi ORCID: orcid.org/0000-0002-5211-825X1, Louiza Douafer2 & Amel Hamdani3 The inventory process is the first method to protect and safeguard animal biodiversity. This study carries out a quantitative and qualitative inventory of terrestrial gastropods at three sites in Skikda province (north-eastern Algeria). The relationship between terrestrial gastropod diversity and soil physicochemical factors was investigated using statistical analyses. The inventory data reveals the presence of four families and eight species showing varied predominance rates of Cornu aspersum species according to each site in the city of Skikda (Azzaba 53.88%; Ben-Azzouz 56.12%; El-Hadaiek 37.92%). The maximal specific richness was registered in the El-Hadaiek site (seven species), and the highest mean richness was noted in the Ben-Azzouz site (392 individuals). Of the eight gastropod species identified, three species (Cornu aspersum, Cantareus apertus and Rumina decollate) were classified as constant species. The Shannon–Weaver diversity and equitability indices vary by site. The presence of certain species in one site and their absence in other sites, as well as the variation in ecological indices, could be attributed to the effect of soil-physicochemical factors. Human industrial and agricultural activities and increasing population growth rates, as well as economic and technological factors, have negatively impacted biodiversity (Aronson et al., 2014; Douglas et al., 2013; Gaston et al., 2013; Mackenzie & Michael, 2018; Yanes, 2012) by inducing marked changes in the structure of biological behaviours and the dysfunction of surrounding ecosystems (Chen & Blume, 1997; Sha et al., 2015). Interestingly, land snails play a crucial role in the functioning and stability of ecosystems due to their contribution to the provision of food for other animals, decomposition of plant material and maintenance of soil calcium content (Lange, 2003). Additionally, their short lifetime and limited dispersal ability make them excellent bioindicators (Watters et al., 2005). Furthermore, snails and slugs can be important links in the transfer of chemicals from vegetation or plant litter to carnivores (Coughtrey et al., 1979; Nica et al., 2012, 2013). Consequently, such transfer along food chains is an important eco-toxicological aspect (Laskowski & Hopkin, 1996). Several studies on land snail inventories have been carried out in several biotopes of Algeria, notably in the north-western (Damerdji, 2008, 2013) and north-eastern regions (Larbaa & Soltani, 2013; Douafer & Soltani, 2014). Recently, a survey of gastropods was conducted in five areas of north-eastern Algeria (Belhiouani et al., 2019). However, we are not aware of a study on the biodiversity and abundance of terrestrial gastropods in other areas of northeast Algeria. The Skikda region (north-eastern Algeria) is the location of highly developed petrochemical industries, which cause serious risks to human and environmental safety by progressively destroying natural resources, water and air quality (Fadel et al., 2016; Kahoul et al., 2014; Zeghdoudi et al., 2019). Researching the biotic and abiotic factors that influence land diversity and abundance is essential to prevent and protect terrestrial ecosystem. Many researchers have demonstrated that climatic factors, soil physicochemical factors and plant communities affect the distribution and abundance of terrestrial gastropods (Gärderforns et al., 1995; Lewis Najev et al., 2020; Nekola, 2003). In Algeria, several studies have been conducted on the effect of environmental factors on the diversity and abundance of land snails (Belhiouani et al., 2019; Douafer & Soltani, 2014). The present study aims to (1) identify and investigate the abundance and diversity of terrestrial gastropod species (snails and slugs) in three sites located in Skikda province, and (2) investigate the relationship between terrestrial gastropod diversity and soil physicochemical factors using statistical analysis (correlation analysis). The city of Skikda (36°52′34 N, 6°54′33° E) is located in the north-east of Algeria, 510 km from Algiers (capital of Algeria). It has a Mediterranean climate, characterised by two seasons: a mild, rainy winter and a hot, dry summer. The average annual precipitation varies between 600 and 800 mm/year. The annual temperature varies from 9 in winter to 27 °C in summer. Humidity during the day is about 70% (Souilah et al., 2019). The study was conducted in three cities of Skikda province (Fig. 1): El-Hadaiek covering an area of 271.75 km2, Azzaba extending over an area of 805.34 km2, and Ben-Azzouz, the largest city of the province, with an area covering 228.28 km2. Table 1 lists the characteristics of the three sampling sites. Location of the three sites of survey in region of Skikda (Northeastern Algeria) Table 1 Characteristics of the study areas Sampling methods and taxa identification Snail sampling was carried out using the quadrat method. Quadrats likely to be suitable breeding habitats for snails and to be sampled were randomly selected by projecting a grid onto a map of the study area. For each site (Fig. 2), a 400 m2 quadrat was established using a tape measure for each sampling site. Snail sampling was carried out by two persons searching each quadrat for 2 h, following the method of Benjamin et al. (2014) with modifications. Live snails and slugs, as well as dead snail shells were collected by hand from different natural habitats (on the ground, under tree trunks, on plants and in crops). All samples obtained were preserved in 70% ethanol at the Laboratory for the Optimization of Agricultural Production in Subhumid Areas (University of Skikda). The snails collected from the three sites were thoroughly identified based on animal morphological features (shape, size, colouration and ornamentation of the shell). Identification was based on the key features reported by Barker (2001) and Bouchet et al. (2005). When a snail was collected, the plant species was noted. Samples of plant species collected in the field were transferred to the laboratory for identification, based on the method previously reported by Quezel and Santa (1962–1963) and Andreas (1998). Pictures taken at sampling sites in the Skikda city: El-Hadaiek (a); Azzaba (b) and Ben-Azzouz (c) The identified snail individuals were counted and subjected to the determination of the constancy index, relative abundance, specific and mean richness, and some diversity indices (Shannon–Weaver and equitability index). The constancy index (C) is calculated according to Dajoz (1985): $${\mathbf{C}} = \left( {{\mathbf{Pa}} \times {\mathbf{100}}} \right)/{\mathbf{P}}$$ where C is the centesimal frequency, Pa is the total number of samples containing the species considered and P is the total number of samples taken. According to Dajoz (1985), three different categories are distinguished: constant species (C ≥ 50%), accessory species (25% < C < 50%) and accidental species (C ≤ 25%). The relative abundance (A) index allows to study the distribution of a species in a given region, and to identify the species as common, rare, or very rare species (Dajoz, 1985). It is calculated by the following formula: $${\mathbf{A}} = \left( {{\mathbf{n}}_{{\mathbf{i}}} \times {\mathbf{100}}} \right)/{\mathbf{N}}$$ where ni is the total number of considered species, and N is the total number of individuals found. According to Dajoz (1985), species can be classified into three different groups: common species (A > 50%), rare species (25% ≤ C ≤ 50%) and very rare species (C < 25%). The specific richness (S) is the number of species found in the study area (Blondel, 1975; Ramade, 1984). The mean richness (S′) is defined according to Blondel (1975) and is calculated by the following formula: $${\mathbf{S}}^{{\prime }} = {\mathbf{n}}_{{\mathbf{i}}} /{\mathbf{P}}$$ where ni is the total number of considered species, and P is the total number of samples taken. The Shannon–Weaver index (H′) index is calculated by the following equation (Shannon & Weaver, 1963): $${\mathbf{H}}^{{\prime }} = - \sum\limits_{{{\mathbf{i = 1}}}}^{{\mathbf{R}}} {\left[ {{\mathbf{p}}_{{\mathbf{i}}} \cdot {\mathbf{Log}}_{{\mathbf{2}}} {\mathbf{p}}_{{\mathbf{i}}} } \right]}$$ where Pi is the relative frequency (ni/N) and R is the total number of species. The equitability index (E) constitutes a second fundamental dimension of diversity (Ramade, 1984). The equitability is expressed as follows: $${\mathbf{E}} = {\mathbf{H}}^{{\prime }} /{\mathbf{Hmax}} = {\mathbf{H}}^{{\prime }} /{\mathbf{lnS}}$$ Soil sampling and determination of physicochemical parameters The analysis of soil physicochemical properties was carried out on samples collected manually using a trowel (Koranteng-Addo et al., 2011) to a depth of about 10 cm. Three representative soil samples were collected from each site using the same quadrate method to study molluscs diversity. In brief, the soils were air-dried for 3- 6 days, crushed and sieved through a 2 mm diameter sieve and then stored in a non-metallic container. Soil pH is measured in soil–water suspension (soil/water ratio = 1/2.5) according Gauchers (1968). The electrical conductivity (EC) can be determined on a soil extract (soil/water ratio = 1/5) using a conductivity meter (Delaunois, 1976). Organic matter (OM) was quantified by the method proposed by Anne (1945), based on the determination of the percentage of organic carbon in the soil. This method is based on the oxidation of organic carbon with potassium bicarbonate and titration of the solution with Mohr salt (0.2 N). The determination of total limestone was calculated according to the method of Duchaufour (1970) based on the reaction of calcium carbonate with hydrochloric acid (HCl). The total porosity (P) is calculated from the apparent and true densities. Soil field capacity was determined using the software of Saxton et al. (1986), while soil humidity (H) was calculated from the difference between the weight of wet soil and dry soil using a precision balance. Data are displayed as mean ± standard deviation (SD). Comparisons of physicochemical factors were tested for statistical significance by one-way ANOVA with Tukey's post hoc test. The relationship between the specific richness of terrestrial gastropods and the physicochemical characteristics of the soils was also examined using the Pearson correlations test. Statistical tests were performed using MINITAB software (version 16, Penn State College, PA, USA) where p < 0.05 was considered significant. Gastropod species inventory The inventory of terrestrial gastropods carried out at the three selected sites reveals the presence of eight species belonging to four malacological families (Milacidae, Helicidae, Geomitridae and Achatinidae). Table 2 summarises the species inventoried in accordance with previously reported classification criteria (Bonnet et al., 1990; Chevallier, 1992; Germain, 1969). The results show that each of the gastropod families Milacidae and Helicidae includes two species; Geomitridae includes three species, and Achatinidae includes one species. Table 2 List of malacological species in the three study sites Flora inventory For the flora inventory in the study sites, lists of plant species were made (Table 3). In all study areas, 12 species belonging to 12 families were identified. Furthermore, we observed that there was no difference in plant species between the three sampling sites and that there was no relationship between snail diversity and plant richness. Table 3 Botanical species identified in the three study sites Terrestrial gastropod structure and distribution in the study sites As shown in Table 4, the species Cornu aspersum presents minimal and maximal abundance rates in El-Hadaiek (37.92%) and Ben-Azzouz (56.12%), as well as maximal and minimal values in Ben-Azzouz (25%) and El-Hadaiek (2.92%). Slugs present a very low abundance (2.04%) in El-Hadaiek and zero-abundance in Azzaba and Ben-Azzouz. In accordance with the findings reported by Dajoz (1985), the constancy values obtained (C%) show the presence of 100% of the species Cornu aspersum, Cantareus apertus and Rumina decollata in the three selected sites. They are therefore considered as constant species (C ≥ 50%). Similarly, Cernuella virgata was found as a constant species in El-Hadaiek and Ben-Azzouz, and as an accessory species in Azzaba (25% < C < 50%), while the species Cochlicella barbara is constant in El-Hadaiek and accessory in Ben-Azzouz and Azzaba. Furthermore, the species Trochoidea elegans was found as a very accidental species in El-Hadaiek and Azzaba (C ≤ 50%) and accessory species in Ben-Azzouz. Slugs are constant in El-Hadaiek and very accidental in Azzaba and Ben-Azzouz. Table 4 Constancy (%) and abundance (A%) of terrestrial gastropods in the three study sites Biodiversity indices The specific richness is represented by seven, six and five gastropod species in El-Hadaiek, Ben-Azzouz and Azzaba respectively (Table 5). However, the maximal values of the mean richness are 392 and 366.5 in Ben-Azzouz and Azzaba respectively (Table 5). As indicated in Table 5, the Shannon–Weaver (H′) diversity index varies between 0.51 in Ben-Azzouz and 0.68 in El-Hadaiek. The equitability index (E) is defined as the fundamental dimension of diversity enabling the comparison of population structure. Thus, the results obtained show that the values of the equitability index vary between 0.28 and 0.35. Table 5 Specific and mean richness and Shannon–Weaver diversity (H) and equitability (E) indices of gastropods in the three study sites Soil physicochemical characteristics The physicochemical parameters studied (organic matter, field capacity, permeability and porosity) vary significantly between the three sites (Table 6). The one-way ANOVA (site) of the soil physicochemical parameters reveals a highly significant effect of site on field capacity (F2,6 = 42.21, p < 0.001), organic matter (F2,6 = 20.67, p < 0.01) and permeability (F2,6 = 50.82, p < 0.001). The site effect on porosity was found significant (F2,6 = 6.66, p < 0.05). Pairwise comparisons (Tukey's test) of the variation in soil physicochemical parameters reveal a significant difference (p < 0.05) between the sites (Table 5). Table 6 Soil physicochemical parameters of the three study sites (m ± SD, n = 3), analysis of variance (ANOVA) and Tukey's test Relationship between specific richness and soil physicochemical characteristics The correlation between the specific richness and physicochemical soil characteristics in all study sites was analysed (Table 7). A highly significant correlation only between the specific richness and organic matter (R = 0.904, p < 0.001) and field capacity (R = 0.956, p < 0.01) can be noted. In contrast, specific richness shows a highly significant negative correlation (R = −0.888, p < 0.001) with permeability. A significant negative correlation is observed between the specific richness and porosity (R = −0.783, p < 0.05). Table 7 Pearson's correlations of terrestrial gastropods specific richness collected in the three study sites with the physicochemical soil characteristics (R: correlation coefficient; P significant at p < 0.05) This study investigated the abundance and diversity of terrestrial gastropod species at three sites located in Skikda province, as well as the impacts of soil physic-chemical factors on snail diversity, was examined. The results revealed an important diversity of the malacological fauna in Skikda province, particularly in the city of El-Hadaiek, and differences in ecological indices (constancy index, relative abundance, specific and mean richness, Shannon–Weaver and equitability indices) between the selected study sites. Furthermore, the soil at the El-Hadaiek site was found to be characterised by high organic matter and field capacity and low porosity and permeability. The results suggest that these parameters are important in determining the richness of terrestrial gastropods in Skikda province, and we do not rule out that other environmental factors may also be important. The biodiversity and distribution of land snails depend on several factors, such as soil characteristics (André, 1982; Douafer & Soltani, 2014; Ondina et al., 1998), climatic factors (Ameur et al., 2019; Hermida et al., 1994), anthropogenic disturbances (Belhiouani et al., 2019) and vegetation (Damerdji, 2013; Damerdji & Amara, 2013; Ondina & Mato, 2001). Several studies have evidenced the need to protect mollusc biodiversity on a global scale (N'dri et al., 2016; Hallgass & Vannozzi, 2016; Nicolai & Ansart, 2017; Heiba et al., 2018; Desoky, 2018; Dedov et al., 2018; Borreda & Martinez-Orti, 2017). In Algeria, some inventories of terrestrial gastropods have been recently carried out in different biotopes (Bouaziz-Yahiatene & Medjdoub-Bensaad, 2016; Hamdi-Ourfella & Soltani, 2016; Ramdini et al., 2021). In the present study, specific richness was lower in the sites of Ben-Azzouz and Azzaba than in El-Hadaiek. Similarly, specific richness is expressed by seven, six and five species respectively at El-Hadaiek, Ben-Azzouz and Azzaba respectively. Previous studies conducted in the northern-eastern region of Algeria have revealed 13 species of terrestrial pulmonate gastropods in El-Kala, El Hadjar and Sidi Kassi (Larba & Soltani, 2013). In addition, Helicidae has been identified as the most abundant family in all three sites with high percentages in Ben-Azzouz and Azzaba, and this is in line with previous results on biodiversity in eastern Algeria (Douafer & Soltani, 2014). This dominance is explained by Chevallier (1992) who assumes the action of the cool and humid environment and selected dark varieties. The abundance results show that Cornu aspersum is a common species in all the study sites (El-Hadaiek, Azzaba and Ben-Azzouz). Moreover, the results of species constancy indicate that the species Cornu aspersum, Cantareus apertus and Rumina decollata are constant in the three study sites (100%) with a significant biomass and a potential for species adaptation via different climates and soils, since the other species present variable constants in various sites. In this regard, Damerdji (2008) reported three constant species and four accidental species in Tlemcen (southern Algeria). The author also reported (Damerdji & Amara, 2013) that the specific richness equals four species (two constants, one accessory, and one accidental) in the region of Naâma (southwestern Algeria). The diversity of the Shannon–Weaver index is lower in El-Hadaiek (0.68 bits) compared to that noticed in El-Kala site (3.05 bits) (Douafer & Soltani, 2014). Also, the equitability index varies between 0.35 and 0.28 (< than 1), suggesting that the distribution of different gastropod species is not in equilibrium with each other (Ramade, 1984). Similar results were obtained in the city of Tlemcen (Northwest Algeria) by Damerdji (2008), while the regions of El Hadjar, Sidi Kaci and El-Kala located in the Northeast Algeria presents an equitability index superior to 0.50 (Larba & Soltani, 2013). This is probably related to the differences in environmental variables between the sites. The distribution and activity of land snails depend on several factors, such as soil characteristics (André, 1982; Gärderforns et al., 1995; Ondina et al., 1998), climatic factors (Hermida et al., 1994) and vegetation (Lewis Najev et al., 2020; Nekola, 2003; Ondina & Mato, 2001). With regard to mollusc nutrition, the flora inventory shows the proliferation of gastropods on all botanical species of the study sites. Several studies have shown a correlation between vegetation and mollusc distribution (Barker & Mayhill, 1999; Millar & Waite, 2002; Martin & Somer, 2004). However, in this study, no relationship was found between the distribution of land snails and dominant plant species in the three study sites. According to the work of Nunes and Santos (2012) conducted in the forests of Ilha (Brazil), this result could be explained by the homogeneity of the study area. Physicochemical factors influence snail diversity in three study sites containing organic matter, field capacity, porosity and permeability. Correlation analysis reveals that organic matter and field capacity are positively correlated with snail specific richness. However, a negative correlation is noted between this parameter (specific richness) and two soil physicochemical factors (permeability and porosity). Organic matter (OM) in the soil provides essential nutrients for plant growth and influences the soil's ability to retain moisture (Chapin et al., 2002) and can also positively affect the abundance of terrestrial gastropods. In this study, the OM content in the soils of the three sites is > 5%, and thus the soils become very rich in organic matter (Abiven et al., 2009), as was found in El-Hadaiek (13.75 ± 0.47%) study area. On the other hand, the field capacity (the maximum volume of water that a soil can retain) is very high at El-Hadaiek (36.07 ± 4.01) compared to the other sites (Azzaba and Ben-Azzouz). This parameter is related to soil texture (amount of clay), which is the most important factor affecting the distribution of gastropods (Outeiro et al., 1993). The soils of the El-Hadaiek and Ben-Azzouz sites are characterised by a clayey-silt texture, while the silt–clay texture characterises the Azzaba site. The clayey-silt soils retain more water than silt–clay soils with a particulate structure. The porosity follows the granulometric nature of the soil; in clay soils (e.g., El Hadaiek), the porosity value is on average ≤ 50. In the other two sites (Azzaba and Ben-Azzouz) where there is less clay, the porosity is around 50%. The presence of clay clogs porous spaces and slows down the circulation of water in the soil. Water circulation (permeability) is slowed down in soils with low porosity, as in the case of El-Hadaiek site (0.25 ± 0.02 cm/h). This is because when soil permeability decreases, the soil pores are filled with water, resulting in higher humidity. Moisture is necessary for the respiration and reproduction of land snails (Coney et al. 1982) and for the production of mucus which is essential for locomotion (Cameron, 2009). 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S., & Papendick, R. I. (1986). Estimating generalized soil-water characteristics from texture. Soil Science Society of America Journal, 50, 1031–1036. https://doi.org/10.2136/sssaj1986.03615995005000040039x Sha, Z., Yuefei, H., Bofu, Y., & Guangqian, W. (2015). Effects of human activities on the eco-environment in the middle Heihe River Basin based on an extended environmental Kuznets curve model. Ecological Engineering, 76, 14–26. https://doi.org/10.1016/j.ecoleng.2014.04.020 Shannon, C. E., & Weaver, W. (1963). The mathematical theory of communication. University of Ilinois Press. Souilah, N., Bendif, H., Djamel Miara, M., & Frahtia, A. (2019). Medicinal plants in floristic regions of El Harrouch and Azzaba (Skikda-Algeria): Production and therapeutic effects. Journal of Floriculture and Landscaping, 4, 05–011. https://doi.org/10.25081/jfcls.2018.v4.3770 Tattersfield, P., Seddon, M. B., Ngereza, C., & Rowson, B. (2006). Elevational variation in diversity and composition of land- snail in Tanzanian forest. African Journal of Ecology, 44, 47–60. https://doi.org/10.1111/j.1365-2028.2006.00612.x Watters, G. T., Menker, T., & O'dee, S. H. (2005). A comparison of land snail faunas between strip-mined land and relatively undisturbed land in Ohio, USA—An evaluation of recovery potential and changing faunal assemblages. Biological Conservation, 126(2), 166–174. https://doi.org/10.1016/j.biocon.2005.05.005 Yanes, Y. (2012). Anthropogenic effect recorded in the live-dead compositional fidelity of land snail assemblages from San Salvador Island Bahamas. Biodiversity and Conservation, 21(13), 3445–3466. https://doi.org/10.1007/s10531-012-0373-4 Zeghdoudi, F., Tanjir, L. M., Ouali, N., Haddidi, I., & Rachedi, M. (2019). Concentrations of trace-metal elements in the superficial sediment and the marine magnophyte, Posidonia oceanica (L.) Delile, 1813 from the Gulf of Skikda (Mediterranean coast, East of Algeria). Cahiers De Biologie Marine, 60, 223–233. This study was supported by the Algerian Fund for Scientific Research (Laboratory for the Optimization of Agricultural Production in Subhumid Areas) and the Ministry of Higher Education and Scientific Research of Algeria (PRFU Projet to Pr. N. Zaidi). We thank Pr. N. Soltani (Laboratory of Applied Animal Biology, University of Annaba) for his advice and Dr. A. Hadef (University of Skikda) for the realization of geographical map. No funding was provided. Laboratory for the Optimization of Agricultural Production in Subhumid Areas (LOPAZS), Department of Natural and Life Sciences, Faculty of Sciences, University of Skikda, 21000, Skikda, Algeria Nedjoua Zaidi Department of Biology, Faculty of Sciences, University of Mila, 43000, Mila, Algeria Louiza Douafer Laboratory of Applied Animal Biology, Department of Biology, Faculty of Sciences, University Badji Mokhtar of Annaba, 23000, Annaba, Algeria Amel Hamdani NZ collected the data, analysed and drafted the MS. LD, AH interpreted data and edited the MS. All authors read and approved the final manuscript. Correspondence to Nedjoua Zaidi. No competing interests. Zaidi, N., Douafer, L. & Hamdani, A. Diversity and abundance of terrestrial gastropods in Skikda region (North-East Algeria): correlation with soil physicochemical factors. JoBAZ 82, 41 (2021). https://doi.org/10.1186/s41936-021-00239-6 Terrestrial gastropod Soil physicochemical factors Skikda city	CommonCrawl
Characterization of weak convergence in $W^{1, p}(\Omega)$ I have to prove that, given $\Omega\subset\mathbb{R}^n$ an open subset, $1\leq p<\infty$ and $\{u_n\}\subset W^{1, p}(\Omega)$, we have $u_n\rightharpoonup u$ in $W^{1, p}(\Omega)$ if and only if $u_n\rightharpoonup u$ in $L^p(\Omega)$ and $Du_n\rightharpoonup Du$ in $L^p(\Omega, \mathbb{R}^n)$. The hint of the exercise is to consider the map $$ T:W^{1, p}(\Omega)\longrightarrow L^p(\Omega)\times L^p(\Omega, \mathbb{R}^n) $$ and prove that it is an isometry. So, my attempt is: by giving $W^{1,p}(\Omega)$ the norm $$ \\|u\\|_{W^{1, p}(\Omega)}=\left(\\|u\\|_{L^p(\Omega)}^p+\sum_{i=1}^n\left\\|\frac{\partial u}{\partial x_i}\right\\|_{L^p(\Omega)}^p\right)^{\frac{1}{p}} $$ and by giving $L^p(\Omega)\times L^p(\Omega, \mathbb{R}^n)$ the norm $$ (u, v) = \left(\\|u\\|^p_{L^p(\Omega)}+\sum_{i=1}^n\\|v_i\\|^p_{L^p(\Omega)}\right)^{\frac{1}{p}}, $$ the application $T$ is an isometry (right?). But now, how can I conclude that the equivalence of the assertions follows? The definition of weak convergence in $W^{1, p}(\Omega)$ is that $u_n\rightharpoonup u$ in $W^{1, p}(\Omega)$ if and only if $L(u_n)\longrightarrow L(u)$ for all $L\in (W^{1, p}(\Omega))'$. By the Riesz Representation Theorem on $W^{1, p}(\Omega)$ I know that there exist $f_0,\ldots,f_n\in L^{p'}(\Omega)$ such that, for every $L\in (W^{1, p}(\Omega))'$, $$ L(u)=\int_{\Omega}\left(f_0(x)u(x)+\sum_{i=1}^nf_i(x)\frac{\partial u}{\partial x_i}(x)\right)\ dx $$ for all $u\in W^{1, p}(\Omega)$ and $$ \\|L\\|_{(W^{1, p}(\Omega))'}=\left(\sum_{i=0}^n\\|f_i\\|_{L^{p'}(\Omega)}^{p'}\right)^{\frac{1}{p'}}. $$ Thank you functional-analysis sobolev-spaces lp-spaces weak-convergence JejiJeji Which implication are you trying to prove? If $u_n\rightharpoonup u$ in $W^{1, p}(\Omega)$ and you take $g\in L^{p'}(\Omega)$, then by Holder's inequality the map $L_g(v)=\int_\Omega gv\,dx$ is linear and continuous in $W^{1, p}(\Omega)$ and so $L_g(u_n)\to L_g(u)$, which shows that $u_n\rightharpoonup u$ in $L^{p}(\Omega)$. Similarly, if $h_1,\ldots, h_n\in L^{p'}(\Omega)$ by Holder's inequality the map $L(v)=\int_\Omega \sum_{i=1}^nh_i(x)\frac{\partial u}{\partial x_i}(x)\,dx$ is linear and continuous in $W^{1, p}(\Omega)$ and so $L(u_n)\to L(u)$, which shows that $Du_n\rightharpoonup Du$ in $L^{p}(\Omega;\mathbb{R}^n)$. Gio67Gio67 $\begingroup$ Ok, I understand this. But what about the converse? I don't understand the hint of the exercise.. $\endgroup$ – Jeji Aug 22 '17 at 8:58 $\begingroup$ By definition I have that $\int_{\Omega}u_ng\rightarrow\int_{\Omega}ug$ for all $g\in L^{p'}(\Omega)$ and $\int_{\Omega}Du_ng\rightarrow\int_{\Omega}Dug$ for all $g\in L^{p'}(\Omega, \mathbb{R}^n)$. Can I conclude that $\int u_ng_o+\sum g_i(x)(u_n(x))_i\rightarrow\int ug_o+\sum g_i(x)u_i(x)$? $\endgroup$ – Jeji Aug 22 '17 at 9:11 $\begingroup$ You have $\int_{\Omega}u_ng_0\rightarrow\int_{\Omega}ug_0$ for all $g_0$ and $\int_{\Omega}Du_ng\rightarrow\int_{\Omega}Dug$ for all $g$. So if you sum them you get $\int_{\Omega}u_ng_0+Du_ng\rightarrow \int_{\Omega}ug_0+Dug$. The hint is to tell you what the dual of $W^{1,p}$ is. $\endgroup$ – Gio67 Aug 22 '17 at 10:50 $\begingroup$ No. No need to use Riesz. For every $g\in L^{p'}(\Omega)$ the functional $L_g$ is linear and continuous. Just use Holder's inequality. $\endgroup$ – Gio67 Aug 22 '17 at 14:37 $\begingroup$ If $X$ is a Banach space, a linear functional $L:X\to \mathbb{R}$ is continuous iff $\|L(x)\|\le c\Vert x\Vert$ for all$x\in X$ and for some constant $c>0$. Now take $X=W^{1,p}$ and $\Vert f\Vert_{W^{1,p}}=\Vert f\Vert_{L^{p}}+\Vert Df\Vert_{L^{p}}$ and apply Holder's inequality to $L_g$. $\endgroup$ – Gio67 Aug 22 '17 at 15:40 Not the answer you're looking for? Browse other questions tagged functional-analysis sobolev-spaces lp-spaces weak-convergence or ask your own question. Proving that weak limit in $L^p$ and strong limit in $H^{-1}$ are the same weak* convergence definition in Sobolev space weak convergence of $L^2$ implies weak convergence of $W_0^{1,2}$ (up to a subsequence)? Weak Convergence of Product Weak Convergence of Composition in Sobolev Space Weak convergence in $L^p$ space. Exercise on equivalence of weak convergence in Sobolev and $L^p$ spaces Prove that the weak convergence in $L^p \left(\mathbb{R}^N\right)$ does not imply the weak convergence of the modulus	CommonCrawl
Time-Dependent Unitary Transformation Method in the Strong-Field-Ionization Regime With the Kramers-Henneberger Picture Je Hoi Mun, Hirofumi Sakai, Dong Eon Kim Subject: Physical Sciences, Acoustics Keywords: Time-dependent Schrödinger equation; Numerical method; Laser-matter interaction; Kramers-Henneberger; Time-dependent unitary transformation Time evolution operators of a strongly ionizing medium are calculated by a time-dependent unitary transformation (TDUT) method. The TDUT method has been employed in quantum mechanical system composed of discrete states. This method is especially helpful for solving molecular rotational dynamics in quasi-adiabatic regimes because the strict unitary nature of the propagation operator allows us to set the temporal step size large; a tight limitation on the temporal step size ($\delta t <<1$) can be circumvented by the strict unitary nature. On the other hand, in a strongly ionizing system where the Hamiltonian is not Hermitian, the same approach cannot be directly applied because it is demanding to define a set of field-dressed eigenstates. In this study, the TDUT method was applied to the ionizing regime using the Kramers-Henneberger frame, in which the strong-field-dressed discrete eigenstates are given by the field-free discrete eigenstates in a moving frame. Although the present work verifies the method for a one-dimensional atom as a prototype, the method can be applied to three-dimensional atoms, and molecules exposed to strong laser fields. Almost Global Stability of Nonlinear Switched System with Stable and Unstable Subsystems Aysegul Kivilcim, Ozkan Karabacak, Rafal Wisniewski Subject: Engineering, Automotive Engineering Keywords: switched systems, stable and unstable subsystems, Lyapunov density, average dwell time, mode-dependent average dwell time This paper presents sufficient conditions for almost global stability of nonlinear switched systems consisting of both stable and unstable subsystems. Techniques from the stability analysis of switched systems have been combined with the multiple Lyapunov density approach - recently proposed by the authors for the almost global stability of nonlinear switched systems composed of stable subsystems. By using slow switching for stable subsystems and fast switching for unstable subsystems lower and upper bounds for mode-dependent average dwell times are obtained. In addition to that, by allowing each subsystem to perform slow switching and using some restrictions on total operation time of unstable subsystems and stable subsystems, we have obtained a lower bound for an average dwell time. Exciton Coupling and Conformational Changes Impacting the Optical Properties of Metal Organic Frameworks Andreas Windischbacher, Luca Steiner, Ritesh Haldar, Christof Wöll, Egbert Zojer, Anne-Marie Kelterer Subject: Materials Science, Nanotechnology Keywords: metal organic frameworks; SURMOF; absorption; emission; time-dependent density functional theory; aggregation In recent years, the photophysical properties of crystalline metal-organic frameworks (MOFs) have become increasingly relevant for their potential application in light-emitting devices, photovoltaics, nonlinear optics and sensing. The availability of high-quality experimental data for such systems makes them ideally suited for a validation of quantum mechanical simulations, aiming at an in-depth atomistic understanding of photophysical phenomena. Here we present a computational DFT study of the absorption and emission characteristics of a Zn-based surface-anchored metal-organic framework (Zn-SURMOF-2) containing anthracenedibenzoic acid (ADB) as linker. Combining band-structure and cluster-based simulations on ADB chromophores in various conformations and aggregation states, we are able to provide a detailed explanation of the experimentally observed photophysical properties of Zn-ADB SURMOF-2: The unexpected (weak) red-shift of the absorption maxima upon incorporating ADB chromophores into SURMOF-2 can be explained by a combination of excitonic coupling effects with conformational changes of the chromophores already in their ground state. As far as the unusually large red-shift of the emission of Zn-ADB SURMOF-2 is concerned, based on our simulations, we attribute it to a modification of the exciton coupling compared to conventional H-aggregates, which results from a relative slip of the centers of neighboring chromophores upon incorporation in Zn-ADB SURMOF-2. The Photochemistry of Fe2(S2C3H6)(CO)6(µ-CO) and its Oxidized Form, Two Simple [FeFe]-Hydrogenase CO-Inhibited Models. A DFT and TDDFT Investigation Federica Arrigoni, Giuseppe Zampella, Luca De Gioia, Claudio Greco, Luca Bertini Subject: Chemistry, Analytical Chemistry Keywords: Metal-carbonyl complexes; [FeFe]-hydrogenases; density functional theory; time-dependent DFT; organometallic photochemistry FeIFeI Fe2(S2C3H6)(CO)6(µ-CO) (1a-CO) and its FeIFeII cationic species (2a+-CO) are the simplest model of the CO-inhibited [FeFe] hydrogenase active site, which is known to undergo CO photolysis within a temperature- dependent process whose products and mechanism are still a matter of debate. Using Density Functional Theory (DFT) and Time-Dependent Density Functional Theory (TDDFT) computations, the ground state and low-lying excited state potential energy surfaces (PESs) of 1a-CO and 2a+-CO have been explored aimed at elucidating the dynamics of the CO photolysis yielding Fe2(S2C3H6)(CO)6 (1a) and Fe2(S2C3H6)(CO)6+ (2a+), two simple models of the catalytic site of the enzyme. Two main results came out from these investigations. First, a-CO and 2a+-CO are both bound with respect to any CO dissociation with lowest free energy barriers around 10 kcal mol-1, suggesting that at least 2a+-CO might be synthetized. Second, focusing on the cationic form, we found at least two clear excited state channels along the PESs of 2a+-CO that are unbound with respect to equatorial CO dissociation. Possible Lattice-Like Medium for Electron Pairing in La2CuO4 Tiege Zhou Subject: Physical Sciences, Condensed Matter Physics Keywords: high temperature copper-oxide superconductors; time-dependent density functional theory; electron-pairing medium Real-time evolution of the electron densities under excitations in La2CuO4 was calculated by the time-dependent density functional theory (TDDFT). The author found, for the first time, under excitations, the electron cloud of Cu2+ changes obviously and the characteristic frequencies are 83 meV and 36 meV, respectively, for two different modes. The results are unexpected and close to that of lattice vibrations. The results show that the electron cloud of Cu2+ (just like the lattice) can be the electron-pairing medium in high temperature copper oxide superconductors. A New Method for Computing the Delay Margin for the Stability of Load Frequency Control Systems Ashraf Khalil, Ang Swee Ping Subject: Engineering, Electrical & Electronic Engineering Keywords: communication time delays; delay margin; delay dependent stability; load frequency control system; sweeping test The open communication is an exigent need for future power system where the time delay is unavoidable. In order to secure the stability of the grid, the frequency must remain within its limited range which is achieved through the load frequency control. The load frequency control signals are transmitted through communication networks which induces time delay that could destabilize the power systems. So, in order to guarantee the stability the delay margin should be computed. In this paper, we present a new method for calculating the delay margin in load frequency control systems. The transcendental time delay characteristics equation is transformed to frequency dependant equation. The spectral radius is used to find the frequencies at which the roots crosses the imaginary axis. The crossing frequencies are determined through the sweeping test and the binary iteration algorithm. A one-area load frequency control system is chosen as case study. The effectiveness of the proposed method has been proved through comparing with the most recent published methods. The method shows its merit with less conservativeness and less computations. The PI controller gains are preferable to be chosen large to reduce the damping, however, the delay margin decreases with increasing the PI controller gains. Far-from-Equilibrium Time Evolution between two Gamma Distributions Eun-jin Kim, Lucille-Marie Tenkès, Rainer Hollerbach Subject: Mathematics & Computer Science, Applied Mathematics Keywords: non-equlibrium; stochastic systems; langevin equation; fokker-planck equation; time-dependent PDFs; gamma distribution Many systems in nature and laboratories are far from equilibrium and exhibit significant fluc- tuations, invalidating the key assumptions of small fluctuations and short memory time in or near equilibrium. A full knowledge of Probability Distribution Functions (PDFs), especially time- dependent PDFs, becomes essential in understanding far-from-equilibrium processes. We consider a stochastic logistic model with multiplicative noise, which has gamma distributions as stationary PDFs. We numerically solve the transient relaxation problem, and show that as the strength of the stochastic noise increases the time-dependent PDFs increasingly deviate from gamma distributions. For sufficiently strong noise a transition occurs whereby the PDF never reaches a stationary state, but instead forms a peak that becomes ever more narrowly concentrated at the origin. The addition of an arbitrarily small amount of additive noise regularizes these solutions, and re-establishes the existence of stationary solutions. In addition to diagnostic quantities such as mean value, standard deviation, skewness and kurtosis, the transitions between different solutions are analyzed in terms of entropy and information length, the total number of statistically distinguishable states that a system passes through in time. Generalizations of the R-Matrix Method to the Treatment of the Interaction of Short Pulse Electromagnetic Radiation with Atoms Barry Schneider, Kathryn R Hamilton, Klaus Bartschat Subject: Physical Sciences, Atomic & Molecular Physics Keywords: B-spline R-matrix; R-matrix with time dependence; intense short-pulse extreme ultra14 violet radiation; time-dependent Schrdinger equation; Arnoldi-Lanczos propagation Since its initial development in the 1970's by Phil Burke and his collaborators, the R-matrix theory and associated computer codes have become the de facto approach for the calculation of accurate data for general electron-atom/ion/molecule collision and photoionization processes. The use of a non-orthonormal set of orbitals based on B-splines, now called the B-spline R-matrix (BSR) approach, was pioneered by Zatsarinny. It has considerably extended the flexibility of the approach and improved particularly the treatment of complex many-electron atomic and ionic targets, for which accurate data are needed in many modelling applications for processes involving low-temperature plasmas. Both the original R-matrix approach and the BSR method have been extended to the interaction of short, intense electromagnetic (EM) radiation with atoms and molecules. Here we provide an overview of the theoretical tools that were required to facilitate the extension of the theory to the time domain. As an example of a practical application, we show results for two-photon ionization of argon by intense short-pulse extreme ultraviolet radiation Updates on the CDK4/6 Inhibitory Strategy and Combinations in Breast Cancer Navid Sobhani, Alberto D'Angelo, Matteo Pittacolo, Giandomenico Roviello, Tobias Otto Subject: Medicine & Pharmacology, Oncology & Oncogenics Keywords: cyclin-dependent kinases; cyclin-dependent kinase 4 and 6 inhibitors; targeted therapies; breast cancer Breast Cancer (BC) is the second most common type of cancer worldwide and displays the highest cancer-related mortality among women worldwide. Targeted therapies have revolutionized the way BC has been treated in the last decades improving life expectancies of millions of women. Among the different molecular pathways that have been of interest for the development of targeted therapies are the Cyclin-Dependent Kinases (CDK). CDK inhibitors are a class of molecules that already exist in nature and those belonging to the INK4 protein family specifically inhibit the CDK4/6 proteins. CDK4/6 inhibitors specifically block the transition from the G1 to the S phase of the cell cycle by dephosphorylation of the retinoblastoma tumor suppressor protein. In the past four years CDK4/6 inhibitors palbociclib, ribociclib, and abemaciclib received their first FDA approval for the treatment of Hormone Receptor (HR)-positive and Human Epidermal growth factor Receptor 2 (HER2)-negative breast cancer after showing significant improvements in progression-free survival in the PALOMA-1, MONALEESA-2 and the MONARCH-2 randomized clinical trials, respectively. After the encouraging results from these clinical trials, CDK4/6 inhibitors have also been investigated in the other BC subtypes. In HER2-positive BC, combination of CDK4/6 inhibitors with HER2-targeted therapies showed promise in preclinical studies and their clinical evaluation is ongoing. Moreover, in triple-negative BC, CDK4/6 inhibitors efficacy has been investigated in combination with other targeted therapies or immunotherapies. This review summarizes the molecular background and clinical efficacy of CDK4/6 inhibitors as single agents or in combination with other targeted therapies for the treatment of BC. Future directions of ongoing clinical trials and predictive biomarkers will be further debated. Nonlocal Symmetries for Time-Dependent Order Differential Equations Andrei Ludu Subject: Mathematics & Computer Science, Applied Mathematics Keywords: time-dependent order of differentiation; fractional calculus; fractional derivative; differential equations; complex systems; Volterra integral equation; VODE; DODE; dynamical evolution A new type of ordinary differential equation is introduced and discussed, namely, the time-dependent order ordinary differential equations. These equations can be solved via fractional calculus and are mapped into Volterra integral equations of second kind with singular integrable kernel. The solutions of the time-dependent order differential equations smoothly deforms solutions of the classical integer order ordinary differential equations into one-another, and can generate or remove singularities. An interesting symmetry of the solution in relation to the Riemann zeta function and Harmonic numbers was also proved. On the Role of Cosmic Mass in Understanding the Relationships among Galactic Dark Matter, Visible Matter and Flat Rotation Speeds U.V.S. Seshavatharam, S. Lakshminarayana Subject: Physical Sciences, Astronomy & Astrophysics Keywords: Planck mass; Mach's principle; distance cosmic mass; galactic visible mass; galactic dark mass; galactic flat rotation speeds; time dependent reference mass; With reference to our recently proposed Planck Scale White Hole Cosmology (PS-WHC) or Flat Space Cosmology (PS-FSC), we make an attempt to quantify galactic dark matter and flat rotation speeds in terms of galactic visible matter and cosmic mass. Considering recently observed dwarf galaxies having very little dark matter and assuming a time dependent reference mass unit of $M_X\cong \left(\mbox{3.0 to 4.0}\right)\times 10^{38}$ kg, we suggest an empirical relation for galactic dark matter $M_d$ via galactic visible mass $M_v$ as,$M_d \cong \frac{M_v^{3/2}}{M_X^{1/2}}$. This relation helps in fitting flat rotation speeds starting from 8 km/sec (for Segue 2) to 500 km/sec (for UGC12591). Modifying MOND's galactic flat rotation speed relation with Hubble mass $M_0\cong \left(\frac{c^3}{2GH_0}\right)$ of the universe, ratio of galactic flat rotation speed $V_G$ to speed of light $c$ can be shown to be approximately $\frac{V_G}{c} \cong 0.5 \left(\frac{M_v}{M_0}\right)^{1/4}$. Considering the sum of galactic dark matter and visible matter, ratio of galactic flat rotation speed to speed of light can be shown to be approximately $\frac{V_G}{c}\cong 0.25 \left(\frac{M_v+M_d}{M_0}\right)^{1/4}$. With further study, dark matter's nature, effect and distribution can be understood in terms of visible matter's extended gravity and extended theories of gravity can be understood with 'distance cosmic mass' rather than the empirical 'minimum acceleration'. Overview on Induced Chirality in Magnetic Field Controlled Electro-Deposition and Induced Magnetic Moment Originating from Chiral Electrodes Claudio Fontanesi, Anup Kumar, Prakash Mondal Subject: Chemistry, Electrochemistry Keywords: Magnetoelectrochemistry; CISS; spin; chirality; spin-dependent electrochemistry Magneto-electrochemistry (MEC) is a unique paradigm in science, where electrochemical experiments are carried out as a function of an applied magnetic field, creating a new horizon of potential scientific and technological applications. Over the time, detailed understanding of this research domain was developed to identify and rationalize the possible effects exerted by a magnetic field on the various microscopic processes occurring in an electrochemical system, such as: electrolyte properties governed by charge-transfer process (electric conductivity, viscosity, and diffusivity), mass transfer, electrochemical kinetics and on the structure/quality of products formed either at the working electrode or in the electrochemical cell. Particularly, magnetic field controlled chiral architecture obtained from deposited metal, alloys and catalyst and their excellent enantio-recognition in experimental frame is highly appealing. Interestingly, Hall effect was also demonstrated in electrolytic medium via an impressive experimental technique which is being employed for further theoretical understanding in the field of magneto-electrochemical science. Later, a highly reproducible local temperature variation was observed in electrochemical electrolytes exposed to perpendicular magnetic and electric fields. However, until recent studies, none of the above mentioned reports considered the possibility of a spin-dependent related charge-transfer process. Recent experimental and theoretical studies reveal that electron's transmission through chiral molecules is spin-selective and this effect has been referred to as chiral-induced spin-selectivity (CISS) effect. The CISS effect pave the way for the building up of a system characterized by a net magnetic moment exploiting the spin-filtering ability of chiral molecules. This interplay between chirality and magnetism may shed light on fundamental scientific aspects underlying the enantio-recognition and highly efficient electron-transfer that occurs in biological process. A Comprehensive Analysis of Proportional Intensity-based Software Reliability Models with Covariates Siqiao Li, Tadashi Dohi, Hiroyuki Okamura Subject: Mathematics & Computer Science, Probability And Statistics Keywords: software reliability models; proportional intensity model; non-homogeneous Poisson process; time-dependent covariate; maximum likelihood estimation; goodness-of-fit performance; predictive performance This paper focuses on the so-called proportional intensity-based software reliability models (PI-SRMs), which are extensions of the common non homogeneous Poisson process (NHPP)-based SRMs, and describe the probabilistic behavior of software fault-detection process by incorporating the time-dependent software metrics data observed in the development process. Especially we generalize the seminal PI-SRM in Rinsaka, Shibata and Dohi (2006) by introducing eleven well-known fault-detection time distributions, and investigate their goodness-of-fit and predictive performances. In numerical illustrations with four data sets collected in real software development projects, we utilize the maximum likelihood estimation to estimate model parameters with three time-dependent covariates; test execution time, failure identification work and computer time-failure identification, and examine the performances of our PI SRMs in comparison with the existing NHPP-based SRMs without covariates. It is shown that our PI-STMs could give better goodness-of-fit and predictive performances in many cases. Temperature-Dependent Physical Characteristics and Varying Heat Effects on Nonlocal Rotating Nanobeams Due to Dynamic Load Ahmed E. Abouelregal, F. A. Mohammed, Mohamed V. Moustapha, Doaa Atta Subject: Materials Science, Nanotechnology Keywords: nonlocal nanobeam; rotation; thermoelasticity; temperature-dependent; varying load A theoretical nonlocal thermoelastic model for studying the effects of the thermal conductivity variability on a rotating nanobeam has been described in the present article. The theory of thermal stress is employed using the Euler–Bernoulli beam model and generalized heat conduction with phase lags. It is believed that the thermal conductivity of the current model varies linearly according to temperature. Due to variable harmonic heat, the considered nanobeam excited and was subjected to a time-varying exponential decay load. Using the Laplace transform process, the analytical solutions for displacement, deflection, thermodynamic temperature and bending moment of rotating nanobeams are provided in final forms and a numerical example has been taken to address the problem. A comparison of the stated results was displayed and additionally, the influences of non-local parameters and varying load were analyzed and examined. We also investigate how the linear changes in the temperature of physical properties can influence both the static and dynamic responses to the rotating nanobeam. Influence of Chiral Compounds on the Oxygen Evolution Reaction (OER) in the Water Splitting Process Mirko Gazzotti, Andrea Stefani, Marco Bonechi, Walter Giurlani, Massimo Innocenti, Claudio Fontanesi Subject: Chemistry, Electrochemistry Keywords: spin dependent electrochemistry; water splitting; nickel; chirality; OER Results are presented concerning the influence on the water splitting process of enantiopure tartaric acid present in bulk solution. Stainless steel and electrodeposited nickel are used as working electrode (WE) surface. The latter is obtained by electrodeposition on the two poles of a magnet. The influence and role played by the chiral compound in solution has been assessed by comparing the current values, in cyclic voltammetry (CV) experiments, recorded in the potential range at which oxygen evolution reaction (OER) occurs. In the case of tartaric acid and nickel WE a spin polarization of about 4 % is found. The use of the chiral environment (bulk solution) and ferromagnetic chiral Ni electrode allows for observing the OER at a more favourable potential: about 50 mV (i.e. a cathodic, less positive, shift of the potential at which the oxygen evolution is observed). An Anti-EpCAM Monoclonal Antibody (EpMab-37-mG2a-f) Exerts Antitumor Activity against Breast Cancer in Mouse Xenograft Model Teizo Asano, Hiroyuki Suzuki, Guanjie Li, Tomokazu Ohishi, Manabu Kawada, Takeo Yoshikawa, Tomohiro Tanaka, Mika K. Kaneko, Yukinari Kato Subject: Medicine & Pharmacology, Oncology & Oncogenics Keywords: EpCAM; breast cancer; antitumor activities; antibody‐dependent cellular cytotoxicity The epithelial cell adhesion molecule (EpCAM) is a stem cell and carcinoma antigen, which mediates cellular adhesion and proliferative signaling by the proteolytic cleavage. In contrast to low expression in normal epithelium, EpCAM is frequently overexpressed in various carcinomas, which correlates with poor prognosis. Therefore, EpCAM has been considered as a promising target for tumor diagnosis and therapy. Using the Cell-Based Immunization and Screening (CBIS) method, we previously established an anti‐EpCAM monoclonal antibody (EpMab-37; mouse IgG1, kappa). In this study, we investigated the antibody‐dependent cellular cytotoxicity (ADCC), complement‐dependent cytotoxicity (CDC), and an antitumor activity by a defucosylated mouse IgG2a-type of EpMab-37 (EpMab-37-mG2a-f) against an EpCAM‐expressing breast cancer cell line (BT-474). EpMab-37-mG2a-f recognized BT-474 cells with a moderate binding-affinity [a dissociation constant (KD): 2.9x10-8 M] by flow cytometry. EpMab-37-mG2a-f exhibited ADCC and CDC for BT-474 cells by murine splenocytes and complements, respectively. Furthermore, administration of EpMab-37-mG2a-f significantly suppressed the BT-474 xenograft tumor development compared with the control mouse IgG. These results indicated that EpMab-37-mG2a-f exerts antitumor activities against the BT-474 xenograft, and could provide valuable therapeutic regimen for the breast cancers. Prevalence of Anti-DENV IgG Among Routine Bangladeshi Blood Donors, and Strategies for the Future Ashraful Hoque, Kashfia Islam, Sushanta Kumar Basak, A.B.M. Al Mamun, Marufur Rahman Subject: Medicine & Pharmacology, General Medical Research Keywords: anti DENV IgM; IgG; Antibody-dependent enhancement; Cross-immunity Background: Dengue is the most common arthropod-borne sickness worldwide, impacting at least 50 million people each year. The dengue virus has four primary serotypes. Infection with one serotype confers homotypic immunity but not heterologous immunity, and secondary infections may be more severe. Although blood transfusions and organ donations have also been observed, the Aedes aegypti mosquito is the primary vector for the transmission of dengue. Infection causes a continuum of clinical illness, from asymptomatic infection to dengue fever, DHF, and dengue shock syndrome (DSS).Aim: To assess the presence of anti DENV IgG and anti DENV IgM antibodies specific to the four dengue serotypes in blood donor service donors and the importance of pre-donation screening in routine blood collection procedures.Method: 3 mL of peripheral venous blood from 507 blood donors was collected in tubes with BD vacutainer gel tube for serum separation after epidemiological records were reviewed. After that, serum was separated and tests were performed by SD Bioline Dengue Duo. Participants in the study completed a social and epidemiological questionnaire that contained information such as age, gender, and dengue diagnosis.Result: Out of the 507 blood samples that were taken, 473 (93.3%) came from male blood donors, while the remaining 34 (6.7%) belonged to female blood donors. The ratio of males to females is 13.91 to 1. The age range is 18–60 years, and the mean and standard deviation are both 27.7 and 6.5. 183 of the 507 samples produced anti DENV IgG positivity, while 324 did not. The ratio of positive to negative was 1.25:2.Conclusion: According to the findings of this study, quantitative methods for determining the presence of anti-dengue antibodies or detecting the dengue virus in blood donors in endemic areas should be devised in order to ensure the quality of blood transfusions. A Preliminary Investigation on Frequency Dependant Cues for Human Emotions Manish Kumar, Thushara D. Abhayapala, Prasanga Samarasinghe Subject: Physical Sciences, Acoustics Keywords: Emotion recognition; Emotion cues; Pure tone; Frequency dependent relationship The recent advances in Human-Computer Interaction and Artificial Intelligence have significantly increased the importance of identifying human emotions from different sensory cues. Hence, understanding the underlying relationships between emotions and sensory cues have become a subject of study in many fields including Acoustics, Psychology, Psychiatry, Neuroscience and Biochemistry. This work is a preliminary step towards investigating cues for human emotion on a fundamental level by aiming to establish relationships between tonal frequencies of sound and emotions. For that, an online perception test is conducted, in which participants are asked to rate the perceived emotions corresponding to each tone. The results show that a crossover point for four primary emotions lies in the frequency range of 417–440 Hz, thus consolidating the hypothesis that the frequency range of 432–440 Hz is neutral from human emotion perspective. It is also observed that the frequency dependant relationships between emotion pairs Happy—Sad, and Anger—Calm are approximately mirrored symmetric in nature. An Advax-adjuvanted Inactivated Cell-culture Japanese Encephalitis Vaccine Induces Broadly Neutralising Anti-flavivirus Antibodies and T-cell Immunity and Provides Single Dose Protection Tomoyoshi Komiya, Yoshikazu Honda-Okubo, Jeremy Baldwin, Nikolai Petrovsky Subject: Medicine & Pharmacology, General Medical Research Keywords: Japanese encephalitis; Vaccine, Flavivirus; Antibody-dependent enhancement; Advax; Adjuvant ccJE+Advax is an inactivated cell culture Japanese encephalitis (JE) vaccine formulated with Advax™, a novel polysaccharide adjuvant based on delta inulin. This vaccine has previously shown promise in murine and equine studies and the current study sought to better understand its mechanism of action and assess the feasibility of single dose vaccine protection. Mice immunised with ccJE-Advax had higher serum neutralisation titres than those immunised with ccJE alone or with alum adjuvant. ccJE+Advax induced extraordinarily broad cross-neutralising antibodies against multiple flaviviruses including West Nile virus (WNV), Murray Valley Encephalitis Virus (MVEV), St Louis Encephalitis virus (SLE) and Dengue-1 and -2 viruses. Notably, the DENV-2 cross-neutralising antibodies from ccJE+Advax immunised mice uniquely had no DENV-2 antibody dependent enhancement (ADE) activity, by contrast to high ADE activity seen with DENV-1 cross-reactive antibodies induced by mbJE or ccJE alone or with alum adjuvant. JEV-stimulated splenocytes from ccJE+Advax immunised mice showed increased IL-17 and IFN-γ production, consistent with a mixed Th1 and Th17 response, whereas ccJE-alum was associated with production of mainly Th2 cytokines. There is an ongoing lack of human vaccines against particular flaviviruses, including WNV, SLE and MVEV. Given its ability to provide single-dose JEV protection as well as to induce broadly neutralising antibodies free of ADE activity, ccJE+Advax vaccine could be highly useful in all situations where rapid protection is desirable but ADE needs to be avoided, e.g. during a local outbreak or for use in travellers or the military requiring rapid travel to JEV endemic regions. PPMaP: Reproducible and Extensible Open-Source Software for Plant Phenological Phase Duration Prediction and Mapping Henri E. Z. Tonnang, Ritter A. Guimapi, Bruce Anani, Dan Makumbi, Bester Mudereri, Tesfaye Balemi, Peter Craufurd Subject: Life Sciences, Other Keywords: plant development rate; temperature-dependent; landscape; multi-location trials Understanding the detailed timing of crop phenology and their variability enhances grain yield and quality by providing precise scheduling of irrigation, fertilization, and crop protection mechanisms. Advances in information and communication technology (ICT) provide a unique opportunity to develop agriculture-related tools that enhance wall-to-wall upscaling of data outputs from point-location data to wide-area spatial scales. Because of the heterogeneity of the worldwide agro-ecological zones where crops are cultivated, it is unproductive to perform plant phenology research without providing means to upscale results to landscape-level while safeguarding field-scale relevance. This paper presents an advanced, reproducible, and open-source software for plant phenology prediction and mapping (PPMaP) that inputs data obtained from multi-location field experiments to derive models for any crop variety. This information can then be applied consecutively at a localized grid within a spatial framework to produce plant phenology predictions at the landscape level. This software supports the development of process-oriented and temperature-driven plant phenology models by intuitively and interactively leading the user through a step-by-step progression to the production of spatial maps for any region of interest. Maize (Zea mays L.) was used to demonstrate the robustness, versatility, and high computing efficiency of the resulting modeling outputs of the PPMaP. The framework is implemented in R, providing a flexible and easy‐to‐use GUI interface. Since this allows appropriate scaling to the larger spatial domain, the software can effectively be used to determine the spatially explicit length of growing period (LGP) of any variety. Increased Zinc and Albumin but Lowered Copper in Children with Transfusion-dependent Thalassemia Zainab Alhillawi, Hussein Al-Hakeim, Shatha Moustafa, Michael Maes Subject: Medicine & Pharmacology, General Medical Research Keywords: Copper; transfusion-dependent thalassemia; zinc; oxidative stress; antioxidants; biomarkers Measurements of copper and zinc in transfusion-dependent thalassemia (TDT) show contradictory results.Aim of the study: To examine serum levels of these minerals in TDT in relation to iron overload indices and erythron variables. Methods: This study recruited 60 children with TDT and 30 healthy children aged 3-12 years old.Results: Zinc was significantly higher in TDT children than in control children, whilst copper and the copper to zinc ratio were significantly lowered in TDT. Serum zinc was significantly associated with the number of blood transfusions and iron overload variables (including serum iron and TS%) and negatively with erythron variables (including hemoglobin, mean corpuscular volume, mean corpuscular hemoglobin). Serum copper was significantly and negatively associated with the same iron overload and erythron variables. The copper to zinc ratio was significantly correlated with iron, TS%, ferritin, hemoglobin, mean corpuscular volume, and mean corpuscular hemoglobin. Albumin levels were significantly higher in TDT children than in control children. Conclusion: Our results suggest that the increase in zinc in children with TDT may be explained by iron loading anemia and hemolysis and the consequent shedding of high amounts of intracellular zinc into the plasma. Increased albumin levels and treatment with Desferral may further contribute towards higher zinc levels in TDT. We suggest that the elevations in zinc in TDT are a compensatory mechanism protecting against infection, inflammation, and oxidative stress. Previous proposals for prophylactic use of zinc supplements in TDT may not be warranted. Identifying Complex lncRNA/Pseudogene-miRNA-mRNA Crosstalk in Hormone-Dependent Cancers Dulari Jayarathna, Miguel E. Rentería, Emilie Sauret, Jyotsna Batra, Neha S. Gandhi Subject: Life Sciences, Genetics Keywords: hormone-dependent cancers; ceRNAs; lncRNAs; microRNAs; pseudogenes; multiple sensitivity correlation The discovery of microRNAs (miRNAs) has fundamentally transformed our understanding of gene regulation. The competing endogenous RNA (ceRNA) hypothesis postulates that not only messenger RNAs but also other RNA transcripts, such as long non-coding RNAs and pseudogenes, can act as natural miRNA sponges. These RNAs influence each other's expression levels by competing for the same pool of miRNAs through miRNA response elements on their target transcripts, thereby modulating gene expression and protein activity. In recent years, these ceRNA regulatory networks have gained considerable attention in cancer research. Several studies have identified cancer-specific ceRNA networks. Nevertheless, prior bioinformatic analyses have focused on long non-coding RNAs-associated ceRNA networks. Here, we identify an extended-ceRNA network (including both long non-coding RNAs and pseudogenes) shared across a group of four hormone-dependent (HD) cancers, i.e., prostate, breast, colorectal, and endometrial cancers, using data from The Cancer Genome Atlas (TCGA). We performed a functional enrichment analysis for differentially expressed genes in the shared ceRNA network of HD cancers, followed by a survival analysis to determine their prognostic ability. We identified two long non-coding RNAs, nine genes, and seventy-four miRNAs in the shared ceRNA network across four HD cancers. Among them, two genes and forty-one miRNAs were associated with at least one HD cancer survival. This study is the first to investigate pseudogene associated ceRNAs across a group of related cancers and highlights the value of this approach to understanding shared molecular pathogenesis in a group of related diseases. A Stepwise GIS Approach for the Delineation of River Valley Bottom within Drainage Basins Using a Cost Distance Accumulation Analysis Gasper L. Sechu, Bertel Nilsson, Bo V. Iversen, Mette B. Greve, Christen D. Børgesen, Mogens H. Greve Subject: Earth Sciences, Atmospheric Science Keywords: river valley bottom; GIS; cost distance accumulation; groundwater dependent ecosystems River valley bottoms have hydrological, geomorphological, and ecological importance and are buffers for protecting the river from upland nutrient loading coming from agriculture and other sources. They are relatively flat, low-lying areas of the terrain that are adjacent to the river and bound by increasing slopes at the transition to the uplands. These areas have under natural conditions, a groundwater table close to the soil surface. The objective of this paper is to present a stepwise GIS approach for the delineation of river valley bottom within drainage basins and use it to perform a national delineation. We developed a tool that applies a concept called cost distance accumulation with spatial data inputs consisting a river network and slope derived from a digital elevation model. We then used wetlands adjacent to rivers as a guide finding the river valley bottom boundary from the cost distance accumulation. We present results from our tool for the whole country of Denmark carrying out a validation within three selected areas. The results reveal that the tool visually performs well and delineates both confined and unconfined river valleys within the same drainage basin. We use the most common forms of wetlands (meadow and marsh) in Denmark's river valleys known as Groundwater Dependent Ecosystems (GDE) to validate our river valley bottom delineated areas. Our delineation picks about half to two-thirds of these GDE. However, we expected this since farmers have reclaimed Denmark's low-lying areas during the last 200 years before the first map of GDE was created. Our tool can be used as a management tool, since it can delineate an area that has been the focus of management actions to protect waterways from upland nutrient pollution. Construction of an Exposure-Pathway-Phenotype in Children with Depression due to Transfusion-Dependent Thalassemia: Results of (Un)supervised Machine Learning Hussein Al-Hakeim, Asawer Najm, Shatha Moustafa, Michael Maes Subject: Medicine & Pharmacology, Psychiatry & Mental Health Studies Keywords: transfusion-dependent thalassemia; depression; neuro-immune; inflammation; biomarkers; oxidative stress Transfusion dependent thalassemia (TDT) patients are treated with continued blood transfusions and show a higher prevalence of depression. TDT with consequent iron overload and inflammation is associated with increased severity of depressive symptoms in TDT children.Aim of the study: To construct a pathway-phenotype which combines iron overload and neuro-immune biomarkers with depressive symptom subdomains in TDT children.Methods: We measured iron status parameters (iron, ferritin, transferrin saturation percentage) and inflammatory (interleukin-1β and tumour necrosis factor-α) biomarkers in TDT (n=111) and healthy (n=53) children and analyzed the results using machine learning.Results: Cluster analysis separated TDT children with depression from those without depression and revealed two depressive subgroups one with low self-esteem and another with increased social-irritability scores. Exploratory factor analysis validated four depressive symptom dimensions as reliable constructs, namely key depressive, physiosomatic, lowered self-esteem and social-irritability dimensions. Partial Least Squares showed that 73.0% of the variance in a latent vector extracted from those four clinical subdomains, immune-inflammatory and iron overload biomarkers was explained by exposure variables including the number of blood transfusions and hospitalizations and use of deferoxamine. The exposure data, iron and immune biomarkers, and symptom subdomains are reflective manifestations of a single latent trait, which shows internal consistency reliability and predictive relevance.Conclusions: The nomological network combining exposure, pathways and behavioral phenome manifestations provides an index of overall severity and disease risk and, therefore, constitutes a new drug target, indicating that iron overload and immune activation should be targeted to treat depression due to TDT. Protein-Encoding RNA-to-RNA Information Transfer in Mammalian Cells: Principles of RNA-Dependent mRNA Amplification Vladimir Volloch Subject: Life Sciences, Molecular Biology Keywords: RNA-dependent amplification of mammalian mRNA; physiologically occurring intracellular PCR, iPCR; RNA-dependent RNA polymerase, RdRp; chimeric RNA; sense-strand RNA; antisense-strand RNA The transfer of protein-encoding genetic information from DNA to RNA to protein, a process formalized as the "Central Dogma of Molecular Biology", has undergone a significant evolution since its inception. It was amended to account for the information flow from RNA to DNA, the reverse transcription, and for the information transfer from RNA to RNA, the RNA-dependent RNA synthesis. These processes, both potentially leading to protein production, were initially described only in viral systems, and although RNA-dependent RNA polymerase activity was shown to be present, and RNA-dependent RNA synthesisfound to occur, in mammalian cells, its function was presumed to be restricted to regulatory. However, recent results, obtained with multiple mRNA species in several mammalian systems, strongly indicate the occurrence of protein-encoding RNA to RNA information transfer in mammalian cells. It can result in the rapid production of the extraordinary quantities of specific proteins as was seen in cases of terminal cellular differentiation and during cellular deposition of extracellular matrix molecules. A malfunction of this process may be involved in pathologies associated either with the deficiency of a protein normally produced by this mechanism or with the abnormal abundanceof a protein or of its C-terminal fragment. It seems to be responsible for some types of familial thalassemia and may underlie the overproduction of beta amyloid in sporadic Alzheimer's disease. The aim of the present article is to systematize the current knowledge and understanding of this pathway. The outlined framework introduces unexpected features of the mRNA amplification such as its ability to generate polypeptides non-contiguously encoded in the genome, its second Tier, a physiologically occurring intracellular polymerase chain reaction, iPCR, a Two-Tier Paradox and RNA Dark Matter. RNA-dependent mRNA amplification represents a new mode of genomic protein-encoding information transfer in mammalian cells. Its potential physiological impact is substantial, it appears relevant to multiple pathologies and its understanding opens new venues of therapeutic interference, it suggests powerful novel bioengineering approaches and its further rigorous investigations are highly warranted. Vitamin B12 May Inhibit RNA-Dependent-RNA Polymerase Activity of nsp12 from the SARS-CoV-2 Virus Naveen Narayanan, Deepak T. Nair Subject: Keywords: nsp12; RNA-dependent-RNA polymerase; SARS-CoV-2; inhibitor; vitamin B12 SARS-CoV-2 is the causative agent for the ongoing COVID19 pandemic, and this virus belongs to the Coronaviridae family. Like other members of this family, the virus possesses a positive-sense single-stranded RNA genome. The genome encodes for the nsp12 protein, which houses the RNA-dependent-RNA polymerase (RdRP) activity responsible for the replication of the viral genome. A homology model of nsp12 was prepared using the structure of the SARS nsp12 (6NUR) as a model. The model was used to carry out in silico screening to identify molecules among natural products, or FDA approved drugs that can potentially inhibit the activity of nsp12. This exercise showed that vitamin B12 (methylcobalamin) may bind to the active site of the nsp12 protein. A model of the nsp12 in complex with substrate RNA and incoming NTP showed that Vitamin B12 binding site overlaps with that of the incoming nucleotide. A comparison of the calculated energies of binding for RNA plus NTP and methylcobalamin suggested that the vitamin may bind to the active site of nsp12 with significant affinity. It is, therefore, possible that methylcobalamin binding may prevent association with RNA and NTP and thus inhibit the RdRP activity of nsp12. Overall, our computational studies suggest that methylcobalamin form of vitamin B12 may serve as an effective inhibitor of the nsp12 protein. An Assessment of Couple Stress Theories Ali R. Hadjesfandiari, Gary F. Dargush Subject: Physical Sciences, Applied Physics Keywords: couple stress theory; size-dependent mechanics; indeterminacies; curvature tensor; torsion tensor In this paper, we examine the mathematical and physical consistencies of the three primary couple stress theories: original Mindlin-Tiersten-Koiter couple stress theory (MTK-CST), modified couple stress theory (M-CST) and consistent couple stress theory (C-CST). As has been known for many years, MTK-CST suffers from some fundamental inconsistencies, such as the indeterminacy of the couple-stress tensor. Therefore, despite the fact that MTK-CST has a fundamental position in the evolution of size-dependent continuum mechanics, it is not a reliable theory within continuum mechanics, for example, in developing new size-dependent multi-physics formulations. We also observe that M-CST not only inherits all inconsistences from the original MTK-CST, but also suffers from new additional inconsistencies, such as the introduction of a new non-physical governing equation. These inconsistencies refute the claim of those who state that the couple-stress tensor may be chosen symmetric. Therefore, the apparent success of MTK-CST and M-CST in describing a size-effect for some problems, such as two-dimensional plate and beam bending, is not enough to justify these theories as suitable for general cases. In fact, the symmetric couple-stresses in M-CST create torsional or anticlastic deformation, not bending. On the other hand, C-CST, with a skew-symmetric couple-stress tensor, is the consistent continuum mechanics suitable for solving different size-dependent solid, fluid and multi-physics problems. Arbidol (Umifenovir): A Broad-spectrum Antiviral Drug that Inhibits Medically Important Arthropod-borne Flaviviruses Jan Haviernik, Michal Stefanik, Martina Fojtikova, Sabrina Kali, Noël Tordo, Ivo Rudolf, Zdenek Hubalek, Ludek Eyer, Daniel Ruzek Subject: Life Sciences, Virology Keywords: flavivirus; arbidol; umifenovir; antiviral activity; cytotoxicity; cell-type dependent antiviral effect Arthropod-borne flaviviruses represent human pathogens of global medical importance, against which no effective small molecule-based antiviral therapy is currently available. Arbidol (umifenovir) is a broad spectrum antiviral compound approved in Russia and China for prophylaxis and treatment of influenza. This compound showed activity against numerous DNA and RNA viruses. Its mode of action is based predominantly on the impairment of critical steps of virus-cell interaction. Here we demonstrate that arbidol possesses a micromolar inhibition activity (EC50 values ranging from 10.57 ± 0.74 to 19.16 ± 0.29 µM) in Vero cells infected with Zika virus, West Nile virus, and tick-borne encephalitis virus, three medically important representatives of arthropod-borne flaviviruses. Interestingly, no antiviral effect of arbidol is observed in porcine stable kidney cells (PS), human neuroblastoma cells (UKF-NB-6), human hepatoma cells (Huh-7 cells) indicating that the antiviral effect of arbidol is strongly cell-type dependent. Arbidol presents a significant increasing in cytotoxicity profiles when tested in various cell lines in the order: Huh-7 < HBCA < PS < UKF-NB-6 < Vero with CC50 values ranging from 18.69 ± 0.1 to 89.72 ± 0.19 µM. Antiviral activity and acceptable cytotoxicity profiles suggest that arbidol could be a promising candidate for further investigation as a potential therapeutic agent in treating flaviviral infections. A Polynomial Algorithm for Sequencing Jobs with Release and Delivery Times on Uniform Machines Nodari Vakhania, Frank Werner Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: scheduling; uniform machines; release time; delivery time; time complexity; algorithm We consider the problem of scheduling $n$ jobs with identical processing times and given release as well as delivery times on $m$ uniform machines. The goal is to minimize the makespan, i.e., the maximum full completion time of any job. This problem is well-known to have an open complexity status even if the number of jobs is fixed. We present a polynomial-time algorithm for the problem which is based on the earlier introduced algorithmic framework blesscmore (``branch less and cut more''). We extend the analysis of the so-called behavior alternatives developed earlier for the version of the problem with identical parallel machines and show how the earlier used technique for identical machines can be extended to the uniform machine environment if a special condition on the job parameters is imposed. The time complexity of the proposed algorithm is $O(\gamma m^2 n\log n)$, where $\gamma$ can be either $n$ or the maximum job delivery time $q_{\max}$. This complexity can even be reduced further by using a smaller number $\kappa<n$ in the estimation describing the number of jobs of particular types. However, this number $\kappa$ becomes only known when the algorithm has terminated. Temozolomide, Simvastatin and Acetylshikonin Combination Induces Mitochondrial Dependent Apoptosis in GBM Cells which is Regulated by Autophagy Sima Hajiahmadi, Shahrokh Lorzadeh, Rosa Iranpour, Saeed Karima, Masoumeh Rajabibazl, Zahra Shahsavari, Saeid Ghavami Subject: Life Sciences, Biochemistry Keywords: statin; natural compounds; Bcl2 family proteins; intrinsic apoptosis pathway; caspase dependent apoptosis Glioblastoma multiforme (GBM) is one of the deadliest cancers. Temozolomide (TMZ) is the most common chemotherapy used for GBM patients. Recently, combination chemotherapy strategies have more effective antitumor effects and focus on slowing down the development of chemotherapy resistance. A combination of TMZ and cholesterol lowering medications (statins) is currently under investigation in in vivo and clinical trials. In our current investigation, we have used a triple combination therapy of TMZ, Simvastatin (Simva), and Acetylshikonin (ASH) and investigated its apoptotic mechanism in GBM cell lines (U87 and U251). We used viability, apoptosis, reactive oxygen species (ROS), mitochondrial membrane potential (MMP), caspase-3/-7, acridine orange (AO) and immunoblotting autophagy assays. Our results showed that TMZ/Simva/ASH combination therapy significantly induced more apoptosis compared to TMZ, Simva, ASH, and TMZ/Simva treatments in GBM cells. Apoptosis via TMZ/Simva/ASH treatment induced mitochondrial damage (increase of ROS, decrease of MMP) and induced caspase-3/7 activation in both GBM cell lines. Compared to all single treatments and the TMZ/Simva treatment, TMZ/Simva/ASH significantly increased positive acidic vacuole organelles. We further confirmed that the increase of AVOs during the TMZ/Simva/ASH treatment was due to partial inhibition of autophagy flux (accumulation of LC3β-II and decrease in p62 degradation) in GBM cells. Our investigation also showed that TMZ/Simva/ASH-induced cell death was depended on autophagy flux as further inhibition of autophagy flux increased TMZ/Simva/ASH-induced cell death in GBM cells. Finally, our results showed that TMZ/Simva/ASH treatment potentially depends on an increase of Bax expression in GBM cells. Our current investigation might open new avenues for more effective treatment of GBM but further investigations are required for better identification of the mechanisms. Ellagic Acid Derivatives: Possible Drugs Against Metapneumovirus? Ekaterina Andreevna Artamonova, Azat Vadimovich Abdullatypov Subject: Life Sciences, Molecular Biology Keywords: metapneumovirus; molecular docking; phenolic compounds; glycosides; ellagic acid; RNA-dependent RNA-polymerase Human metapneumovirus is one of major causes of common cold among children, especially infants. Its key enzyme is RNA-dependent RNA-polymerase, which performs both replication and transcription, including capping and cap methylation. The goal of the work is to find possible inhibitors of RNA-dependent RNA-polymerase across the active compounds of Rosaceae plants. The candidates were selected by molecular docking to cap-transferring domain of RNA-polymerase (PDB ID: 4UCZ) in Autodock VINA. Among all the substances tested by docking, ellagic acid derivatives showed the most promising results (affinity values below -10 kcal/mol). Hence, they could be treated as possible candidate drugs against metapneumoviral infection after experimental examination. The main advantage of using these substances should be their low toxicity, which is quite uncommon for selective RNA polymerase inhibitors used in clinical practice. Occurrence of ellagic acid derivatives among the plants from Rosaceae family like raspberry could explain their effect during common cold. Pseudo-static Simplified Analysis Method of the Pile-liquefiable Soil Interaction Considering Rate-dependent Characteristics Xinlei Zhang, Zhanpeng Ji, Hongmei Gao, Zhihua Wang, Wenwen Li Subject: Engineering, Civil Engineering Keywords: soil liquefaction; pile-soil interaction; rate-dependent; simply analysis; influence factors analysis The lateral pressure generated by liquefied soil on pile is a critical parameter in the analysis of soil-pile interaction in liquefaction-susceptible sites. Previous studies have shown that liquefied sand behaves like a non-Newton fluid, and its effect on piles has rate-dependent properties. In this study, a simplified pseudo-static method for liquefiable soil-pile interaction analysis is proposed by treating the liquefied soil as a thixotropic fluid, which considers the rate-dependent behavior. The viscous shear force generated by the relative movement between the viscous fluid (whose viscosity coefficient varies with excess pore pressure and shear strain rate) and the pile was assumed to be the lateral load on the pile. The results from the simplified analysis show that the distribution of bending moment is in good agreement with experiments data. Besides, the effects of various parameters, including relative density, thickness ratio of non-liquefiable layer to liquefiable layer, and frequency of input ground motion, on the pile-soil rate-dependent interaction were discussed in detail. Dirac Oscillator in Dynamical Noncommutative Space Ilyas Haouam Subject: Physical Sciences, Mathematical Physics Keywords: Dynamical noncommutative space; τ -space; position-dependent noncommutativity; noncommutative space; Dirac oscillator In this paper, we address the energy eigenvalues of two-dimensional Dirac oscillator perturbed by dynamical noncommutative space. We derived the relativistic Hamiltonian of Dirac oscillator in dynamical noncommutative space ( τ -space), in which the space-space Heisenberg–like commutation relations and noncommutative parameter are position-dependent. Then used this Hamiltonian to calculate the first-order correction to the eigenvalues and eigenvectors, based on the second quantization and using the perturbation theory. It is shown that the energy shift depends on the dynamical noncommutative parameter τ . Knowing that with a set of two-dimensional Bopp-shift transformation, we mapped the noncommutative problem to the standard commutative one. Prognostic Significance of CKS2 and CD47 Expression in Patients With Gastric Cancer Who Underwent Radical Gastrectomy Yang zhou, Jing zeng, Haoran zhuang, wei zhou, keyan wu, weigan shen Subject: Life Sciences, Biochemistry Keywords: Gastric cancer; Cyclin-dependent protein kinase; Cluster of differentiation (CD) 47; Prognosis Objective: To investigate the protein expression levels of cyclin‑dependent kinase subunit 2 (CKS2) and cluster of differentiation (CD) 47 in gastric cancer (GC) and their clinical significances. Methods: A total of 126 GC patients who underwent radical resection were selected as study subjects. Additionally, 32 patients with benign gastric tumor, 42 patients with low-grade intraepithelial neoplasia (LGIEN), and 49 patients with high-grade intraepithelial neoplasia (HGIEN) who underwent surgery were selected as the control groups. Immunohistochemistry was used to detect the expression of CKS2 and CD47 in surgical specimens. We statistically analyzed the clinical significance of the expression of the two factors. Results: (1) The positivity rates for CKS2 in benign gastric tumor tissue, LGIEN tissue, HGIEN tissue, and GC tissue gradually increased, i.e., 6.3% (2/32), 30.9% (13/42), 38.8% (19/49), and 60.3% (76/126), respectively, and the positivity rates for CD47 were 18.8% (6/32), 38.1% (16/42), 46.9% (23/49), and 65.9% (83/126), respectively. (2) High expression of CKS2 and CD47 were associated with tumor diameter, Lauren classification, number of lymph node metastases, and TNM stage. In addition, the immunohistochemical scores for CKS2 and CD47 were positively correlated (r=0.625, P=0.000). (3) The median follow-up time of 126 patients was 46.5 months, and the overall survival rate was 40.5% (51/126). Survival analysis showed that compared with that in the CKS2 (-) group, the overall survival rate for patients in the CKS2 (+) group was significantly worse (25.0% vs 64.0%, 2=15.67, P=0.000) and that compared with the CD47 (-) group, the CD47 (+) group had significantly worse overall survival (30.1% vs 60.5%, 2=15.67, P=0.000). (4) The overall survival rates of CKS2(+)CD47(+) group, CKS2(+)CD47(-) group, CKS2(-)CD47(+) group, and CKS2 (-)CD47 (-) group were 20.0%(13/65), 58.3%(7/12), 57.1%(8/14), 65.7% (23/35), respectively, the prognosis of patients in CKS2(+)CD47(+) group was significantly poor. Conclusion: High expression levels of CKS2 and CD47 were closely related to the occurrence of GC and can be used as independent risk factors to assess the prognosis of patients. Using Potential Dependent Special Relativity, Gauss's Law, and Schrodinger Equation to Find Vacuum Quantized Energy and Elementary Particles Mass Zoalnoon Ahmed Abeid Allah Saad, Mubarak Dirar Abd-Alla Yagoubb, Mohamed Yahia Shirgawi Mohammed, Mashair Ahmed Mohammed Yousef Subject: Physical Sciences, General & Theoretical Physics Keywords: potential dependent special relativity; Gauss law; gravity; vacuum energy; Schrödinger equation; spherical symmetry Potential dependent special relativity and Gauss's law for the electric field have been used for gravity by assuming vacuum energy to be generated when the energy is a minimum useful expression for vacuum energy has been found. This expression shows that elementary particles are generated by gravity vacuum filling their hollow balls; using Schrödinger equation for spherically symmetric particles vacuum energy is quantized. Treating mass as vibrating spheres thus solving Schrödinger, coordinate harmonic oscillator energy relation has been found. Preprint TECHNICAL NOTE \| doi:10.20944/preprints202203.0166.v1 A Note on Novel Normal-Power Non-Linear Function Matthew Iwada Ekum Subject: Mathematics & Computer Science, Probability And Statistics Keywords: Bimodal Dependent Variable; Normal-Power; Non-Linear; Least Square Estimation; Economy-Tourism Model Regression models are mostly used in all fields of sciences for modelling the relationship between a dependent variable and independent variable(s). The least square method is often used to estimate the parameters in a linear model because it is the best linear unbiased estimator. These estimates can only be reliable if the assumption of normality is satisfied. In some cases the dependent variable might be bimodal and shows a non-linear relationship with the independent variable(s). In this case, a non-linear model should be used. In non-linear model, the standard errors are often obtained by linearizing the nonlinear function around the parameter, assuming central limit theorem. After the linearization, the least square parameter estimates are obtained. It should be noted that the error of the non-linear model is different from that of the transformed linear model. Thus, there is a need to transform back to the original non-linear model. In this note, a novel non-linear function was developed into a non-linear regression model, called Normal-Power model. The least square method was used to estimate the parameter of the transformed model. Its usefulness in regression model was demonstrated using real data of Nigeria Economy-Tourism model. Modeling Dengue Immune Responses Mediated by Antibodies: a Qualitative Study Afrina Andriani Sebayang, Hilda Fahlena, Vizda Anam, Damián Knopoff, Nico Stollenwerk, Maíra Aguiar, Edy Soewono Subject: Biology, Anatomy & Morphology Keywords: Within-host modeling; Dengue fever; immune response; antibodies; viral load; Antibody-Dependent Enhancement Dengue fever is a viral mosquito-borne infection, a major international public health concern. With 2.5 billion people at risk of acquiring the infection around the world, disease severity is influenced by the immunological status of the individual, seronegative or seropositive, prior to natural infection. Caused by four antigenically related but distinct serotypes, DENV-1 to DENV-4, infection by one serotype confers life-long immunity to that serotype and a period of temporary cross-immunity (TCI) to other serotypes. The clinical response on exposure to a second serotype is complex with the so-called Antibody-Dependent enhancement (ADE) process, a disease augmentation phenomenon when pre-existing antibodies to previous dengue infection do not neutralize but rather enhance the new infection, used to explain the etiology of severe disease. In this paper, we present a minimalistic mathematical model framework developed to describe qualitatively the dengue immunological response mediated by antibodies. Three models are analyzed and compared: i) primary dengue infection, ii) secondary dengue infection with the same (homologous) dengue virus and iii) secondary dengue infection with a different (heterologous) dengue virus. We explore the features of viral replication, antibody production, and infection clearance over time. The model is developed based on body cells and free virus interactions resulting in infected cells activating antibody production. Our mathematical results are qualitatively similar to the ones described in the empiric immunology literature, providing insights on the immunopathogenesis of severe disease. Results presented here are of use for future research directions to evaluate the impact of dengue vaccines. Evaluation of Thiol-dependent Enzymes on the Pharmacological Effects Induced by the Catalytically Active PLA2 from Bothrops jararacussu Marcos Hikari Toyama, Caroline R. C. Costa, Mariana Novo Belchor, Adeilso Bispo dos Santos Junior, Laila Lucyane Ferreira de Moraes, Airam Roggero dos Santos Silva, Marcos Antonio de Oliveira Subject: Medicine & Pharmacology, Allergology Keywords: Secretory Phospholipase A2, Bothrops jararacussu, Oxidative Stress, Edema, Myonecrosis and Thiol Dependent Antioxidant Background: Clinical cases reports with snake accidents show that venom bite induces increased oxidative stress including several markers of lipid peroxidation and other oxidative stress marker in plasma. Methods: The main findings of this work were performed with BthTx-II on paw edema of animals treated with the toxin and biochemical measurement of COX-2, PGE2, MDA and the effects of peroxiredoxin inhibitors on edema and myotoxicity were also evaluated. Results: The results show that edema and myotoxocity induced by PLA2 (BthTx-II) induces a strong mobilization of arachidonic acid and an increase in cellular oxidative stress as measured by increased malondialdehydo (MDA) concentration and protein carbonylation. Thus, these findings establish the strong link between oxidative stress, arachidonic acid mobilization and that these events may explain the presence of oxidative stress markers in snake-bitten patients. Experiments performed with animals previously treated with commercially purchased inhibitors showed enzymes such as thioredoxin (TXN), thioredoxin reductase (TXNRD) and other glutathione (GSH)-related antioxidant defenses could play an essential role controlling and defining the end of edema on the late phase of PLA2 BthTx-II-induced process. Conclusion. This study showed that thioate-dependent antioxidant enzymes play an important role in resolving the edema induced by BthTx-II. Structural Insights into Thermotoga maritima FtsH Periplasmic Domain on Substrate Recognition Jun Yop An, Humayun Sharif, Gil Bu Kang, Kyung Jin Park, Jung-Gyu Lee, Sukyeong Lee, Mi Sun Jin, Ji-Joon Song, Jimin Wang, Soo Hyun Eom Subject: Life Sciences, Biochemistry Keywords: ATP-dependent proteolysis, Non-native membrane proteins, Periplasmic domain, Crystal structure, Photosystem II. Prompt removal of misfolded membrane proteins and misassembled membrane protein complexes is essential for membrane homeostasis. However, the elimination of these toxic proteins from the hydrophobic membrane environment has high energetic barriers. Transmembrane FtsH is the only known ATP-dependent protease responsible for this task, unlike other well-studied soluble ATP-dependent proteases. The mechanisms by which FtsH recognizes, unfolds, translocates, and proteolyzes its substrates remain unclear. Here, we report the crystal structures of the Thermotoga maritima FtsH periplasmic domain (PD) in an associative trimeric state at a 1.5-1.95 Å resolution. We also describe the pH-dependent oligomerization states of the isolated PD using dynamic light scattering. These observations help us understand how FtsH recognizes membrane-anchored misfolded proteins. An Emergy-Based Hybrid Method for Assessing Sustainability of an Resource-Dependent Region Lulu Qu, Xueyi Shi, Chang Liu Subject: Biology, Other Keywords: sustainability; resource-dependent city; emergy analysis; IPAT (Human Impact Population Affluence Technology); Taiyuan As the natural resources are getting exhausted, the concept of sustainable development of region has received increasing attentions, especially for resource-dependent cities. In this paper an innovative method that emergy analysis and IPAT (Human Impact Population Affluence Technology) model were combined in order to analyze the quantitative relationship of economic growth and energy consumption and further to evaluate its overall sustainability level. Taiyuan, a traditional, resource-dependent city in China, is selected as the case study region. The main results show that total emergy of Taiyuan increased from 9.023× 1023 sej in 2007 to 9.116× 1023sej in 2014, with 38% reduction on non-renewable emergy and 125% growth on imported emergy. Regional emergy money ratio (RMB) was reduced by 48% from 5.31× 1013sej/$ in 2007 to 2.74× 1013sej/$ in 2014, indicating that the increasing speed of consuming resources and energy was faster than the increase of GDP, and that Taiyuan's money purchasing power declined. The lower emergy sustainability index (ESI) indicates that Taiyuan was explored and produced large quantities of mineral resources, which puts more stress on the environment as a consequence, and that this is not sustainable in the long run. The IPAT analysis demonstrates that Taiyuan sticks to the efforts of energy conservation and environmental protection, in order to promote regional sustainable development, it is necessary to take an integrated effort. Policy insights suggest that resourceful regions should improve include energy and resource efficiency, optimizing energy and resourceful structure. The Real Cause of Differential Aging in the Twin "paradox" Gordon Liu Subject: Physical Sciences, General & Theoretical Physics Keywords: Twin paradox; Relativity; Space-time; Time dilation; Differential aging Physicists have employed various approaches to solve the "paradox" and offered a consistent conclusion that the traveller twin is younger than the homebody twin. However, some authors attribute the cause of differential aging to acceleration, while others believe that acceleration should not be regarded as the source of differential aging, but frame switch is. So far there is no agreement on this issue. Actually, acceleration and frame switch should not be regarded as the source of differential aging. The author will introduce a thought experiment in which two very long spacecraft are moving in opposite directions at a speed close to the speed of light to discuss the real cause of differential aging. The author found that the real cause of differential aging in the twin "paradox" is because of the asymmetry of destination choice. People always choose their destinations in the universe rather than in spacecraft. The destinations are always stationary relative to the homebody twin and moving relative to the traveller twin. Once we choose a destination in a reference frame, the distance is the proper length in this reference frame, but the distance will contract in another moving reference frame, thus the recording time will be shorter. Addendum to "The VIT Transform Approach to Discrete-Time Signals and Linear Time-Varying Systems" Edward Kamen Subject: Engineering, General Engineering Keywords: VIT transform, discrete-time signals, linear time-varying systems This addendum contains clarifications and a sharpening of some of the results on the VIT transform framework developed in [1]. The focus is on the right-coefficient and left- coefficient forms of the transform, the extraction of a first-order term from a left polynomial fraction, and the application to linear time-varying systems. Energy Vector and Time Vector in the Dirac Theory Christian Rakotonirina Subject: Physical Sciences, Acoustics Keywords: Tunnelling time; helicity; time dilation; Dirac equation; superluminal velocity We have introduced a sign operator of energy, analogous to the operator helicity, but in the direction of what we call energy vector. However, this energy vector needs a time vector. To give physical senses to the components of such a time vector, we try to explain the time dilation in special relativity and try to relate the components of the time vector to the tunneling times when an electron crosses a potential barrier. Climate Change Impacts Assessment in Coastal Lagoons Using Available Modelling Tools Bruno Primo, Fernanda Achete, Sarith Mahanama, Marcus Thatcher, Mark Hemer, Sutat Weesakui, Trang Duong Subject: Earth Sciences, Oceanography Keywords: water quality; hydrodynamics; flushing time; residence time; downscaling; stratification Climate change such as sea level rise, change in temperature, precipitation, and storminess are expected to impact significantly coastal lagoons. The nature and magnitude of these impacts are uncertain. The objective of the research is to determine the climate change impacts on mixing and circulation at Songkhla lagoon, Thailand. Songkhla lagoon is the largest lagoonal water resource in Thailand and Southeast Asia. The lagoon is a combined freshwater and estuarine complex of high productivity which represents an extraordinary combination of environmental resources believed to be unique in the region. This work is part of a Climate Change impact assessment framework. It is the validation phase (step 5) of the framework applying a case study. Delft 3D was used to simulate CC scenarios in the climate downscaling models, part of the previous framework steps. These results were compared to the current conditions to determine the main changes in mixing and circulation in the coastal lagoon. Three indicators were applied to quantify the impacts: flushing time, salinity intrusion and stratification. The results suggest an increase in water velocities at the inlet in future scenarios and a decrease of flushing time. Salinity and stratification showed more complex changes in futures scenarios. Testing the Orientability of Time Mark Hadley Subject: Physical Sciences, General & Theoretical Physics Keywords: quantum theory; time orientability; time reversal; topology of spacetime A number of experimental tests of time orientability are described as well as clear experimental signatures from non time orientability (time reversal). Some tests are well known, while others are based on more recent theoretical work. Surprisingly, the results all suggest that time is not orientable at a microscopic level; even definitive tests are positive. At a microscopic level the direction of time can reverse and a consistent forward time direction cannot be defined. That is the conclusion supported by a range of well-known experiments. The conflict between quantum theory and local realism; electrodynamics with electric charges; and spin half transformation properties of fermions; can all be interpreted as evidence of time reversal. While particle-antiparticle annihilation provides a definitive test. It offers both a new view of space-time and an novel interpretation of quantum theory with the potential to unify classical and quantum theories. Osteocyte-Derived CaMKK2 Regulates Osteoclasts and Bone Mass in a Sex-Dependent Manner Through Secreted Calpastatin Justin N Williams, Mavis Irwin, Yong Li, Anuradha Valiyakambrath, Brett T Mattingly, Sheel Patel, Mizuho Kittaka, Rebecca N Collins, Nicholas Clough, Emma H Doud, Amber L Mosley, Teresita M Bellido, Angela Bruzzaniti, Lilian I. Plotkin, Jonathan C. Trinidad, William R Thompson, Lynda F. Bonewald, Uma Sankar Subject: Life Sciences, Cell & Developmental Biology Keywords: Extracellular calpastatin, Ca2+/ calmodulin (CaM)-dependent protein kinase kinase 2, osteocytes, osteoclasts, bone remodeling Calcium/calmodulin (CaM)-dependent protein kinase kinase 2 (CaMKK2) regulates bone remodeling through its effects on osteoblasts and osteoclasts. However, its role in osteocytes, the most abundant bone cell type, and the master regulator of bone remodeling, remains unknown. Here we report that the conditional deletion of CaMKK2 from osteocytes using Dentine matrix protein 1 (Dmp1)-8kb-Cre mice led to enhanced bone mass only in female mice owing to a suppression of osteoclasts. Conditioned media isolated from female CaMKK2-deficient osteocytes inhibited osteoclast formation and function in in vitro assays, indicating a role for osteocyte-secreted factors. Proteomics analysis revealed significantly higher levels of extracellular calpastatin, a specific inhibitor of calcium-dependent cysteine proteases calpains, in female CaMKK2 null osteocyte conditioned media, compared to media from female control osteocytes. Further, exogenously added non-cell permeable recombinant calpastatin domain I elicited a marked, dose-dependent inhibition of female wild-type osteoclasts and depletion of calpastatin from female CaMKK2-deficient osteocyte conditioned media reversed the inhibition of matrix resorption by osteoclasts. Our findings reveal a novel role for extracellular calpastatin in regulating female osteoclast function and unravel a novel CaMKK2-mediated paracrine mechanism of osteoclast regulation by female osteocytes. The Cationic Amphiphilic Drug Hexamethylene Amiloride Eradicates Bulk Breast Cancer Cells and Therapy-Resistant Subpopulations With Similar Efficiencies Anastasia L Berg, Ashley Rowson-Hodel, Michelle Hu, Michael Keeling, Hao Wu, Kacey VanderVorst, Jenny J Chen, Jason Hatakeyama, Joseph Jilek, Courtney A Dreyer, Madelyn R Wheeler, Ai-Ming Yu, Yuanpei Li, Kermit L Carraway Subject: Medicine & Pharmacology, Oncology & Oncogenics Keywords: breast cancer; cancer stem cell; therapy resistance; cationic amphiphilic drug; lysosome-dependent cell death The resistance of cancer cell subpopulations, including cancer stem cell (CSC) populations, to apoptosis-inducing chemotherapeutic agents is a key barrier to improved outcomes for cancer patients. The cationic amphiphilic drug hexamethylene amiloride (HMA) has been previously demonstrated to efficiently kill bulk breast cancer cells independent of tumor subtype or species, but acts poorly toward non-transformed cells derived from multiple tissues. Here we demonstrate that HMA is similarly cytotoxic toward breast CSC-related subpopulations that are resistant to conventional chemotherapeutic agents, but poorly cytotoxic toward normal mammary stem cells. HMA inhibits the sphere-forming capacity of FACS-sorted human and mouse mammary CSC-related cells in vitro, specifically kills tumor but not normal mammary organoids ex vivo, and inhibits metastatic outgrowth in vivo, consistent with CSC suppression. Moreover, HMA inhibits viability and sphere formation by lung, colon, pancreatic, brain, liver, prostate and bladder tumor cell lines, suggesting that its effects may be applicable to multiple malignancies. Mechanistically, HMA elicits the permeabilization of the limiting lysosomal membrane, a hallmark feature of the lysosome-dependent cell death pathway. Our observations expose a key vulnerability intrinsic to cancer stem cells, and point to novel strategies for the exploitation of cationic amphiphilic drugs in cancer treatment. Preprint BRIEF REPORT \| doi:10.20944/preprints202102.0110.v1 Zika E Glycan Loop Region and Guillain-Barré Syndrome-Related Proteins: A Possible Molecular Mimicry to be Taken in Account for Vaccine Development Lebeau Grégorie, Frumence Etienne, Turpin Jonathan, Hoarau Jean-jacques, Gadea Gilles, Krejbich Pascale, Despres Philippe, Wildriss Viranaicken Subject: Life Sciences, Biochemistry Keywords: ZIKV; Guillain-Barré Syndrome; Molecular Mimicry; Calcium Channel Voltage Dependent; Heat Shock Protein; Vaccine Neurological complications of infection by the mosquito-borne Zika virus (ZIKV) include Guillain-Barré syndrome (GBS), an acute inflammatory demyelinating polyneuritis. GBS was first associated with recent ZIKV epidemics caused by the emergence of ZIKV Asian lineage in South Pacific. Here, we hypothesize that ZIKV-associated GBS relates to a molecular mimicry between viral envelope E (E) protein and neural proteins involved in GBS. Analysis of ZIKV epidemic strains showed that glycan loop (GL) region of the E protein includes an IVNDT motif which is conserved in voltage-dependent L-type calcium channel subunit alpha-1C (Cav1.2) and Heat Shock 70 kDa protein 12A (HSP70 12A). Both VSCC-alpha 1C and HSP70 12A belong to protein families which have been associated with neurological autoimmune diseases in central nervous system. The purpose of our in silico analysis is to point out that IVNDT motif of ZIKV E-GL region should be taken in consideration for the development of safe and effective anti-Zika vaccines by precluding the possibility of adverse neurologic events including autoimmune diseases such as GBS. An iterative scheme for feature-based positioning using a weighted dissimilarity measured Caifa Zhou, Andreas Wieser Subject: Engineering, Other Keywords: weighted dissimilarity measure; feature-based indoor positioning; signals of opportunity; location-dependent standard deviation We propose an iterative scheme for feature-based positioning using a new weighted dissimilarity measure with the goal of reducing the impact of large errors among the measured or modeled features. The weights are computed from the location-dependent standard deviations of the features and stored as part of the reference fingerprint map (RFM). Spatial filtering and kernel smoothing of the kinematically collected raw data allow efficiently estimating the standard deviations during RFM generation. In the positioning stage, the weights control the contribution of each feature to the dissimilarity measure, which in turn quantifies the difference between the set of online measured features and the fingerprints stored in the RFM. Features with little variability contribute more to the estimated position than features with high variability. Iterations are necessary because the variability depends on the location, and the location is initially unknown when estimating the position. Using real WiFi signal strength data from extended test measurements with ground truth in an office building, we show that the standard deviations of these features vary considerably within the region of interest and are neither simple functions of the signal strength nor of the distances from the corresponding access points. This is the motivation to include the empirical standard deviations in the RFM. We then analyze the deviations of the estimated positions with and without the location-dependent weighting. In the present example the maximum radial positioning error from ground truth are reduced by 40% comparing to kNN without the weighted dissimilarity measure. Multiple Tensor Train Approximation of Parametric Constitutive Equations in Elasto-Viscoplasticity Clément Olivier, David Ryckelynck, Julien Cortial Subject: Engineering, Mechanical Engineering Keywords: parameter-dependent model; surrogate modeling; tensor-train decomposition; gappy POD; heterogeneous data; elasto-viscoplasticity This work presents a novel approach to construct surrogate models of parametric Differential Algebraic Equations based on a tensor representation of the solutions. The procedure consists in building simultaneously, for every output of the reference model, an approximation given in tensor-train format. A parsimonious exploration of the parameter space coupled with a compact data representation allows to alleviate the curse of dimensionality. The approach is thus appropriate when many parameters with large domains of variation are involved. The numerical results obtained for a nonlinear elasto-viscoplastic constitutive law show that the constructed surrogate model is sufficiently accurate to enable parametric studies such as the calibration of material coefficients. The Vestigial Esterase Domain of Haemagglutinin of H5N1 Avian Influenza A Virus: Antigenicity and Contribution to Viral Pathogenesis Zhiqiang Zheng, Subha Sankar Paul, Xiaobing Mo, Yu-Ren Adam Yuan, Yee-Joo Tan Subject: Life Sciences, Virology Keywords: influenza; neutralising antibodies; vestigial esterase; antibody dependent cell-mediated cytotoxicity; pH-induced conformational changes Initial attempts to develop monoclonal antibodies as therapeutics to resolve influenza infections focused mainly on searching for antibodies with the potential to neutralise the virus in vitro with classical haemagglutination inhibition and micro-neutralisation assays. This led to the identification of many antibodies that bind to the head domain of haemagglutinin (HA) which generally have potent neutralisation capabilities that block viral entry or viral membrane fusion. However, this class of antibodies has a narrow breadth of protection in that they are usually strain specific. This led to the emphasis on stalk targeting antibodies which are able to bind a broad range of viral targets that span across different influenza subtypes. Recently, a third class of antibodies targeting the vestigial esterase (VE) domain have been characterised. In this review, we describe the key features of neutralising VE targeting antibodies and compare them with head and stalk class antibodies. A study of controllability of impulsive neutral evolution integro-differential equations with state dependent delay in Banach space Dimplekumar Chalishajar, A. Anguraj, Kulandhivel Karthikeyan, Malar Ganeshan Subject: Mathematics & Computer Science, Applied Mathematics Keywords: Impulsive conditions, Controllability, Neutral evolution integrodi erential equa- tions, Resolvent operators, State dependent delay In this paper, we study the problem of controllability of impulsive neutral evolution integrodifferential equations with state dependent delay in Banach spaces. The main results are completely new and are obtained by using Sadovskii's fixed point theorem, theory of resolvent operators, and an abstract phase space. An example is given to illustrate the theory. Inconsistency of Time-symmetry Model Srečko Šorli, Štefan Čelan Subject: Physical Sciences, Acoustics Keywords: time; space; symmetry Can physical objects be in time-symmetry? Physical objects can only exist in a medium that has physical attributes, which means this medium is a type of energy. Is time energy? This article will show that time is not energy and there is no possibility that physical objects could be in time-symmetry. Physical objects only can be in symmetry in the time-invariant space in which they exist. In this perspective time measured with clocks is the result of the observer's measurement in the time-invariant space. The time-symmetry model is flawed. The Error induced by Using Representative Periods in Capacity Expansion Models Lina Reichenberg, Frederik Hedenus Subject: Engineering, Energy & Fuel Technology Keywords: electricity system models; time representation; time reduction methods; representative days Capacity Expansion Models (CEMs) are optimization models used for long-term energy planning on national to continental scale. They are typically computationally demanding, thus in need of simplification, where one such simplification is to reduce the temporal representation. This paper investigates how using representative periods to reduce the temporal representation in CEMs distorts results compared to a benchmark model of a full chronological year. The test model is a generic CEM applied to Europe, equipped with a novel formulation for storage in model versions with reduced temporal representation. We test the performance of reduced models at penetration levels of wind and solar of 90%. Three measures for accuracy are used: (i) system cost, (ii) total capacity mix and (iii) regional capacity. We find that: (i) the system cost is well represented (~5% deviation from benchmark) with as few as ten representative days, (ii) the capacity mix is in general fairly well (~20% deviation) represented with 50 or more representative days, and (iii) the regional capacity mix displays large deviations (>50%) from benchmark for as many as 250 representative days. We conclude that modelers should be aware of the error margins when presenting results on these three aspects. The Associations between Screen Time and Sleep Duration, and Body Mass Index (BMI) in under Five-Year-Old Children Hossein Sourtiji, Mehdi Rassafiani, Seyed Ali Hosseini, Mohammad Esmaeil Motlagh, Mehdi Noroozi Subject: Medicine & Pharmacology, Other Keywords: screen time; sleep duration; body mass index (BMI); time use Today, due to recent developments in technology, children devote plenty of time for screen viewing. However, its harmful effects are not yet clear. The purpose of present study was to examine the associations among screen viewing and sleep duration, and body mass index (BMI) in under-five years old children. This cross-sectional study was conducted with 322 under-five healthy children that were selected using multistage stratified cluster sampling method in 2017. The data that were gathered by time-use diary method were analyzed using Kolmogorov-Smirnov test, Spearman correlation tests, multiple linear regression analysis, one-way ANCOVA, two-way ANCOVA. There was a negative correlation between screen time and sleep duration (rs = -0.42, p = 0.00), positive correlation between screen time and BMI (rs = 0.38, p = 0.00) and sleep duration negatively correlated with BMI (rs = -0.22, p = 0.00). screen viewing was a predictive factor for both sleep duration (β = -0.26, p = 0.00) and BMI (β = -0.26, p = 0.00). screen viewing had a significant impact on sleep duration (4, 314) = 5.02, P = 0.001) and BMI (F (4, 314) = 1.16, P=0.298). Results of this study indicated that screen viewing is related to sleep duration and BMI in under-five children. furthermore, screen time has an impact on sleep duration and BMI scores of children. findings of our study suggest that sleep duration negatively is associated with BMI in under-five-year-old children. Structural Proteomics-Driven Targeted Design of Favipiravir-Binding Site in The RdRp of SARS-CoV-2 Unravels Susceptible Hotspots and Resistance Mutations Aditya K. Padhi, Jagneshwar Dandapat, Vladimir N. Uversky, Timir Tripathi Subject: Life Sciences, Biochemistry Keywords: Drug resistance; nsp12; protein design; fitness; RNA-dependent RNA polymerase; resistance mutations; SARS-CoV-2. Favipiravir is a broad-spectrum inhibitor of viral RNA-dependent RNA polymerase (RdRp) currently being used to manage COVID-19 in several countries. By acting as a substrate for RdRp, favipiravir gets incorporated into the nascent viral RNA and prevents strand extension. A high mutation rate of SARS-CoV-2 RdRp may facilitate antigenic drift as an answer to the host immune response, thereby generating resistance of virus to favipiravir. Therefore, it is extremely crucial to predict potential mutational sites in the RdRp and the emergence of structural modifications contributing to drug resistance. Here, we used high-throughput interface-based protein design to generate >100,000 designs and identify mutation hotspot residues in the favipiravir-binding site of RdRp. Several mutants had lower binding affinities to favipiravir, out of which hotspot residues with a high propensity to undergo positive selection were identified. The results showed that the designs retained an average of 97 to 98% sequence identity, suggesting that SARS-CoV-2 can develop favipiravir resistance with just a few mutations. Notably, we observed that out of 134 mutations predicted designs, 63 specific mutations were already present in the CoV-GLUE database, thus attaining ~47% correlation match with the clinical sequencing data. The findings improve our understanding of the potential signatures of adaptation in SARS-CoV-2 against favipiravir and management of COVID-19. Furthermore, they can help develop exhaustive strategies for robust antiviral design and discovery. Acute Low-intensity Treadmill Running Induces Intestinal Glucose Transporters via GLP-2 in Mice Kai Aoki, Takuji Suzuki, Fang Hui, Takuro Nakano, Koki Yanazawa, Masato Yonamine, Shinichiro Fujita, Takehito Sugasawa, Yasuko Yoshida, Naomi Omi, Yasushi Kawakami, Kazuhiro Takekoshi Subject: Life Sciences, Biochemistry Keywords: low intensity exercise; intestine; sodium-dependent glucose transporter; glucose transporter 2; glucagon like peptide 2 Exercise affects various organs. However, its effects on nutrient digestion and absorption in the intestinal tract are not well understood. A few studies have reported that exercise training in-creases the expression of carbohydrate digestion and absorption molecules. Exercise was also shown to increase the concentration of blood glucagon like peptide-2(GLP-2), which regulates carbohydrate digestion and absorption in small intestinal epithelium. Therefore, we investigated the effects of exercise on intestinal digestion and absorption molecules and the levels of GLP-2. 6-wk-old of male mice were divided into 2 groups; sedentary (SED) and low-intensity exercise (LEx). LEx mice were required to run on a treadmill (12.5 m/min, 60 min), whereas SED mice rested. All mice were euthanized 1 h after exercise or rest and plasma, jejunum, ileum, and colon were sampled. Samples were analyzed using EIA and immunoblotting. The levels of plasma GLP-2 and the expression of the GLP-2 receptor, sucrase-isomaltase (SI), and glucose transporter (GLUT2) in the jejunum were increased in LEx group. We showed that acute low-intensity exer-cise affects the intestinal carbohydrate digestion and absorption molecules via GLP-2. Our results suggest that exercise might provide new benefits to the small intestine for people with intestinal frailty. Nsp7 and Spike Glycoprotein of SARS-CoV-2 Are Envisaged as Potential Targets of Vitamin D and Ivermectin Jhimli Dasgupta, Udayaditya Sen, Abhisek Bakshi, Abhijit Dasgupta, Krishnendu Manna, Chinmay Saha, Rajat K. De, Satinath Mukhopadhyay, Nitai P. Bhattacharyya Subject: Life Sciences, Virology Keywords: SARS-CoV-2; Vitamin D; Ivermectin; RNA-dependent-RNA polymerase; Spike glycoprotein; Knowledge based docking COVID-19 has emerged as deadly pandemic worldwide with no vaccine or suitable antiviral drugs to prevent or cure the disease. Because of the time-consuming process to develop new vaccines or antiviral agents, there has been a growing interest in repurposing some existing drugs to combat SARS-CoV-2. Vitamin D is known to be protective against acute respiratory distress syndrome (ARDS), pneumonia and cytokine storm. Recently it has been used as a repurposed drug for the treatment of H5N1 virus-induced lung injury. Circumstantial evidences indicate that people with low level of vitamin D are more susceptible to SARS-CoV-2. Although, vitamin D was suggested to interfere with viral replication, its interaction with any SARS-CoV-2 protein is unexplored yet. Beside this, ivermectin, a well-known anti-parasitic agent, exhibits potent anti-viral activities in vitro against viruses such as HIV-1 and dengue. Very recently, ivermectin has been found to reduce viral load of SARS-CoV-2 in vitro. We have analyzed available structures of SARS-CoV-2 proteins to identify probable binding partner(s) of vitamin D and ivermectin through knowledge-based docking studies and figured out possible implication of their binding in SARS-CoV-2 infection. Our observations suggest that the non-structural protein nsp7 possesses a potential site to house 25-hydroxyvitamin D3 (VDY) or the active form of Vitamin D, calcitrol. Binding of vitamin D with nsp7 likely to hamper the formation of nsp7-nsp8 complex which is required to bind with RNA dependent RNA polymerase (RdRP), nsp12 for optimal function. On the other hand, potential binding site of ivermectin has been identified in the S2 subunit of trimeric spike(S) glycoprotein of SARS-CoV-2. We propose that deeply inserted mode of ivermectin binding at three inter-subunit junctions may restrict large scale conformational changes of S2 helices which is necessary for efficient fusion of viral and host membrane. Our study, therefore, opens up avenues for further investigations to consider vitamin D and ivermectin as potential drugs against SARS-CoV-2. Presenting Different Time Steps, at the Start of Inflation, Using Kiefer Density Matrix, for the Use of an Inflaton, in Determining Different Conceivable Time Intervals for Time Flow Analysis Andrew W Beckwith Subject: Physical Sciences, Acoustics Keywords: Minimum scale factor; cosmological constant; space-time bubble; Arrow of time We are using the book "Towards Quantum Gravity with an article by Claus Kiefer as to a quantum gravity interpretation of the density matrix in the early universe. The density matrix we are using is a one loop approximation, with inflaton value and potential terms, like V(phi) using the Padmanabhan values one can expect if the scale factor is a ~ a(Initial) times t ^ gamma , from early times . In doing so, we isolate out presuming a very small initial time step candidates initial time values which are from a polynomial for time values due to the Kiefer Density value. Parisian Time of Reflected Brownian Motion With Drift on Rays Angelos Dassios, Junyi Zhang Subject: Mathematics & Computer Science, Algebra & Number Theory Keywords: Brownian motion; Parisian time; exact simulation; real-time gross settlement system In this paper, we study the Parisian time of a reflected Brownian motion with drift on a finite collection of rays. We derive the Laplace transform of the Parisian time using a recursive method, and provide an exact simulation algorithm to sample from the distribution of the Parisian time. The paper is motivated by the settlement delay in the real-time gross settlement (RTGS) system. Both the central bank and the participating banks in the system are concerned about the liquidity risk, and are interested in the first time that the duration of settlement delay exceeds a predefined limit, we reduce this problem to the calculation of the Parisian time. The Parisian time is also crucial in the pricing of Parisian type options; to this end, we will compare our results with the existing literature. Methods for Large-Scale Time-Triggered Network Scheduling Francisco Pozo, Guillermo Rodriguez-Navas, Hans Hansson Subject: Engineering, Industrial & Manufacturing Engineering Keywords: Real-Time Networks; Scheduling; Time-Triggered; SMT Solvers; Cyber-Physical Systems Future cyber-physical systems may extend over broad geographical areas, like cities or regions, thus requiring the deployment of large real-time networks. A strategy to guarantee predictable communication over such networks is to synthesize an offline time-triggered communication schedule. However, this synthesis problem is computationally hard (NP-complete), and existing approaches do not scale satisfactorily to the required network sizes. This article presents a segmented offline synthesis method which substantially reduces this limitation, being able to generate time-triggered schedules for large hybrid (wired and wireless) networks. We also present a series of algorithms and optimizations that increase the performance and compactness of the obtained schedules while solving some of the problems inherent to segmented approaches. We evaluate our approach on a set of realistic large-size multi-hop networks, significantly larger than those considered in the existing literature. The results show that our segmentation reduces the synthesis time up to two orders of magnitude. Irreversibility as Thermodynamic Time Charles C. Hwang Subject: Physical Sciences, Other Keywords: time; availability; irreversibility; time dilation; biological clock; metabolic efficiency; telomere; mitochondria In Newtonian mechanics, time as well as space are perceived as absolute entities. In 2 Einstein's special relativity, time is frame dependent. Time is also affected by gravitational field 3 and as the field varies in space, time also varies throughout space. In the present article, a 4 thermodynamic-based time is investigated. The entity is called "irreversibility", which is generated 5 when availability (also known as exergy) is destroyed. Since each thermodynamic system may 6 generate different amount of irreversibility, this quantity is system dependent. The time's arrow is 7 automatically satisfied, since irreversibility generation always proceeds in one direction (toward 8 future). We have demonstrated that, like common time, irreversibility is frame dependent, and 9 affected by gravity in the similar manner as the common time. For this reason, we propose to 10 assign the entity irreversibility of the system as thermodynamic time. A possible application of the 11 thermodynamic time is an interpretation and managing of the aging of biological systems. The 12 metabolic efficiency is related to the irreversibility of the chemical processes and affect the aging of 13 the system. Our sensation of time-flow may be attributed to the flow of availability and destruction 14 of it through the living system. It is shown by other authors that entropy generation (equivalent to 15 irreversibility) is a parameter for the human life span. Since the thermodynamic time is based on a 16 concept of thermodynamics that is universal, further applications to other subjects, such as biological 17 clock, telomere, and cosmology are possible. An Entropy-based Approach for Evaluating Travel Time Predictability Based on Vehicle Trajectory Data Tao Xu, Xiang Li Subject: Earth Sciences, Geoinformatics Keywords: travel time predictability; multiple entropy; travel time series; vehicle trajectory data With the great development of intelligent transportation systems (ITS), travel time prediction has attracted the attentions of many researchers and a large number of prediction methods have been developed. However, as an unavoidable topic, the predictability of travel time series is the basic premise for travel time prediction has received less attention than the methodology. Based on the analysis of the complexity of travel time series, this paper defines travel time predictability to express the probability of correct travel time prediction and proposes an entropy-based method to measure the upper bound of travel time predictability. Multiscale entropy is employed to quantify the complexity of travel time series, and the relationships between entropy and the upper bound of travel time predictability are presented. Empirical studies are made with vehicle trajectory data in an express road section. The effectiveness of time scales, tolerance, and series length to entropy and travel time predictability are analysis, and some valuable suggestions about the accuracy of travel time predictability are discussed. Finally, the comparisons between travel time predictability and actual prediction results from two prediction models, ARIMA and BPNN, are conducted. Experimental results demonstrate the validity and reliability of the proposed travel time predictability. Field Equations in C4 Space-Time Dimitris Mastoridis, K. Kalogirou Subject: Physical Sciences, General & Theoretical Physics Keywords: general relativity; geometric uni cation; dark matter-energy; mass geometrisation; complex space-time; symplectic space-time; extended space-time We explore the field equations in a 4-d complex space-time, in the same way, that general relativity does for our usual 4-d real space-time, forming this way, a new "general relativity" in C4 space-time, free of sources. Afterwards, by embedding our usual 4-d real space-time in C4 space-time, we describe geometrically the energy-momentum tensor Tμν as the lost geometric information of this embedding. We further give possible explanation of dark eld and dark energy. KERRA, Mixed Medicinal Plant Extracts, Inhibits SARS-CoV-2 Targets Enzymes and Feline Corona Virus Supaphorn Seetaha, Phatcharin Khamplong, Panatda Wanaragthai, Thitinan Aiebchun, Siriluk Ratanabunyong, Sucheewin Krobthong, Yodying Yingchutrakul, Jatuporn Rattanasrisomporn, Kiattawee Choowongkomon Subject: Medicine & Pharmacology, General Medical Research Keywords: COVID-19 pandemic; KERRA; SARS-CoV-2 main protease; RNA-dependent RNA polymerase; anti-FIPV activity The COVID-19 pandemic affects all parameters, especially health care professionals, drugs and medical supplies. The KERRA is a mixed medicinal plant capsule that is used for the treatment of patients with high fever with food and drug administration approved by FDA Thailand. Recently, KERRA showed quicker recovery for COVID-19 patients. Therefore, it is possible that some ingredients in KERRA could inhibit SARS-CoV-2. In this study, two important replication-related enzymes in SARS-CoV-2, a main protease and an RNA-dependent RNA polymerase (RdRp), were used to study the effect of KERRA. The results showed that KERRA inhibited the SARS-CoV-2 main protease and SARS-CoV-2 RdRp with IC50 values of 49.91 ± 1.75 ng/mL and 36.23 ± 5.23 µg/mL, respectively. KERRA displayed no cytotoxic activity on macrophage cells at concentrations lower than 1 mg/mL and exhibited anti-inflammatory activity. Additionally, KERRA was against a feline coronavirus (feline infectious peritonitis [FIP]) infection with an EC50 value of 134.3 g/mL. This study supports the potential use of KERRA as a candidate drug for COVID-19. Usefulness of a Concept Called Autonomous Selection Idan S. Solon Subject: Biology, Other Keywords: extended evolutionary synthesis; inheritance of acquired characters; stress-induced mutagenesis; fitness-dependent sex; horizontal gene transfer Here, I introduce a concept called autonomous selection to refer to a source of selection that is part of the individuals upon which it acts. The concept is motivated by a set of phenomena with the following characteristics: Natural selection shaped a variant (e.g., gene, epigenetic mark, or combination thereof) to act in a manner that reduces the frequency of one or more heritable traits of the individual in which it is located if those traits are detrimental to individual or group fitness. Phenomena with these characteristics are peculiar to traditional evolutionary theory but have been identified rather frequently in recent decades. They are also relevant to adaptive evolution: By reducing the frequency of a trait detrimental to fitness, the variant accelerates the evolution of adaptations, which allows its holders to adapt better to constantly changing environments. The variant is shaped by (natural) selection, but also does (autonomous) selection. Several phenomena with these characteristics have been invoked by proponents of the extended evolutionary synthesis (EES). The concept of autonomous selection helps resolve some of the controversy surrounding the EES: EES proponents call attention to the incompleteness of contemporary theory, emphasizing individuals' processes that influence which adaptations those individuals evolve. I argue for the special importance of individuals' processes that do not just influence those individuals' adaptations, but also accelerate the adaptive evolution of those individuals. All known phenomena that fit this description are examples of autonomous selection. Other phenomena raised by EES proponents do not meet this threshold. Research on Retailer Pricing Based on Extended Regret Theory in E-commerce Environment Ge Qiu Subject: Social Sciences, Econometrics & Statistics Keywords: Retailers' Optimal Pricing Strategy; Expected Utility Theory (EUT); Regret Theory; Regret Reference Point; Price-dependent Demand Based on the Expected Utility Theory and Regret Theory, the Extended Regret Theory (ERT) is proposed in this paper to study the optimal pricing strategy of retailers in e-commerce environment. Taking the diversity of sales channels and the uncertainty of consumers in e-commerce environment into consideration, author of the paper designs an extended regret utility function which comprehensively considers both pessimistic and optimistic attitudes of decision makers in retailing industry to describe their regret-avoidance behavior. According to the sensitivity analysis, it is found that the optimal retail price decreases as the consumer price sensitivity coefficient increases, yet does not show variation with changes of the consumers pessimism degree. Moreover, the optimal retail price(s) obtained under EUT, ERT and combination of EUT and ERT represent the same. Phosphorylation-Dependent Inhibition of Akt1 Nileeka Balasuriya, McShane McKenna, Xuguang Liu, Shawn S. C. Li, Patrick O'Donoghue Subject: Life Sciences, Biochemistry Keywords: genetic code expansion, protein kinase B, phosphoinositide dependent kinase 1 (PDK1), phosphoseryl-tRNA synthetase (SepRS), tRNASep Akt1 is a proto-oncogene that is over active in most cancers. Akt1 activation requires phosphorylation at Thr308; phosphorylation at Ser473 further enhances catalytic activity. Akt1 activity is also regulated via interactions between the kinase domain and the N-terminal auto-inhibitory pleckstrin homology (PH) domain. As it was previously difficult to produce Akt1 in site-specifically phosphorylated forms, the contribution of each activating phosphorylation site to auto-inhibition was unknown. Using a combination of genetic code expansion and in vivo enzymatic phosphorylation, we produced Akt1 variants containing programmed phosphorylation to probe the interplay between Akt1 phosphorylation status and the auto-inhibitory function of the PH domain. Deletion of the PH domain increased the enzyme activity for all three phosphorylated Akt1 variants. For the doubly phosphorylated enzyme, deletion of the PH domain relieved auto-inhibition by 295-fold. We next found that phosphorylation at Ser473 provided resistance to chemical inhibition by Akti-1/2 inhibitor VIII. The Akti-1/2 inhibitor was most effective against pAkt1T308 and showed 4-fold decreased potency with Akt1 variants phosphorylated at Ser473. The data highlight the need to design more potent Akt1 inhibitors that are effective against the doubly phosphorylated and most pathogenic form of Akt1. Real Time Fault Location Using the Retardation Method Moneer Nabwani, Michael Suleymanov, Yosef Pinhasi, Asher Yahalom Subject: Engineering, Electrical & Electronic Engineering Keywords: fault location; real time A new method for short circuit fault location is proposed based on instantaneous signal measurement and its derivatives, and is based on the retardation phenomena. The difference between the times in which a signal is registered in two detectors is used to locate the fault. Although a description of faults in terms of a lumped circuit is useful for elucidating the methods for detecting the fault. This description will not suffice to describe the fault signal propagation hence a distributed models is needed which is given in terms of the telegraph equations. Those equations are used to derive a transmission line transfer function, and an exact analytical description of the short circuit signal propagating in the transmission line is obtained. The analytical solution was verified both by numerical simulations and experimentally. Time, Causality, and Entropy Amrit Šorli, Štefan Čelan Subject: Physical Sciences, General & Theoretical Physics Keywords: time; causality; entropy; observer How to build an optimal model where three terms "time, causality, and entropy" will be interrelated in a most correct way? This task has a semantic and physical aspect. We give in this article the solution that is based only on elementary perception. In physics, we experience time with our senses as the duration of material change running in space. This fact is the standpoint for our model where causality is only a principle, it is not a physical actuality and entropy runs only in space and not in time. Time is merely a duration of entropy increasing and is entering existence when measured by the observer. Chlorella sp Microalgae Suspensions—Rheological Behaviour Analyzes at Different Culture Times Daniela Guimarães, Messias Silva, Carla Loures Subject: Engineering, Energy & Fuel Technology Keywords: Chlorella; rheology; culture time Taking into account the growing interest in microalgae to be used as raw material for biodiesel production, this research is aimed at analyzing the rheological behaviour of microalgae suspensions (Chlorella sp) at different culture times under eight different conditions (temperature, salinity and CO2, NO3 and PO4 levels) in order to estimate the energy demands of each step, with the purpose of optimizing a continuous feed tubular bioreactor construction. For each condition, it was calculated the biomass and oil yields, so as to correlate these results with rheological parameters. The suspension results indicated that the microalgae Chlorella sp is a non-Newtonian material with dilatant characteristics; the processing time hardly exerted an influence on the rheograms of the suspension of the microalgae Chlorella sp, except for the simultaneous conditions of low salinity and low CO2 content; NO3 and PO4 contents and the amount of supplements influenced the rheological parameters of the suspension of the microalgae Chlorella sp, when in low concentration of CO2 and low salinity levels. Using Machine Learning to Improve Performance of a Low-Cost Real-Time Stormwater Control Measure Marzieh Khosravi, Sara Baghalian, Michael Burns, Andrea L. Welker, Michael Golub Subject: Engineering, Civil Engineering Keywords: Real-Time; Stormwater; Control Measure; Low-Cost; Machine Learning; Time-series; LSTM The alteration of natural land cover to impervious surfaces during development increases stormwater runoff. Stormwater Control Measures (SCMs) are used to manage water quantity and enhance water quality by restoring the hydrologic cycle altered by development. Often, SCMs have an outflow pipe to handle overflows or to manage the release of water detained when infiltration is not possible. Traditionally, these are static controls (e.g. a small orifice is used to restrict the volume of outflow), however, these systems can be improved by instituting real-time controls (RTC). RTC improve the functionality of SCMs by dynamically controlling outflows to adjust to environmental conditions. A major impediment to the widespread implementation of RTC is the high cost of installation and operation. This study utilized machine learning methods to develop a forecasting approach for the implementation of low-cost RTC that were implemented on a programmable gate of the outlet structure of a multi-stage basin in southeastern Pennsylvania. The goals were to decrease the peak flow exiting the basin during rain events, increase the volume of water detained, decrease the number of overtopping events, maintain healthy vegetation in the basin, and protect the downstream vegetation from erosion. Multiple popular data science algorithms were evaluated including multiple linear regression and long short-term memory. These algorithms were used with a dataset, which consisted of four years of historical sensor data, collected in 5-minute intervals, to train models to predict water levels to optimize operations. The accuracy of 30 models with three different methods of handling missing values were compared. A long short-term memory model configured with a 30-minute lead time produced the best results. Having an approximate same lag time of 30 minutes for the contributing drainage area of the SCM provided a sufficient RTC functioning period to improve the performance of the outlet structure. Hybrid Algorithm for Anomaly Removal in Time Series Data Mining Abdul Razaque, Marzhan Abenova, Munif Alotaibi, Bandar Alotaibi, Hamoud Alshammari, Salim Hariri, Aziz Alotaibi Subject: Engineering, Control & Systems Engineering Keywords: time series; NMP algorithm; anomalies; data mining; similarities in time series; clustering Time series data are significant and are derived from temporal data, which involve real numbers representing values collected regularly over time. Time series have a great impact on many types of data. However, time series have anomalies. We introduce hybrid algorithm named novel matrix profile (NMP) to solve the all-pairs similarity search problem for time series data. The proposed NMP inherits the features from two state-of-the art algorithms: similarity time-series automatic multivariate prediction (STAMP), and short text online microblogging protocol (STOMP). The proposed algorithm caches the output in an easy-to-access fashion for single- and multidimensional data. The proposed NMP algorithm can be used on large data sets and generates approximate solutions of high quality in a reasonable time. The proposed NMP can also handle several data mining tasks. It is implemented on a Python platform. To determine its effectiveness, it is compared with the state-of-the-art matrix profile algorithms i.e., STAMP and STOMP. The results confirm that the proposed NMP provides higher accuracy than the compared algorithms. Pattern Matching Trading System Based on the Dynamic Time Warping Algorithm Sang Hyuk Kim, Hee Soo Lee, Hanjun Ko, Seung Hwan Jeong, Hyun Woo Byun, Kyong Joo Oh Subject: Mathematics & Computer Science, Information Technology & Data Management Keywords: dynamic time warping; pattern matching trading system; time series data; sliding window The futures market plays a significant role in hedging and speculating by investors. Although various models and instruments are developed for real-time trading, it is difficult to realize profit by processing and trading a vast amount of real-time data. This study proposes a real-time index futures trading strategy that uses the pattern of KOSPI 200 index futures time series data. We construct a pattern matching trading system (PMTS) based on a dynamic time warping algorithm that recognizes patterns of market data movement in the morning and determines the afternoon's clearing strategy. We adopt 13 and 27 representative patterns and conduct simulations with various ranges of parameters to find optimal ones. Our experimental results show that the PMTS provides stable and effective trading strategies with relatively low trading frequencies. Investor communities that have sustained financial markets are able to make more efficient investments by using the PMTS. In this sense, the system developed in this paper is a sustainable investment technique and helps financial markets achieve efficient sustainability. Comparing Markov Chain Samplers for Molecular Simulation Robert D. Skeel, Youhan Fang Subject: Physical Sciences, Atomic & Molecular Physics Keywords: Markov chain Monte Carlo; stochastic dynamics integrators; decorrelation time; integrated autocorrelation time Markov chain Monte Carlo sampling propagators, including numerical integrators for stochastic dynamics, are central to the calculation of thermodynamic quantities and determination of structure for molecular systems. Efficiency is paramount, and to a great extent, this is determined by the integrated autocorrelation time (IAcT). This quantity varies depending on the observable that is being estimated. It is suggested that it is the maximum of the IAcT over all observables that is the relevant metric. Reviewed here is a method for estimating this quantity. For reversible propagators (which are those that satisfy detailed balance), the maximum IAcT is determined by the spectral gap in the forward transfer operator, but for irreversible propagators, the maximum IAcT can be far less than or greater than what might be inferred from the spectral gap. This is consistent with recent theoretical results (not to mention past practical experience) suggesting that irreversible propagators generally perform better if not much better than reversible ones. Typical irreversible propagators involve a parameter controlling the mix of ballistic and diffusive movement. To gain insight into the effect of the damping parameter for Langevin dynamics, its optimal value is obtained here for a multidimensional quadratic potential energy function. On the Wave Solutions of Conformable Fractional Evolution Equations Alper Korkmaz Subject: Mathematics & Computer Science, Applied Mathematics Keywords: time fractional KdV equation; time fractional Burgers equation; Kudryashov method; wave solution The exact solutions in the wave form are derived for the time fractional KdV and the time fractional Burgers' equations in conformable fractional derivative sense. The fractional variable change using the fundamental properties of the conformable derivative reduces both equations to some nonlinear ODEs. The predicted solution is assumed to be a finite series form of a function satisfying a particular first-order ODE whose solution contains an exponential function in the denominator. The solutions are represented in the explicit forms and illustrated by some choices of the parameters for various fractional orders of the equations. Sine-Gordon Expansion Method for Exact Solutions to Conformable Time Fractional Equations in RLW-Class Alper Korkmaz, Ozlem Ersoy Hepson, Kamyar Hosseini, Hadi Rezazadeh, Mostafa Eslami Subject: Keywords: Sine-Gordon Expansion Method; conformable time fractional RLW equation; conformable time fractional modified RLW equation; conformable time fractional symmetric-RLW equation The Sine-Gordon expansion method is implemented to construct exact solutions some conformable time fractional equations in Regularized Long Wave(RLW)-class. Compatible wave transform reduces the governing equation to classical ordinary differential equation. The homogeneous balance procedure gives the order of the predicted polynomial-type solution that is inspired from well-known Sine-Gordon equation. The substitution of this solution follows the previous step. Equating the coefficients of the powers of predicted solution leads a system of algebraic equations. The solution of resultant system for coefficients gives the necessary relations among the parameters and the coefficients to be able construct the solutions. Some solutions are simulated for some particular choices of parameters. Who is More Likely to Complete the Appointments, and What Factors Determine the Appointment Wait Time? Wafa K. Alnakhi, Heba Mamdouh, Hamid Y. Hussain, Mohamed S. Mudawi, Gamal M. Ibrahim, Amal J. Al Balushi, Noora Al Zarooni, Abdulsalam Elnaeem, Nabil Natafgi Subject: Materials Science, Other Keywords: Telehealth; telemedicine; Dubai Health Authority (DHA); wait time; turn-around time; appointment completion Background: Digital health significantly affects healthcare delivery. Moreover, empirical studies on the utilization of telehealth in Dubai are limited. Accordingly, this study examines the utilization of telehealth services in Dubai Health Authority (DHA) facilities and the factors associated with telehealth appointment completion and turnaround time. Methods: This cross-sectional study examines patients who used telehealth services in DHA from 2020 through 2021 using 241,822 records. A binary logistic regression model was constructed to investigate the association between appointment turnaround time as a dependent variable and patient and visit characteristics as independent variables. Results: Of the total scheduled telehealth visits, more than three-quarter (78.55%) were completed. Older patients, non-Emiratis, patients who had their visits in 2020, patients who had video visits, and those who sought family medicine as a specialty had a shorter turn-around time to receive their appointment. Conclusions: This study identifies several characteristics associated with the turn-around time. Moreover, technological improvements focusing on specialties that can readily be addressed through telehealth and further research in this domain will improve service provision and support building an evidence base. A simple Spectral Observer Lizeth Torres, Javier Jiménez-Cabas, José Francisco Gómez-Aguilar, Pablo Pérez-Alcazar Subject: Engineering, Control & Systems Engineering Keywords: Signal Processing; Fourier Series; State Observer; Short Time Fourier Transform; Time-Frequency Analysis The principal aim of a spectral observer is twofold: the reconstruction of a signal of time via state estimation and the decomposition of such a signal into the frequencies that make it up. A spectral observer can be catalogued as an online algorithm for time-frequency analysis because is a method that can compute on the fly the Fourier transform (FT) of a signal, without having the entire signal available from the start. In this regard, this paper presents a novel spectral observer with an adjustable constant gain for reconstructing a given signal by means of the recursive identification of the coefficients of a Fourier series. The reconstruction or estimation of a signal in the context of this work means to find the coefficients of a linear combination of sines a cosines that fits a signal such that it can be reproduced. The design procedure of the spectral observer is presented along with the following applications: (1) the reconstruction of a simple periodical signal, (2) the approximation of both a square and a triangular signal, (3) the edge detection in signals by using the Fourier coefficients, (4) the fitting of the historical Bitcoin market data from 2014-12-01 to 2018-01-08 and (5) the estimation of a input force acting upon a Duffing oscillator. To round out this paper, we present a detailed discussion about the results of the applications as well as a comparative analysis of the proposed spectral observer vis-à-vis the Short Time Fourier Transform (STFT), which is a well-known method for time-frequency analysis. Synthesis and Thrombin, Factor Xa and U46619 Inhibitory Effects of Non-amidino and Amidino N2-Thiophenecarbonyl- and N2-Tosylanthranilamides Soo Hyun Lee, Wonhwa Lee, Nguyen Thi Ha, Il Soo Um, Jong-Sup Bae, Eunsook Ma Subject: Chemistry, Other Keywords: N2-Arylcarbonyl/sulfonylanthranilamides; Prothrombin time; Activated partial thromboplastin time; Thrombin; Factor Xa; U46619 Thrombin (factor IIa) and factor Xa (FXa) are key enzymes at the junction of the intrinsic and extrinsic coagulation pathways and are the most attractive pharmacological targets for the development of novel anticoagulants. Twenty non-amidino N2-thiophencarbonyl- and N2-tosyl anthranilamides 1-20 and six amidino N2-thiophencarbonyl- and N2-tosylanthranilamides 21-26 were synthesized and evaluated prothrombin time (PT) and activated partial thromboplastin time (aPTT) using human plasma at concentration 30 μg/mL in vitro. From these results, compounds 5, 9, and 21-23 were selected to study the further antithrombotic activity. The anticoagulant properties of 5, 9, and 21-23 significantly exhibited a concentration-dependent prolongation of in vitro PT and aPTT, in vivo bleeding time, and ex vivo clotting time. These compounds concentration-dependently inhibited the activities of thrombin and FXa and inhibited the generation of thrombin and FXa in human endothelial cells. In addition, data showed that 5, 9, and 21-23 significantly inhibited thrombin catalyzed fibrin polymerization and mouse platelet aggregation and inhibited platelet aggregation induced U46619 in vitro and ex vivo. N-(3'-Amidinophenyl)-2-((thiophen-2''-yl)carbonyl amino)benzamide (21) was most active. Explicit Exact Solutions to Some One Dimensional Conformable Time Fractional Equations Subject: Mathematics & Computer Science, Applied Mathematics Keywords: modified Kudryashov method; conformable time fractional RLW-Burgers Equation; conformable time fractional potential KdV Equation; conformable time fractional CRWP equation; conformable derivative The exact solutions of some conformable time fractional PDEs are presented explicitly. The modified Kudryashov method is applied to construct the solutions to the conformable time fractional Regularized Long Wave-Burgers (RLW-Burgers, potential Korteweg-de Vries (KdV) and clannish random walker's parabolic (CRWP) equations. Initially, the predicted solution in the finite series of a rational form of an exponential function is substituted to the ODE generated from the conformable time fractional PDE by using wave transformation. The coefficients used in the finite series are determined by solving the algebraic system derived from the coefficients of the powers of the predicted solution. Normative Values of Skeletal Muscle Contractile Parameters and Lateral Symmetry in Artistic and Rhythmic Gymnasts Mitija Samardžija Pavletić, Almir Atiković, Ekrem Čolakhodžić, Selma Sijerčić, Emilija Petković, Amra Nožinović Mujanović Subject: Biology, Other Keywords: tensiomyography; gymnastics; contraction time; asymmetry Introduction: The purpose of this study was to determine the normative values of muscles' contractile properties, lateral symmetry, and the impact of aging on muscle contractility in gymnastics. Materials and Methods: A survey of 81 athletes from different disciplines was undertaken: MAG (n = 26), WAG (n = 28), and RG (n = 27). The athletes' average age was 15.41 ± 5.03 years. We try to establish the normative values for contraction time (muscle pairs) in gymnastics for Slovenian athletes for ten skeletal muscles. Results: Athletes' age affects contractility in a negative way. Differences between the duration of contractility and age were found in all disciplines: m. BF (r = 0.48, p < 0.001), m. TB (r = 0.37, p < 0.013), m. ES (r = 0.17, p < 0.025), m. VL (r = 0.36, p < 0.00) and m. VM (r = 0.40, p < 0.000) at a statistical significance of p < 0.05. Conclusions: A comparison between the left and right sides shows little asymmetry in WAG and that the occurrence of injuries is in the middle range. In RG we see a bigger deviation, which could trigger the emergence of pain or injury in m. BF (13%) and m. GL (14.5%), but in MAG the deviation is greater in m. BB (12%), m. BF (11%) and m. GM (13%). Anomaly Detection over Time Series Data Zhenyi Zhu Subject: Mathematics & Computer Science, Other Keywords: Anomaly Detection; Time Series; EWMA The anomaly detection task is very important in computer science. And there are a lot of anomaly detection methods. Different from some thresholding methods, some unsupervised methods could make us get more accurate and faster result, which is the object of the project. In this paper, I tried to use EWMA and some other methods in two datasets: Webank time consuming indicators dataset and AIOps Challenge dataset. The paper consists nine parts: background of the project, related work, description of algorithms, implementation details, experimental setup and data sets used, experimental results and discussion, future directions, reference and meeting notes. Solving the 'Two Times Problem' With an Information Gathering and Utilizing System (IGUS) Ronanld P. Gruber, Carlos Montemayor, Richard A. Block Subject: Physical Sciences, General & Theoretical Physics Keywords: IGUS; flow of time; passage There is a long standing 'two times problem' in that a satisfactory reconciliation between the time of physics and that of psychology has not been realized. A partial solution to the past/present/future phenomenon has been successfully given by the Hartle information gathering and processing system (IGUS) view. That model IGUS robot is enhanced here for the entire 'two times problem' to deal with not only the temporal experiences of the flow of time but also those of manifest time. A dualistic robot is proposed which has a veridical system of temporal experiences that are compatible with various spacetime cosmologies. It also has an illusory system of corresponding temporal experiences. This dualistic IGUS robot was made possible by discovering temporal experience within the brain that correspond to those of physics. The dualistic theory suggests that the veridical system, as a result of evolution, begets the illusory system to enhance behavioral adaptation. Thus, there is just one fundamental physical time which the brain does, indeed, possess and then enhances with illusory counterparts. Therefore, there should no longer be a need to reify illusory temporal experiences as modern spacetime cosmologies tend to do. Physical time already resides within human time. A Procustes's Procedure for Obtaining Divergences Leonardo Riveaud, Mateos Diego, Pedro Walter Lamberti Subject: Physical Sciences, Acoustics Keywords: Divergences; Kernels; Time series analysis Divergences have become a very useful tool for measuring similarity (or dissimilarity) between probability distributions. Depending on the field of application a more appropriate measure may be necessary. In this paper we introduce a family of divergences we call gamma-divergences. They are based on the convexity property of the functions that generate them. We demonstrate that these divergences verify all the usually required properties, and we extend them to weighted probability distribution. We investigate their properties in the context of kernel theory. Finally, we apply our findings to the analysis of simulated and real time series. What is the Shape of Geographical Time-Space? A Three Dimensional Model made of Curves and Cones Alain L'Hostis, Farouk Abdou Subject: Social Sciences, Accounting Keywords: Geographical Time-Space; Transport; Cartography We propose a geographical time-space model extending time-space relief cartography introduced by Mathis and L'Hostis [,,,]. The novelty of the model resides in the use of cones to describe the terrestrial surface instead of graph faces, and in the use of curves instead of broken segments for edges. The approach lies a the intersection of two domains involving graphic representation: cartography, and three dimensional computer graphics. We implement the model on the Chinese space. The Chinese geographical time-space of the reference year 2006 is produced by the combination and the confrontation of the fast air transport system and of the 7.5 times slower road transport system. Slower, short range flights are represented as curved lines above the earth surface with longer length than the geodesic, in order to account for a slower speed. The very steep slope of cones expresses the relative difficulty of crossing terrestrial time-space, as well as the comparably extreme efficiency of long-range flights for moving between cities. Finally, the whole image proposes a coherent representation of the geographical time-space where fast city to city transport is combined with slow terrestrial systems that allow to reach any location. Linear Regression Analysis for Time-Point Datasets Janardan Patil, Li Len, Abhinav Bharat, Xi Li Subject: Keywords: regression; time point data; modelling In this paper, we present a relapse based demonstrating way to deal with investigate various arrangement MTC information. A commonplace use of this displaying approach incorporates three stages: first, define a model that approximates the connection between quality articulation and trial factors, with boundaries consolidated to address the exploration premium; second, utilize least-squares and assessing condition methods to gauge boundaries and their relating standard blunders; third, register test insights, P-qualities and NFD as proportions of factual criticalness. The benefits of this methodology are as per the following. To begin with, it tends to the exploration interest in a particular, precise way, and maximally uses all the information and other important data. Second, it represents both orderly and irregular varieties related with the information, and the consequences of such examination give not just quality explicit data applicable to the exploration objective, yet additionally its dependability, in this way helping agents to settle on better choices for subsequent investigations. Third, this methodology is truly adaptable, and can undoubtedly be stretched out to different sorts of MTC considers or other microarray explores by detailing various models dependent on the test plan of the investigations. Face Detection with a portable architecture in Real Time Francesco De Feo, Pasquale De Luca Subject: Mathematics & Computer Science, Artificial Intelligence & Robotics Keywords: Face detection; Drone; Real Time Nowadays, security is a top priority. In fact, biometrics uses cutting-edge technologies to identify terrorists and criminals. But the practice of distinguishing humans based on intrinsic physical or behavior traits goes back thousands of years. With the widespread use of computers in the late 20th century, new possibilities for digital biometrics emerged and new technologies were generously used. Among these, we remember high resolution security video cameras and drones. So, the aim of the present project is to study and explain the features of these technologies, especially the ones of the the Phantom 4 Pro+ aircraft and analyze its operating methods in order to identify human faces during live streaming of videos. For this purpose, it will be used Paul Viola and Michael Jones' face detection algorithm, which includes Haar features and cascade classifiers to identify faces, eyes and ears of an individual. Travelling Surface Plasmons with Interference Envelope and A Vision for Time Crystals Amir Djalalian-Assl Subject: Physical Sciences, General & Theoretical Physics Keywords: surface plasmons; time crystal; thin film The influence of the film thickness and the substrate's refractive index on the surface mode at the superstrate is an important study step that may help clearing some of the misunderstandings surrounding their propagation mechanism. A single sub-wavelength slit perforating a thin metallic film is among the simplest nanostructure capable of launching Surface Plasmon Polaritons on its surrounding surface when excited by an incident field. Here, the impact of the substrate and the film thickness on surface waves is investigated. When the thickness of the film is comparable to its skin depth, SPP waves from the substrate penetrate the film and emerge from the superstrate, creating a superposition of two SPP waves, that leads to a beat interference envelope with well-defined loci which are the function of both the drive frequency and the dielectric constant of the substrate/superstrate. As the film thickness is reduced to the SPP's penetration depth, surface waves from optically denser dielectric/metal interface would dominate, leading to volume plasmons that propagate inside the film at optical frequencies. Interference of periodic volume charge density with the incident field over the film creates charge bundles that are periodic in space and time. Galactic Symmetry Richard Oldani Subject: Physical Sciences, Astronomy & Astrophysics Keywords: time; clocks; quantum mechanics; relativity theory; conjugate variables; non-inertial; space-time linearity; energy Differences between the quantum mechanical and relativistic concepts of time are explained by applying the strong equivalence principle to the electron in an atomic clock. The resulting clock model calls for the microscopic equations of motion of the electron to be formulated in Minkowski space, and for the photon to be described relativistically as a four-dimensional localization of energy. The resulting Lagrangian formulation of quantum mechanics is completely analogous to the more familiar nonrelativistic Hamiltonian model based on the Schrödinger equation. It accounts for the 720 degree rotation of a wave function as the absorption of one 360 degree electromagnetic wave cycle and the emission of another, yielding two wave cycles to correspond with one clock cycle. Because the properties of energy are universal the equations are able to be extended to include galaxies in spite of vast differences in lifetime. They show that symmetry exists between the electromagnetic fields of atoms and the gravitational fields of galaxies due to the presence in both of radial and transverse fields. The description of galaxy structure is fundamentally distinct because it is based on the conjugate variables energy and time. Determinants of Surgical Case On-Time Start and On-Time Finish in Perioperative Services Majbah Uddin, Lawrence Fredendall, Nathan Huynh, Kevin Taaffe, Robert Allen Subject: Keywords: case on-time start; case on-time finish; perioperative services; team familiarity; OR efficiency Efficient use of the operating room (OR) is crucial for any hospital. One of the major inefficiencies in the OR is surgical cases not starting or finishing on time as scheduled. When a case is delayed, it affects all subsequent cases in that OR. This study uses discrete choice analysis to determine the significant factors, including team familiarity, that influence OR case on-time start and finish. A case is considered on-time if the documented procedure start and finish times are no more than 10 minutes after the scheduled start and finish times. The analysis uses surgical case data from a large tertiary referral hospital and academic center in Greenville, South Carolina. The case data includes all surgical cases (15,091) performed during regular workdays in 2013. Two binary logit models are developed: one for case on-time start and one for case on-time finish. Results indicate that higher team familiarity between surgeon and anesthesiologist, surgeon and circulating nurse, surgeon and scrub nurse, and surgeon and CRNA improve the likelihood of an OR case on-time start and on-time finish. This finding indicates that the OR scheduling staff in the study hospital make a concerted effort to schedule the surgical teams with members who have worked well together in the past. Novel Dead-Time Compensation Strategy for Wide Current Range in a Three-Phase Inverter Jeong-Woo Lim, Hanyoung Bu, Younghoon Cho Subject: Engineering, Electrical & Electronic Engineering Keywords: DTCS; dead-time compensation; trapezoidal compensation voltage; dead-time effects; three-phase VSI compensation This paper proposes a novel three-phase voltage source inverter dead-time compensation strategy for accurate compensation in wide current regions of the inverter. In particular, an analysis of the output voltage distortion of the inverter, which appears as parasitic components of the switches, has been conducted for proper voltage compensation in the low current region, and an on-line compensation voltage controller has been proposed. Also, a new trapezoidal compensation voltage implementation method using the current phase is proposed to simplify realizing the trapezoidal shape of the three-phase compensation voltages. Finally, when the proposed dead-time compensation strategy is applied, the maximum phase voltage magnitude in the linear modulation voltage regions is defined to achieve smooth operation even at high modulation index. Simulations and experiments were conducted to verify the performance of the proposed dead-time compensation scheme. Binding Mechanism of Remdesivir to SARS-CoV-2 RNA Dependent RNA Polymerase Leili Zhang, Ruhong Zhou Subject: Chemistry, Physical Chemistry Keywords: COVID-19; SARS-CoV-2; RNA-dependent RNA polymerase (RdRp); remdesivir; homology model; molecular dynamics; free energy perturbation Starting from December 2019, coronavirus disease 2019 (COVID-19) has emerged as a once-in-a-century pandemic with deadly consequences, which urgently calls for new treatments, cures and supporting apparatuses. Remdesivir was reported by World Health Organization (WHO) as the most promising drug currently available for the treatment of COVID-19. Here, we use molecular dynamics simulations and free energy perturbation methods to study the inhibition mechanism of remdesivir to its target SARS-CoV-2 virus RNA-dependent RNA polymerase (RdRp). In the absence of a crystal structure of the SARS-CoV-2 RdRp, we first construct the homology model of this polymerase based on a previously available structure of SARS-CoV NSP12 RdRp (with a sequence identify of 95.8%). We then build the putative binding mode by aligning the remdesivir + RdRp complex to the ATP bound poliovirus RdRp. The putative binding structure is further optimized with molecular dynamics simulations and demonstrated to be stable, indicating a reasonable binding mode for remdesivir. The relative binding free energy of remdesivir is calculated to be -8.28 ± 0.65 kcal/mol, much stronger than the natural substrate ATP (-4.14 ± 0.89 kcal/mol) which is needed for the polymerization. The ~800-fold improvement in the Kd from remdesivir over ATP indicates an effective replacement of APT in blocking of the RdRp binding pocket. Key residues D618, S549 and R555 are found to be the contributors to the binding affinity of remdesivir. These findings demonstrate that remdesivir can potentially act as a SARS-CoV-2 RNA-chain terminator, effectively stopping its RNA reproduction, with key residues also identified for future lead optimization and/or drug resistance studies. Improved Immune Responses against Zika Virus after Sequential Dengue and Zika Virus Infection in Human Felix G. Delgado, Karina I. Torres, Jaime E. Castellanos, Consuelo Romero-Sánchez, Etienne Simon-Lorière, Anavaj Sakuntabhai, Claude Roth Subject: Life Sciences, Virology Keywords: Dengue virus; Zika virus; T-cell epitopes; cross-reactive T cells; immunodominance; neutralizing antibodies; antibody-dependent-enhancement (ADE) The high level of dengue virus (DENV) seroprevalence in areas where Zika virus (ZIKV) is circulating and the cross-reactivity between these two viruses have raised concerns on the risk of increased ZIKV disease severity for patients with a history of previous DENV infection. To determine the role of DENV pre-immunity in ZIKV infection, we analysed the T and B cell responses against ZIKV in donors with or without previous DENV infection. Using PBMCs from donors living in an endemic area in Colombia, we have identified, by interferon (IFN)-γ enzyme-linked immunospot (ELISPOT) assay, most of the immunodominant ZIKV T-cell epitopes in the non-structural proteins NS1, NS3 and NS5. Analyses of the T and B-cell responses in the same donors revealed a stronger T-cell response against peptides conserved between DENV and ZIKV, with a higher level of ZIKV-neutralizing antibodies in DENV-immune donors, in comparison with DENV-naïve donors. Strikingly, the potential for antibody mediated enhancement of ZIKV infection was reduced in donors with sequential DENV and ZIKV infection in comparison with donors with DENV infection only. Altogether, these data suggest that individuals with DENV immunity present improved immune responses against ZIKV. Absolute Time, Length Expansion, Particle Mass Origins, Quantum Entanglement, Pauli Exclusion Principle and Higgs Boson on the 4-D Euclidean Space Jae-Kwang Hwang Subject: Physical Sciences, Particle & Field Physics Keywords: Absolute time; Length expansion; Absolute time simultaneity; Twin paradox; Quantum entanglement; 4-D Euclidean space; Pauli exclusion principle; Higgs boson; Time clicking; Quantum base The absolute time and relative time are defined in terms of the 4-D Euclidean space. Our universe is the 3-D x1x2x3 quantized photon space which follows the absolute time simultaneity when the universe moves along the absolute time axis of ct. The length expansion of Dx = gDx0 is derived under the condition of the absolute time (ct) simultaneity. From the similarity between this length expansion of Dx = gDx0 and the energy increasing of E = gE0, it is assumed that the energy is proportional to the particle size of Dx. The extension of this assumption to the 4-D Euclidean space gives the new definition that the particle energy (E) is the 4-D volume. Then, the particle mass energy is defined as E= mc2 = cDtDV = gE0. The masses of the elementary particles are originated from the 4-D warped volume of the photon space because the particle is the warped photon space with the velocity of v < c. Therefore, the Higgs boson concept in the standard model (SM) is not needed in the present 3-D quantized space model (TQSM). The scalar boson with the spin of zero, photon with the spin of 1 and graviton with the spin of 2 are the two-boson states. Therefore, the observed Higgs boson is reinterpreted as the two-boson state of the scalar boson with the spin of zero. The cosmic muon observation and twin paradox are explained by using the absolute time and relative time. The relative time is the observed time in the twin paradox and cosmic muon observation. In the twin paradox, a person who travels the long distance is more aged than a person on the earth in terms of the relative time ages because of the space and time conversion effect (STCE effect) of the moving space distance (x). But twins are in the same ages in terms of the absolute time without STCE effect. The fast-moving cosmic muon has the expanded half-life from the time expansion of the relative time. Also, the quantum entanglement and Pauli exclusion principle are explained. The quantum base of the photon space line connects two entangled particles. Two particles and quantum base system is fluctuated along the absolute time axis by the time clicking when one particle is measured. Another particle is instantly selected by the time clicking. This is called as the quantum entanglement. The photons which are the flat photon space with the constant speed of c along the space axis and absolute time axis have the 4-D photon velocity of ceff = 20.5 c. Total 10-D Euclidean space including three 3-D quantized spaces and one absolute time axis is required for the electric charges (EC), lepton charges (CC) and color charges (CC) of the elementary particles. The 3-D photon space is very stiff along the absolute time (ct) axis and very soft along the space axes. The Coulomb force through the photons (2EM waves) of the space fluctuations is much stronger than the Gravitational force through the gravitons (G waves) of the time fluctuations between two electrons. Explaining Bad Forecasts in Global Time Series Models Jože Rožanec, Elena Trajkova, Klemen Kenda, Blaž Fortuna, Dunja Mladenić Subject: Engineering, Electrical & Electronic Engineering Keywords: Explainable Artificial Intelligence; XAI; Time Series Forecasting; Global Time Series Models; Machine Learning; Artificial Intelligence While increasing empirical evidence suggests that global time series forecasting models can achieve better forecasting performance than local ones, there is a research void regarding when and why the global models fail to provide a good forecast. This paper uses anomaly detection algorithms and Explainable Artificial Intelligence (XAI) to answer when and why a forecast should not be trusted. To address this issue, a dashboard was built to inform the user regarding (i) the relevance of the features for that particular forecast, (ii) which training samples most likely influenced the forecast outcome, (iii) why the forecast is considered an outlier, and (iv) provide a range of counterfactual examples to understand value changes, in the feature vector or the predicted value, can lead to a different outcome. Moreover, a modular architecture and a methodology were developed to iteratively remove noisy data instances from the train set, to enhance the overall global time series forecasting model performance. Finally, to test the effectiveness of the proposed approach, it was validated on two publicly available real-world datasets. Towards a Framework for Observational Causality from Time Series: When Shannon Meets Turing David Sigtermans Subject: Keywords: information theory; transfer entropy; time-delayed mutual information; data processing inequality; time series; causal tensor We propose a novel tensor-based formalism for inferring causal structures from time series. An information theoretical analysis of transfer entropy (TE), shows that TE results from transmission of information over a set of communication channels. Tensors are the mathematical equivalents of these multi-channel causal channels. A multi-channel causal channel is a generalization of a discrete memoryless channel (DMC). We consider a DMC as a single-channel causal channel. Investigation of a system comprising three variables shows that in our formalism, bivariate analysis suffices to differentiate between direct and indirect relations. For this to be true, we have to combine the output of multi-channel causal channels with the output of single-channel causal channels. We can understand this result when we consider the role of noise. Subsequent transmission of information over noisy channels can never result in less noisy transmission overall. This implies that a Data Processing Inequality (DPI) exists for transfer entropy. Genome Wide Identification of Key Components of RNA Silencing in Two Phaseolus vulgaris Genotypes of Contrasting Origin and Their Expression Analyses in Response to Fungal Infection Juan Camilo Alvarez-Diaz, Manon Richard, Vincent Thareau, Gianluca Teano, Christine Paysant-Le-Roux, Guillem Rigaill, Stéphanie Pflieger, Ariane Gratias, Valérie Geffroy Subject: Biology, Plant Sciences Keywords: Phaseolus vulgaris; Colletotrichum lindemuthianum; RNA silencing; Argonaute; double-stranded RNA binding (DRB); RNA-dependent RNA polymerase (RDR); Pol IV RNA silencing serves key roles in a multitude of cellular processes, including development, stress responses, metabolism, and maintenance of genome integrity. Dicer, Argonaute (AGO), double-stranded RNA binding (DRB), RNA-dependent RNA polymerase (RDR) and DNA-dependent RNA polymerases known as Pol IV and Pol V form core components to trigger RNA silencing. Common bean (Phaseolus vulgaris) is an important staple crop worldwide. In this study, we aimed to unravel the components of the RNA-guided silencing pathway in this non-model plant taking advantage of the availability of two genome assemblies of Andean and Meso-American origin. We identified six PvDCLs, thirteen PvAGOs, 10 PvDRB, 5 PvRDR, in both genotypes, suggesting no recent gene amplification or deletion after the gene pool separation. In addition, we identified one PvNRPD1 and one PvNRPE1 encoding the largest subunits of Pol IV and Pol V, respectively. These genes were categorized into subgroups based on phylogenetic analyses. Comprehensive analyses of gene structure, genomic localization and similarity among these genes were performed. Their expression patterns were investigated by means of expression models in different organs using online data and quantitative RT-PCR after pathogen infection. Several of the candidate genes were up-regulated after infection with the fungus Colletotrichum lindemuthianum. Efficiency of True-Green Light Emitting Diodes: Non-Uniformity and Temperature Effects Ilya E. Titkov, Sergey Yu Karpov, Amit Yadav, Denis Mamedov, Vera L. Zerova, Edik Rafailov Subject: Physical Sciences, Condensed Matter Physics Keywords: InGaN green LEDs; active region non-uniformity; temperature-dependent electroluminescence; internal quantum efficiency; light extraction efficiency; extended defects; modeling External quantum efficiency of industrial-grade green InGaN light-emitting diodes (LEDs) has been measured in a wide range of operating currents at various temperatures from 13 K to 300 K. Unlike blue LEDs, the efficiency as a function of current is found to have a multi-peak character, which could not be fitted by a simple ABC-model. This observation correlated with splitting of LED emission spectra into two peaks at certain currents. The characterization data are interpreted in terms of non-uniformity of the LED active region, which is tentatively attributed to extended defects like V-pits. We suggest a new approach to evaluation of temperature-dependent light extraction and internal quantum efficiencies taking into account the active region non-uniformity. As a result, the temperature dependence of light extraction and internal quantum efficiencies have been evaluated in the temperature range mentioned above and compared with those of blue LEDs.	CommonCrawl
One $$kg$$ of a diatomic gas is at a pressure of $$8 \times {10^4}\,N/{m^2}.$$ The density of the gas is $$4kg/{m^3}$$. What is the energy of the gas due to its thermal motion ? $$5 \times {10^4}\,J$$ $$Volume\,\, = \,\,{{mass} \over {density}} = {1 \over 4}{m^3}$$ $$K.E = {5 \over 2}PV$$ $$ = {5 \over 2} \times 8 \times {10^4} \times {1 \over 4}$$ $$ = 5 \times {10^4}J$$ Statement - 1: The temperature dependence of resistance is usually given as $$R = {R_0}\left( {1 + \alpha \,\Delta t} \right).$$ The resistance of wire changes from $$100\Omega $$ to $$150\Omega $$ when its temperature is increased from $${27^ \circ }C$$ to $${227^ \circ }C$$. This implies that $$\alpha = 2.5 \times {10^{ - 3}}/C.$$ Statement - 2: $$R = {R_0}\left( {1 + \alpha \,\Delta t} \right)$$ is valid only when the change in the temperature $$\Delta T$$ is small and $$\Delta T = \left( {R - {R_0}} \right) < < {R_0}.$$ Statement - 1 is true, Statement - 2 is true; Statement - 2 is the correct explanation of Statement - 1 Statement - 1 is true, Statement - 2 is true; Statement - 2 is not the correct explanation of Statement - 1 Statement - 1 is false, Statement - 2 is true Statement - 1 is true, Statement - 2 is false The relation $$R = {R_0}\left( {1 + \alpha \,\Delta t} \right)$$ is valid for small values of $$\Delta t$$ and $${R_0}$$ is resistance at $${0^ \circ }C$$ and also $$\left( {R - {R_0}} \right)$$ should be much smaller than $${R_0}.$$ So, statement $$(1)$$ is wrong but statement $$(2)$$ is correct. An insulated container of gas has two chambers separated by an insulating partition. One of the chambers has volume $${V_1}$$ and contains ideal gas at pressure $${P_1}$$ and temperature $${T_1}$$. The other chamber has volume $${V_2}$$ and contains ideal gas at pressure $${P_2}$$ and temperature $${T_2}$$. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be $${{{T_1}{T_2}\left( {{P_1}{V_1} + {P_2}{V_2}} \right)} \over {{P_1}{V_1}{T_2} + {P_2}{V_2}{T_1}}}$$ $${{{P_1}{V_1}{T_1} + {P_2}{V_2}{T_2}} \over {{P_1}{V_1} + {P_2}{V_2}}}$$ Same as $$A.$$ $$20$$ The speed of sound in oxygen $$\left( {{O_2}} \right)$$ at a certain temperature is $$460\,\,m{s^{ - 1}}.$$ The speed of sound in helium $$(He)$$ at the same temperature will be (assume both gases to be ideal) $$1421\,\,m{s^{ - 1}}$$ $$500\,\,m{s^{ - 1}}$$ The speed of sound in a gas is given by $$v = \sqrt {{{\gamma RT} \over M}} $$ $$\therefore$$ $${{{v_{{O_2}}}} \over {{v_{He}}}} = \sqrt {{{{\gamma _{{O_2}}}} \over {{M_{{O_2}}}}} \times {{{M_{He}}} \over {{\gamma _{He}}}}} $$ $$ = \sqrt {{{1.4} \over {32}} \times {4 \over {1.67}}} = 0.3237$$ $$\therefore$$ $${v_{He}} = {{{v_{{O_2}}}} \over {0.3237}}$$ $$ = {{460} \over {0.3237}}$$ $$ = 1421\,m/s$$ Questions Asked from Heat and Thermodynamics AIEEE 2002 (10)	CommonCrawl
Benedikt Bitterli Star Stacker: Astrophotography with C++11 If you've ever taken a photo of the night sky with a cell phone or a consumer camera, you might have been disappointed with the results. The problem is that stars are actually surprisingly dim, and to properly capture them on film, the camera sensor needs to be exposed to the sky for a long time. However, most consumer cameras use only a short exposure time, and you might end up with a picture that looks like the raw input image in the video above: A dim image with only a handful of bright stars visible - certainly not worth sharing on your social medias. Since I'm a programmer and not a photographer, the obvious question to ask was this: Maybe we can't take better pictures - but if we had a lot of such low quality input images, could we somehow extract a single, higher quality picture of the night sky from them? This is what this project is all about. If we throw plenty of math at the problem, the answer is yes! - with enough input images, we can reconstruct hundreds of stars from what used to be a black night sky. However, getting there turns out to be quite difficult. In the following, I will briefly outline my approach to the problem, what worked and what didn't work. There will also be plenty of pretty pictures along the way. Before I dive into the details of this project, I should add a quick disclaimer. I am neither a photographer nor a computer vision person, and my approach to solve this problem may be clumsy at times. But I wanted to play with computer vision for a while now, and it was a refreshing side project to work on. To that end, most of the code was written from scratch, since I wanted to avoid big dependencies like OpenCV - it's not much of a learning experience otherwise. If you have any suggestions or corrections to make, feel free to contact me. It's also worth mentioning that these things are not new. There are already software packages that can enhance your star photos for you (pixinsight, DeepSkyStacker, AstroArt, just to name a few). The problem I found with these is that they are either quite expensive or performed substandard when it comes to aligning images. It's possible that these just need more manual preprocessing and dialing in the right settings before they produce better results, but this is unsatisfying: My goal was to have a piece of software that won't need any user adjustment or complicated setup to work. After all, what is the fun in having a program do the work for you when you have to spend just as much time setting it up! The basic problem we're trying to solve is that we have a photo of something that's very dim taken with a short exposure, and as a result we can't see anything. Our first instinct is to simply turn up the image brightness, and this is almost the correct thing to do. If we do this to our input image, we get a result like this: If we take an input star image (left) and just increase its brightness, we don't get great results (right). There are three problems here: Our color channels only have 8 bits of precision, so we can't just make the image brighter and expect more detail to appear. Additionally, multiplying the image brightness also multiplies the noise level and leaves us with nasty red and green image speckles in the result. Finally, making the image brighter also reveals the problem of light pollution: City lights that get reflected by the atmosphere and occlude the stars we want to see, leading to an orange film in front of the night sky: Increasing the image brightness reveals the light pollution that occludes the night sky. Removing light pollution Even if we can remove noise and increase precision, light pollution puts a hard limit on how much we can boost the image brightness; eventually, we'll just end up with a white image. Of course, the ideal solution is to avoid the problem in the first place, i.e. drive far away from civilization and take photos unpolluted by man-made lights. But that's a non-software solution. Let's instead try to get the most out of the photos we have! What helps us is that light pollution looks completely different to the stars we want to extract: Stars are tiny bright dots, and light pollution is a smoothly changing tint over the whole image. Using these properties, we can build a simple process to remove light pollution: First, we will come up with a mathematical model that can express "smoothly changing tint" as a simple formula with few parameters. Then, we build a crude guess of which pixels contain stars and which are part of the background. We can then fit the parameters of the formula so that it best matches the background of the image. If all goes well, the fitted formula then closely predicts the value of light polution over the whole image. Then we can simply subtract the fitted model from the input, and what is left should hopefully be just stars. Coming up with a formula that can describe light pollution over the whole image is quite difficult, and we're not going to do that. Instead, we're going to use a classic modelling trick: We will use a very simple formula, but only use it to model a small patch of pixels (say, a 50x50 pixel square). Then we simply use an ensemble of many such simple formulas to cover the whole image. Simple is better than complex, and I'm going to assume that we can model light pollution within a small square of pixels as a linear gradient. Building a star mask Our first step in removing light pollution is to build a binary mask that roughly classifies pixels into "probably stars" and "probably background". This mask does not have to be perfect - as long as we can exclude most of the stars, we will be fine. I'm going to use the fact that light pollution is smooth and low frequency, whereas stars are small dots significantly brighter than the background. This means that if we take the average brightness over a small patch of pixels, then background pixels will be "close" to the average, whereas stars will be a lot brighter. We need to be careful how we measure the "closeness" of two brightness values. Our input is polluted by camera noise and has an unknown dynamic range, which means that hardcoding an absolute threshold is going to be fragile and will only work for some inputs. Instead, we're going to model our background pixels to be polluted by Gaussian noise. To use this model, we estimate the mean and sample variance of all pixels within a small image patch surrounding the pixel we want to classify. We then compare the target pixel to the mean; if its difference to the mean is smaller than two standard deviations, the fluctuation can likely be explained as noise and we classify the pixel as "probably background". A larger deviation suggests this pixel cannot be explained by our model for background pixels and we classify it as "probably stars". If we do this for our input image, we get a mask as shown below: An input image (left) with a rough binary mask (right) classifying pixels into stars (black) and background (white). We can see some spurious background pixels that get classified as stars, but overall the result looks quite good. It will definitely suffice for our purposes. Estimating the light pollution Now that we have roughly classified unwanted star pixels, we can fit our model for light pollution to the remaining background pixels. As mentioned before, we model light pollution within small patches of pixels as a linear gradient. Such a gradient has three parameters: Its brightness, its x-slope and its y-slope. Our goal now is to estimate these parameters so that the linear gradient best matches the input image. This problem is best known as Weighted Least Squares and is well-studied. We can write the optimal fit in terms of a set of linear equations $$(\mathbf{X}^T \mathbf{W} \mathbf{X}) \beta = \mathbf{X}^T \mathbf{W} y,$$ where $y$ is the vector of input pixels, $\beta$ are the parameters of our model, $\mathbf{X}$ is the feature matrix (pixel positions + a column of constant 1s) and $\mathbf{W}$ is a diagonal matrix containing our image mask. This will not make much sense unless you are familiar with linear regression (I won't go into the details), but just assume that this allows us to compute the optimal parameters. Arbitrary sized matrix math is inconvenient to implement, and I've opted to use the excellent Eigen matrix library to solve this system of equations. Once we have estimated the parameters $\beta$, we can go in the reverse direction: Evaluating $X \beta$ retrieves the value of the model for all pixels in the patch. If we do this over the whole image, this is what we get: An input image (left) and its model of light pollution (right) estimated from the input using weighted linear least squares. Not too bad! Here's what happens when we subtract our model from our input image: Subtracting our fitted model of light polution from the input reveals a clean, black night sky with stars left intact. This is exactly what we were after. The light pollution is completely gone, but our stars were left intact. And all that with just software - no need to leave the comfort of our bedroom. Stacking Frames With a single image, this is about as good as it gets. With light pollution removed, we can boost the image brightness by a bit and extract a few more stars. However, we still struggle with a lack of dynamic range and speckles of camera noise, which only get worse the brighter we make the image. The solution here is to use not just one, but multiple images taken a short time apart. With some assumptions, the noise in different images is uncorrelated and just fluctuates around zero - i.e. sometimes pixels come out darker and sometimes brighter than they should be, but on average we get the correct value. By the law of large numbers, if we had a lot of pictures of the same scene and averaged them, we will get a noise-free and very precise result of what the scene actually looks like. Let's try this for a sequence of images taken of the night sky: Naively averaging an input sequence smears stars into star trails. Woah! This looks nothing like our input image. What we're seeing here is an effect called star trails. Even though the camera was static, the earth moved while we were taking pictures. This causes stars to wander between pictures and leave trails if we naively average the images. While this certainly looks cool, it's not the effect we want. Because the stars move between exposures, we won't get more accurate pixel data for each star when we average images - all we get is a smeared version of the star. The solution to this problem needs a bit more math. The basic idea is that we need to undo the rotation of the earth and align all the pictures with each other before we average them. This will make it possible to extract a much more precise image of each star. We don't know the exact rotation, so we need to estimate it from the images. To do this, we will need several steps; here's a rough outline: Star extraction: We first need to precisely locate all the stars in the image. These are our reference points that we want to track between images. Coarse alignment: We then need to match stars between images and compute a rough initial guess for how the images are rotated with respect to each other. This algorithm needs to be fast and robust, but it doesn't need to be too accurate. Fine alignment: With each frame roughly aligned to the next frame and correspondences between stars established, we run a more sophisticated optimization algorithm to precisely align frames. Merging: After all frames are finely aligned, we subtract light pollution and transform each image through a camera model. This allows us to average the aligned images and obtain a merged output. The reason why we need both a rough and fine alignment step is that the fine alignment algorithm I'm using will fail spectacularly unless the frames are already fairly close to each other. To solve this problem, we first run a completely different rough alignment algorithm that gets us most of the way there, while we use fine alignment to get precisely matching images. Finding stars The first step in our alignment pipeline is to precisely locate stars in an input image. In computer vision this falls under the umbrella term of "feature extraction", which extracts "trackable" features from an image. There's a wide range of established algorithms to do this, such as SIFT, SURF, GLOH and HOG, just to name a few. However, I am not going to use any of these. Stars have very few distinctive features (they're just white blobs), and these general-purpose algorithms would be overkill. Additionally, unlike these general-purpose methods, we can leverage specific knowledge about our stars to compute their location very precisely. And finally, it's a lot more educational to build something of our own than to implement someone else's ideas. Blob transform We know that stars are more or less white blobs in a dark background. Therefore, the first step in extracting stars is to try and locate "blob-like" objects in the image. This is not easy when operating on the RGB data directly, and we will instead pre-process our image using an algorithm called Difference of Gaussians The basic idea is that we take an input image, blur it slightly and subtract the blurred image from the input. In uniform regions, the blur won't change much and the output will be zero. However, close to edges and corners, the blurring will change the image significantly, and the magnitude of the difference will be large. For blob-like objects, the difference of gaussians algorithm will react particularly strongly, which makes it very useful for our purposes. Another cool thing is that we can repeat the blurring and subtracting to obtain a whole chain of filtered outputs - this allows us to detect blobs of different sizes. I've illustrated this below for an input image of a Cornell box: An illustration of the Difference of Gaussians on a Cornell box image. From left to right, the amount of blur increases, and the size of features detected by the algorithm increases accordingly. As an optimization, you would usually combine a blur step with a downsampling step (e.g. halve the image size after blurring), which results in what is called a Gaussian pyramid. Rough star extraction After running the difference of gaussians, we end up with a stack of grayscale images. If a pixel in one of these images has a large value, it means that at that location in the input image, there was a blob-like object. For a fixed pixel location, we can also look at all the images in the stack so check which one has the brightest value at that point. This tells us the size of the blob: Images obtained from larger blurs capture larger blobs, and vice-versa. The exact formula for the radius can be obtained from the blur parameters. To make these images useful, we now need to convert the pixel data into a concrete list of blob positions and radii. We're interested in the most "blob-like" features in the input, which corresponds to finding local maxima in the image stack. I'm going to use a very simple algorithm for this: First, I will pick the most blob-like feature (i.e. the brightest pixel) in the entire image stack, and add it to my list of potential stars. Then I will remove all other blobs that overlap with the one I picked. This amounts to going through all images in the stack and blacking out a circle with the radius of the blob we picked. We then simply repeat this process until we've obtained a sufficient number of stars. I've illustrated a run of this algorithm on an example input image. The estimated blob locations and radii are shown on the right: An input image (left) and its roughly estimated star positions and radii (right). The results look quite decent. It manages to extract all directly visible stars, as well as a lot of extremely dim stars that are tough to detect by eye. There are also some false positives, but we can filter these out later. Precise star extraction The algorithm described above will give us a rough initial guess of where the stars in the image are. The extracted star positions are very inaccurate however, which is unfortunate - we want to use the stars as fixpoints to align images, so we need the positions to be as accurate as possible. To do this, we will refine the star positions with a second algorithm. We will use the knowledge that stars are very much blob-like. This means they can be well approximated with a 2D Gaussian: A controllable "blob function". To illustrate, here's a heatmap of a 2D Gaussian with some hand-picked parameters: The nice thing about Gaussians is that, given a 2D point set, we can directly compute the parameters of a Gaussian that best fits the input data. This allows us to create the following refinement algorithm: We use the rough blob positions as an initial guess, and extract a small image patch (say, 64x64 pixels) around each blob position. If the initial guess is correct and there is a star close to that blob, then we should be able to reproduce it well with a Gaussian. Therefore, as a next step we fit a 2D Gaussian that best fits the image patch we extracted. The mean value of the Gaussian is the star position. If we apply this to a sample input, we obtain an image like this: An input image (left) and a naive Gaussian estimation of star location and shapes. Awful! These Gaussians do not reproduce the stars well at all. The problem here is that the input image is polluted by a constant level of background noise. A constant value added to a blob generally cannot be modelled with a 2D Gaussian, and as a result the best fit ends up being an extremely large Gaussian that tries to account for both the noise and the star. However, we can just apply the same trick here that we used earlier for subtracting the light pollution. We first measure the mean and variance within the image patch; anything that falls within a few standard deviations of the background is most likely noise and should be ignored when fitting the Gaussian. If we apply this in a weighted Gaussian fitting scheme, we get this result: An input image (left) and corresponding star Gaussians (right) estimated using a model accounting for background noise. This is really quite good! The great thing is that fitting the Gaussian uses the information of a whole neighborhood of pixels, and the resulting estimated star position has sub-pixel accuracy. This algorithm has a few other desirable properties too, such as being robust with respect to rotation and noise. This ensures we will be able to accurately track stars across a whole sequence of images Our initial coarse detection step is bound to have a few false positives, and we should filter these out in a final pruning step. We can use a lot of information from the Gaussian fit to determine whether there really was a star or not. If the Gaussian has a very large radius, or is very dim, then we likely just captured a piece of the background and should remove this star. With a list of precise star locations computed for each image, we are starting to have enough data to start aligning images in our sequence. But before we figure out how we do this, we first need to discuss what exactly it is that we are doing. In order to make image alignment easy, we are first going to make a few assumptions. Our first assumption is that stars are infinitely far away, which means that there is no parallax: If we move the camera, nothing will change in the image; only when things rotate do we start to see change. This way, we don't have to worry about solving for camera translation. Additionally, we'll assume that the stars stay fixed in place while the camera (or, rather, the earth) rotates. Finally, we'll assume our camera is well-behaved: It has a centered image plane and negligible distortion. In a camera model, we're interested in relating 3D points, i.e. $v = (X, Y, Z)$, to points on the camera image plane, i.e. $p = (x, y, 1)$. We can do this using the transformation $$ p \propto \mathbf{V} \mathbf{R} v, $$ where $$ \mathbf{V} = \begin{bmatrix} f & 0 & 0 \\ 0 & f & 0 \\ 0 & 0 & 1 \end{bmatrix} $$ is the intrinsic camera matrix and $\mathbf{R}$ is the extrinsic camera matrix. The intrinsic matrix describes properties of the camera apparatus, such as distortion and offset. In our case, we only include the camera's focal length (described by the $f$ parameter). The extrinsic matrix describes the camera pose, which in our case reduces to a rotation matrix. Note that I've used the proportional sign rather than an equality in the projection equation above. This is because we will do a perspective division after the linear transformation. We first compute $(\overline{x}, \overline{y}, \overline{z}) = \mathbf{V} \mathbf{R} v$, and then obtain $p = (\overline{x}/\overline{z}, \overline{y}/\overline{z}, \overline{z}/\overline{z}) = (x, y, 1)$. I will make the reasonable assumption that all the images in our sequence were taken by the same camera, which means we will have to deal with only a single intrinsic matrix. However, each image will have a different camera pose. We will index the images in our sequence and assign a rotation matrix to each; frame $l$ gets orientation $\mathbf{R}_l$ and so forth. In order to align images, we need to solve for an orientation $\mathbf{R}_l$ for all frames, and a single global $f$ parameter. To do this, we'll frequently make use of image correspondences. An image correspondence is a single 3D point that appears in two different frames - for example, a star that has been captured by two images in the input sequence. Let's call our 3D point $v$, and its projections $p_l$ and $p_k$ in frames $l$ and $k$ of the input sequence. We can relate these points with $$\begin{align} p_l &= \mathbf{V} \mathbf{R}_l v \\ p_k &= \mathbf{V} \mathbf{R}_k v . \end{align}$$ Of course, if we just have the images, then we don't know $v$ in general. However, if we know that $p_l$ and $p_k$ are projections of the same point, then we can rewrite the equations above into $$\begin{align} p_l &= \mathbf{V} \mathbf{R}_l \mathbf{R}_k^{-1} \mathbf{V}^{-1} p_k \\ &= \mathbf{V} \mathbf{R}_{lk}^{-1} \mathbf{V}^{-1} p_k, \end{align}$$ where $\mathbf{R}_{kl}$ is the relative pose between frames $k$ and $l$. Given enough correspondences, we can use the equation above to solve for both $\mathbf{V}$ and $\mathbf{R}_{lk}$. This is what alignment does. Coarse star alignment Unfortunately, correspondences are information we don't have right now: All we have is a list of stars for each image, and have no idea which star in one frame corresponds to which star in another frame. If we knew a "good enough" relative pose between two frames, then finding correspondences is easy. We simply take a star in one frame, project it into the other frame, and check which star on the other frame it is closest to. If our estimated pose is good enough, this will work - but it turns this issue into a chicken and egg problem. If we have a pose, we can find correspondences, and if we have correspondences, we can solve for a pose. We will solve this problem using a bootstrapping process. First, we'll guess a few promising correspondences (say, two pairs of stars) and then solve for a pose that aligns them. Then we will assign an error score to this alignment: We'll compute correspondences for all stars assuming the pose we just obtained is the correct one. Then we sum the squared distances from each star to its aligned correspondence. If this sum is large, the computed pose a bad one, and our initial two correspondences we guessed are likely incorrect. We'll repeat this process with a large set of guesses and pick the pose that has the lowest error score. To make things easy, I will only solve for pose (i.e. extrinsic parameters) and will assume the focal length is 1. This makes the rough alignment not as good, but in practice it is sufficient for our purposes. How do we get good initial guesses? Here's a few ideas: Feature Matching In computer vision, the usual way of finding correspondences is to just compare the pixels (or some compressed version) of potential feature points to each other. This will work well in most images, but it's a poor fit for astrophotography. The features we want to compare are stars, which happen to all look pretty much identical - there's not much difference from one white blob to another. Random Guessing Another potential option is to use a RANSAC style approach and just pick two pairs of stars at random and check the resulting alignment. For a low number of stars, this can actually do quite well! But as the number of stars increases, our chances of finding a good initial alignment is poor. For example, for two frames with 1000 stars each, we need to try more than 7500 random pairs to be 99.9% sure we find at least one good one. This can get very expensive very quickly. Constellation Matching This last idea is the one I chose to go with, because it's not too expensive and worked the best out of the three approaches I tried (also, it's a cool idea). The basic approach is very intuitive: When humans try to track stars, they look at the arrangement of stars - i.e. constellations - instead of individual stars in isolation. Can we somehow replicate this in code and match star arrangements across different images? There are many ways you could try to measure star arrangements, but I've decided to go with the simplest (and hopefully robust) approach, which is to track triangles of stars. For each star, I am extracting its 100 closest neighbors. Then I build an exhaustive list of all triangles that could be formed with the initial star and its 100 neighbors, giving us roughly $100^2/2=5000$ possible "constellations" the star is a part of. We do this for all stars in each frame, and end up with a big list of constellation triangles for each frame. In order to get initial correspondences between two frames, we start comparing triangles between them. For each star, we check all triangles it is a part of and search for the most similar triangle in the other frame. There are many different ways we could do this, but I've opted for something simple: We first measure the side lengths of the triangle and store them as a vector of three floats - in other words, each triangle is now represented as a 3D point. To compare two triangles, we just take the euclidian distance between their respective 3D points. The reason I picked this representation is so we can make searching fast: If we store each triangle as a 3D point in a kD-tree, we can very quickly search for the best matching triangle by just traversing the tree. That is, each frame is now represented as a kD-tree of triangles. For each star, we check its containing triangles and find the best matching triangle in the other frame. The vertices of the best matching triangle are now candidate correspondences that we will test in our alignment pipeline. Below is an illustration of this process. First, let's look at two input frames to the algorithm, which were taken relatively far apart: Two frames (A and B) of our input sequence. Now, let's draw the best matching star triangles between the two frames: Matched and tracked star constellations between the two input images. This looks quite good! Although there are a handful of incorrectly matched triangles, the vast majority are correctly tracked across frames. Remember that all we need for a rough alignment are two pairs of correct star correspondences, and for these frames this technique delivers more than 100. Finally, below I'm showing the rough alignment with the lowest error score, which was ultimately picked by the algorithm: Overlayed star constellations from both frames after rough alignment. This looks quite good! Near the edges the alignment is a bit off - most likely because we don't solve for intrinsic parameters - but the fitted pose is very usable. Remember that we only need this alignment to be good enough for the fine alignment step, and this will definitely be sufficient. Fine star alignment With a rough alignment in place and correspondences computed, it's time for the final alignment step. In the rough alignment step we've estimated the pose using only two pairs of correspondences. In theory, two pairs of correspondences are enough to estimate both intrinsic and extrinsic parameters; however, we have hundreds of correspondences! Somehow we want to extract intrinsic and extrinsic parameters that accomodate all correspondences and not just two - this is what fine alignment is all about. The general term for the problem we're dealing with is an overdetermined system of equations. The go-to solution technique is least squares, which is what we will be using. I won't go into detail about least squares, but what it allows us to do is to find a set of parameters that minimizes the combined error over all aligned correspondences. If our system is linear, we can even compute the optimal solution in closed form. Unfortunately, this is not the case for our problem - rotation matrices, matrix inversion and perspective division cause significant non-linearity, and we will turn to an approximate minimization technique. The simplest such technique is gradient descent, which is what I've opted to use. The basic idea is this: We have some formula to compute the total alignment error. Changing the intrinsic and extrinsic parameters will change the error in some way - it will either become larger or smaller. The measure of this change is the derivative of the error with respect to the parameters. If we want to reduce the error as much as possible, we simply need to follow its negative derivative. Doing this minimization actually turns out to be quite difficult. The error we want to minimize is highly non-linear and derivatives are inconvenient and unstable to compute. Additionally, depending on which space we formulate the problem in, the minimization can be extremely unstable and produce unusable results. For production code I would recommend using a library like OpenCV, which already ships with well-engineered and tested code to do this. However, in a personal project, the pain of the learning process is quite valuable, and I've instead dug into literature to figure out how to solve this using a hand-rolled solution. Over the course of a few weeks I implemented several optimization models, and all except one turned out to be very unreliable. Reproducing the working algorithm here would exceed the scope of this (already long) post, but there were two publications I found extremely helpful: Construction of Panoramic Image Mosaics (relevant bits: pages 10-14) and Image Alignment and Stitching. I would recommend these to anyone implementing image alignment. With the boring bits out of the way, let's look at some actual results! Below are the same images we've seen before, animated over several iterations of the optimization algorithm. At each iteration, the pose and focal length are re-estimated and refined, leading to a better and better alignment: Overlayed star constellations from both frames, over several iterations of the fine alignment algorithm. Given a good enough initial guess (the rough alignment), a robust implementation of this optimization converges surprisingly quickly. Usually we're done after 10 iterations or less, rendering this the cheapest step of the program - even though it took the longest to implement. Now we're almost done! Using rough & fine alignment, we can align all successive images in our input sequence to each other. Doing this is called pairwise alignment, because we only align two images at a time. It turns out we can do slightly better than this. When we do pairwise alignment, we align a star with its correspondence in one other frame. However, usually a star appears in more than just one frame - it could even appear in every frame in the sequence. To make use of this additional information, we perform one final global alignment step after we complete pairwise alignment. The global alignment optimizes all poses simultaneously to lign up all correspondences of all stars across all frames. A dizzying amount of data! The math for global alignment is pretty much the same as for pairwise alignment, except we add some more derivatives. There is definitely not enough space here to describe the process in detail, but please see the papers linked earlier if you're interested. With all alignments computed, we can at last produce the final output image. Doing this is quite simple: We first pick a reference camera, which in my case is always the first camera in the sequence. Then we reproject all images in the sequence into the reference camera. In other words, we iterate over all points on the image plane of the reference camera, and project those points into the image plane of every other frame in the sequence. Then we simply look up the pixel values there and average them. The output of this process is the average of the aligned images. But enough text - let's look at the final results. Below are the first six images in the sequence, after light pollution removal and significantly boosted in brightness. I'm showing the images after alignment, and I'm averaging more and more images together: Merging increasing numbers of aligned frames greatly reduces noise. It may be hard to make out in this low-resolution version, but the images start out extremely noisy. This is because we boosted the image brightness quite a lot. However, the more images we add, the lower the noise level becomes. The cool thing is that unlike naive averaging, the stars stay perfectly sharp! Our alignment pipeline makes sure stars stay put and don't get smeared out into star trails. Finally, here is a fast forward of the merging process of all 64 images in this sequence: An animation of iteratively merging all images in our input sequence. We can see that there is some additional red background tint due to parts of the light pollution we didn't catch in the first processing step. To get rid of it, we do a second light pollution subtraction after merging and tonemap the result. And we're done! Here are the full resolution results. On the top is the first image in the input sequence, on the bottom is the final merged output image: The first image in the input sequence (top) and the final output after subtracting light pollution, aligning and merging (bottom). This project was a fun experiment in how much you can extract out of a low quality input image. Originally the purpose of this was just to learn more about computer vision, but I was surprised at the results obtained in the end. Although this is not production ready code, it produces nice images. If I had more time to spend on this project, there are definitely a few things I would fix. I'm not doing any kind of dark frame subtraction, meaning that static sensor noise and dead pixels will stick around in the merged image. Additionally, I'm working with 8 bit JPEGs as input, rather than higher-precision RAW files, which limits the quality of the output a bit. Finally, all alignment is done on estimated star positions, which may be inaccurate - a final alignment step using the pixel data directly could make the results even sharper. While working on this, I was also playing with an interesting idea for a future project: Only in a few places in the processing pipeline did we assume that all images were taken by the same camera. Additionally, we don't require input frames to be very similar to each other - the alignment algorithm is robust enough to handle arbitrary camera orientation changes between images. This opens up an interesting avenue for a crowd-sourced stargazing service. It would ask people around the globe to upload night sky images to a website, and an algorithm behind the scenes would combine all of these images into a single, high-resolution star map spanning the globe. There's definitely more work to be done on top of this project to make something like that possible, but it's an interesting idea. Big thanks go to the dashingly handsome Andrew Chin for providing the images in this post and sparking the initial idea for this project.	CommonCrawl
Confusion with the Periodic Table The periodic table has 7 periods and they have 2,8,8,18,18... elements respectively from 1 to 7. But from what I understand, the periods each state the number of electron shells that the elements in that period has. So if that is the case, shouldn't period 3 have more elements, since it can hold up to 18 electrons, and therefore it can have up to 18 more protons from the largest atomic number element in period 2? (Since period 3 has a M electron shell, it can also have a p orbital, and in total therefore can have 18 elements.) The same could be said for elements in group 4, group 5, group 6 and so on since they can have f,g, and h orbitals as well. Am I missing something here? periodic-table phi2kphi2k $\begingroup$ There are a couple assumptions in your question that are really confusing me: (1) "shouldn't period 3...hold up to 18 electrons?" Why should you expect that? (2) "Since period 3 has a M electron shell" I haven't really been in a chemistry classroom for a while--what's an M electron shell? (3) " group 4, group 5, group 6...can have f,g, and h orbitals as well" No naturally-occurring element has electrons in anything higher than an f-shell. If you could explain these three points, I might be able to figure out where the confusion is coming from. $\endgroup$ – chipbuster Jul 30 '15 at 17:10 $\begingroup$ @chipbuster - M corresponds to principle quantum number 3 (K is 1, L is 2, and so on). It's old-style (or X-ray) notation. I would argue that f, g, h (and higher) atomic orbitals exist, but aren't populated for the elements in question. $\endgroup$ – Todd Minehardt Jul 30 '15 at 17:32 $\begingroup$ The standard periodic table isn't arranged according to electronic configuration; it's arranged so that elements with similar properties appear in the same group. There are alternative versions of the periodic table arranged in different ways, including by electronic configuration. $\endgroup$ – bon Jul 30 '15 at 17:44 $\begingroup$ @ToddMinehardt thanks, I had never heard x-ray notation used before. And agreed about the higher atomic orbitals. $\endgroup$ – chipbuster Jul 30 '15 at 17:52 So if that is the case, shouldn't period 3 have more elements, since it can hold up to 18 electrons, and therefore it can have up to 18 more protons from the largest atomic number element in period 2? Indeed, elements of the same period have the same number of electron shells, but the "problem" is that in accordance with the Madelung/Janet/Klechkowski rule, the $\mathrm{4s}$ orbital is occupied before the $\mathrm{3d}$ orbital. As a result, the $\mathrm{3d}$ orbital could be filled only when the $\mathrm{4s}$ orbital is already filled, i.e. only for elements of the 4th period. Similarly, the $\mathrm{5s}$, the $\mathrm{5p}$, and the $\mathrm{6s}$ orbitals are occupied before the $\mathrm{4f}$ orbital. As a result, the $\mathrm{4f}$ orbital could be filled only when the $\mathrm{5s}$, the $\mathrm{5p}$, and the $\mathrm{6s}$ orbitals are already filled, i.e. only for elements of the 6th period. WildcatWildcat Not the answer you're looking for? Browse other questions tagged periodic-table or ask your own question. What are the alternatives to the Periodic Table of the Elements? What is a "period" of the periodic table? What is the group number or name for elements between group 3 and 4 (F-block) on the periodic table? Periodic trends: why is effect of protons greater than electrons? Reading number of outer shell electrons and other properties from periodic table? What do the numerals on the top right corner of the cells in the periodic table represent? Periodic table- quantum numbers Electronic configuration and the periodic table Structure of the periodic table	CommonCrawl
NERSC Annual Reports HPC Requirements for Science HPC Workshop Reports Home » News & Publications » Publications & Reports » NERSC User Publications » 2014 2014 Publications Resulting from the Use of NERSC Resources On their Allocation Year 2015 ERCAP Request Forms Principal Investigators reported 1,808 refereed publications (published or in press) for the preceding 12 months, based on using, at least in part, NERSC resources. Agarwal, Deborah Valerie Hendrix, Lavanya Ramakrishnan, Youngryel Ryu, Catharine van Ingen, Keith R. Jackson, and Deborah Agarwal. Camp: Community access modis pipeline. October 2013. (doi:10.1016/j.future.2013.09.023) Aldering, Greg Scalzo, R., Aldering, G., Antilogus, P., Aragon, C., Bailey, S., Baltay, C., Bongard, S., Buton, C., Cellier-Holzem, F., Childress, M., Chotard, N., Copin, Y., Fakhouri, H.~K., Gangler, E., Guy, J., Kim, A.~G., Kowalski, M., Kromer, M., Nordin, J., Nugent, P., Paech, K., Pain, R., Pecontal, E., Pereira, R., Perlmutter, S., Rabinowitz, D., Rigault, M., Runge, K., Saunders, C., Sim, S.~A., Smadja, G., Tao, C., Taubenberger, S., Thomas, R.~C., Weaver, B.~A., and Nearby Supernova Factory, Type Ia supernova bolometric light curves and ejected mass estimates from the Nearby Supernova Factory, Monthly Notices of the Royal Astronomical Society, 440, 1518 Kim, A.~G., Aldering, G., Antilogus, P., Aragon, C., Bailey, S., Baltay, C., Bongard, S., Buton, C., Canto, A., Cellier-Holzem, F., Childress, M., Chotard, N., Copin, Y., Fakhouri, H.~K., Feindt, U., Fleury, M., Gangler, E., Greskovic, P., Guy, J., Kowalski, M., Lombardo, S., Nordin, J., Nugent, P., Pain, R., Pecontal, E., Pereira, R., Perlmutter, S., Rabinowitz, D., Rigault, M., Runge, K., Saunders, C., Scalzo, R., Smadja, G., Tao, C., Thomas, R.~C., and Weaver, B.~A., Type Ia Supernova Hubble Residuals and Host-galaxy Properties, The Astrophysical Journal, 784, Feindt, U., Kerschhaggl, M., Kowalski, M., Aldering, G., Antilogus, P., Aragon, C., Bailey, S., Baltay, C., Bongard, S., Buton, C., Canto, A., Cellier-Holzem, F., Childress, M., Chotard, N., Copin, Y., Fakhouri, H.~K., Gangler, E., Guy, J., Kim, A., Nugent, P., Nordin, J., Paech, K., Pain, R., Pecontal, E., Pereira, R., Perlmutter, S., Rabinowitz, D., Rigault, M., Runge, K., Saunders, C., Scalzo, R., Smadja, G., Tao, C., Thomas, R.~C., Weaver, B.~A., and Wu, C., Measuring cosmic bulk flows with Type Ia supernovae from the Nearby Supernova Factory, Astronomy and Astrophysics, 560, A90 Rigault, M., Copin, Y., Aldering, G., Antilogus, P., Aragon, C., Bailey, S., Baltay, C., Bongard, S., Buton, C., Canto, A., Cellier-Holzem, F., Childress, M., Chotard, N., Fakhouri, H.~K., Feindt, , U., Fleury, M., Gangler, E., Greskovic, P., Guy, J., Kim, A.~G., Kowalski, M., Lombardo, S., Nordin, J., Nugent, P., Pain, R., P{\'e}contal, E., Pereira, R., Perlmutter, S., Rabinowitz, D., Runge, K., Saunders, C., Scalzo, R., Smadja, G., Tao, C., Thomas, R.~C., and Weaver, B.~A., Evidence of environmental dependencies of Type Ia supernovae from the Nearby Supernova Factory indicated by local H-alpha, Astronomy and Astrophysics, 560, A66 Alhassid, Yoram C.N. 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Biochemistry 52: 7703-7706 (2013) supporting information S0-State Model of the Oxygen-Evolving Complex of Photosystem II, Rhitankar Pal, Christian F. A. Negre, Leslie Vogt, Ravi Pokhrel, Mehmed Z. Ertem, Gary W. Brudvig, and Victor S. Batista. Biophys. J 105: 2323-2332 (2013) Membrane permeation induced by aggregates of human islet amyloid polypeptides, Chetan Poojari, Dequan Xiao, Victor S. Batista, Birgit Strodel. J. Am. Chem. Soc. 135: 19064-19067 (2013) Spectral Tuning of Ultraviolet Cone Pigments: An Interhelical Lock Mechanism, Sivakumar Sekharan, Victoria L. Mooney, Ivan Rivalta, Manija A. Kazmi, Maureen Neitz, Jay Neitz, Thomas P. Sakmar, Elsa C. Y. Yan, Victor S. Batista. Dalton Trans. 43: 576-583 (2014) EXAFS Simulation Refinement Based on Broken-Symmetry DFT Geometries for the Mn (IV)-Fe(III) Center of Class I RNR from Chlamydia trachomatis, Sandra Luber, Sophie Leung, Carmen Herrmann, Wen-Ge Han, Louis Noodleman and Victor S. Batista. J. Phys. Chem. A 118: 3090-3099 (2014). Excited State Intramolecular Hydrogen Transfer (ESIHT) of 1,8-Dihydroxy-9,10-Anthraquinone (DHAQ) Characterized by Ultrafast Electronic and Vibrational Spectroscopy and Computational Modeling. Omar Mohammed, Dequan Xiao, Victor S. Batista, Erik T. J. Nibbering. J. Chem. Theory Comput accepted (2014). The MoD-QM/MM Structural Refinement Method: Characterization of Hydrogen Bonding in the Oxytricha nova G-quadruplex Junming Ho, Michael B. Newcomer, Christina M. Ragain, Jose A. Gascon, Enrique R. Batista, J. Patrick Loria and Victor S. Batista. J. Phys. Chem. Lett. 4: 745-748 (2013) Functional Role of Pyridinium During Aqueous Electrochemical Reduction of CO2 on Pt(111), Mehmed Z. Ertem, Steven J. Konezny, C. Moyses Araujo and Victor S. Batista. Inorg. Chem. 52: 6752-6764 (2013) Hydroxamate Anchors for Improved Photoconversion in Dye- Sensitized Solar Cells, Timothy Brewster, Steven J. Konezny, Lauren Martini, Stafford Sheehan, Charles A. Schmuttenmaer, Victor S. Batista and Robert H. Crabtree. J. Phys. Chem. A 117: 5269-5279 (2013) Photoinduced Proton Coupled Electron Transfer in 2-(2'- Hydroxyphenyl)benzothiazole, Sandra Luber, Katrin Adamczyk, Erik Nibbering and Victor S. Batista. Solar Energy Conversion: Dynamics of Interfacial Electron and Excitation Transfer (2013) The Royal Society of Chemistry, Chapter 1, p. 1-36, Ed. Piotr Piotrowiak Computational Modeling of Photocatalytic Cells by Steven Konezny and Victor S. Batista. J. Phys. Chem. C 117: 24462-24470 (2013). Efficiency of Interfacial Electron Transfer from Zn-Porphyrin Dyes into TiO2 Correlated to the Linker Single Molecule Conductance, Christian F. A. Negre, Rebecca L. Milot, Lauren A. Martini, Wendu Ding, Robert H. Crabtree and Victor S. Batista. Chem. Phys. Chem. 15: 1138-1147 (2014) Linker Rectifiers for Covalent Attachment of Transition Metal Catalysts to Metal-Oxide Surfaces, Wendu Ding, Christian F. A. Negre, Julio L. Palma, Alec C. Durrell, Laura J. Allen, Karin J. Young, Rebecca L. Milot, Charles A. Schmuttenmaer, Gary W. Brudvig, Robert H. Crabtree and Victor S. Batista. J. Phys. Chem. C 118: 8316-8321 (2014). High-conductance conformers in histograms of current- voltage characteristics Wendu Ding, Christian F. A. Negre, Leslie Vogt, and Victor S. Batista. J. Chem. Theory Comput 10: 3393−3400 (2014). Single Molecule Rectification Induced by the Asymmetry of a Single Frontier Orbital Wendu Ding, Christian F. A. Negre, Leslie Vogt, and Victor S. Batista. Topics in Catalysis [Special Issue on CO2 Reduction] accepted (2014). Electrochemical Reduction of Aqueous Imidazolium on Pt (111) by Proton Coupled Electron Transfer, Kuo Liao, Mikhail Askerka, Elizabeth L. Zeitler, Andrew B. Bocarsly and Victor S. Batista. J. Phys. Chem. B accepted (2014). Steered Quantum Dynamics for Energy Minimization, Micheline Soley, Andreas Markmann, and Victor S. Batista. Bazavov, Alexei 1. A. Bazavov et al, Phys. Rev. D88 (2013) 094021 2. A. Bazavov et al, J. Phys. Conf. Ser. 535 (2014) 012031 Bell, Alexis Getsoian, A; Zhai, Z; Bell, A.T. J. Am. Chem. Soc. In Press 2014 Getsoian, A; Bell, A.T. J. Phys. Chem. C 2013, 117, 25562-25578. Max Duarte, Ann S. Almgren, and John B. Bell, "A Low Mach Number Model for Moist Atmospheric Flows," submitted for publication. M. Cai, A. Nonaka, B. E. Griffith, J. B. Bell, and A. Donev, "Efficient Variable-Coefficient Finite-Volume Stokes Solvers," Commun. Comput. Phys., 16, 1263-1297, 2014. Ann Almgren, John Bell, Andy Nonaka and Michael Zingale, "Low Mach Number Modeling of Stratified Flows," Finite Volumes for Complex Applications VII -- Methods and Theoretical Apsects, Springer Proceedings in Mathematics and Statistics, eds. J. Fuhrmann, M. Ohlberger, C. Rohde, Berlin, June 2014. A. Dubey, A. Almgren, J. Bell, M. Berzins, S. Brandt, G. Bryan, P. Colella, D. Graves, M. Lijewski, F. Loffler, B. O'Shea, E. Schnetter, B. Van Straalen, K. Weide "A Survey of High Level Frameworks in Block-Structured Adaptive Mesh Refinement Packages", Journal of Parallel and Distributed Computing, to appear, 2014. Zarija Lukic, Casey Stark, Peter Nugent, Martin White, Avery Meiksin, Ann Almgren, "The Lyman-alpha forest in optically-thin hydrodynamical simulations," submitted for publication. C. M. Malone, M. Zingale, A. Nonaka, A. S. Almgren, and J. B. Bell, "Multidimensional Modeling of Type I X-ray Bursts. II. Two-Dimensional Convection in a Mixed H/He Accretor", Astrophysical Journal, 788, 115, 2014. J.C. Dolence, A. Burrows, and W. Zhang, "Two-Dimensional Core-Collapse Supernova Models with Multi-Dimensional Transport," submitted to ApJ. K. Balakrishnan, A. Garcia, A. Donev, and J. Bell, "Fluctuating hydrodynamics of multispecies nonreactive mixtures" Physical Review E, vol. 89, No. 1, January 2014. Woosley, Stan Ke-Jung Chen, Alexander Heger, Stan Woosley, Ann Almgren, and Daniel Whalen, "Pair Instability Supernovae of Very Massive Population III Stars" Astrophysical Journal, 792, 44, 2014. Ke-Jung Chen, Alexander Heger, S.E. Woosley, Ann S. Almgren, and Daniel J. Whalen, "Two-Dimensional Simulations of Pulsational Pair-Instability Supernova", Astrophysical Journal, 792, 28, 2014. Ke-Jung Chen, Alexander Heger, S.E. Woosley, Ann Almgren, and Daniel J. Whalen, and Jarrett L. Johnson, "The General Relativitistic Instability Supernova of a Supermassive Population III Star", Astrophysical Journal, 790, 162, 2014. A. J. Aspden, M. S. Day and J. B. Bell, "Turbulence-Chemistry Interaction in Lean Premixed Hydrogen Combustion," Proceedings of the Combustion Institute, to appear, 2014. M. Emmett, W. Zhang, J.B. Bell, "High-Order Algorithms for Compressible Reacting Flow with Complex Chemistry", Combustion Theory and Modelling, pp. 361-387, May 2014. Ke-Jung Chen, Alexander Heger, and Ann S. Almgren, "Numerical Approaches for Multidimensional Simulations of Stellar Explosions", Astronomy and Computing, 3-4, pp. 70-78, Nov.-Dec. 2013. Bellan, Josette 1.G. Borghesi and J. Bellan, Irreversible entropy production rate in high- pressure turbulent reactive flows, Proc. of the Comb. Inst., doi. 10.1016/j.proci.2014.05.016, 2014 2.G. Borghesi and J. Bellan, Models for the Large Eddy Simulation equations to describe multi-species mixing occurring at supercritical pressure, accepted for publication in Int. J. Energ. Mat. Chem. Prop., 7/28/2014 Benedek, Roy First-Principles Analysis of Phase Stability in Layered-Layered Composite Cathodes for Lithium-Ion Batteries Iddir, H, Benedek, R CHEMISTRY OF MATERIALS Volume: 26 Issue: 7 Pages: 2407-2413 DOI: 10.1021/cm403256a Published: APR 8 2014 Berg, Bernd B.A. Berg and Hao Wu, SU(3) deconfining phase transition with finite volume corrections due to a confined exterior, Phys. Rev. D 88 (2013) 074507. Berg, Larry Berhanu, Workalemahu Full length amylin oligomer aggregation: insights from molecular dynamics simulations and implications for design of aggregation inhibitors By Berhanu, Workalemahu Mikre; Masunov, Artem E. From Journal of Biomolecular Structure and Dynamics (2014), 32(10), 1651-1669 Atomistic mechanism of polyphenol amyloid aggregation inhibitors: Molecular Dynamics study of Curcumin, Exifone and Myricetin interaction with the segment of tau peptide oligomer By Berhanu Workalemahu M; Masunov Artem E From Journal of biomolecular structure & dynamics (2014), 1-52. E.J. Alred, E.G. Scheele, Workalemahu M. Berhanu and U.H.E. Hansmann (2014) Stability of Iowa Mutant and Wild Type Aβ-peptide Aggregates, submitted for publication. Blanquart, Guillaume Xuan, Y., Blanquart, G. Effects of aromatic chemistry-turbulence interactions on soot formation in a turbulent non-premixed flame, Proceedings of the Combustion Institute (2014), in press. Verma, S., Xuan, Y., Blanquart, G. An Improved Bounded Semi-Lagrangian Scheme for the Turbulent Transport of Passive Scalars, Journal of Computational Physics (2014), 272, 1-22. Xuan, Y., Blanquart, G., A flamelet-based a priori analysis on the chemistry tabulation of polycyclic aromatic hydrocarbons in non-premixed flames, Combustion and Flame (2014), 161, 1516-1525. Xuan, Y., Blanquart, G., Mueller, M.E., Modeling curvature effects in diffusion flames using a laminar flamelet model, Combustion and Flame (2014), 161, 1294-1309. Boman, Erik Scalable Matrix Computations on Scale-Free Graphs Using 2D Graph Partitioning, E.G. Boman, K.D. Devine, S. Rajamanickam, SC13, Nov. 2013. Bonoli, Paul N. Bertelli, E. F. Jaeger, J. C. Hosea, C. K. Phillips, L. Berry, S. P. Gerhardt, D. Green, B. LeBlanc, R. J. Perkins, P. M. Ryan, G. Taylor, E. J. Valeo, and J. R.Wilson, "Full wave simulations of fast wave heating losses in the scrape-off layer of NSTX and NSTX-U", Nuclear Fusion 54, 083004 (2014). P. T. Bonoli, "Review of recent experimental and modeling progress in the lower hybrid range of frequencies at ITER relevant parameters", The Physics of Plasmas 21, 061508 (2014). Jungpyo Lee and John C. Wright, "A block-tridiagonal solver with two-level parallelization for finite element-spectral codes", Computer Physics Communications 185, 2598?2608 (2014). J. C. Wright and N. Bertelli, "The effects of finite electron temperature and diffraction on lower hybrid wave propagation", Plasma Physics and Controlled Fusion 56, 035006 (2014). J. C. Wright, A. Bader, L. A. Berry, P. T. Bonoli, R. W. Harvey, E. F. Jaeger, J.-P. Lee, A. Schmidt, E. D?Azevedo, I. Faust, C. K. Phillips, and E. Valeo, ?Time dependent evolution of RF-generated non-thermal particle distributions in fusion plasmas?, Plasma Physics and Controlled Fusion 56, 045007 (2014). C. Yang, P. T. Bonoli, J. C. Wright, B. Ding, R. Parker, S. Shiraiwa, and M. H. Lia, "Modelling of the EAST lower-hybrid current drive experiment using GENRAY/CQL3D and TORLH/CQL3D", accepted for publication in Plasma Physics and Controlled Fusion (2014). Borrill, Julian "Measurement of the Cosmic Microwave Background Polarization Lensing Power Spectrum with the POLARBEAR experiment". PolarBear collaboration. Physical Review Letters accepted on 25 April 2014. "Evidence for Gravitational Lensing of the Cosmic Microwave Background Polarization from Cross- Correlation with the Cosmic Infrared Background". Physical Review Letters, Volume 112, Issue 13, id.131302 Title: Planck intermediate results. XIV. Dust emission at millimetre wavelengths in the Galactic plane Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Title: Planck intermediate results. XV. A study of anomalous microwave emission in Galactic clouds Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Title: Planck intermediate results. XVI. Profile likelihoods for cosmological parameters Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Title: Planck intermediate results. XVII. Emission of dust in the diffuse interstellar medium from the far-infrared to microwave frequencies Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Title: Planck intermediate results. XVIII. The millimetre and sub-millimetre emission from planetary nebulae Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Title: Planck intermediate results. XIX. An overview of the polarized thermal emission from Galactic dust Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Title: Planck intermediate results. XX. Comparison of polarized thermal emission from Galactic dust with simulations of MHD turbulence Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Title: Planck intermediate results. XXI. Comparison of polarized thermal emission from Galactic dust at 353GHz with optical interstellar polarization Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Title: Planck intermediate results. XXII. Frequency dependence of thermal emission from Galactic dust in intensity and polarization Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Planck intermediate results. XXIII. Galactic plane emission components derived from Planck with ancillary data Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Planck intermediate results. XXVI. Optical identification and redshifts of Planck clusters with the RTT150 telescope Authors: Planck Collaboration Reference: Submitted to Astronomy & Astrophysics Bourg, Ian Hamm L.M., Bourg I.C., Wallace A.F., Rotenberg B. Molecular simulation of CO2- and CO3-brine-mineral systems. Rev. Mineral. Geochem. 77: 189-228 (2013). Holmboe M., Bourg I.C. Molecular dynamics simulations of water and sodium diffusion in smectite interlayer nanopores as a function of pore size and temperature. J. Phys. Chem. C 118:1001-1013 (2014). Bowen, Benjamin Oliver Rübel, Annette Greiner, Shreyas Cholia, Katherine Louie, E. Wes Bethel, Trent R. Northen, and Benjamin P. Bowen, "OpenMSI: A High-Performance Web-Based Platform for Mass Spectrometry Imaging" Analytical Chemistry 2013 85 (21), 10354-10361, DOI: 10.1021/ac402540a. Katherine B. Louie, Benjamin P. Bowen, Xiaoliang Cheng, James E. Berleman, Romy Chakraborty, Adam Deutschbauer, Adam Arkin, and Trent R. Northen, Replica-Extraction-Transfer Nanostructure-Initiator Mass Spectrometry Imaging of Acoustically Printed Bacteria, Analytical Chemistry 2013 85 (22), 10856- 10862. Bin Dong, Suren Byna, and John Wu, "Expediting Scientific Data Analysis with Reorganization," IEEE Cluster 2013 Bragg, Arthur Yu, W.; Donohoo-Vallett, P. J.; Zhou, Z.; Bragg, A. E. Ultrafast photo-induced nuclear relaxation of a conformationally disordered conjugated polymer probed with transient absorption and femtosecond stimulated Raman spectroscopies. Journal of Chemical Physics, 141, 044201 (2014). (Selected for Editor's Picks, August 8th, 2014) Brown, Virginia Brush, Charles Bryantsev, Vyacheslav 1. Sun, XQ; Tian, GX; Xu, C; Rao, LF; Vukovic, S.; Kang, SO; Hay, PB. Quantifying the binding strength of U(VI) with phthalimidedioxime in comparison with glutarimidedioxime. DALTON TRANSACTIONS, 2014, Volume: 43, Issue: 2, pages: 551-557. Buluc, Aydin H. M. Aktulga, A. Buluc, S. Williams, and C. Yang. "Optimizing sparse matrix-multiple vectors multiplication for nuclear conguration interaction calculations". In Proceedings of the IPDPS. IEEE Computer Society, 2014. E. Georganas, A. Buluc, J. Chapman, L. Oliker, D. Rokhsar, and K. Yelick. "Parallel de bruijn graph construction and traversal for de novo genome assembly". In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis (SC'14), 2014. A. Lugowski, S. Kamil, A. Buluc, S. Williams, E. Duriakova, L. Oliker, A. Fox, and J. Gilbert. "Parallel processing of filtered queries in attributed semantic graphs". Journal of Parallel and Distributed Computing (JPDC)), 2014 (in press). Cahill, Kevin Cameron-Smith, Philip Stefanie Kirschke, et al., "Three decades of global methane sources and sinks", Nature Geosci., 6, 813-823, doi:10.1038/ngeo1955, 2013. Hsu, J., M.J. Prather, D. Bergmann, and P. Cameron-Smith, "Sensitivity of stratospheric dynamics to uncertainty in O3 production", Journal of Geophysical Research: Atmospheres, 118(16), 8984-8999, doi:10.1002/jgrd.50689, 2013. Santra, Biswajit [1] R. A. DiStasio Jr., B. Santra, Z. Li, X. Wu, and R. Car, "The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water. J. Chem. Phys. 141, 084502 (2014). Carlson, Joseph "Spin Response and Neutrino Emissivity of Dense Neutron Matter", G. Shen, S. Gandolfi, S. Reddy, J. Carlson, Phys. Rev. C 87, 025802 (2013). "Effects of the two-body and three-body hyperon-nucleon interactions in Lambda hypernuclei", D. Lonardoni, S. Gandolfi, F. Pederiva,, Phys. Rev. C 87, 041303(R) (2013). "Properties of trapped neutrons interacting with realistic nuclear Hamiltonians", Pieter Maris, James P. Vary, S. Gandolfi, J. Carlson, Steven C. Pieper, Phys. Rev. C 87, 054318 (2013). "Quantum Monte Carlo Calculations with Chiral Effective Field Theory Interactions", A. Gezerlis, I. Tews, E. Epelbaum, S. Gandolfi, K. Hebeler, A. Nogga, A. Schwenk, Phys. Rev. Lett. 111, 032501 (2013). "Accurate determination of the interaction between Lambda hyperons and nucleons from Auxiliary Field Diffusion Monte Carlo calculations", D. Lonardoni, F. Pederiva, S. Gandolfi, Phys. Rev. C 89, 014314 (2014). "Coupled-cluster calculations of nucleonic matter", G. Hagen, T. Papenbrock, A. Ekstrom, K. A. Wendt, G. Baardsen, S. Gandolfi, M. Hjorth-Jensen, C. J. Horowitz, Phys. Rev. C 89, 014319 "Quantum Monte Carlo calculations of light nuclei using chiral potentials", J. E. Lynn, J. Carlson, E. Epelbaum, S. Gandolfi, A. Gezerlis, A. Schwenk, arXiv:1406.2787, Physical Review Letters (in press). "In- Medium Similarity Renormalization Group with Chiral Two- Plus Three-Body Interactions?, H. Hergert, S. K. Bogner, S. Binder, A. Calci, J. Langhammer, R. Roth, and A. Schwenk, Phys. Rev. C 87, 034307 (2013) "Ab Initio Calculations of Even Oxygen Isotopes with Chiral Two- Plus Three-Body Interactions", H. Hergert, S. Binder, A. Calci, J. Langhammer, and R. Roth, Phys. Rev. Lett. 110,242501 (2013) "Nonperturbative Shell Model Interactions from the In-Medium Similarity Renormalization Group", S. K. Bogner, H. Hergert, J. D. Holt, A. Schwenk, S. Binder, A. Calci, J. Langhammer, and R. Roth, arXiv:1402.1407 [nucl-th], accepted for publication in Phys. Rev. Lett. "Predicting energies of small clusters from the inhomogeneous unitary Fermi gas", J Carlson, S Gandolfi, Physical Review A90 (R), 011601, 2014. "Neutral Weak Current Two-Body Contributions in Inclusive Scattering from Carbon-12", A Lovato, S Gandolfi, J Carlson, SC Pieper, R Schiavilla, Physical Review Letters 112 (18), 182502, 2014. "Exploiting Intrinsic Triangular Geometry in Relativistic He3+ Au Collisions to Disentangle Medium Properties", JL Nagle, et al., Phys. Rev. Letters (in press) 2014. "Corrections to nuclear energies and radii in finite oscillator spaces", R. J. Furnstahl, G. Hagen, and T. Papenbrock, Phys. Rev. C 86, 031301 (2012). "Universal properties of infrared oscillator basis extrapolations:, S. N. More, A. Ekstrom, R. J. Furnstahl, G. Hagen, and T. Papenbrock, Phys. Rev. C 87, 044326 (2013). "Systematic expansion for infrared oscillator basis extrapolations", R. J. Furnstahl, S. N. 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Phan, "On the 3-D structure and dissipation of reconnection-driven flow-bursts," Geophys. Res. Lett., 41, 3710 (2014) Ceder, Gerbrand [1] J. Lee, A. Urban, X. Li, D. Su, G. Hautier and G. Ceder, Unlocking the Potential of Cation- Disordered Oxides for Rechargeable Lithium Batteries, Science 343 (2014) 519-522. [2] A. Urban, J. Lee and G. Ceder, The Configurational Space of Rocksalt-Type Oxides for High- Capacity Lithium Battery Electrodes, Adv. Energy Mater. 4 (13) (2014) 1400478. [3] Y. Mo, S. P. Ong and G. Ceder, Insights into Diffusion Mechanisms in P2 Layered Oxide Materials by First-Principles, Chem. Mater., online published [4] J. Kim, X. Li, C. J. Moore, S. H. Bo, P. G. Khalifah, C. P. Grey and G. Ceder, Chem. Mater. 26 (14) (2014) 4200-4206. Hsiao, Eric "Extensive HST ultraviolet spectra and multiwavelength observations of SN 2014J in M82 indicate reddening and circumstellar scattering by typical dust", Foley, Ryan J., Fox, O. D., McCully, C., Phillips, M. M., Sand, D. J., Zheng, W., Challis, P., Filippenko, A. V., Folatelli, G., Hillebrandt, W., Hsiao, E. Y., Jha, S. W., Kirshner, R. P., Kromer, M., Marion, G. H., Nelson, M., Pakmor, R., Pignata, G., Röpke, F. K., Seitenzahl, I. R., Silverman, J. M., Skrutskie, M., & Stritzinger, M. D.. 1, Monthly Notices of the Royal Astronomical Society, 2014 Cenko, Stephen "Constraints on the Progenitor System of the Type Ia Supernova 2014J from Pre-explosion Hubble Space Telescope Imaging", Kelly, Patrick L., Fox, Ori D., Filippenko, Alexei V., Cenko, S. Bradley, Prato, Lisa, Schaefer, Gail, Shen, Ken J., Zheng, WeiKang, Graham, Melissa L., & Tucker, Brad E.. 1, The Astrophysical Journal, 2014 Sako, Masao "Hubble Space Telescope and Ground-based Observations of the Type Iax Supernovae SN 2005hk and SN 2008A", McCully, Curtis, Jha, Saurabh W., Foley, Ryan J., Chornock, Ryan, Holtzman, Jon A., Balam, David D., Branch, David, Filippenko, Alexei V., Frieman, Joshua, Fynbo, Johan, Galbany, Lluis, Ganeshalingam, Mohan, Garnavich, Peter M., Graham, Melissa L., Hsiao, Eric Y., Leloudas, Giorgos, Leonard, Douglas C., Li, Weidong, Riess, Adam G., Sako, Masao, Schneider, Donald P., Silverman, Jeffrey M., Sollerman, Jesper, Steele, Thea N., Thomas, Rollin C., Wheeler, J. Craig, & Zheng, Chen. 1, The Astrophysical Journal, 2014 "Three Gravitationally Lensed Supernovae behind CLASH Galaxy Clusters", Patel, Brandon, McCully, Curtis, Jha, Saurabh W., Rodney, Steven A., Jones, David O., Graur, Or, Merten, Julian, Zitrin, Adi, Riess, Adam G., Matheson, Thomas, Sako, Masao, Holoien, Thomas W.-S., Postman, Marc, Coe, Dan, Bartelmann, Matthias, Balestra, Italo, Benítez, Narciso, Bouwens, Rychard, Bradley, Larry, Broadhurst, Tom, Cenko, S. Bradley, Donahue, Megan, Filippenko, Alexei V., Ford, Holland, Garnavich, Peter, Grillo, Claudio, Infante, Leopoldo, Jouvel, Stéphanie, Kelson, Daniel, Koekemoer, Anton, Lahav, Ofer, Lemze, Doron, Maoz, Dan, Medezinski, Elinor, Melchior, Peter, Meneghetti, Massimo, Molino, Alberto, Moustakas, John, Moustakas, Leonidas A., Nonino, Mario, Rosati, Piero, Seitz, Stella, Strolger, Louis G., Umetsu, Keiichi, & Zheng, Wei. 1, The Astrophysical Journal, 2014 "Estimating the First-light Time of the Type Ia Supernova 2014J in M82", Zheng, WeiKang, Shivvers, Isaac, Filippenko, Alexei V., Itagaki, Koichi, Clubb, Kelsey I., Fox, Ori D., Graham, Melissa L., Kelly, Patrick L., & Mauerhan, Jon C.. 1, The Astrophysical Journal, 2014 "The Type IIb Supernova 2013df and its Cool Supergiant Progenitor", Van Dyk, Schuyler D., Zheng, WeiKang, Fox, Ori D., Cenko, S. Bradley, Clubb, Kelsey I., Filippenko, Alexei V., Foley, Ryan J., Miller, Adam A., Smith, Nathan, Kelly, Patrick L., Lee, William H., Ben-Ami, Sagi, & Gal-Yam, Avishay. 1, The Astronomical Journal, 2014 "The Afterglow of GRB 130427A from 1 to 1016 GHz", Perley, D. A., Cenko, S. B., Corsi, A., Tanvir, N. R., Levan, A. J., Kann, D. A., Sonbas, E., Wiersema, K., Zheng, W., Zhao, X.-H., Bai, J.-M., Bremer, M., Castro-Tirado, A. J., Chang, L., Clubb, K. 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Taylor, S.M. Hagos, and L.R. Leung. 2013. Observed Scaling in Clouds and Precipitation and Scale Incognizance in Regional to Global Atmospheric Models. J. Clim., 26, 9313-9333, doi: 10.1175/JCLI-D-13-00005.1. Xu, Ye Xu, Y., R. Bahadur, C. Zhao, and L.R. Leung. 2013. Estimating the Radiative Forcing of Carbonaceous Aerosols Over California Based on Satellite and Ground Observations. J. Geophys. Res., 118, 11,148-11,160, doi: 10.1002/jgrd.50835. Yang, Q., L.R. Leung, S. Rauscher, T. Ringler, and M. Taylor. 2014. Spatial Resolution Dependence of Precipitation Extremes From Atmospheric Moisture Budgets in Aqua-Planet Simulations. J. Clim., 27(10), 3565-3581, doi: 10.1175/jcli-d-13-00468.1. Zhao, C., S. Chen, L.R. Leung, Y. Qian, J. Kok, R. Zaveri, and J. Huang. 2013. Uncertainty in Modeling Dust Mass Balance and Radiative Forcing From Size Parameterization. Atmos. Chem. Phys., 13, 10733-10753, doi:10.5194/acp-13-10733-2013. Li, Xiaoye (Sherry) 1) A.~Druinsky, B.~Austin, X.S.~ Li, O.~Marques, E.~Roman, S.~Williams, "A Roofline Performance Analysis of an Algebraic Multigrid PDE Solvers", poster, SC14, Nov. 16-21, 2014, New Orleans. 2) A. Napov and X.S. Li, "An algebraic multifrontal preconditioner that exploits the low-rank property", Numerical Linear Algebra with Applications, 2014 (in revision). Li, Yan "Characterization of One-Dimensional Molecular Chains of 4,4'-Biphenyl Diisocyanide on Au(111) by Scanning Tunneling Microscopy", Jing Zhou, Yan Li, Percy Zahl, Peter Sutter, Dario J. Stacchiola and Michael G. White, J. Chem. Phys., accepted in Special Topics Issue "Supramolecular Self-Assembly at Surfaces". Ligeti, Zoltan 1) Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents Sheer El-Showk (CERN), Miguel F. Paulos (Brown U.), David Poland (Yale U.), Slava Rychkov (CERN & Ecole Normale Superieure & Paris U., VI-VII & Ecole Normale Superieure, LPS), David Simmons-Duffin (Princeton, Inst. Advanced Study), Alessandro Vichi (LBL, Berkeley & UC, Berkeley). Published in J.Stat.Phys. xx (2014) xx http://link.springer.com/article/10.1007/s10955-014-1042-7 http://arxiv.org/abs/1403.4545 2) Jet Veto Clustering Logarithms Beyond Leading Order Simone Alioli, Jonathan R. Walsh (LBNL, Berkeley & UC, Berkeley). Published in JHEP 1403 (2014) 119 http://arxiv.org/abs/1311.5234 3) Conformal Field Theories in Fractional Dimensions S. El-Showk (IPhT, Saclay), M. Paulos (Brown U.), D. Poland (Yale U.), S. Rychkov (CERN & Ecole Normale Superieure & Paris U., VI-VII), D. Simmons-Duffin (Princeton, Inst. Advanced Study), A. Vichi (LBL, Berkeley & UC, Berkeley). Published in Phys.Rev.Lett. 112 (2014) 141601 http://arxiv.org/abs/1309.5089 4) Jet p_TResummation in Higgs Production at NNLL' + NNLO Iain W. Stewart (MIT, Cambridge, CTP), Frank J. Tackmann (DESY), Jonathan R. Walsh, Saba Zuberi (LBNL, Berkeley). Published in Phys.Rev. D89 (2014) 054001 http://arxiv.org/abs/1307.1808 5) Combining Higher-Order Resummation with Multiple NLO Calculations and Parton Showers in GENEVA Simone Alioli, Christian W. Bauer, Calvin J. Berggren (LBL, Berkeley), Andrew Hornig (Washington U., Seattle), Frank J. Tackmann (DESY), Christopher K. Vermilion, Jonathan R. Walsh, Saba Zuberi (LBL, Berkeley). Published in JHEP 1309 (2013) 120 http://arxiv.org/abs/1211.7049 Lin, Guang Bilionis I, N. Zabaras, B Konomi, and G Lin. Multi-output separable Gaussian process: Towards an efficient, fully Bayesian paradigm for uncertainty quantification, Journal of Computational Physics, 241:212-239, 2013. B. Konomi, G. Karagiannis, A. Sarkar, X. Sun, G. Lin, Bayesian Treed Multivariate Gaussian Process with Adaptive Design: Application to a Carbon Capture Unit, Technometrics, 56(2), 145158, 2014. B. Konomi, G. Karagiannis, G. Lin, On the Bayesian Treed Multivariate Gaussian Process with Linear Model of Coregionalization, Journal of Statistical Planning and Inference, in press. B. Konomi, G. Lin, Low-Cost Multi-output Gaussian Process with Application to Uncertainty Quantification, International Journal for Uncertainty Quantification, in press. G. Karagiannis, B. Konomi, G. Lin, Mixed shrinkage prior procedure for basis selection and global evaluation of gPC expansions in Bayesian framework: Applications to elliptic SPDEs, Journal of Computational Physics, in review. Konomi, B., G. Karagiannis, G. Lin, Bayesian treed Calibration: an application to Carbon capture with AX sorbent, Journal of American Statistical Association, under revision. D. Meng, B. Zheng, G. Lin, M.L. Sushko, Numerical Solution of 3D Poisson-Nernst- Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in Confined Environment, Communications in Computational Physics, in press. S. Xing, G. Lin, Modeling the Sedimentation of Red Blood Cells in Flow under Strong External Magnetic Body Force using a Lattice Boltzmann Fictitious Domain Method, Special Issue in Numerical Mathematics: Theory, Methods and Applications, in press. J. Liu, G. Lin, F. Sadre-Marandi, A comparative study of the weak Galerkin, discontinuous Galerkin, and mixed finite element methods Journal of Computational and Applied Mathematics, in press, DOI: 10.1016/j.cam.2014.06.024 Z. Zhang, X. Hu, T.Y. Hou, G. Lin, P. Yan, An adaptive ANOVA-based data-driven stochastic method for elliptic PDE with random coefficients, Communications in Computational Physics, 16: 571-598, 2014. doi:10.4208/cicp.270913.020414a G. Lin, J. Bao, Z. Xu, A three-dimensional phase field model coupled with lattice kinetics solver for modeling crystal growth in furnaces with accelerated crucible rotation and traveling magnetic field, Computers and Fluids, DOI:10.1016/j.compfluid.2014.07.027. Bao J, Z Hou, Y Fang, H Ren, and G. Lin, Uncertainty quantification for evaluating the impacts of fracture zone on pressure buildup and ground surface uplift during geological CO2 sequestration, Greenhouse Gases: science and technology, DOI: 10.1002/ghg.1362 M. J. Del Razo, W. Pan, H. Qian, G. Lin, Fluorescence Correlation Spectroscopy and Nonlinear Stochastic Reaction-Diffusion, Biological Physics, in press. E. Sousa, G. Lin, U. Shumlak, Uncertainty Quantification of the GEM Challenge Magnetic Reconnection Problem using the Multi-level Monte Carlo Method, International Journal for Uncertainty Quantification, in press. I. Bright, G. Lin, N. Kutz, Compressive Sensing Based Machine Learning Strategy For Characterizing The Flow Around A Cylinder With Limited Pressure Measurements, Physics of Fluids, 25, 127102 (2013); http://dx.doi.org/10.1063/1.4836815 W. Li, G. Lin, D. Zhang, An Adaptive-ANOVA-based PCKF for High-Dimensional Nonlinear Inverse Modeling, Journal of Computational Physics, Volume 258, 2014, Pages 752772 G. Lin, J. Liu, L. Mu, X. Ye, Weak Galerkin Finite Element Methods for Darcy Flow: Anisotropy and Heterogeneity, Journal of Computational Physics, DOI: 10.1016/j.jcp.2014.07.001. Z. Hou, D.W. Engel, D.H. Bacon, G. Lin, Y. Fang, H. Ren, Z. Fang, Uncertainty Analyses of CO2 Plume Expansion subsequent to Wellbore CO2 Leakage into Aquifers, International Journal of Greenhouse Gas Control, 27:69-80, 2014. doi:10.1016/j.ijggc.2014.05.004. S. Shao, N. Abdolrahim, D. F. Bahr, G. Lin, and H.M. Zbib, Stochastic Effects in Plasticity in Small Volumes, International Journal of Plasticity, 52, 117- 132, 2014. Lin, Zhihong 1.Particle simulation of lower hybrid wave propagation in fusion plasmas, J. Bao, Z. Lin, A. Kuley, and Z. X. Lu, Plasma Phys. Contr. Fusion 56, 095020 (2014). 2.Microturbulence in DIII-D Tokamak Pedestal. I. Electrostatic Instabilities, D. Fulton, Z. Lin, I. Holod, and Y. Xiao, Phys. Plasmas 21, 042110 (2014). 3.Radial Localization of Toroidicity-Induced Alfven Eigenmodes, Zhixuan Wang, Zhihong Lin, Ihor Holod, W. W. Heidbrink, Benjamin Tobias, Michael Van Zeeland, and M. E. Austin, Phys. Rev. Lett. 111, 145003 (2013). 4.Nonlinear generation of zonal fields by the beta-induced Alfven eigenmode in tokamak, H. S. Zhang and Z. Lin, Plasma Sci. Technol. 15, 969 (2013). 5.Verification of particle simulation of radio frequency waves in fusion plasmas, A. Kuley, Z. X. Wang, Z. Lin, and F. Wessel, Phys. Plasmas 20, 102515 (2013). 6.Does the orbit-averaged theory require a scale separation between periodic orbit size and perturbation correlation length? Wenlu Zhang and Zhihong Lin, Phys. Plasmas 20, 102306 (2013). 7.Nonlinear dynamics of beta-induced Alfven eigenmode in tokamak, H. S. Zhang, Z. Lin, W. Deng, I. Holod, Z. X. Wang, Y. Xiao, W. L. Zhang, Phys. Plasmas 20, 012510 (2013). 8.Comparison of toroidicity-induced Alfven eigenmodes and energetic particle modes by gyrokinetic particle simulations, Chenxi Zhang, Wenlu Zhang, Zhihong Lin, Ding Li, Phys. Plasmas 20, 052501 (2013). 9.R. E. Waltz, E. M. Bass, and G.M. Staebler, "Quasilinear model for energetic particle diffusion in radial and velocity space", Phys. Plasmas 20, 042510 (2013). 10.E. M. Bass and R. E. Waltz, "Gyrokinetic simulation of global and local Alfven eigenmodes driven by energetic particles in a DIII-D discharge", Phys. Plasmas 20, 012508 (2013). 11.The effect of the fast-ion profile on Alfven eigenmode stability, W.W. Heidbrink, M.A. Van Zeeland, M.E. Austin, E.M. Bass, K. Ghantous, N.N. Gorelenkov, B.A. Grierson, D.A. Spong, and B.J. Tobias, Nucl. Fusion 53, 093006 (2013). 12.Measurements of the eigenfunction of reversed shear Alfven eigenmodes that sweep downward in frequency, W. W. Heidbrink, M. E. Austin, D. A. Spong, B. J. Tobias, and M. A. Van Zeeland, Phys. Plasmas 20, 082504 (2013). 13.Energetic ion transport by microturbulence is insignificant in tokamaks, D. C. Pace, M. E. Austin, E. M. Bass, R. V. Budny, W. W. Heidbrink, ��, M. A. Van Zeeland, R.E. Waltz, et al., Phys. Plasmas 20 (2013) 056108. 14.D. A. Spong, "Simulation of Alfvén frequency cascade modes in reversed shear-discharges using a Landau- closure model," Nuclear Fusion 53, 053008 (2013). 15.GTC simulation of ideal ballooning mode in tokamak plasmas, Z. Li, G. Sun, I. Holod, Y. Xiao, W. Zhang, and Z. Lin, Plasma Sci. Technol. 15, 499 16.Verification of Electromagnetic Fluid-Kinetic Hybrid Electron Model in Global Gyrokinetic Particle Simulation, I. Holod and Z. Lin, Phys. Plasmas 20, 032309 (2013). Liu, Adrian i) Adrian Liu, Aaron R. Parsons, Cathryn M. Trott, Epoch of reionization window. I. Mathematical formalism, Physical Review D 90, 023018 (2014) ii) Adrian Liu, Aaron R. Parsons, Cathryn M. Trott, Epoch of reionization window. II. Statistical methods for foreground wedge reduction, Phys. Rev. D 90, 023019 (2014) A, Liu and U. Thumm, `Laser-assisted XUV double ionization of helium', PRA 89, 063423 (2014) Being selected as KALEIDOSCOPE. Liu, Bin 1. Lei, Y., Liu, B., Lu, J., Libera, J.A., Greeley, J., and Elam, J.W., "Effects of Chlorine in Titanium Oxide on Palladium Atomic Layer Deposition", Journal of Physical Chemistry C (accepted) 2. Lei, Y., Zhao, H., Rivas, R. D., Lee, S., Liu, B, Lu, J., Stach, Eric S., Winans, R. E., Chapman, K. W., Greeley, J. P. Greeley, Miller, J. T., Chupas, P. J., and Elam, J. W., "Adsorbate-Induced Structural Changes in 1-3 nm Platinum Nanoparticles", Journal of the American Chemical Society, 2014 136, 9320-9326. 3. Liu, B., Cheng, L., Curtiss, L., and Greeley, J.P., Effects of van der Waals density functional calculations on trends in furfural adsorption and hydrogenation on close-packed transition metal surfaces, Surface Science 2014, 622, 51-59. 4. Cheng, L., Yin, C., Mehmood, F., Liu, B., Greeley, J., Lee, S., Lee, B., Seifert, S., Winans, R., Teschner, D., Schloegl, R., Vajda, S., and Curtiss, L. Reaction Mechanism for Direct Propylene Expodation by Alumina-Supported Silver Aggregates: The Role of the Particle/Support Interface, ACS Catalysis, 2014 4, 1, 32-39. Liu, Da-Jiang Realistic multisite lattice-gas modeling and KMC simulation of catalytic surface reactions: Kinetics and multiscale spatial behavior for CO-oxidation on metal(100) surfaces, D.-J. Liu, J.W. Evans, Progress in Surface Science, 88, 393-521 (2013). Dissociative adsorption of O2 on unreconstructed metal(100) surfaces: Pathways, energetics, and sticking kinetics, D.-J. Liu, J.W. Evans, Phys. Rev. B 89, 205406 (2014) Statistical mechanical models for dissociative adsorption of O2 on metal(100) surfaces with blocking, steering, and funneling, J.W. Evans, D.-J. Liu, J. Chem. Phys . 140, 194704 (2014). Real-time ab-initio KMC simulation of the self-assembly and sintering of bimetallic nanoclusters on fcc(100) surfaces: Au+Ag on Ag(100), Y. Han, D.-J. Liu, J.W. Evans, Nano Letters, 14, 4646 (2014). Transition and Noble Metals on the (0001) Surface of Graphite: Fundamental Aspects of Adsorption, Diffusion, and Morphology, D. Appy, H. Lei, C.-Z. Wang, M.C. Tringides, D.-J. Liu, J.W. Evans, and P.A. Thiel, Progress in Surface Science, in press (2014). A search for the structure of sulfur-induced reconstruction on Cu(111), D.-J. Liu, H. Walen, J. Oh, H. Lim, J.W. Evans, Y. Kim, P.A. Thiel, J. Phys. Chem. C, in press (2014). Analytic formulations for one-dimensional decay of rectangular homoepitaxial islands during coarsening on anisotropic fcc (110) surfaces, C.-J Wang, Y Han, H. Walen, S. M. Russell, P. A. Thiel, and J. W. Evans, Phys. Rev. B, 88, 155434 (2013). Liu, Feng 1. M. Zhou, Z. Liu, Z. Wang, Z. Bai, Y. Feng, M. G. Lagally, and Feng Liu, "Strain-Engineered Surface Transport in Si(001): Complete Isolation of the Surface State via Tensile Strain", Phys. Rev. Lett. 111,246801 (2013). 2. Z. F. Wang, S. Jin and Feng Liu, "Spatially separated spin carriers in spin- semiconducting graphene nanoribbons", Phys. Rev. Lett. 111, 096803 (2013). 3. C. Si, W. Duan, Z. Liu, and Feng Liu, First-Principles Calculations on the Effect of Doping and Biaxial Tensile Strain on Electron-Phonon Coupling in Graphene, Phys. Rev. Lett. 111, 196802 (2013). 4. Z. F. Wang, Z. Liu and Feng Liu,Quantum anomalous Hall effect in 2D organic topological insulator, Phys. Rev. Lett. 110, 196801 (2013). 5. Z. Liu, Z. F. Wang, J.-W. Mei, Y. Wu and Feng Liu, Flat Chern Band in a Two-Dimensional Organometallic Framework, Rev. Lett. 110, 106804 (2013). 6. Z. F. Wang, Zheng Liu and Feng Liu, Organic topological insulators in organometallic lattices, Nature Commun. 4, 1471 (2013) 7. Z. F. Wang, Li Chen, and Feng Liu, Tuning Topological Edge States of Bi(111) Bilayer Film by Edge Adsorption, Nano Lett., 14, 2879 (2014) 8. M. Liu and Feng Liu, Quantum Manifestation of Elastic Constants in Nanostructures, Nanotechnology 25, 135706 (2014) Jian Liu, 'Path integral Liouville dynamics for thermal equilibirum systems', J. Chem. Phys. 140, 224107 (2014) Liu, Keh-Fei Non-perturbative renormalization of overlap quark bilinears on 2+1-flavor domain wall fermion configurations. chiQCD Collaboration (Zhaofeng Liu et al.). [arXiv:1312.7628 [hep-lat]]. Phys.Rev. D90 (2014) 034505. From Nuclear Structure to Nucleon Structure. Keh-Fei Liu, [arXiv:1404.3754 [hep-ph]]. Nucl. Phys. A 928 (2014), 99. Oscillatory behavior of the domain wall fermions revisited. Jian Liang, Ying Chen, Ming Gong, Long-Cheng Gui, Keh-Fei Liu, Zhaofeng Liu, Yi-Bo Yang. [arXiv:1310.3532 [hep-lat]]. Phys.Rev. D89 (2014) 094507. Strangeness and charmness content of the nucleon from overlap fermions on 2+1-flavor domain-wall fermion configurations. XQCD Collaboration (M. Gong et al.). [arXiv:1304.1194 [hep-ph]]. Phys.Rev. D88 (2013) 014503. 1.Y. Zhang, Y. Hsieh, V. Volkov, D. Su, W. An, R. Si, Y. Zhu, P. Liu, J. X. Wang, R. R. Adzic, High performance Pt monolayer catalysts produced via core-catalyzed coating in ethanol, ACS Catalysis 4 (2014) 738-742. Liu, Ping 1.W. An, A. E. Baber, F. Xu, M. Soldemo, J. Weissenrieder, D. Stacchiola, P. Liu, ¡§Mechanistic study of CO titration on CuxO/Cu(111) (xT2) surfaces¡¨, ChemCatChem 6 (2014) 2364-2372. Louie, Steven S. Coh, L.Z. Tan, S.G. Louie, and M.L. Cohen, "Theory of the Raman Spectrum of Rotated Double-layer Graphene," Phys. Rev. B 88, 165431 (2013). D.Y. Qiu, F.H. da Jornada, and S.G. Louie,"Optical Spectrum of MoS2: Many-body Effects and Diversity of Exciton States," Phys. Rev. Lett. 111, 216805 (2013). Y. Sakai, G.D. Nguyen, R.B. Capaz, S. Coh, I.V. Pechenezhskiy, X. Hong, F. Wang, M.F. Crommie, S. Saito, S.G. Louie, and M.L. Cohen, "Intermolecular Interactions and Substrate Effects for an Adamantine Monolayer on a Au(111) surface," Phys. Rev. B 88, 235407 (2013). T. Bazhirov, S. Coh, S.G. Louie, and M.L. Cohen, "Importance of Oxygen Octahedra Tilts for the Electron-phonon Coupling in K-doped BaBiO3," Phys. Rev. B 88, 224509 (2013). Q. Zhou, S. Coh, M.L. Cohen, S.G. Louie, and A. Zettl, "Imprint of Transition Metal d Orbitals on a Graphene Dirac Cone," Phys. Rev. B 88, 235431 (2013). M.G. Menezes, R.B. Capaz, and S.G. Louie, "Ab Initio Quasiparticle Band Structure of ABA- and ABC-stacked Graphene Trilayers," Phys. Rev. B 89, 035431 (2014). A. Malashevich, M. Jain, and S.G. Louie, "First-principles DFT+GW Study of Oxygen Vacancies in Rutile TiO2," Phys. Rev. B 89, 075205 (2014). J. Lischner, D. Vigil-Fowler, and S.G. Louie, "Satellite Structures in the Spectral Functions of the Two-dimensional Electron Gas in Semiconductor Quantum Wells: A GW Plus Cumulant Study," Phys. Rev. B 89, 125430 (2014). K. F. Mak, F. H. da Jornada, K. He, J. Deslippe, N. Petrone, J. Hone, J. Shan, S. G. Louie, and T. F. Heinz, "Tuning Many-body Interactions in Graphene: The Effects of Doping on Excitons and Quasiparticle Lifetimes," Phys. Rev. Lett. 112, 207401 (2014). K. Liu, X. Hong, S.K. Choi, C. Jin, R.B. Capaz, J. Kim, W. Wang, X. Bai, S.G. Louie, E. Wang, and F. Wang, "Systematic Determination of Absolute Absorption Cross-section of Individual Carbon Nanotubes," Proc. National Academy of Sciences 111, 7564 (2014). M. Bernardi, D. Vigil-Fowler, J. Lischner, J.B. Neaton, and S.G. Louie, "Ab Initio Study of Hot Carriers in the First Picosecond after Sunlight Absorption in Silicon," Phys. Rev. Lett. 112 (25) 257402 (2014). G. Samsonidze, F.J. Ribeiro, M.L. Cohen, and S.G. Louie, "Quasiparticle and Optical Properties of Polythiophene-derived Polymers," Phys. Rev. B 90, 035123 (2014). S.K. Choi, C.-H. Park, and S.G. Louie, "Electron Supercollimation in Graphene and Dirac Fermion Materis Using One-dimensional Disorder Potentials," Phys. Rev. Letters 113, 026802 (2014). G. Samsonidze, M.L. Cohen, and S.G. Louie, "First-principles Study of Quasiparticle Energies of a Bipolar Molecule in a Scanning Tunneling Microscope Measurement," Comp. Mat. Sci 91, 187 (2014). J.I. Mustafa, B.D. Malone, M.L. Cohen, and S.G. Louie, "Band Offsets in c-Si/Si-XII Heterojunctions," Solid State Comm. 191, 6 (2014). Lu, Deyu 1. K. Müller, D. Lu, S. D. Senanayake, and D. E. Starr, "Monoethanolamine Adsorption on TiO2(110): Bonding, Structure, and Implications for Use as a Model Solid-Supported CO2 Capture Material," J. Phys. Chem. C 118, 1576 (2014). 2. Samuel A. Tenney, Deyu Lu, Feng He, Niv Levy, Uduwanage G. E. Perera, David E. Starr, Kathrin Müller, Hendrik Bluhm, and Peter Sutter, "Key StructureProperty Relationships in CO2 Capture by Supported Alkanolamines", J. Phys. Chem. C, 118 (33), 1925219258, (2014). 3. D. Lu, "Evaluation of model exchange-correlation kernels in the adiabatic connection fluctuation-dissipation theorem for inhomogeneous systems," J. Chem. Phys. 140, 18A520 (2014). Luk, Kam-Biu The Muon System of the Daya Bay Reactor Antineutrino Experiment Daya Bay Collaboration (Submitted on 1 Jul 2014 (v1), last revised 2 Jul 2014 (this version, v2)) Comments: 18 pages, 23 figures, submitted to NIM-A Subjects: Instrumentation and Detectors (physics.ins-det); High Energy Physics - Experiment (hep-ex) Cite as: arXiv:1407.0275 [physics.ins-det] Search for a Light Sterile Neutrino at Daya Bay F. P. An, A. B. Balantekin, H. R. Band, W. Beriguete, M. Bishai, S. Blyth, I. Butorov, G. F. Cao, J. Cao, Y. L. Chan, J. F. Chang, L. C. Chang, Y. Chang, C. Chasman, H. Chen, Q. Y. Chen, S. M. Chen, X. Chen, X. 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Amylin oligomer aggregation: insights from molecular dynamics simulations and implications for design of aggregation inhibitors By Berhanu, Workalemahu Mikre; Masunov, Artem E. From Journal of Biomolecular Structure and Dynamics (2014), 32(10), 1651- 1669. The atomic level interaction of polyphenols with the Aβ oligomer aggregate, a molecular dynamic guidance for rational drug design By Berhanu, Workalemahu Mikre; Masunov, Artem E. Edited By Watson, Ronald Ross; Preedy, Victor R.; Zibadi, Sherma From Polyphenols in Human Health and Disease (2014)1, 59-70,, 2 plates. Amylin oligomer aggregation: insights from molecular dynamics simulations and implications for design of aggregation inhibitors By Berhanu Workalemahu Mikre; Masunov Artem E From Journal of biomolecular structure & dynamics (2014), 32(10), 1651-69. 1) "Mechanism of Nonlinear Optical Enhancement and Supramolecular Isomerism in 1D Polymeric Zn(II) and Cd(II) Sulfates with Pyridine-aldoxime Ligands" Croitor, Lilia; Coropceanu, Eduard B.; Masunov, Artem E.; Rivera- Jacquez,Hector J.; Siminel, Anatolii V.; Fonari, Marina S. Journal of Physical Chemistry C (2014), 118(17), 9217-9227 2) Design of a New Optical Material with Broad Spectrum Linear and Two- Photon Absorption and Solvatochromism" Moreshead, William V.; Przhonska, Olga V.; Bondar, Mykhailo V.; Kachkovski, Alexei D.; Nayyar, Iffat H.; Masunov, Artem E.; Woodward, Adam W.; Belfield, Kevin D. 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Jansang, and E.A. Kotomin, First principles calculations of (Ba,Sr)(Co,Fe)O3- structural stability, Solid State Ionics, 2013, 230, 2126 . 11. O. Sharia, M.M.Kuklja, Rapid materials degradation induced by surfaces and voids: ab initio modeling of beta-octotetramethylene tetranitramine, J. Am. Chem. Soc. 2012, 134, 11815-11820. 12. L.G. Salamanca-Riba, R.A. Isaacs, J. Wan, K. Gaskell, Y. Jiang, M. Wuttig, A.N. Mansour, S.N. Rashkeev, M. Kukla, M. LeMieux, P.Y. Zavalij, J. Santiago, L. Hu, Three Dimensional Epitaxy of Carbon Nanostructures in Silver, submitted to Advanced Functional Materials 13. William Joost, Sreeramamurthy Ankem, Maija M. Kuklja, A Modified Embedded Atom Method Potential for the Titanium-Oxygen System, submitted to Mod. and Simul. Mat. Science and Engineering. 14. R. Tsyshevsky, S. Rashkeev, M. Kuklja, Electronic States and Optical Transitions at OrganicInorganic Interfaces: Pentaerythritol Tetranitrate on MgO Surface, submitted to Journal of Physical Chemistry C. 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Frenkel, "Effects of Adsorbate Coverage and Bond-Length Disorder on the d- Band Center of Carbon-Supported Pt Catalysts", Chem. Phys. Chem. 15 (2014) 1569. A.I. Frenkel, M.W. Cason, A. Elsen, U. Jung, M.W. Small, R.G. Nuzzo, F.D. Vila, J.J. Rehr, E.A. Stach, J.C. Yang, "Critical review: Effects of complex interactions on structure and dynamics of supported metal catalysts", J. Vac. Sci. Technol., A 32 (2014) 020801. M. Guzzo, J.J. Kas, L. Sponza, C. Giorgetti, F. Sottile, D. Pierucci, M.G. Silly, F. Sirotti, J.J. Rehr, L. Reining, "Multiple satellites in materials with complex plasmon spectra: From graphite to graphene", Phys. Rev. B 89 (2014) G.F. Bertsch and A.J. Lee, "Time-dependent mean-field theory for x-ray near-edge", Phys. Rev. B 89 (2014) 075135. R.S. Markiewicz, J.J. Rehr, A. Bansil, "Lattice Model of Resonant Inelastic X-Ray Scattering in Metals: Relation of a Strong Core Hole to the X-Ray Edge Singularity", Phys. Rev. Lett. 112 (2014) 237401. Reichler, Thomas Staten, P. W., T. Reichler, and J. Lu (2014): The transient circulation response to radiative forcings and surface warming, J. Climate Staten, P. W., and T. Reichler (2014): On the ratio between shifts in the eddy-driven jet and the Hadley cell edge, Clim. Dyn., 42 (5-6), 1229-1242, DOI: 10.1007/s00382-013-1905-7 Charlton-Perez, A., M. Baldwin, T. Birner, R. Black, A. Butler, N. Calvo, N. Davis, E. Gerber, N. Gillett, S. Hardiman, J. Kim, K. Krueger, Y. Lee, E. Manzini, B. McDaniel, L. Polvani, T. Reichler, T. Shaw, M. Sigmond, S. Son, M. Tohey, L. Wilcox, S. Yoden, B. Christiansen, F. Lott, D. Shindell, S. Yukimoto, S. Watanabe, (2013): On the lack of stratospheric dynamical variability in low-top versions of the CMIP5 models, J. Geophys. Res., 118 (6), 2494-2505, DOI: 10.1002/jgrd.50125 Ren, Chuang 2. R. Yan, J. Li, and C. Ren, Intermittent laser-plasma interactions and hot electron generation in shock ignition, Phys. Plasmas 21, 062705 (2014); http://dx.doi.org/10.1063/1.4882682 Rivera Jacquez, Hector Molecular Packing in Organic Solar Cell Materials: Insights from the Emission Line Shapes of P3HT/PCBM Polymer Blend Nanoparticles Crotty, Angela M.; Gizzi, Alicia N.; Rivera-Jacquez, Hector J.; Masunov, Artem E.; Hu, Zhongjian; Geldmeier, Jeff A.; Gesquiere, Andre J. Journal of Physical Chemistry C (2014), 118(34), 19975-19984. Polymeric Luminescent Zn(II) and Cd(II) Dicarboxylates Decorated by Oxime Ligands: Tuning the Dimensionality and Adsorption Capacity Croitor, Lilia; Coropceanu, Eduard B.; Masunov, Artem E.; Rivera-Jacquez, Hector J.; Siminel, Anatolii V.; Zelentsov, Vyacheslav I.; Datsko, Tatiana Ya.; Fonari, Marina S. Crystal Growth & Design (2014), 14(8), 3935-3948 Mechanism of Nonlinear Optical Enhancement and Supramolecular Isomerism in 1D Polymeric Zn(II) and Cd(II) Sulfates with Pyridine-4-aldoxime Ligands Croitor, Lilia; Coropceanu, Eduard B.; Masunov, Artem E.; Rivera-Jacquez, Hector J.; Siminel, Anatolii V.; Fonari, Marina S. From Journal of Physical Chemistry C (2014), 118(17), 9217-9227 Rodero, Ivan Javier Diaz Montes, Yu Xie, Ivan Rodero, Jaroslaw Zola, Baskar Ganapathysubramanian, Manish Parashar: Federated Computing for the Masses-Aggregating Resources to Tackle Large-Scale Engineering Problems. 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Ruebel, Oliver - Peterka, T., Morozov, D., Phillips, C.: High-Performance Computation of Distributed-Memory Parallel 3D Voronoi and Delaunay Tessellation. Proceedings of SC14, New Orleans, LA, 2014. - Ciprian Docan, Fan Zhang, Tong Jin, Hoang Bui, Qian Sun, Julian Cummings, Norbert Podhorszki Scott Klasky, Manish Parashar, ActiveSpaces: Exploring Dynamic Code Deployment for Extreme Scale Data Processing, Concurrency and Computation: Practice and Experience, 2014. (Accepted) - Solomon Lasluisa, Fan Zhang, Tong Jin, Ivan Rodero, Hoang Bui, Manish Parashar, In-situ Feature-based Objects Tracking for Data-Intensive Scientific and Enterprise Analytics Workflows, Cluster 2014. (Accepted) - Tong Jin, Fan Zhang, Qian Sun, Hoang Bui, Norbert Podhorszki, Scott Klasky, Hemanth Kolla, Jacqueline Chen, Robert Hager, Choong-Seock Chang, Manish Parashar, Leveraging Deep Memory Hierarchies for Data Staging in Coupled Data Intensive Simulation Workflows, Poster, IEEE Cluster 2014 (Accepted) - Hoang Bui, Robert Dyja, Fan Zhang, Qian Sun, Tong Jin, Baskar Ganapathysubramanian, Manish Parashar, Accelerating AMR-based Finite Element Simulation Workflows Using DataSpaces, Data-Intensive Scalable Computing Systems Workshop, SC 2014 (Submitted) - Marc Gamell, Ivan Rodero, Manish Parashar, Janine Bennett, Hemanth Kolla, Jacqueline Chen, Peer-Timo Bremer, Aaditya G. Landge, Attila Gyulassy, Patrick McCormick, Scott Pakin, Valerio Pascucci, Scott Klasky: Exploring power behaviors and trade-offs of in-situ data analytics. SC 2013 - S. Kumar, J. Edwards, P.-T. Bremer, A. Knoll, C. Christensen, V. Vishwanath, P. Carns, J. Schmidt, V. Pascucci. 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T. Heron1, M. Trassin, Y. Gao, J. Bosse, Q. He, J. Liu, C. Wang, S. Salahuddin, D. C. Ralph, D. G. Schlom, J. Iniguez, B. D. Huey and R. Ramesh, Deterministic Electrical Switching of Magnetism at Room Temperature, (accepted in Nature) Diana Berman, Sanket A. Deshmukh, Subramanian K.R.S. Sankaranarayanan, Ali Erdemir, and Anirudha V. Sumant "Extraordinary Macroscale Wear Resistance of One Atom Thick Graphene Layer" Advanced Functional Materials DOI: 10.1002/adfm.201401755 Ganesh Kamath, and Subramanian K. R. S. Sankaranarayanan. In Silico Based Rank-Order Determination and Experiments on Nonaqueous Electrolytes for Sodium Ion Battery Applications. Journal of Physical Chemistry C. 2014, 118 (25), pp 13406�13416. Diana Berman, Sanket A. Deshmukh, Subramanian K.R.S. Sankaranarayanan, Ali Erdemir, and Anirudha V. Sumant "Origin of macroscale superlubricity enabled by graphene nanoscroll formation" Science (Under review) Ganesh Kamath and Subramanian K.R.S. Sankaranarayanan "Atomistic mechanism of formation of hollow iron oxide nanoparticles" Manuscript submitted to Nanoletters Ganesh Kamath and Subramanian K.R.S. Sankaranarayanan. "Atomistic simulations of electric field sintering of nanoscale oxides" Manuscript Submitted to Applied Physics Letters Subramanian Sankaranarayanan, Badri Narayanan, Ganesh Kamath and Shriram Ramanathan. Role of chloride ions in inducing pitting corrosion and oxide breakdown in FeOx. Electrochem Acta journal special issue (Invited) (2014) Aspuru-Guzik, Alan Car, Roberto [1] R. A. DiStasio Jr., B. Santra, Z. Li, X. Wu, and R. Car, "The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water". J. Chem. Phys. 141, 084502 (2014). Savage, Martin Baryon masses at nonzero isospin/kaon density William Detmold, Amy N. Nicholson Phys.Rev. D88 (2013) 074501 Nuclear \sigma-terms and Scalar-Isoscalar WIMP-Nucleus Interactions from Lattice QCD S.R. 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Haranczyk - In-silico design of porous polymer networks: high-throughput screening for methane storage materials- Journal of the American Chemical Society 136 (2014) 5006-5022 2) L. Sarkisov, R.L. Martin, M. Haranczyk, B. Smit - On the flexibility of metal �organic frameworks- Journal of the American Chemical Society 136 (2014) 2228-2231 3) C. M. Simon, J. Kim, L-C. Lin, R. L. Martin, M. Haranczyk, B. Smit -Optimizing nanoporous materials for gas storage- Physical Chemistry Chemical Physics 16 (2014) 5499-5513 (featured on the issues cover) 4) M. Haranczyk, L.-C. Lin, K. Lee, R.L. Martin, J.B. Neaton, B. Smit -Methane storage capabilities of diamond analogues - Physical Chemistry Chemical Physics 15 (2013) 20937-20942 5) D. Holden, K. Jelfs, A. Trewin, D. Willock, M. Haranczyk, A. Cooper - Gas Diffusion in a Porous Organic Cage: Analysis of Dynamic Pore Connectivity using Molecular Dynamics Simulations- Journal of Physical Chemistry C 118 (2014) 12734-12743 6) J. Perry, S. Teich-McGoldrick, S. Meek, J. Greathouse, M. Haranczyk, M. Allendorf - Noble Gas Adsorption in Metal-Organic Frameworks Containing Open-Metal Sites- Journal of Physical Chemistry C 118 (2014) 11685-11698 7) Lin, L.-C., Lee, K., Gagliardi, L., Neaton, J. & Smit, B. Force-Field Development from Electronic Structure Calculations with Periodic Boundary Conditions: Applications to Gaseous Adsorption and Transport in MetalOrganic Frameworks.Journal of Chemical Theory and Computation(2014). doi:10.1021/ct500094w 8) Kim, J., Lin, L., Lee, K. & Neaton, J. Efficient Determination of Accurate Force Fields for Porous Materials Using ab Initio Total Energy Calculations. (2014). doi:10.1021/jp412368m Smith, Jeremy 1.D. Riccardi, H.-B. Guo, J. M. Parks, B. Gu, A.O. Summers, S.M. Miller, L. Liang and J.C. Smith, Why mercury prefers soft ligands. J. Phys. Chem. Lett., 2013, 4, 2317-2322. 2.D. Riccardi, H.-B. Guo, J. M. Parks, B. Gu, L. Liang, and J. C. Smith, Cluster-continuum calculations of hydration free energies of anions and group 12 divalent cations J. Chem. Theory Comput. 2013, 9, 555569. 3.Wymore, J.M. Parks, Z.-K. Yang, B.L. Hanson, Z. Fisher, S. Mason, M.P. Blakeley, T. Forsyth, J.P. Glusker, H.L. Carroll, J.C. Smith, D.A. Keen, D.E. Graham and A. Kovalevsky, L-arabinose binding, isomerization and epimerization by D-xylose isomerase: A combined X-ray/neutron crystallographic and molecular simulation study. P. Langan, A.K. Sangha, T. Structure, 2014, 22, 1-14. 4.J. Zhou, D. Riccardi, A. Beste, J.C. Smith and J.M. Parks, Mercury methylation by HgcA: Theory supports carbanion transfer to Hg(II) Inorg. Chem. 2014, 53, 772777. 5.A.K. Sangha, B.H. Davison, R.F. Standaert, M.F. Davis, J.C. Smith and J.M. Parks,Chemical factors that control lignin polymerization J. Phys. Chem. B., 2014, 118, 164170. 6.Alekozai E, GhattyVenkataKrishna P, Crowley M, Uberbacher E, Smith JC and Cheng X. Simulation Analysis of the Cellulase Cel7A Carbohydrate Binding Module on the Surface of the Cellulose Iβ. Cellulose, 2014, 21(2), 951-971 7.Ghattyvenkatakrishna P, Uberbacher E, Cheng X. Effect of the amyloid β hairpin's structure on the handedness of helices formed by its aggregates. FEBS Lett, 2013, 587(16):2649-55 8.Pan J, Cheng X, Monticelli L, Heberle FA, Kučerka N, Tieleman P, Katsaras J. The Molecular Structure of a Phosphatidylserine Bilayer Determined by Scattering and Molecular Dynamics Simulations. Soft Matter. 2014, 10(21):3716-25 9.Le RK, Harris BJ, Iwuchukwu IJ, Bruce BD, Cheng X, Qian S, Heller WT, O'Neill H, Frymier PD. Analysis of the solution structure of Thermosynechococcus elongatus photosystem I in n-dodecyl-β-d-maltoside using small-angle neutron scattering and molecular dynamics simulation. Arch Biochem Biophys. 2014, 550-551C:50-57 Snurr, Randall Y.J. Colon, R. Krishna, R.Q. Snurr, Strong influence of the H2 binding energy on the Maxwell-Stefan diffusivity in NU-100, UiO-68, and IRMOF-16, Micropor. Mesopor. Mater. 185, 190-196 (2014) Y.J. Colon, D. Fairen-Jimenez, C.E. Wilmer, R.Q. Snurr, High-throughput screening of porous crystalline materials for hydrogen storage capacity near room temperature, J. Phys. Chem. C, 118, 5383-5389 (2014). D. A. Gomez-Gualdron, O.V. Gutov, V. Krungleviciute, B. Borah, J. E. Mondloch, J. T. Hupp, T. Yildirim, O.K. Farha, R. Q. Snurr, "Computational design of metal-organic frameworks based on stable zirconium building units for storage and delivery of methane", Chem. Mat. DOI: 10.1021/cm502304e Solar-Lezama, Armando The following paper has been accepted for publication: Zhilei Xu, Shoaib Kamil, Armando Sola-Lezama, "MSL: A Synthesis Enabled Language for Distributed Implementations", SuperComputing 2014 Sonnad, Kiran Investigation into electron cloud effects in the International Linear Collider positron damping ring Phys. Rev. ST Accel. Beams 17, 031002 ? Published 17 March 2014 Sovinec, Carl F. Ebrahimi, E. B. Hooper, C. R. Sovinec, and R. Raman, "Magnetic reconnection process in transient coaxial helicity injection," Physics of Plasmas 20, 090702 (2013). E. B. Hooper, C. R. Sovinec, R. Raman, F. Ebrahimi, and J. E. Menard, "Resistive MHD simulations of helicity- injected startup plasmas in NSTX," Physics of Plasmas 20, 092510 (2013). J. B. O'Bryan and C. R. Sovinec, "Simulated flux-rope evolution during non-inductive startup in Pegasus," Plasma Physics and Controlled Fusion 56, 064005 (2014). E. C. Howell and C. R. Sovinec, "Solving the Grad-Shafranov equation with spectral elements," Computer Physics Communications 185, 1415 (2014). F. Ebrahimi, R. Raman, E. B. Hooper, C. R. Sovinec, and A. Bhattacharjee, "Physics of forced magnetic reconnection in coaxial helicity injection experiments in National Spherical Torus Experiment," Physics of Plasmas 21, 056109 (2014). Spera, Frank Lesher, C. and Spera, F., Thermodynamic and Transport Properties of silicate melts and magma, In: Encyclopedia of Volcanoes, H. Sigurdsson, Ed. (Academic Press, New York, 2015), In Press (ms available at http://magma.geol.ucsb.edu/index.html). Bohrson, W., Spera, F., Ghiorso, M., Brown, G., Creamer, J. and Mayfield, A. (2014), Thermodynamic model for energy-constrained open system evolution of crustal magma bodies undergoing simultaneous assimilation, recharge and crystallization: The magma chamber simulator. J. Petrology (2014) 55 (9): 1685-1717.doi: 10.1093/petrology/egu036 (ms available at http://magma.geol.ucsb.edu/index.html) Dane Tikunoff and Spera, F. (2014), Thermal conductivity of molten and glassy NaAlSi3O8, CaMgSi2O6 and Mg2SiO4 by Non Equilibrium Molecular Dynamics at elevated Temperature and Pressure: Part 1- Methods and Results. American Mineralogist, November/December 2014 issue. Spong, Don D. A. Spong, Long-term Landau-fluid simulation of RSAE/TAE instabilities, Plasma and Fusion Research, Volume 8, 3403077 (March, 2014), available online at http://www.jspf.or.jp/PFR/PFR_articles/pfr2014S2/pfr2014_09-3403077.html. D. A. Spong, "Simulation of Alfvén frequency cascade modes in reversed shear-discharges using a Landau- closure model," Nuclear Fusion 53, 053008 (2013). Kunihiro Ogawa, Mitsutaka Isobe, Kazuo Toi, Akihiro Shimizu, Donald A. Spong, Masaki Osakabe, Satoshi Yamamoto and the LHD Experiment Group, Energetic ion losses caused by magnetohydrodynamic activity resonant and non-resonant with energetic ions in Large Helical Device, Plasma Phys. Control. Fusion 56 (2014) 094005. A.W. Clark, M. Doumet, K.C. Hammond, Y. Kornbluth, D.A. Spong, R. Sweeney, F.A. Volpe, Proto- CIRCUS tilted-coil tokamaktorsatron hybrid: Design and construction, Fusion Engineering and Design, available online 29 August (2014) at: http://dx.doi.org/10.1016/j.fusengdes.2014.07.012. W.W. Heidbrink, M.A. Van Zeeland, M.E. Austin, E.M. Bass, K. Ghantous, N.N. Gorelenkov, B.A. Grierson, D.A. Spong, and B.J. Tobias, The effect of the fast-ion profile on Alfvén eigenmode stability, Nucl. Fusion 53 (September, 2013) 093006. Martin, P. ; Puiatti, M.E.; Agostinetti, P.; Agostini, M.; Alonso; et al., Overview of the RFX-mod fusion science programme, Nuclear Fusion, v 53, n 10, October 2013. W.W. Heidbrink, M.E. Austin, D.A. Spong, B.J. Tobias, and M.A. Van Zeeland, Measurements of the eigenfunction of reversed shear Alfvén eigenmodes that sweep downward in frequency, Phys. Plasmas 20 (August, 2013) 082504. Stan, Cristiana Stan, C., and L. Xu, 2014: Climate simulations and projections with a super-parameterized climate model. Environmental Modeling and Software, 60, 134-152, doi:10.1016/j.envsoft.2014.06.013 Zhu, X., L. Xu and C. Stan, 2014: Projected changes of the tropical Atlantic vertical wind shear and its relationship with ENSO in the SP-CCSM4. Journal of Climate, doi: doi: http://dx.doi.org/10.1175/JCLI-D- 14-00002.1 Stocks, G. Malcolm 1)Samolyuk, GD; Osetsky, YN; Stoller, RE. The influence of transition metal solutes on the dislocation core structure and values of the Peierls stress and barrier in tungsten. J Phys.-Cond. Matter. 25 (2013) p. 025403. 2)Samolyuk, GD; Golubov, SI; Osetsky, YN; Stoller, RE. Self-interstitial configurations in hcp Zr: a first principles analysis. Phil. Mag. Lett. 93 (2013) pp. 93-100. 3)G.D. Samolyuk, A.V. Barashev, S.I. Golubov, Y.N. Osetsky, R.E. Stoller, Analysis of the anisotropy of point defect diffusion in hcp Zr, Acta Mater. 78 (2014) p 173. 4)Chandrima Mitra, Randy S. Fishman, Satoshi Okamoto, Ho Nyung Lee and Fernando A. Reboredo, Ground-state and spin-wave dynamics in Brownmillerite SrCoO2.5a combined hybrid functional and LSDA + U study, J. Phys.: Condens. Matter 26 036004 (2014). 5)Chandrima Mitra, Tricia Meyer, Ho Nyung Lee, and Fernando Reboredo, Oxygen Diffusion Pathways in Brownmillerite SrCoO2.5: Influence of Structure and Chemical Potential, Accepted in Journal of Chemical Physics (in press) (2014). 6)C. Park, G. A. Rojas, S. Jeon, S. J. Kelly, S. Smith, B. G. Sumpter, M. Yoon, P. Maksymovych, Weak competing interactions control assembly of strongly bonded TCNQ ionic acceptor molecules on silver surfaces (2014, Phys. Rev. B, accepted). 7)X. Li, M.-W. Lin, A. A. Puretzky, J. C. Idrobo, M. Chi, M. Yoon, C. Ma, C. M. Rouleau, I. I. Kravchenko, D. B. Geohegan, K. Xiao, Controlled Vapor Phase Growth of Single Crystalline, Two-Dimensional GaSe Crystals with High Photoresponse (2014, Scientific Report 4, 5497). 8)P.A. Hu, J. Zhang, M. Yoon, W. Feng, P. Tan, W. Zheng, J. Liu, X. Wang, J.C. Idrobo, D.B. Geohegan, K. Xiao, Highly Sensitive Phototransistors Based on Two-Dimensional GaTe Nanosheets with Direct Bandgap (2014, Nano Research 7, 694). 9)Hybrid density functional theory meets quasiparticle calculations: a consistent electronic structure approach" by V. Atalla, M. Yoon, F. Caruso, P. Rinke, M. Scheffler, Phys. Rev. B. 88, 165122 (2013). 10)D.B. Geohegan, A.A. Puretzky, M. Yoon, G. Eres, C. Rouleau, K. Xiao, J. Jackson, J. Readle, M. Regmi, N. Thonnard, G. Duscher, M. Chisholm, K. More, Laser Interactions for the Synthesis and In Situ Diagnostics of Nanomaterials, book chapter of Lasers in Materials Science, Springer International Publishing Switzerland (2014). 11)T. Iwashita, D. M. Nicholson, and T. Egami , Elementary excitations and crossover phenomena in liquids, Phys. Rev. Lett 110 205504 (2013). 12)D. M. Nicholson, Madhusudan Ojha, and T. Egami , First principles local stress in crystalline and amorphous metals, accepted for publication in J. Phys. Cond. Matt. (2013). 13)Jarrahi, Zeynab, Cao, Yunhao, Hong, Tu, Puzyrev, Yevgeniy, Wang, Bin, Lin, Junhao, Huffstutter, Alex, Pantelides, Sokrates, Xu, Yaqiong , "Enhanced Photoresponse in Curled Graphene Ribbons", accepted in Nanoscale 14)Li, Q; Owens, JR; Han, CB; Sumpter, BG; Lu, WC; Bernholc, J; Meunier, V; Maksymovych, P; Fuentes-Cabrera, M; Pan, MH, Self-Organized and Cu-Coordinated Surface Linear Polymerization. Scientific Reports 3, 2102 (2013). 15)A.A. Aczel, G.E. Granroth, G.J. MacDougall, W.J.L. Buyers, D.L. Abernathy, G.D. Samolyuk, G.M. Stocks, S.E. Nagler, Quantum oscillations of nitrogen atoms in uranium nitride, Nature Comm. 3, 1124 (2013). 16)Michio Okada, Eli Rotenberg, S D Kevan, J Schäfer, Balazs Ujfalussy, G Malcolm Stocks, B Genatempo, E Bruno and E W Plummer, Evolution of the electronic structure in Mo1−xRex alloys, New J. Phys. 15, 093010 (2013). Striolo, Alberto R.K. Kalluri, M.M. Biener, M.E. Suss, M.D. Merrill, M. Stadermann, J.D. Santiago, T.F. Baumann, J. Biener, A. Striolo, Unraveling the Potential and Pore-Size Dependent Capacitance of Slit-Shaped Graphitic Carbon Pores in Aqueous Electrolytes, Physical Chemistry Chemical Physics 15 (2013) 2309-2320. T.A. Ho, A. Striolo, Polarizability Effects in Molecular Dynamics Simulations of the Graphene-Water Interface, J. Chem. Phys. 138 (2013) 054117/1-9. M. Suttipong, N.R. Tummala, A. Striolo, C. Silvera Batista, J. Fagan, Salt-Specific Effects in Aqueous Dispersions of Carbon Nanotubes, Soft Matter 9 (2013) 3712-3719. Also featured in the cover art of Soft Matter, volume 9, issue # 14, April 14th, 2013. D.R. Cole, Ok Salim, A. Phan, G. Rother, A. Striolo, L. Vlcek, Carbon-Bearing Fluids at Nanoscale Interfaces, Procedia Earth and Planetary Science 7 (2013) 175-178. X.-C. Luu, J. Yu, A. Striolo, Nanoparticles Adsorbed at the Water/Oil Interface: Coverage Effects on Structure and Diffusion, Langmuir 29 (2013) 7221-7228. A. Phan, D.R. Cole. A. Striolo, Liquid Ethanol Simulated on Crystalline Alpha Alumina, J. Phys. Chem. B 117 (2013) 3829-3840. D. Argyris, A. Phan, P.D. Ashby, A. Striolo, Hydration Structure at the α-Al2O3 (0001) Surface: Insights from Experimental AFM Force Spectroscopy Data and Atomistic Molecular Simulations, J. Phys. Chem. C 117 (2013) 10433-10444. T.A. Ho, R.K. Kalluri, M.M. Biener, J. Biener, A. Striolo, Partition and Structure of Aqueous NaCl and CaCl2 Electrolytes in Carbon-Slit Electrodes, J. Phys. Chem. C 117 (2013) 13609-13619. M. Hu, D.P. Linder, M. Buongiorno Nardelli, A. Striolo, Hydrogen Adsorption on Platinum-Gold Nanoparticles: A Density Functional Theory Study, J. Phys. Chem. A 117 (2013) 15050-15060. D. Konatham, J. Yu, T.A. Ho, A. Striolo, Simulation Insights for Graphene-Based Water Desalination Membranes, Langmuir 29 (2013) 11884-11897. Also featured in the cover art of Langmuir, volume 29, issue # 38, September 24th, 2013. X.-C. Luu, J. Yu, A. Striolo, Ellipsoidal Janus Nanoparticles Adsorbed at Water-Oil Interface: Some Evidence of Emergent Behavior, J. Phys. Chem. B 117 (2013) 13922-13929. T.A. Ho, A. Striolo, Capacitance Enhancement via Electrode Patterning, J. Chem. Phys. 139 (2013) 204708. A. Phan, D.R. Cole, A. Striolo, Aqueous Methane in Slit-Shaped Silica Nanopores: High Solubility and Traces of Hydrates, J. Phys. Chem. C 118 (2014) 4860-4868. M. Suttipong, B.P. Grady, A. Striolo, Self-Assembled Surfactants on Patterned Surfaces: Confinement and Cooperative Effects on Aggregates Morphology, Phys. Chem. Chem. Phys. 16 (2014) 16388-16398. Also A. Phan, D.R. Cole, A. Striolo, Preferential Adsorption from Liquid Water-Ethanol Mixtures in Alumina Pores, Langmuir 30 (2014) 8066-8077. T.A. Ho, A. Striolo, Molecular Dynamics Simulation of the Graphene-Water Interface: Comparing Water Models, Mol. Simul. (2014) in Press. Z. Liu, J.-G. Yu, E.A. ORear, A. Striolo, Aqueous Dual-Tailed Surfactants Simulated on the Alumina Surface, J. Phys. Chem. B (2014) in Press. T. Le, D.R. Cole, A. Striolo, Propane Simulated in Silica Pores: Adsorption Isotherms, Molecular Structure, and Mobility, Chem. Eng. Sci. (2014) in press. Sun, Jianwei Surendran Assary, Rajeev Please see the Project proposal Teranishi, Keita Keita Teranishi and Michael A. Heroux. 2014. Toward Local Failure Local Recovery Resilience Model using MPI-ULFM. In Proceedings of the 21st European MPI Users' Group Meeting (EuroMPI/ASIA '14). ACM, New York, NY, USA, , Pages 51 , 6 pages. DOI=10.1145/2642769.2642774 http://doi.acm.org/10.1145/2642769.2642774 Tillett, Jason Comparison of temporal and spectral scattering methods using acoustically large breast models derived from magnetic resonance images: A. J. Hesford, J. C. Tillett, J. P. Astheimer, and R. C. Waag. J. Acoust. Soc. Am., 136:Pages 682-692 (2014). PMC JournalIn Process Tilson, Jeffrey J. L. Tilson and W. C. Ermler, Massively Parallel Spin-Orbit Configuration Interaction, Theoretical Chemistry Accounts (2014), 133, 1564-72. Toussaint, Doug The Fermilab Lattice and MILC Collaborations: A. Bazavov, C. Bernard, C. Bouchard, C. DeTar, D. Du, A.X. El-Khadra, J. Foley, E.D. Freeland, E. Gamiz, Steven Gottlieb, U.M. Heller, J. Kim, A.S. Kronfeld, J. Laiho, L. Levkova, P.B. Mackenzie, E.T. Neil, M.B. Oktay, Si-Wei Qiu, J.N. Simone, R. Sugar, D. Toussaint, R.S. Van de Water, and Ran Zhou, Determination of \\|V_us\| from a lattice-QCD calculation of the K to pi l nu semileptonic form factor with physical quark masses, Phys. Rev. Lett. 112, 112001 (2014) [arXiv:1312.1228]. The Fermilab Lattice and MILC Collaborations: J. Bailey, A. Bazavov, C. Bernard, C. Bouchard, C. DeTar, D. Du, A.X. El-Khadra, J. Foley, E.D. Freeland, E. Gamiz, Steven Gottlieb, U.M. Heller, A.S. Kronfeld, J. Laiho, L. Levkova, P.B. Mackenzie, E.T. Neil, Si-Wei Qiu, J.N. Simone, R. Sugar, D. Toussaint, R.S. Van de Water, and Ran Zhou, Update of \|V_cb\| from the B-bar to D* l nu form factor at zero recoil with three-flavor lattice QCD, Phys. Rev. D 89, 114504 (2014) [arXiv:1403.0635]. Ludmilla Levkova and Carleton DeTar, Quark-gluon plasma in an external magnetic field, Phys. Rev. Lett. 112, 012002 (2014) [arXiv:1309.1142]. Trebotich, David D. Trebotich, M. F. Adams, C. I. Steefel, S. Molins and C. Shen, High Resolution Simulation of Pore Scale Reactive Transport Processes Associated with Carbon Sequestration, Computing in Science and Engineering, Nov/Dec Leadership Computing Issue, 2014. Sergi Molins, David Trebotich, Li Yang, Jonathan B. Ajo-Franklin, Terry J. Ligocki, Chaopeng Shen and Carl Steefel, Pore-Scale Controls on Calcite Dissolution Rates from Flow-through Laboratory and Numerical Experiments, Environmental Science and Technology, accepted May 27, 2014. dx.doi.org/10.1021/es5013438 C. Steefel, S. Molins, D. Trebotich, Pore scale processes associated with subsurface CO2 injection and sequestration, Reviews in Mineralogy and Geochemistry, 77, pp. 259-303, 2013. doi:10.2138/rmg.2013.77.8 D. Trebotich and D. T. Graves, An Adaptive Finite Volume Method for Incompressible Navier-Stokes Equations in Complex Geometries", under revision Comm. App. Math. Comp. Sci. Tretiak, Sergei Trinkle, Dallas 1. Calculation of strain effects on vacancy-mediated diffusion of impurities in fcc structures: General approach and application to Ni1-xSi x. T. Garnier, Z. Li, Maylise Nastar, V. R. Manga, P. Bellon, and D. R. Trinkle. 2. Diffusion of Si impurities in Ni under stress: A first-principles study. T. Garnier, V. R. Manga, P. Bellon, and D. R. Trinkle. Phys. Rev. B 90, 024306 (2014), doi://10.1103/PhysRevB.90.024306, Database: hdl.handle.net/11115/239 3. Quantitative modeling of solute drag by vacancies in face-centered-cubic alloys. T. Garnier, D. R. Trinkle, M. Nastar, and P. Bellon. Phys. Rev. B 89, 144202 (2014), doi://10.1103/PhysRevB.89.144202 Tsung, Frank B. J. Winjum, F. S. Tsung, W. B. Mori, Interactions of laser speckles due to stimulated Raman scattering. In preparation. B. J. Winjum, V. K. Decyk, W. B. Mori, J. W. Banks, R. L. Berger, T. Chapman, S. Brunner, Kinetic simulations of externally driven and instability driven nonlinear electron plasma waves relevant to stimulated Raman scattering. In preparation. Turner, Alexander Tyson, Trevor 1. T. Yu, P. Gao, T. Wu, T. A. Tyson, and R. Lalancette, "Ferroelectricity in Single Crystal InMnO3", Appl. Phys. Lett. 102, 172901 (2013). 2. T. A. Tyson, T. Wu, H. Y. Chen, J. Bai, K. H. Ahn, K. I. Pandya, S. B. Kim and S. W. Cheong, "Measurements and ab initio molecular dynamics simulations of the high temperature ferroelectric transition in hexagonal RMnO3", J. Appl. Phys. 110 , 084116 (2011). 3. P. Gao, Z. Chen, T. A. Tyson, T. Wu, K. H. Ahn, Z. Liu, R. Tappero, S. B. Kim, and S.-W. Cheong, High-pressure structural stability of multiferroic hexagonal RMnO3 (R=Y, Ho, Lu) (2011), Phys. Rev. B 83, 224113 (2011). Van Der Ven, Anton Alexandra Emly, Emmanouil Kioupakis, and Anton Van der Ven; "Phase Stability and Transport Mechanisms in Antiperovskite Li3OCl and Li3OBr Superionic Conductors", Chemistry of Materials Van Veenendaal, Michel 1. "Novel High-Pressure Monoclinic Metallic Phase of V2O3", Yang Ding, Cheng-Chien Chen, Qiaoshi Zeng, Heung-Sik Kim, Myung Joon Han, Mahalingam Balasubramanian, Robert Gordon, Fangfei Li, Ligang Bai, Dimitry Popov, Steve M. Heald, Thomas Gog, Ho-kwang Mao, and Michel van Veenendaal, Physical Review Letters 112, 056401 (2014) [Editor's Suggestion]. 2. "Persistent spin excitations in doped antiferromagnets revealed by resonant inelastic light scattering", C. J. Jia, E. A. Nowadnick, K. Wohlfeld, Y. F. Kung, C.-C. Chen, S. Johnston, T. Tohyama, B. Moritz and T. P. Devereaux, Nature Communications 5, 3314 (2014). 3. "Spin chain in magnetic field: limitations of the large-N mean-field theory", Krzysztof Wohlfeld, Cheng-Chien Chen, Michel van Veenendaal, and Thomas P. Devereaux, accepted for publication in Acta Physica Polonica A. Van de Walle, Chris E. Kioupakis, Q. Yan, D. Steiauf, and C. G. Van de Walle, Temperature and carrier-density dependence of Auger and radiative recombination in nitride optoelectronic devices, New J. of Phys. 15, 125006 (2013). A. Alkauskus, Q. Yan, and C. G. Van de Walle, First-principles theory of nonradiative carrier capture via multiphonon emission, Phys. Rev. B 90, 075202 (2014). [Editors suggestion] A. Alkauskas, B. Buckley, D. D. Awschalom, and C. G. Van de Walle, First-principles theory of the luminescence lineshape for the triplet transition in diamond NV centres, New J. Phys., 16, 073026 (2014). J. L. Lyons, A. Janotti, and C. G. Van de Walle, "Effects of hole localization on limiting p-type conductivity in oxide and nitride semiconductors'', J. Appl. 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Wu, Journal of Chemical Physics, 140, 044714, 2014. 14. "A contact-corrected density functional theory for electrolytes at an interface", J. Jiang, D. Cao, D. Henderson, and J. Wu, Phys. Chem. Chem. Phys., 16, 3934, 2014. 15."Fast prediction of hydration free energies for SAMPL4 blind test from a classical density functional theory", The Journal of Computer-Aided Molecular Design, 28:299�304, 2014. 16."Molecular density functional theory for multiscale modeling of hydration free energy", J. Fu, Y. Liu, J. Wu, Chemical Engineering Science, submitted, 2014. 17. "A liquid-state theory for electron correlation functions and thermodynamics", S. Zhao, P. Feng, and J. Wu, Chemical Physics Letters, 556, 336�340, 2013. 18. "Morphological control and growth mechanism of branched titanium dioxide nanowires", D. Li, F. Soberanis, J. Fu, J. Wu, and D. Kisailus, Crystal Growth & Design, 13 (2), 422-428, 2013. Wu, John (Kesheng) 1. Parallel Data Analysis Directly on Scientific File Formats. S Blanas, K Wu, S Byna, B Dong, A Shoshani. SIGMOD 2014. 2. Hello ADIOS: the challenges and lessons of developing leadership class I/O frameworks. Q Liu, J Logan, Y Tian, H Abbasi, N Podhorszki, JY Choi, S Klasky, et al. Concurrency and Computation: Practice and Experience 26 (7), 1453-14733. Parameter Analysis of the VPIN (Volume synchronized Probability of Informed Trading) Metric. JH Song, K Wu, HD Simon. In Quantitative Financial Risk Management: Theory and Practice. 2014. 4. Exploring Irregular Time Series Through Non-Uniform Fourier Transform. JH Song, M Lopez de Prado, HD Simon, K Wu. 2014. 5. SDS: a framework for scientific data services. B Dong, S Byna, K Wu. Proceedings of the 8th Parallel Data Storage Workshop, 27-32. 2013. 6. Fast Change Point Detection for electricity market analysis W Gu, J Choi, M Gu, H Simon, K Wu. Big Data, 2013 IEEE International Conference on, 50-57. 2013 7. Expediting scientific data analysis with reorganization of data. B Dong, S Byna, K Wu. Cluster Computing (CLUSTER), 2013 IEEE International Conference on, 1-8. 2013 8. Accelerating gene context analysis using bitmaps. A Romosan, A Shoshani, K Wu, V Markowitz, K Mavrommatis. SSDBM 2013. 9. Optimizing fastquery performance on lustre file system. KW Lin, S Byna, J Chou, K Wu. SSDBM. 2013. Wu, Ruqian J. Hu and R.Q. Wu, "Control of the Magnetism and Magnetic Anisotropy of a Single-Molecule Magnet with an Electric Field", Phys. Rev. Lett. 110, 097202 (2013). L. Lang, C.D. Dong, G.H. Chen, J.H. Yang,X. Gu, H.J. Xiang, R.Q. Wu, and X.G. Gong, Self-Stopping Effect of Lithium Penetration into Silicon Nanowires, NanoScale, 5, 12394 (2013). J. Karel, Y.N. Zhang, C. Bordel, K.H. Stone, T.Y. Chen, C.A. Jenkins, D. J. Smith, J. Hu, R. Q. Wu, S.M. Heald, J.B. Kortright and F. Hellman, Enhanced Magnetism in Amorphous FexSi1-x Thin Films, Matter. Res. Exp. 1, 026102 (2014). P. V. Ong, N. Kioussis, P. K. Amiri, J. G Alzate, K. L. Wang, G.P. Carman, J. Hu and R.Q. Wu, Electric field control and effect of Pd capping on magnetocrystalline anisotropy in FePd thin films: A first-principles study, Phy. Rev. B 89, 094422 (2014). J. Hu and R.Q. Wu, Giant magnetic anisotropy of transition-metal dimers on defected graphene, Nano. Lett, 14, 1853 (2014). L. Ma, J. Hu, M. Costa, Z. Shi, J. Li, X. G. Xu, Y. Jiang, G. Y. Guo, R. Q. Wu, and S. M. Zhou, Magneto- optical Kerr effect in L10 FePdPt ternary alloys: Experiments and first-principles calculations, J. Appl. Phys. 115, 183903 (2014). Wu, Xifan Robert A. DiStasio Jr.1, Biswajit Santra, Zhaofeng Li, Xifan Wu and Roberto Car, The individual and collective effects of exact exchange and dispersion, J. Chem. Phys., 141, 084502 (2014). Hongwei Wang, Igor V. Solovyev, Wenbin Wang, Xiao Wang, Philip J. Ryan, David J. Keavney, Jong-Woo Kim, Thomas Z. Ward, Leyi Zhu, Jian Shen, X. M. Cheng, Lixin He, Xiaoshan Xu, and Xifan Wu, Structural and electronic origin of the magnetic structures in hexagonal LuFeO3, Physical Review B, 90, 014436 (2014). Wu, Zhigang 1.Marc Dvorak and Zhigang Wu, Geomatrically induced transitions between semimetal and semiconductor in graphene, Phys. Rev. B 90, 115415 (2014). 2.Huashan Li, Tianlei Zhou, Zhigang Wu, Alan Sellinger and Mark T. Lusk, Tailoring the optical gap of silicon quantum dots without changing their size, Phys. Chem. Chem. Phys. 16, 19275 (2014). 3.Marc Dvorak, Xiao-Jia Chen and Zhigang Wu, Quasiparticle energies and excitonic effects in dense solid hydrogen near metallization, Phys. Rev. B 90, 035103 (2014). 4.Huashan Li, Zhigang Wu, Tianlei Zhou, Alan Sellinger, and Mark T. Lusk, Double superexchange in quantum dot mesomaterials, Energy Environ. Sci. 7, 1023 (2014). 5.Huashan Li, Zhigang Wu, and Mark T. 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Adversarial Attacks on Copyright Detection Systems Revision as of 09:57, 15 November 2020 by T34sun (talk \| contribs) (→‎3.2. Interpreting the fingerprint extractor as a CNN) 3 3.2. Interpreting the fingerprint extractor as a CNN 4 3.3 Formulating the adversarial loss function 5 5. Conclusion Luwen Chang, Qingyang Yu, Tao Kong, Tianrong Sun Copyright detection system is one of the most commonly used machine learning systems; however, the hardiness of copyright detection and content control systems to adversarial attacks, inputs intentionally designed by people to cause the model to make a mistake, has not been widely addressed by public. Copyright detection system are vulnerable to attacks for three reasons. 1. Unlike to physical-world attacks where adversarial samples need to survive under different conditions like resolutions and viewing angles, any digital files can be uploaded directly to the web without going through a camera or microphone. 2. The detection system is open which means the uploaded files may not correspond to an existing class. In this case, it will prevent people from uploading unprotected audio/video whereas most of the uploaded files nowadays are not protected. 3. The detection system needs to handle a vast majority of content which have different labels but similar features. For example, in the ImageNet classification task, the system is easily attacked when there are two cats/dogs/birds with high similarities but from different classes. 3.2. Interpreting the fingerprint extractor as a CNN The generic neural network model consists two convolutional layers and a max-pooling layer, depicted in the figure below. As mentioned above, the convolutional neural network is well-known for its properties of temporarily localized and transformational invariant. The purpose of this network is to generate audio fingerprinting signals that extract features that uniquely identify a signal, regardless of the starting and ending time of the inputs. File:cov network.jpg 3.3 Formulating the adversarial loss function In the previous section, local maxima of spectrogram are used to generate fingerprints by CNN, but a loss has not been quantified how similar tow fingerprints are. After the loss is found, standard gradient methods can be used to find a perturbation $\delta$, which can be added to a signal so that the copyright detection system will be tricked. Also, a bound is set to make sure the generated fingerprints are close enough to the original audio signal. $$\text{bound:}\ \|\|\delta\|\|_p\le\epsilon$$ where $\|\|\delta\|\|_p\le\epsilon$ is the $l_p$-norm of the perturbation and $\epsilon$ is the bound of the difference between the original file and the adversarial example. To compare how similar two binary fingerprints are, Hamming distance is employed. Hamming distance between two strings is the number of digits that are different. For example, the Hamming distance between 101100 and 100110 is 2. Let $\psi(x)$ and $\psi(y)$ be two binary fingerprints outputted from the model, the number of peaks shared by $x$ and $y$ can be found through $\|\psi(x)\cdot\psi(y)\|$. Now, to get a differentiable loss function, the equation is found to be $$J(x,y)=\|\phi(x)\cdot\psi(x)\cdot\psi(y)\|$$ This is effective for white-box attacks with knowing the fingerprinting system. However, the loss can be easily minimized by modifying the location of the peaks by one pixel, which would not be reliable to transfer to black-box industrial systems. To make it more transferable, a new loss function which involves more movements of the local maxima of the spectrogram is proposed. The idea is to move the locations of peaks in $\phi(x)$ outside of neighborhood of the peaks of $\phi(y)$. In order to implement the model more efficiently, two max-pooling layers are used. One of the layers has a bigger width $w_1$ while the other one has a smaller width $w_2$. For any location, if the output of $w_1$ pooling is strictly greater than the output of $w_2$ pooling, then it can be concluded that no peak in that location with radius $w_2$. The loss function is as the following: $$J(x,y) = \sum_i\bigg(ReLU\bigg(c-\bigg(\underset{\|j\| \leq w_1}{\max}\phi(i+j;x)-\underset{\|j\| \leq w_2}{\max}\phi(i+j;x)\bigg)\bigg)\cdot\psi(i;y)\bigg)$$ The equation above penalizes the peaks of $x$ which are in neighborhood of peaks of $y$ with radius of $w_2$. The activation function uses $ReLU$. $c$ is the difference between the output of two max-pooling layers. Lastly, instead of the maximum operator, smoothed max function is replaced here: $$S_\alpha(x_1,x_2,...,x_n) = \frac{\sum_{i=1}^{n}x_ie^{\alpha x_i}}{\sum_{i=1}^{n}e^{\alpha x_i}}$$ $\alpha$ is a smoothing hyper parameter. When $\alpha$ approaches positive infinity, $S_\alpha$ is closer to the actual max function. To summarize, the optimization problem can be formulated as the following: $$ \underset{\delta}{\min}J(x+\delta,x)\\ s.t.\|\|\delta\|\|_{\infty}\le\epsilon $$ where $x$ is the input signal, $J$ is the loss function with the smoothed max function. In conclusion, many industrial copyright detection systems used in the popular video and music website such as YouTube and AudioTag are significantly vulnerable to adversarial attacks established in the existing literature. By building a simple music identification system resembling that of Shazam using neural network and attack it by the well-known gradient method, this paper firmly proved the lack of robustness of the current online detector. The intention of this paper is to raise the awareness of the vulnerability of the current online system to adversarial attacks and to emphasize the significance of enhancing our copyright detection system. More approach, such as adversarial training needs to be developed and examined, in order to protect us against the threat of adversarial copyright attack. Retrieved from "http://wiki.math.uwaterloo.ca/statwiki/index.php?title=Adversarial_Attacks_on_Copyright_Detection_Systems&oldid=44467"	CommonCrawl
mildbyte's notes tagged 'games' Travelling murderer problem: planning a Morrowind all-faction speedrun with simulated annealing, part 3 @mildbyte 4 years, 9 months ago \| programming \| games \| morrowind \| python \| Last time, I showed a way to generate a decent route through the quest graph as well as came up with a rough character progression that can be used to quickly complete all faction questlines in Morrowind. Today, I'll analyse Mark/Recall and other miscellaneous transport modes, deal with an interesting Temple quest, showcase the final route and finally publish the code for the route planner. Here's a map of the route for those of you who like migraines: The points of interest here are joined with colour-coded lines. White is walking or flying, red is Mages Guild teleports, blue is Almsivi/Divine Intervention spells, yellow is travel by boat/silt strider and green is Recalls. Mark/Recall are a pair of spells in Morrowind that allow the player to teleport around the game world. Casting Mark remembers a given place and Recall teleports the player to the last position the Mark was cast. Only one Mark can be active at a given time: casting it again removes the previous Mark. Imagine casting Mark at the beginning of a dungeon (unlike Skyrim, Morrowind dungeons don't have a quick shortcut back to the start of the dungeon from its end) and teleporting there, or placing a Mark next to an NPC providing transport services. This could shave a considerable amount of time from the route. There are several questions here. Firstly, given a route, what's the most efficient arrangement of Mark and Recall casts for it? Secondly, can we change the optimiser to take into account the Mark/Recall spells? The most optimal route through the quest graph might not be the most optimal when Mark/Recall spells are used. Single Mark For now, imagine we have already settled on a route and can only place a Mark once in the game, in fact only at one node in the quest graph (and not anywhere on the route between nodes). What's the best place for it? Since we have a matrix of fastest node-to-node travel times, given a Mark position, at each node in the route we can decide whether we want to proceed to the next node directly or by first teleporting to the Mark and then going to the next node. Try placing a Mark at each the nodes in the route and see which one gives the fastest overall time: def get_best_mark_position(route): return min( # can't use the mark until we've placed it (sum(get_node_distance(r1, r2) for r1, r2 in zip(route[:i], route[1:i])) + sum( # after placing the mark, we have a choice of recalling to it and going to the next node # or going to the next node directly min(get_node_distance(r, r2), get_node_distance(r1, r2)) for r1, r2 in zip(route[i:], route[i + 1:])), i, r) for i, r in enumerate(route) I ran that and found out that by far the best position for a single Mark was right at the questgiver who's standing next to the Mages Guild teleport. This makes a lot of sense: a Recall to the Mages Guild gives the player instant access to 4 cities. Coupled with Intervention spells, this lets the player reach essentially any town in the game within a matter of minutes, if not seconds. Multiple Marks Now, again, given a single route through the quests, let's allow the player to place multiple Marks so that they can Recall to the last one they placed. I first tried the same idea that I did for the route optimiser: take multiple possible arrangements of Marks (basically a Boolean array of the same length as the route that determines whether, at each node, we place a Mark there or not after we visit it), mutate each one (by randomly adding or removing Marks) and score it (sum up the decreased travel costs by considering at each node whether it's better to proceed to the next node directly or via a previous Mark). I let this run for a while but it wasn't giving good results, quickly getting stuck in local minima. A big problem with this approach was that it didn't consider placing Marks in places visited between nodes, which excluded strategies like placing a Mark at the beginning of a dungeon (while a door to the dungeon is a point in the travel graph, it isn't a point in the quest graph). To do that, I'd have to have a matrix of best travel times between each pair of nodes in the travel graph, not just the quest graph. Given how long my implementation of Dijkstra took to create the matrix for 100 nodes, I wasn't going to get away with reusing it. Speeding things up Floyd-Warshall is the nuclear option of pathfinding algorithms. Instead of finding shortest paths from a single source like Dijkstra would, it finds the shortest paths between any two vertices in the graph. Not only that, but it does in $ \Theta(V^3) $, independently of the number of edges, making it perfect for dense graphs. It took about 15 minutes to run my Python implementation of Floyd-Warshall on the coalesced 700-node graph. But this wasn't enough. I realised that coalescing vertices in the same in-game cell to a single one was giving strange results, too: for example, each node had an Almsivi/Divine Intervention edge towards the nearest Temple/Imperial Cult Shrine that has a weight considerably larger than zero (due to the fact that the central vertex for that cell was far away from the actual teleportation destination) and I was wondering if that could be skewing the route. I hence decided to rerun the route planner on the full unprocessed 6500-node graph and rewrote the Floyd-Warshall implementation in C++. It still took 15 minutes to run it, but this time it was on the whole graph. Most of this time, in fact, was spent loading the input and writing the output matrices, since I serialised those into text and not binary. And by that point I was on a roll anyway and rewrote the route planner in C++ as well. The Python program would now instead export the quest node distance matrix and the dependency graph to a text file. I didn't perform detailed measurements, but it definitely became a couple of orders of magnitude faster. Adding Mark/Recall awareness to the optimizer I tried rerunning the Mark/Recall planner on the fully expanded route (which enumerates each vertex on the travel graph) but by this point, it was getting more and more clear that simply maintaining a Mark at any Mages Guild teleporter was a really good option that was difficult to improve on. This is a slightly trippy picture, but it's basically a contour plot that shows the average travel time (in real seconds, assuming a travel speed of about 750 units per second, which is achievable with an artifact that I'll talk about later) to any node in the quest graph from any point in the travel graph, interpolated using nearest-neighbour on pixels that didn't map to any points on the travel graph. I also added a travel cost of 5 seconds to public transport and Mages Guild teleporters. This was to account for the time spent in the game's UI as well as to nudge the optimiser into flailing less around multiple towns. Strictly speaking, I should have actually calculated the average time at each pixel, but this picture is good enough. The colour map here ranges from blue (smallest average travel time) to green (largest). For example, Vivec (south of the game map) has the largest average travel times to any point of interest in the route. This is because the Temple of Vivec (one possible destination of an Almsivi Intervention spell) is on the other side of the city from other transport modes (boats/silt striders/Mages Guild) and so anyone near Vivec would have to first teleport to the Temple and then walk across the city to continue their journey. On the other hand, despite being basically a wasteland, the southeast corner of the map has good travel connections: this is because a Divine Intervention spell takes the player to Wolverine Hall on the east side, right next door to the Mages Guild. Silent Pilgrimage There's a cool quest in Morrowind's Temple questline that involves the player completing a pilgrimage from the southernmost part of the game map to the northernmost. Sounds easy, right? Well, the only problem is that the player can't speak to anyone during the pilgrimage, which means the player can't use any public transport or Mages Guild teleports. The honest way to do this is to actually walk or levitate the whole distance, which would take a few minutes even with Speed-increasing spells. The mostly-honest way to do this would be casting Divine/Almsivi Intervention spells in strategic places that would teleport the player part of the way between the spheres of influence of different Temples/Imperial Cult shrines. The dishonest way would be casting a Mark at the shrine during a previous visit and simply Recalling there when the pilgrimage starts. However, the first version of the route planner wasn't really aware of that quest. I had a "Set Mark at Sanctus Shrine" graph node and a "Do the Sanctus Shrine quest" node, but the optimiser wasn't encouraged to put them close together. In the best route it had come up with, those two nodes were far apart and about 3/4 of the route was with the Mark stuck at the Shrine. Hence, if we want to maintain a Mark at a Mages Guild, we also have to juggle that with having a Mark at the Sanctus Shrine in order to complete the Silent Pilgrimage. So the question now was kind of an inverse one: given that we can teleport to a Guild at any time (except for when the Mark is at the Shrine and so we'd get teleported there instead), what's the best route through the game quests? I decided to produce two travel graphs: when there's a recall edge to a Mages Guild (it doesn't matter which one, since we can almost instantaneously teleport to any of them once we're there) and when there's a recall edge to the Sanctus Shrine. The optimiser would get these two versions of the node-to-node distance matrix as well as the instructions specifying which matrix to use when. That way, it could also try to exploit the Mark in the northern part of the game map. The best route it could come up with (not counting time spent in dialogue, combat, training or getting all required items/money at the start at the game) now took about 2500 seconds of real time, which looked quite promising. Propylon Chambers There's a mode of transport in Morrowind that I hadn't mentioned at all: Propylon Chambers. They're located inside 10 ancient Dark Elf strongholds that are scattered roughly in a circle around the map. Each stronghold has a Propylon Index that's hidden somewhere in the game world, and discovering a given stronghold's Index allows the player to travel to that stronghold from either of the two adjacent to it. (from http://stuporstar.sarahdimento.com/other-mods/books-of-vvardenfell/key-to-the-dunmer-strongholds/) Can they be useful here? After looking at their placement, it sadly doesn't seem so. Firstly, there are very few strongholds that are closer to quest objectives than ordinary towns and secondly, their Indices are often in inconvenient places (for example, the Rotheran Index is located in Rotheran itself). But perhaps it's worth including Propylon Chambers in the route anyway? To test that, I assumed that the player has all Propylon indices from the beginning and regenerated the travel graph with the addition of teleportation between adjacent Dunmer strongholds. This would provide a lower bound on the route length and show whether there is enough time saving to make getting any of the Indices worthwhile. Turns out, there really isn't. The best route without Propylon Chambers takes about 2500 seconds, whereas including them improves the route by only two minutes. There are a few places the optimiser decided to exploit this method of teleportation: When performing quests around Suran, going to Marandus and teleporting to Berandas in order to get the Boots of the Apostle in that stronghold. Then teleporting from Berandas to Falensarano on the eastern part of the game map to get Ring of the Wind from the cave nearby as well as (later on) deliver an item to a mine. Teleporting to Valenvaryon several times for easier access to the island north of the map. Teleporting from Hlormaren (a stronghold west of Balmora) to Falasmaryon where the Marksman master trainer lives. Teleporting from Berandas to Rotheran close to the end of the route to grab the Ice Blade of the Monarch (located in that stronghold). Given that simulating actually getting the Indices would also be a pain (I'd have to keep track of the optimal travel time between any two quest nodes for when the player has any combination of indices out of $ 2^{10} = 1024 $), I decided to skip them for now. Opening gambit and various exploits There are a few things that are worth doing at the beginning of the game to ensure a smooth progression through the route as well as raise enough money to pay our way through training and some faction quests. I'd use enchantments for most of the in-game activities, including dealing damage, teleporting and movement. Enchantments are spells that can be put on equipment. They require a soul gem to produce, which determines how much charge the item will have, but enchanted items recharge over time, don't use up player's Magicka reserves and spells cast from them can't fail and are instantaneous. This means that teleporting takes a few seconds faster since we don't need to wait for the cast animation, but more importantly, casts can't be interrupted by someone hitting the player. The items enchanted with all three types of teleportation (Divine/Almsivi intervention and Recall) are easily obtained at the beginning of the game: the first two during Edwinna Elbert's initial questline and the final one can be bought from a merchant in Caldera. I hence changed the optimiser a bit to always have these two starting nodes (Ajira and Edwinna's Mages Guild quests) at the beginning of the route and would do some more preparation as part of these before proceeding. Dealing damage I had played around with various ways of dealing damage to NPCs. I first thought of using Blunt weapons, since the player would have to train that skill anyway and one of the best Blunt weapons has to be acquired as a part of an Imperial Cult quest, but it still takes several swings to kill anyone with it, since the player can miss, especially at lower skill levels. Then I remembered about the Drain Health enchantment: it reduces the target's maximum health by a given number of points. It's supposed to be used as a cheap way to weaken the enemy, but it can also be exploited. If one casts Drain Health 100pt on someone, even for one second, they will die if they have fewer than 100 hit points. Paired with a 100-point Weakness to Magicka effect, this allows for a cheap way to kill anybody with fewer than 200 hit points, which is an overwhelming majority of game characters. Despite all the teleportation, there still is a lot of walking to be done in the game. While the character will have access to Fortify Speed potions, I only wanted to use them for long movement segments, since making enough of them to cover the whole route would take too much time. Thankfully, there is an artifact in the game that gives the player a constant Fortify Speed effect: Boots of Blinding Speed. They boost the player's speed by 200 points (essentially tripling it) at the expense of blinding (it's in the name) the player. The blinding effect can be resisted: if the player has a Resist Magicka spell active for the split second when they put the boots on, the effect is nullified. Moreover, levitation is important, since it allows the player to bypass various obstacles as well as avoid annoying enemies. Due to the way levitation speed is calculated (the main component is the sum of player's Speed and the levitation effect magnitude), 1 point of Levitation is sufficient for the player to start flying and it's cheaper to increase speed by manipulating the character's Speed attribute. 1 point of Levitation for about 90 seconds would be another enchantment. Unlock, frenzy Chests and doors in Morrowind can have a lock with a level ranging from 1 to 100. Hence, we'd need to also enchant a piece of clothing with Open 100pt. There are quite a few times in the route where we need to kill someone who's not attacking us without attracting the guards' attention (like when doing Morag Tong assassinations before the actual quest starts). One way to do it is taunting the NPC until they attack, which takes time and needs a moderately high Speechcraft skill. Luckily, there's a magic effect for that, too. Frenzy increases the Fight rating of an NPC and 100pt for 1 second is enough to make them attack the player. When the effect wears off, they don't stop attacking and can be slain in self defence without legal issues. Alchemy feedback loop and fundraising When a player creates a potion in Morrowind, their chance of success as well as the potion's strength, duration and value is partially governed by the player's Intelligence attribute. The player can also create a potion that boosts their Intelligence attribute. Do you see how the game can be broken with this? There's no limit on how many potions the player can consume per second and there's no cap on the player's Intelligence. Hence we can have all our monetary problems taken care of by exploiting this and repeatedly creating stronger and stronger Intelligence potions to sell. Not only that, but we can also use this to create Restore Health potions that restore player's health faster than anybody can damage it as well as use the Intelligence boost to create enchanted items manually (instead of paying a specialist to do it). Finally, we can also create Fortify Speed potions that increase the player's raw speed. There are merchants in Morrowind that restock some of their ingredients as soon as the player stops trading with them and lots of them sell ingredients for Fortify Intelligence and Restore Health potions. We need about 75000 gold pieces to get through the game, including all training and faction quests. Luckily, there's a merchant in the game that has 5000 gold in his inventory and buys items at face value. My tests showed I needed about 150 Health potions to get me through the game, so I'd sell any extra ones to the Creeper to get me to the target number. Fortifying player's Speed (beyond the boost provided by the Boots) is more difficult: there are only two ingredients in the game that restock and provide the Fortify Speed attribute, Kagouti Hide and Shalk Resin. However, they are quite expensive (52 gold pieces in total for the two) and also have a Drain Fatigue side effect (which makes the player lose consciousness when their Fatigue is close to zero). Hence they have to be paired with another two ingredients that have a Restore Fatigue effect. Final route Here's the final route that I came up with: it opens with the sequence of money-making and enchantments that I had described before and then continues with the list of things to do that was produced by the optimiser. This initial sequence took me about 28 minutes to complete and the rest of the route is located here. I also uploaded the route that assumes the player can use all Propylon Chambers here. Create the character (build). Steal the Limeware Platter from the Census & Excise office before leaving and pick up the Ring of Healing from the barrel on the way. Give the ring to Fargoth to boost relationship with Arrille. Go there, sell the platter, buy a Resist Magicka Spell, 2 Drathis' Winter Guest scrolls and an Iron Warhammer. On the way to the silt strider, grab the 4 types of mushrooms (needed for Ajira's first quest). Take the silt strider to Balmora. Join the Mages Guild, take all supplies from the chest and take the Ceramic Bowl from Ranis Athrys' table. Go downstairs to Estirdalin and make a spell of Resist Magicka 100% on Self. Hand in the first Ajira quest. Teleport to Caldera Mages Guild. Steal the alchemy set from the tower in the Guild as well as 1 Dreugh Wax (needed for the Seven Graces quest). Go north-west towards Gnaar Mok to meet Pemenie. Kill her with a combination of Thunder Fist (Nord racial power), the Drathis' scrolls and the Warhammer. Use the Fortify Willpower and Restore Magicka potions from the supplies chest to successfully cast Resist Magicka spell and equip the Boots. Use the Almsivi Intervention scroll to go to Ald-Ruhn. Go to the Mages Guild, take all supplies from the chest there. Buy 2 Mark scrolls from Tanar Llervi (she sells one at a time but they restock after leaving the Barter menu). Take Mages Guild teleport to Balmora, place a Mark while facing Masalinie Merian (Guild teleporter). Do all remaining Ajira quests: Make sure to steal the Grand, the Large and the two Common Soul gems as well as the Platter and any other Soul Gem (needed as a donation for a Temple quest) during the second quest. Flowers: Willow Anther and Heather can be bought from Ajira herself. The other two can be stolen from Millie Hastien's shop. On the way there, sell the Platter to Ra'Virr next door. Sell all rewards (potions) back to Ajira to have roughly 1000 gold for the next part. Mages Guild teleport to Sadrith Mora, Go to Aunius Autrus in the Imperial Shrine. Alchemy loop time! Use all money to continuously buy 10 Ash Yam, 5 Bloat and 5 Netch Leather from Aunius Autrus (should roughly end up with 260, 130 and 130 of each, respectively). Use all Bloat and half of Ash Yams to make Intelligence potions, drink them all. Use all Netch Leather and Ash Yams to make Intelligence potions, sell enough to Aunius to get all his money, drink the rest. Go to Scelian Plebo and buy 10 Saltrice and 10 Marshmerrow 30 times. Make 300 Restore Health potions with these ingredients. Sell enough Health potions to Scelian to get all his money. Buy Drain Blood (has the Drain Health effect) and Frenzying Touch (has the Frenzy Humanoid effect) from Uleni Heleran in the Mages Guild on the way back. Teleport to Balmora, Almsivi Scroll to the Temple. Go to Nalcarya of White Haven. Buy 1 diamond (future Thieves Guild quest) and 4 Daedra Hearts (future Temple quest), sell her enough potions to drain her of money. Go to Millie Hastien next door. Buy 1 Exquisite Amulet, 1 Exquisite Ring, 1 Extravagant Pants and an Extravagant Belt. Back to Balmora MG, buy spells from Marayn Dren: Levitate, Ondusi's Open Door, Dire Weakness to Magicka. Whilst still under the effect of Intelligence potions, make the following enchantments: Exquisite Amulet: Weakness to Magicka 100% on Touch, Drain Health 100% on Touch (use the stolen Grand Soul Gem). Expensive Belt: Levitate 1pt 90s on Self (use the stolen Greater Soul Gem) Exquisite Ring: Open 100pt on Touch (Common Soul Gem) Expensive Pants: Frenzy Humanoid 100pt on Touch (Common Soul Gem) Do hotkeying. I prefer having the Amulet on 1, Belt on 7, Ring on 8 and Pants on 9. Whilst still under the effect of Intelligence potions, teleport to Sadrith Mora. Buy 100 Shalk Resin and 100 Kagouti hide from Pierlette Rostorard (will need to sell her Health potions a couple of times in order to afford the ingredients). Buy 100 Hound Meat and 100 Scuttle from Threvul Serethi. Make 100 potions of Fortify Speed (+ Restore Fatigue) from these 4 ingredients. Alchemy should be slightly beyond 70 by this point (requirement for some Guild promotions). Hotkey Speed potions to 2. Recall and teleport to Caldera. Sell Restore Health potions to Creeper until have about 75000 gold. Hotkey remaining ones to 3. Recall, buy 6 Drathis' Winter Guest scrolls from Galbedir and buy Chronicles of Nchuleft from Dorisa Darvel, then steal a Dwemer Tube from Vorar Helas' house. Recall, teleport to Ald-Ruhn and do all Edwinna Elbert quests up to and including Dwemer Tube. Should be rewarded with the Almsivi and Divine Intervention amulets. Hotkey those to 4 and 5, respectively. Proceed as per the rest of the route. Finally, there are several NPCs that have to be killed as part of the run and have to be damaged first before they can be killed with the Amulet, either with the Drathis' scrolls or with the Iron Warhammer/Skull Crusher when it's picked up: Relas Arothan has one Sanguine Item required for extra Morag Tong reputation. Lorbumol gro-Aglakh needs to be killed as part of the Fighters Guild questline. While he has 199 health, he has some natural magic resistance, decreasing the effect of the amulet. Burub gra-Bamog also has some natural resistance to Magicka. Orvas Dren, brother of the Duke and head of the local criminal syndicate, has to be killed as part of the House Hlaalu questline and has 250 hit points. Varus Vantinius is the current head of the Imperial Legion and has to be killed in a duel to finish that faction's questline. I think that's it! The code to produce most of this is on my GitHub, together with the code from the previous set of articles. One day I might even actually record myself trying to follow this route, but I'm sure actually planning it out is more fun that running it. Finally, feel free to follow me on Twitter at twitter.com/mildbyte! Previously, we left off by converting the problem of finding a route that completes all faction questlines in Morrowind into the general case of the travelling salesman problem with dependency constraints. Today, we'll come up with a way to produce a good enough solution to it. Generating a travel time matrix There are two graphs I'm talking about here: one is the quest dependency graph from the previous part and the other one is the travel graph that I had generated back in an earlier article. The dependency graph had about 110 geographically distinct nodes at this point, so the first order of business was creating a matrix of fastest routes and travel times between any two of those nodes, since the final route could indeed include travelling between any two points. To do that, I used Dijkstra's algorithm: since it's an single-source-shortest-path algorithm, if I ran it for one geographical node in the quest dependency graph, I'd get shortest routes (on the travel graph) to all other points. Hence I only had to run it a hundred times. There was a problem, though: the travel graph had about 6500 vertices and 16000 teleportation edges (that is, travelling with public transport or using an Almsivi/Divine Intervention spell: this doesn't include actual physical travel edges between points in the same cell). It took about 10 minutes to run Dijkstra for a single source, so I was looking at spending about a day generating the travel time matrix. Hence I decided to prune the travel graph a bit by coalescing vertices that were in the same cell. For every cell (interior or exterior), I'd replace all vertices in it with a single one with average coordinates and then recalculate the cost of travelling between them: def coalesce_cells(vertices, edges): # Replaces all vertices in the graph in the same cell with a single one (average location) vertices_map = defaultdict(list) for v in vertices: vertices_map[v.cell].append(v) # Calculate the average vertex for each cell average_vertices = {} for cell, vs in vertices_map.items(): coords = tuple(sum(v.coords[i] for v in vs) / float(len(vs)) for i in range(3)) average_vertices[cell] = Location(coords=coords, cell_id=vs[0].cell_id, cell=vs[0].cell) new_vertices = set([average_vertices[v.cell] for v in vertices]) # Group edges by average vertices they belong to grouped_edges = defaultdict(lambda: defaultdict(list)) for v1 in edges: av1 = average_vertices[v1.cell] for v2 in edges[v1]: # Calculate the new edge cost grouped_edges[av1][av2].append((edges[v1][v2][0], get_distance(av1.coords, v1.coords) / WALKING_SPEED + edges[v1][v2][1] + get_distance(v2.coords, av2.coords) / WALKING_SPEED)) new_edges = defaultdict(dict) for av1 in grouped_edges: for av2 in grouped_edges[av1]: # Replace all possible edges between the two new vertices with the cheapest one new_edges[av1][av2] = min(grouped_edges[av1][av2], key=lambda md: md[1]) return new_vertices, new_edges With this pruning, the travel graph shrunk to about 800 vertices and 2200 teleportation edges and I successfully managed to create a matrix of fastest travel times between any two nodes on the dependency graph. Here's one of cool things you can do with such a distance matrix: use a clustering algorithm to visualize clumps in which quest points of interest are organized (the image is clickable). For example, the top left corner of this heatmap has a group of NPCs that are all located on a set of remote islands at the north of the game map. Getting to them is a pain and takes a lot of time, hence it's worth arranging our quests in such a way so that we only have to visit there once. Simulated annealing (genetic algorithm?) Let's now say we have a candidate route, which is one of topological sorts of the dependency graph. We can see how long this route takes by simply adding up the cost of travel between consecutive nodes using our cost matrix. How would we find an optimal route? Brute force won't help here. I decided to do a slightly less stupid thing: let's take a route and randomly perturb it. Sure, the route we end up with might be less efficient than it was before. But imagine we do that for tens of thousands of randomly generated routes, keeping a fraction of them that's the most efficient, randomly perturbing the best routes again and again. Eventually we'd converge on a decent route, if not the most optimal one. The final algorithm I used is: Start with a pool of candidate routes: take a single topological sort and repeat it 20000 times Do until I get bored and terminate the optimization: sort the routes by their total time, keep top 1000 for each remaining route: generate 20 candidate routes from it: pick a random point in the route and move it a random number of steps up or down check the dependency graph is still satisfied, if not, try again do this perturbation 30 times the pool now has 20000 routes again, repeat Of course, the actual constants can be played with and the termination condition could be better defined. Some call this a genetic algorithm (where we kind of simulate evolution and random mutations in the gene pool), some call it simulated annealing (where the magnitude of random perturbations decreases over time until the solution pool settles down). "Genetic algorithm" sounds sexier, which is why I mentioned it in this paragraph. I left this to run overnight and in the morning came back what seemed to be a decent route through the game. The times here were inferred from in-game travel distances, assuming the minimum walking speed of about 100 game units per second. Of course, there are potions and spells to increase the player's walking speed. In addition, this doesn't account for the time spent in the menus or actually killing whatever the player is supposed to kill. Overall, there are some things the optimiser came up with that made me go "aha!". I wrote a pretty printer that would take the graph nodes and expand them into an actual travel plan that uses Almsivi/Divine Intervention spells and public transport. In this fragment, for example, the route planner set up the faction questline progress just right so that all six objectives in the desolate southwest corner of the map could be completed in one go (lines 592-618). However, there are a few problems with this route: It doesn't account for the uses of Mark/Recall spells. These are immensely powerful: a Recall teleports the player to the location of the last time a Mark spell was cast. It doesn't account for skills training in order to progress through faction quests. Advancement in Morrowind factions requires not only quest completion, but also skills training. I had already mentioned that while we can pay to train a skill, it can't be trained above its governing attribute. Attributes can only be raised when the player levels up. A game character has 5 out of 27 skills as major skills (which lets them level faster and gives a flat +25 bonus to them at the beginning of the game) and 5 minor skills (which also lets them level faster, albeit not as fast as major skills, and adds a +10 bonus). The character levels up when they have gotten 10 points in their major or minor skills. This is where it gets weird. At level up, the player picks 3 attributes to raise. How much they are raised by is determined by the skills the player had trained. For example, if they got 10 points in Alchemy (governed by Intelligence), then, if Intelligence is picked at level up, it will increase by 5 points instead of 1. However, if the player had leveled up by training 1 point in Long Blade (governed by Strength) and 9 points in Alchemy, they'll only get a 4x multiplier to Intelligence and 1x to Strength. The player can also train skills that aren't major or minor to get enough points to boost the attribute multiplier. Let's say the player also trains 1 point in Security (governed by Intelligence) which isn't their major or minor skill. It won't count towards the 10 points required for a level up, but it will count towards the attribute multiplier calculations. Hence the player will be able to raise their Intelligence by 5. I hence had to tactically choose my character's major/minor skills as well as the race (which gives bonuses to certain skills and attributes) in order to be able to quickly meet each faction's expectations. Overview of factions and required skill levels This is a list of skill levels that each faction requires in order for the player to be able to become the head of that faction. Note that this might not necessarily meet the skill requirements for the highest rank of that faction, since most factions stop checking the player's credentials during their final questlines and just promote the player to the highest rank once the questline is completed. Mages Guild: Alteration, Destruction, Alchemy, Enchant, Illusion, Mysticism. One skill at 70, two at 25, Intelligence and Willpower 33. Fighters Guild: Axe, Long Blade, Blunt Weapon, Heavy Armor, Armorer, Block; 70/25/25, Strength and Endurance 33. Thieves Guild: Marksman, Short Blade, Light Armor, Acrobatics, Sneak, Security; 80/30/30, Agility and Personality 34. Tribunal Temple: Alchemy, Blunt Weapon, Conjuration, Mysticism, Restoration, Unarmored; 80/30/30, Intelligence and Personality 34. Morag Tong: Acrobatics, Illusion, Marksman, Light Armor, Short Blade, Sneak; 80/30/30. Speed and Agility 34. Imperial Cult: Speechcraft, Unarmored, Restoration, Mysticism, Enchant, Blunt Weapon; 90/35/35. Personality and Willpower 35. Imperial Legion: Athletics, Spear, Long Blade, Blunt Weapon, Heavy Armor, Block; 70/25/25. Endurance and Personality 33. House Hlaalu: Speechcraft, Mercantile, Marksman, Short Blade, Light Armor, Security; 70/25/25. Speed and Agility 33. Character planning With that in mind, I decided to have Alchemy, Blunt and Marksman as high level skills. Alchemy (main skill for the Mages Guild) could be trained really quickly by making potions. Blunt was shared between 4 factions (Fighters Guild, Temple, Imperial Cult and Imperial Legion) and would have to be trained to 90. Marksman would cover the other 3 factions (Thieves Guild, Morag Tong and House Hlaalu) and trained to 80. The other skills had to be chosen partially to cover the remaining, weaker requirements, partially so that training them would boost either Strength or Agility to 90 or 80, respectively (otherwise Blunt or Marksman wouldn't be possible to be trained). I hence decided to go for a character that starts with high Strength and a bonus to Blunt weapons and train Long Blade to boost Strength (and cover the Fighters Guild/Imperial Legion secondary skill requirement). For Agility, I would train Block, Light Armor and Sneak. All three of those are governed by Agility and training them to required levels would result in Agility being boosted enough to allow me to train Marksman to 80. Enchant and Mysticism would cover the secondary requirements for the Temple, the Mages Guild and the Imperial Legion. Here's the final character sheet. The major and minor skills that she starts with are: Alchemy: 35. To be trained to 70 by making potions (main skill for MG, secondary skill for T). Blunt: 40. To be trained to 90 (main skill for FG, IL, IC and T). Marksman: 30. To be trained to 80 (main skill for TG, MT and HH). Mysticism: 35, doesn't need to be trained (secondary skill for MG, T and IC). Enchant: 35, doesn't need to be trained (secondary skill for MG and IC). Minor: Long Blade: 25. To be trained to 45 to get extra Strength points (secondary skill for FG and IL). Sneak: 15. To be trained to 30 (secondary skill for TG and MT). Block: 15. To be trained to 30 (secondary skill for FG and IL). Speechcraft: 15. To be trained to 25 for extra 5 Personality points (secondary skill for HH). Light Armor: 15. To be trained to 30 (secondary skill for TG, MT and HH). Encoding training in the quest dependency graph I decided not to load up Morrowind trainer data in order to incorporate it into the route planner. Instead, I looked up the best trainers for Blunt and Marksman (since they're the only ones that will let the player reach the required level) as well as some second best ones and tried to come up with people that the player character would meet en route anyway. There were some hilarious coincidences, like Alveleg who has to be killed as part of a Fighters Guild quest but who can also train the player in Block, Sneak and Marksman up to fairly high levels. I then added some extra nodes to the dependency graph to reflect the new training sessions: # Training nodes training_alveleg: # we're killing him as part of the FG quest and he trains Marksman (45), Sneak (42) and Block (38) description: Train Block x10 (up to 25), Sneak x15 (up to 30), Marksman x15 (up to 45), should get Agi 60 giver: alveleg training_bolnor: description: Train Light Armor x15 (up to 30), Marksman x5 (up to 50), should get Agility 70 giver: bolnor andrani - training_alveleg training_eydis: description: Train Long Blade x20 (up to 40), Blunt x30 (up to 70), Strength 85 giver: eydis fire-eye training_ernse: description: Train Blunt x20 (up to 90) giver: ernse llervu - training_eydis training_missun: description: Train Marksman x30 (up to 80) giver: missun akin - training_bolnor training_falvel: description: Train Mercantile x10 (should get Personality 35) giver: falvel arenim They would then become prerequisites for some later quests in faction questlines: tt_tharer_1: description: Get and hand in all Tharer Rotheloth quests giver: tharer rotheloth - tt_7graces_vivec - tt_7graces_gnisis - tt_7graces_kummu - tt_7graces_gg - tt_cure_lette - tt_mount_kand - tt_mawia - tt_kill_raxle_berne - training_eydis # Curate (50 blunt) to hand in Galom Daeus quest In some cases, the requirements I added were stronger than necessary. For example, one could get promoted to Master of Fighters Guild with a Blunt skill of 80, yet it depends on a graph node training Blunt to 90. The reasoning behind it was that we don't want to visit the Master Blunt trainer more than once: if we're visiting her, we might as well train Blunt to the maximum we'll need. Next up, we'll try to add the usage of Mark and Recall spells to the route as well as discuss some miscellaneous Morrowind tricks and glitches that can help during a speedrun. Well, not even last night's storm could wake you. I heard them say we've reached Morrowind, I'm sure they'll let us go and do a speedrun. Jiub There's the famous speedrun of Morrowind's main quest that involves basically travelling to the final game location using a few scrolls and spells and killing the boss. However, there isn't a Morrowind speedrun category where someone tries to become the head of all factions. For all its critical acclaim and its great story, most of quests in Morrowind are basically fetch-item or kill-this-person and there aren't many quests that require anything else. But planning such a speedrun route could still be extremely interesting for many reasons: There are 10 joinable factions in Morrowind (Mages/Thieves/Fighters Guild, Imperial Cult, Imperial Legion, Tribunal Temple and the Great Houses: Hlaalu, Redoran, Telvanni). The player can only be a member of one Great House in a playthrough, but that still leaves 8 factions to do. The transport system. It's not just a matter of fast travelling to certain locations like one would do in Skyrim or Oblivion. Instead travel is by several transportation modes including boats, caravans and teleportation spells that I had previously investigated. Walking is required a lot and so it's important to manage faction questlines to avoid unnecessary redundant trips to different cities. There are many ways to become the head of a given faction. Faction questlines use a promotion system where new questlines open up as the character attains higher ranks at a faction. Promotion is a matter of not only reputation points (awarded by quests) but also player skills and attributes. Some quest objectives can be pre-completed or done in a different way. For example, if the quest giver wants the player to kill someone, that someone can often be killed before the quest even starts, at which point, most of the time, the quest giver will give the player the reward anyway. However, sometimes this might not work and the player will lose out on reputation points required to unlock further questlines. Similarly, in most fetch quests the questgiver suggests where the player can get a given item, but doesn't care if it was bought in a nearby shop a few minutes ago. So given those features, this can get really complicated. On the way to a given quest objective the player can pick up another quest or pick up an item that might be needed at some point for a quest for a different faction that they aren't even a member of. What could be an efficient route through one faction's quests might be inferior to a slower route when all factions are played through since it could be that points in that route are visited in other factions' quests anyway, and so on. In other words, planning an efficient route through all factions would be a fun computer science problem. A note on skill requirements and Morrowind's levelling system There are a couple factions where the final quest can be completed immediately, but that just results in a journal entry saying that the player character is now the head of the faction (and the advancement is not reflected in the character stats). I decided I wanted to rise to the top the mostly-honest way instead. Unlike Skyrim and Oblivion, advancement in Morrowind factions requires the player to have certain skills at a certain level. There are 27 skills in Morrowind and each faction has 6 so-called "favoured skills". Becoming head of a faction requires the player to have one of these skills at a very high level (roughly 80-90 out of 100) and 2 of them at a medium level (about 30-35). Morrowind characters also have 7 attributes, each of which "governs" several skills. Attributes also play a role in faction advancement. So that's kind of bad news, since in a speedrun we won't have enough time to develop our character's skills. The good news is there are trainers scattered around Morrowind that will, for a certain fee, instantly raise these skills. The bad news is that these trainers won't train skills above their governing attributes. Raising attributes requires levelling and levelling in Morrowind is a very long story. I'll get into the actual levelling strategy later. Different routes through a given faction I quickly gave up on scraping quest data from the game files (since most quests are driven and updated by a set of dialogue conditions and in-game scripts) and instead used the UESP's Morrowind Quests page to manually create a series of spreadsheets for each faction that included quests, their reputation gain and rough requirements. Here's an example of one such spreadsheet: This spreadsheet already shows the complexity of Morrowind factions. There are two intended ways to reach the top of the Mages Guild: by having enough reputation and skills to become a Master Wizard and either completing all of Edwinna Elbert's quests and challenging the current Arch-Mage to a duel or completing all of Skink-in-Tree's-Shade's quests and getting a letter from the upper management telling the current Arch-Mage to step down. I later found another way, by reaching the rank of Wizard (one rank below Master Wizard) and then talking to the current Arch-Mage about a duel, which is quicker. Other than that, there's also multiple ways to complete a quest. Edwinna Elbert's final 3 quests requiring the player to bring her some Dwarven artifacts don't require the player to actually go to the places she recommends: the artifacts can be acquired from different locations or even bought. Generating all possible routes through a faction ...turned out to be tricky. The first cut of this was encoding each quest in a YAML file as a set of prerequisites and required items/actions for completion. For example: edwinna_2: giver: edwinna elbert rank: Conjurer quest: Chimarvamidium 2 - Dwemer Tube: items: misc_dwrv_artifact60 - Nchuleftingth: go_person: anes vendu This encodes the start of Edwinna Elbert's advanced questline, Dwemer Tube from Arkngthunch-Sturdumz, which requires the player to have become a Conjurer in the Guild and completed Edwinna's previous quest. To complete this quest, the player needs to have the tube in their inventory (I used the in-game item ID). Completion gives the player 5 faction reputation points. The questline continues with Nchuleftingth Expedition and to complete that quest, the player needs to go to a certain NPC (he's an archaeologist who has, as it turns out, perished). Unlike the previous quest, this action (of going to a person and interacting with them) requires us to have started the quest. So with that in mind, we can generate a set of all possible ways to complete a guild using breadth-first search: set of all sequences completing the guild S = empty for each sequence in S: if it already completes the guild, ignore it otherwise, get all possible next quests that can be done in this sequence: where the quest prerequisites have been met (e.g. a previous/required quest in the questline has been completed) where there's enough reputation to start a new questline add each one of these possible quests to a sequence to create several new sequences replace the current sequence with the newly generated ones until S stops changing Combinatorial explosions, combinatorial explosions everywhere What could possibly go wrong? Well, firstly there's an issue of ordering. If the player is juggling two parallel questlines from different questgivers, each possible interleaving of those is counted, which causes a combinatorial explosion. Secondly, routes that are strictly worse than existing routes are generated too. For example, if completing a certain guild requires us to only complete quests A, B, D and E, there's no point in generating a route A, B, C, D, E: there's no way doing D won't take extra time. I hence did some culling by making sure that during generation we wouldn't consider a sequence if it were a superset of an already existing quest sequence. This brought the number of generated routes (subsets, really) down to a mildly manageable 300. Is this good? Well, not really. This only accounted for which sets of quests could be completed. There was no mention of the order in which these quests could be completed (yielding probably millions of permutations), the ordering of actual actions that would complete a given quest (for example, completing a given quest could involve killing someone and that could happen even before the player character was aware of a quest) or the alternative routes (like fetching a required item from a different place or doing an extra objective to get more faction reputation). Worse even, this was just the route generation for one faction. There were 7 more factions to do (and I had to pick a Great House that would be the quickest to complete too) and even if they didn't have that many ways to complete them, brute-forcing through all the possible routes with all factions would definitely be unreasonable. This method also wouldn't let me encode some guild features. For example, Morag Tong, Morrowind's legal assassin guild, has several questgivers around the world, any of which can give the player their next contract. Furthermore, the reputation required for the final questline to open can be gathered not only by doing assassination contracts, but also by collecting certain items spread around the world, each yielding about the same reputation as a contract. These items can quite often be found in dungeons that the player has to visit for other factions anyway and it could be the case that doing those quests to collect these items is overall faster. Attempt 2: a single quest dependency graph I hence decided to drop the idea of combining all possible routes from all guilds and instead did some experimentation to find out if there are obviously quick routes through most guilds. Turns out, there were and so instead of solving a few million instances of the Travelling Salesman Problem, I could do with just one. Still impossible, but less impossible. Quick overview of fastest routes for a given faction In the Mages Guild, the introductory questline can be completed in a matter of minutes and yield 22 reputation points and then Edwinna's quests can be completed en route to other quest locations that will likely have to be visited anyway. Those two questgivers would bring the player character over the 70 reputation limit required to challenge the current Arch-Mage (at that point, I wasn't looking at skills training yet). The Fighters Guild could be completed by doing all quests from one questgiver (most of which involved killing bandits in roughly the same area which can be done even before the quest begins), a couple from another one and then proceeding on to a final questline (which does have a quest requiring to bring some items to the middle of nowhere, but the alternative ending requires many more reputation points). The Thieves Guild has some conflicts with the Fighters Guild and so the two questlines have to be carefully managed together. Almost all quests in the Thieves Guild need to be done (since doing some Fighters' Guild quests decreases reputation with the Thieves Guild), but the good news is that they share the antagonist and so after reaching a certain reputation with the Thieves Guild, finishing the Fighters Guild promotes the character to Master Thief. Morag Tong can basically be completed in one go: after the initial contract required to join the Guild, the player collects enough Sanguine items to skip all contracts straight on to the final questline and the location of the final boss is visited twice in other guilds' quests. Tribunal Temple starts with a mandatory pilgrimage that visits a few locations around the game map. There are several more pilgrimages as part of the questline and some of those can be completed even without having joined the faction. Imperial Legion has a questline that takes place in a single town and requires the player to visit the location that's visited anyway in Edwinna Elbert's questline in the Mages Guild. In addition, one quest gives additional reputation with the Temple, allowing to skip one quest there. Imperial Cult has three questlines. One of them involves fundraising and, just like in real life, the player can simply give the money to the questgiver on the spot instead of asking others for it. The other one involves fetching several powerful artifacts and visiting a couple of locations that are visited in other guilds' questlines. After eyeballing the Great Houses' questlines, I settled on House Hlaalu. House Redoran has a way too long questline, most of the action in House Telvanni happens on the East side of the game map that mostly isn't visited in other quests and the final Hlaalu questline that leads to becoming Grandmaster can be started at an earlier rank. Quest dependency graph Now that I had a single route for each guild, instead of encoding each and every quest requirement and location in a graph, I opted for an easier way. Each node in a quest dependency graph would be something that's fairly quick to complete and happens in the same location. It could be a quest, or a series of quests, or the action of clearing out some dungeon that is featured in several future quests. A node contains two things: where this node is located (for example, the in-game ID of the questgiver or an NPC in the location that the player needs to clear out or find a certain item) and nodes that the player needs to have completed before. # Coalesced Ajira questline mg_ajira_1: giver: ajira # Edwinna's quests up until Nchuleftingth expedition, all done in one go (Dwemer tube stolen # from Vorar Helas in Balmora, then Chimarvamidium, Skink and Huleen) mg_edwinna_1: # also gives Almsivi/Divine amulets - mg_ajira_1 mg_edwinna_2: - mg_edwinna_1 - mg_edwinna_nchuleftingth - mg_edwinna_scarab_plans - mg_edwinna_airship_plans # locations of items we need to collect to complete Edwinna's quests mg_edwinna_nchuleftingth: giver: anes vendu # can discover his body before the quest begins mg_edwinna_scarab_plans: giver: Khargol gro-Boguk # orc in Vacant Tower with the other copy of the plans mg_edwinna_airship_plans: giver: lugrub gro-ogdum # located near the orc in Gnisis Eggmine that is also a part of the IL quest mg_master: giver: trebonius artorius In this case, the Dwarwen plans required by Edwinna can be collected even before the questline begins and then all handed in at the same time. When talking to someone had to be done as a part of the quest, I encoded it as several nodes that depended on each other: fg_eydis_1_start: # join FG and start first quest fg_eydis_1_do: giver: drarayne thelas # actually do the first quest - fg_eydis_1_start fg_eydis_1_end: # hand the quest in - fg_eydis_1_do Here's the final quest dependency graph: This was much better than messing around with reputation points and quest prerequisites. Any topological sorting of this dependency graph would be a valid route through the game's quests (assuming I encoded my dependencies correctly). Since each node had a fixed geographical location, I could use a pathfinding algorithm and the data from my previous project to find out the time that any given route satisfying this dependency graph (using teleportation and public transport) takes. However, there's still a problem: there are many possible topological sortings of a given graph and counting them is #P-complete. This is a general case of the travelling salesman problem: if here we need to find the shortest tour that visits all nodes subject to a set of dependencies (e.g. we can't visit A before we've visited C), then in TSP we need to visit all nodes without any dependencies. Having dependencies decreases our search space (in the most extreme case the dependency graph is a line and so there's only one possible route), but not by enough. I hence had to develop some approximations to turn this graph and the matrix of travel times between its nodes into a good-enough route. Next up, I'll try a couple of random approximations to solve this problem, including simulated annealing (also kind of known as a genetic algorithm). There's also the matter of planning out the player character and his/her skill development in order to minimize the amount of time we need to spend training up to get promoted in various guilds. Stay tuned! Let's go on a treasure hunt! @mildbyte 5 years, 6 months ago \| programming \| games \| python \| telegram \| bots \| Chatbots are basically a clunky commandline interface to things that sometimes really need a custom UI. But what if I do want to make something that uses some of the features (a GPS receiver, a camera, a microphone) that a modern phone has? I'm too lazy to write device-specific code and dig around in the intrinsics of Android/iOS APIs. So after doing some research on modern messenger apps (I kind of fell behind on what was going on after the WhatsApp acquisition and turns out billions more have popped up since then) I stumbled upon the Telegram bot API. And it's actually pretty simple. In a nutshell, you create a bot (by messaging another bot) which gives you a token. The token is the only thing your bot needs to communicate with the Telegram servers (so no coding up handshakes or managing session keys): it makes up your REST endpoint that you can throw queries at. The connection is over SSL, so that takes care of your ISP or a kid with a WiFi dongle and Wireshark grabbing hold of your token. Bot chats aren't end-to-end encrypted though, so Telegram are still able to read whatever you talk to the bot about. With that in mind, receiving messages is easy: just shoot a GET request at https://api.telegram.org/bot(TOKEN)/getUpdates (reference) and it will come back with a JSON-serialised list of events (message sent, message edited etc) that happened to your bot. Each one has a unique sequence number which you can use to seek around in the update log (to say get updates only starting from the last one you processed). Updates related to messages have in them a chat ID identifying your conversation with a given user -- and you include that chat ID in your POST requests to https://api.telegram.org/bot(TOKEN)/sendMessage (reference) in order to send messages back to that user. You can also send around various other things besides text messages, like locations (latitude-longitude pairs), photos (your bot gets some links to various-sized thumbnails of the photo), contacts etc. So I managed to write Indiana, a treasure hunt bot that comes up with a random location inside Hyde Park (well, the rectangle whose all 4 points lie within Hyde Park and yes, that means it can sometimes put the treasure in the water or in some restricted areas and I take no responsibility for you ending up there) and, when sent a location, replies back with a rough estimate of how far the treasure is. Sort of like Pokemon Go without having to lug around an extra power pack. Note you also can send the bot a manual location -- it can't distinguish between that and a physical location read from GPS (thankfully). project Morrowind, part 7 So that you don't think that the 1-year delay in posting part 6 was due to me manually drawing the population heatmaps in Paint, I finally split the code I used to produce all the plots into a set of modules and uploaded them to GitHub. You'll need the usual scientific Python stack (NumPy, SciPy, matplotlib as well as PIL) and a C++ compiler. Since I wasn't sure if it's a good idea to post the game data dump that I produced, you'll have to make it yourself: you'll need the original Morrowind.esm data file and Enchanted Editor (instructions on how to produce the dump are in the README). With all that in mind, I've run the code end-to-end and it spit out a similar set of images to what I have on the blog, which makes me incredibly happy. Now it's time to get back to Cookie Clicker! I told you I'd be back in a year's time. With Aryon safe back in his tower and with all inhabitants of the island maximising the efficiency of their travel, it was time to approach a new challenge and create some more pretty pictures. The next question was simple: where the hell are all the people and what do they do? Let's try and use our cool matrix that converts in-game coordinates to coordinates on a map to its full extent and create some sort of a population heatmap. This isn't difficult to do since we already have all the pieces of the puzzle: we know where all the NPCs are located and what their occupation, race and gender are. The only problem is dealing with NPCs that are in the interior: remember how interiors are completely separate mini-worlds? This means that we can't simply infer someone's location in the exterior by taking the coordinates of the two doors and adding up an offset of the NPC from the door, since interiors often are bigger on the inside than what they look like from the outside. Since we'd only be looking at a world-scale overview, I decided not to bother with precision: the actual exterior location of an NPC is simply the location of the closest exterior door they can get to (by number of cells they have to traverse to get outside). Armed with these tools, I went through all the NPCs in the world, getting their exterior location, and converted that location into coordinates on the map. I had a map-sized matrix where I accumulated those coordinates: the number at each pixel was the number of NPCs whose exterior coordinates fell within that square. This meant that I'd get disproportionately large amounts of people piling up at the doors of densely-populated interiors, which wasn't optimal as it was difficult to see on the image (after all, it's just one pixel) and wasn't representing the in-game reality well: after all, we are interested in the population in a given city/region and people don't really stand in one spot either, instead roaming around. Hence I applied a Gaussian blur to my matrix so that instead of 10 people assigned to one pixel we'd be looking at something like 2.2 people on that pixel, 1.1 people one pixel away, 0.5 people 2 pixels away etc. If this feels like chopping people into parts and throwing those body parts around so they form a nice hill, it's because it kind of is. With that out of the way, I normalised the matrix so that all values were between 0 and 1, applied one of the numerous colormaps that matplotlib has (I quite liked the one called blues) and blended it with the original map. I also toyed around with applying a transfer function to the inputs before pushing them into the colormap since I didn't like the way it looked by default -- I chose a logistic function: \[ f(t) = \frac{1}{1 + e^{-k(t-c)}} \] I didn't really have a methodology here: varying $k$ changes the steepness of the curve (how quickly things go from the left side of the colormap to the right side, getting brighter) and varying $c$ changes where it's centered, so I tinkered with them for each picture until it looked good. With that in mind, let's see what we ended up with! draw_npcs(filter_sigma=25, sigmoid_k=8, sigmoid_c=0.2, output='map_population.png') (full) We get dark blobs in large population centres like, bottom to top, Vivec (and Ebonheart next to it), then Balmora (southwestern part of the island), Sadrith Mora (far east), Ald'ruhn (north of Balmora) and Gnisis (northwest of Ald'ruhn). There are also some minor places highlighted around -- these are either smaller settlements or larger dungeons/strongholds/shrines. What else can we do with it? How about mapping out all the Dark Elves? Easy, just don't go through all the NPCs: draw_npcs(filter_sigma=25, mark_npcs=[n for n in npcs if n.race == 'Dark Elf'], sigmoid_k=8, sigmoid_c=0.2, output='map_population_darkelf.png') (full) Yes, it looks just like the population heatmap. How about seeing where they are overrepresented or underrepresented? We can divide the two overlays by one another to essentially get fractions of Dark Elves amongst the population: draw_npcs(relative=True, filter_sigma=50, mark_npcs=[n for n in npcs if n.race == 'Dark Elf'], sigmoid_k=4, sigmoid_c=0.5, output='map_population_darkelf_relative.png') (full) I did have to play around with the parameters for this one (increasing the blur radius and moving the centre of the sigmoid to 0.5), but we can sort of see how the Dark Elves (natives of Morrowind) are less represented in the southwestern part of the island (which is more cosmopolitan and welcoming towards foreigners) and more represented in the eastern territories as well around the Ashlander camps (which almost completely consist of them). What else can we do? Morrowind has slavery! Let's find out where all the slaves are concentrated: draw_npcs(relative=True, filter_sigma=25, mark_npcs=[n for n in npcs if n.class_name == 'Slave'], sigmoid_k=8, sigmoid_c=0.2, output='map_population_slave_relative.png') (full) No blobs around big cities and towns -- which makes sense since this is a relative fraction. Instead what we have highlighted for us are random dungeons and plantations around the world where slaves are held, including Abebaal Egg Mine or Dren Plantation or some slave markets or Rotheran or Hlormaren (interestingly, for the latter the blob (west of Balmora by the sea) is west of the actual stronghold -- this is because the slaves are held in sewers from where the exit is around there). Of course we would never use this tool for our own selfish purposes: draw_npcs(relative=True, filter_sigma=50, mark_npcs=[n for n in npcs if n.is_female], sigmoid_k=12, sigmoid_c=0.7, output='map_population_female_relative.png') (full) There are very few places on the island where females are overrepresented (note I set the centre of the sigmoid at 70%) -- the only one of them that's a town is Tel Mora in the northeast. That's because the councilor of that town "does not enjoy the presence of men" and all residents of that town are indeed women. Another place is Odirniran in the southeast, a Telvanni stronghold under attack by House Hlaalu. Northwest of that we have Assu with two sorceresses and north of that is Tel Uvirith -- a stronghold that gets built for the player as part of the Telvanni questline. It's disabled at the start of the game (and is invisible), but the scraper obviously didn't care about that. Next year on project Morrowind, I promise I'll actually get around to cleaning up the source code that was used to make all this and releasing it. Promise. Look what I found in my drafts folder. Welcome back to project Morrowind. The nice visualization of where Aryon could be was very close now. I went with the stupidest approach: go through all pixels on the map, convert each one into a point in the game world and find how long it would take Aryon to get there (by using the method I mentioned previously: go through all points in the graph we know the shortest travel time to and find the one for which the total travel time (shortest time to travel to that point + time to walk from that point to the destination) is the smallest). Except I forgot this was Python and I was going to go through, for each point on the map, about 2400 possible routes through exterior points. And there were 1650x1900 = about 3 million points. Sure, I could be smart about it and use various optimisations (like coalescing exterior points that are close enough to each other and treating them as one or exploiting the triangle inequality (as mentioned in the previous post) or looking at 2x2 blocks on the map instead of each pixel or using all 4 cores of my CPU instead of one). Or I could farm it out to a C++ program. So I dumped the list of known exterior coordinates and times of the shortest routes to those to a file as well as the in-game coordinates of the 3-ish million points on the map I was interested in. The program would take those and spit out, for each sought coordinate, the shortest time it would take for Aryon to get there from his tower. In fact, it took 40 lines and ran in about 10 seconds. It's pretty amazing how fast you can be if you speak to the bare metal. I then used matplotlib's contour plot to visualize the heatmap I got. I didn't manage to get it to actually overlay on the map in the map's original resolution, but the wizards were still extremely impressed and said that I should speak to them whenever I was interested in seed funding for my startup. So this actually makes sense. There's a 2h circle around Aryon's home (northeast portion of the island) from where he could either walk or teleport to Wolverine Hall through Divine Intervention (an island east of Vvardenfell). Wolverine Hall has a Mages' Guild, so that means he could instantaneously get to four other major towns (a blob along the west edge of the island). So there are quite a few places he could get in 2 hours! After that, he would have to take the Silt Strider or a boat, which would slow him down. In 4 hours he would barely be able to reach Gnisis (northwest corner of the island) or Maar Gan (the little arc at the top of the 4h contour around the main population centres). He, of course, could walk from his original location for 4 hours but he wouldn't get very far. In 6 hours he could be anywhere on the island and in 8 he would be able to reach the northern edges of Dagon Fel, a small island north of Vvardenfell. Finally, in about 11 hours he could very possibly be having breakfast with Big Head in the most desolate corner of Morrowind. Perhaps he had some business there? The wizards said last time they ever saw Aryon was at about 2am, so he'd been gone for almost 10 hours by that point. Luckily as we were trying to figure out if he would deliberately take the most efficient route to get as far away from his tower as possible, we heard a loud noise from a nearby wardrobe and an asleep but still alive Aryon fell out of it. In the end, he loved my contour plot as well and hung it up on his wall. Some people say the tower steward still uses it to track down people who go missing in action during Aryon's wild parties. Next year on project Morrowind, we'll talk about my assignment with Vvardenfell Office for National Statistics to make sense of the island's demographics. Welcome back to project Morrowind, in which we use technology to oppress people for our own political gains. A couple of hungover Telvanni wizards came by to my house this Saturday morning. They went to Master Aryon's tower the night before for a round of drinks, which quickly escalated to several rounds of drinks. Long story short, Aryon managed to wander away somewhere and hasn't been seen since. Worse even, a Council meeting was supposed to take place next Monday and Aryon not attending it would be disastrous. The wizards wondered if I could map out the locations Aryon might possibly be in so they would be able to better concentrate their agents' efforts across various cities in Vvardenfell and recover him before the meeting. Imagining all kinds of blog posts I could write about this, I agreed. Regenerating the graph I first had to alter the weights between the edges on the travel graph, since in actual game time travel by silt strider or boat isn't instantaneous. But it's easy to calculate from the distance anyway: the speed of travel is in a game setting that defaults to 16000 units per game hour. For example, the distance between Seyda Neen and Balmora is about 55000 units, so if in the beginning of the game you decided to spend money on public transport instead of walking, you would get to Balmora and finish your first quest in less than 3.5 game hours. Determining the walking time between locations also required some digging. The minimum walking speed in the game is 100 game units per real-world second and the game time by default flows 30 times faster than real time. So walking 16000 units would take about 16000 / 100 * 30 / 3600 = 1h20m of game time. As you see, this is not much slower than taking the silt strider and if you saw one you would realise why. Obviously, if our travel NPC has "Guild Guide" in his class name, traveling with him doesn't take any time - because magic. Having rebuilt the graph and re-run Dijkstra on it, we can easily determine how long it would take Aryon to reach any point in the game world, assuming he uses the fastest route. Go through all points in the graph we know the shortest travel time to and find the one for which the total travel time (shortest time to travel to that point + time to walk from that point to the destination) is the smallest. There is an optimisation which I haven't done: we actually only care about points on the graph where we can get by any other route than plain walking. Consider this: if a shortest path to a point is formed by first teleporting to some point A, then walking to point B and then finally walking to point C (all in a straight line), why not walk from A to C directly (we're assuming here that Aryon can levitate and move between the points as-the-crow-flies, so any 3 points that are in the exterior follow the triangle inequality). But of course just giving the Telvanni wizards a list of in-game coordinates would be a faux pas. They required a map, and a map I would provide. An affine map, of all things. A quick, incomplete and mostly wrong introduction to linear algebra The problem here is that we want to find a way to convert a pair of pixel coordinates on the game map to coordinates in the game world. Luckily, this transformation has an important property: a line between any two points on the game map is also a line in the actual world. Such transformations are called affine: they can be composed out of primitive operations like translation, rotation, reflection etc. The good news is, they can be represented by a matrix product. $$ \begin{pmatrix}x_{GAME} \\ y_{GAME} \\ 1 \end{pmatrix} = M \begin{pmatrix}x_{MAP} \\ y_{MAP} \\ 1\end{pmatrix} $$ So if we have a pair of map coordinates and this 3x3 matrix M, we'll be able to calculate the actual in-game coordinates, and vice versa. The third component of the vector being 1 is an ugly hack that allows us to encode translations (movement), since otherwise the vector (0, 0) on the map would map (he-he) to the vector (0, 0) in the game. More on Wikipedia. How do we find such a matrix? Well, we can use it to transform several vectors at the same time: $$ \begin{pmatrix}x_{GAME, 1} & x_{GAME, 2} & x_{GAME, 3} \\ y_{GAME, 1} & y_{GAME, 2} & y_{GAME, 3} \\ 1 & 1 & 1 \end{pmatrix} = M \begin{pmatrix}x_{MAP, 1} & x_{MAP, 2} & x_{MAP, 3} \\ y_{MAP, 1} & y_{MAP, 2} & y_{MAP, 3} \\ 1 & 1 & 1 \end{pmatrix} $$ And (by inverting the matrix on the right and multiplying the whole equation by it) this can be rewritten to $$ M = \begin{pmatrix}x_{GAME, 1} & x_{GAME, 2} & x_{GAME, 3} \\ y_{GAME, 1} & y_{GAME, 2} & y_{GAME, 3} \\ 1 & 1 & 1 \end{pmatrix} \begin{pmatrix}x_{MAP, 1} & x_{MAP, 2} & x_{MAP, 3} \\ y_{MAP, 1} & y_{MAP, 2} & y_{MAP, 3} \\ 1 & 1 & 1 \end{pmatrix}^{-1} $$ Essentially, if we get 3 sets of coordinates in the game world and on the map, we can use those to recover our mapping. These 3 points also can't be on the same line because then the determinant of the matrix of map coordinates is zero and it doesn't have an inverse. So I picked the game coordinates of 3 locations that were fairly well spread (to minimize the error) and tried to pinpoint the corresponding pixel coordinates on the map. In the end this is the matrix I found: $$ M = \begin{pmatrix}185.38 & -0.43327 & -126720 \\ 1.2986 & -0.018372 & 218470 \\ 0 & 0 & 1 \end{pmatrix} $$ To test it out, I plotted the three reference points I used to calculate it (in red) as well as Aryon's initial location (in blue): the exterior door to his house is located at game coordinates (85730.77, 117960.3, 5081.284) which he matrix mapped to (1147.33, 555.21). I can see your house from here! (the actual map comes from http://thegamersjournal.com/rpg/pc/morrowind/maps/map_rendered_m.jpg) This edition of project Morrowind was overdue by about two months, so I sadly have to stop here. But next time I'll definitely tell you how we managed to track Aryon and save the Telvanni council from collapse. @mildbyte 6 years, 10 months ago \| programming \| games \| morrowind \| python \| Today on project Morrowind, we take decades of research into rendering 3D scene descriptions to beautiful photorealistic worlds and throw it away. I finally give up on any nontrivial formatting in WordPress and hope it can't mangle text in pictures. Loading cell data There are a few catches to parsing cells in Morrowind, the first one being how we can uniquely name one. It's easy with interiors, since each interior has a NAME field, like "Uncle Sweetshare's Workshop" (and that's not a joke). However, there are about three types of exteriors. The first one is cities and notable landmarks - like the example in the picture, those will have a RGNN, a NAME and some coordinates of where the massive exterior square cell is located. However, there are many Vivec cells (since Vivec is really big) and so we'll use the region coordinates as well to identify one. Secondly, wilderness cells like other parts of the Ascadian Isles Region will be named just using that and their exterior coordinates. Finally, there are exterior cells without neither a cell nor a region name but with coordinates - those are named Wilderness [x, y] in TES Construction Set, so let's use that as well. Each one of these cantons is a city by itself and they are all joined by bridges. Also, it's on the water. Who wouldn't want to live here? (from http://www.uesp.net/wiki/File:MW_Map_Vivec.jpg) The next step is parsing out the contents of each cell, which is basically an ID of an object and other data about the given instance of the reference (for example, the position, the number of hit points (for an NPC) or possible destinations (for doors or NPCs offering travel services)). Oh, also, references can sometimes be deleted - but instead of them being removed from the data file, they are just marked as deleted. This could be because actually wiping them from the file would imply rewriting the whole file over (since all the pointers in the file would have to be recalculated), a joke now but something that would probably take up way too many resources back in 2002. One thing that should be noted is that the actual object definitions can appear before or after they are referenced and so we have to parse the file in two passes - first recording just the reference IDs as strings and then linking those to actual Python objects. Whew, we're done! In [1]: mages Out[1]: Vivec, Guild of Mages In [2]: mages.is_interior Out[2]: True In [3]: mages.destinations Out[3]: [(Vivec, Foreign Quarter Plaza, (-826.792800, 357.833600, 309.695400))] I haven't included the locations that NPCs in the cell can take the player to (like the teleportation services) in the cell destinations' list - it only lists where the doors in the cell lead to. The full version is at https://mildbyte.files.wordpress.com/2016/03/graph-2016-2.png, but beware - it's about 10MB large and might break your browser's assumptions about how large PNGs can get. But even with this information, we can create cool-looking graphs. For example, I produced the picture above with GraphViz, on it the nodes are cells and they are joined with an edge if there's a door between them. The large clump in the middle is Vivec. There are some smaller clusters dotted around, being slightly smaller cities (like Balmora, Caldera or Ald'runh). There are also some hub-spoke formations in there as well, the hub being a named exterior cell and the cells joined to it being the interiors that are accessible through it - these are smaller settlements. Yet this is not what we came here for. We want to know how to get from point A to point B while exploiting everything this world has to offer us -- not just the doors. So let's talk about how we will define the actual travel graph. Building a travel planner Clearly, there's an infinite number of points in the game, but we don't need to look at them all. We only need to consider our start point, our end point and all potential points of interest our travel can go through. So we can easily define the nodes in our graph: For every object offering travel "services" (NPCs/doors), the object's location and the travel destination. The location of every Divine/Almsivi Intervention marker. That's it. A description of our route would then be something along the lines of "From the starting point, go to this door (point 1), go through it to a different cell (point 2), walk to the person offering travel services (point 3), travel to a different city (point 4), walk to your destination (point 5)". So let's see how the nodes in the graph can be joined. A travel "service" provider's location (a door or an actual teleporter/silt strider driver NPC) is joined to its destination with an edge of length 0. If two nodes are in the same cell (or both are in the exterior world), they're joined with an edge of length proportional to the distance between them (so we ignore, say, mountains in the exterior world or impassable obstacles in the interior). Every single node is joined to the nearest Temple/Imperial Fort to it (using the straight as-the-crow-flies Euclidean distance for exteriors or the distance from the nearest exterior cell for the interiors). With this method, I ended up with a travel graph that had 6424 vertices and 16065 teleport-only edges - that includes doors/transport services/Intervention spells but not direct within-cell travel, as it's very easy to find the distance between any two points in that case on the fly. One interesting thing about shortest-paths algorithms is that finding the shortest path between two nodes (single-pair shortest-path) is as computationally expensive (has the same asymptotic complexity) as finding the shortest path from a fixed node to everywhere in the graph (single-source shortest-path). Intuitively, this is because our ideal path in a single-pair problem could include any point in the graph and so we are calculating the shortest path to that point from our source anyway. Dijkstra's Algorithm works pretty well for these kinds of things, finding the shortest paths from a single source to everywhere in O(\|V\|²) (where \|V\| is the number of nodes in the graph). This can be improved by using a Fibonacci Heap to store unexamined vertices and fetch the closest ones in O(1), giving a time complexity of O(\|E\| + \|V\|log\|V\|). I didn't think just 6000 vertices would make the search take too much time, so didn't implement one, but perhaps will do later. I used Aryon as a guinea pig for this experiment - he becomes your main questgiver in the latter stages of the House Telvanni questline and happens to live in a fairly isolated tower in the middle of nowhere with almost no travel services. So while you can use Mark/Recall to get to him, his quests can send you across the game world to places reaching which quickly can be nontrivial. After unleashing Dijkstra upon this graph (which admittedly took 10 minutes, slightly too long) we get two lists: first, for each point, the weight of the cheapest (fastest in this case) route from Aryon to that point. Second, for each point, what is the previous point in the fastest route. Hence we can easily reconstruct the optimal route for a point of interest by following those links. For example, how do we get from Aryon to Hlormaren, a Dunmer stronghold on the other edge of the island? Like this: Out[35]: (Hlormaren, Dome, (384.000000, -408.000000, 384.000000)) route = chain_prev(prev, target) [(Tel Vos, Aryon's Chambers, (3905.517000, 2935.360000, 15752.000000)), (Wolverine Hall, [18,3], (148881.700000, 28453.790000, 1495.193000)), (Sadrith Mora, Wolverine Hall: Imperial Shrine, (-64.000000, -96.000000, 0.000000)), (Sadrith Mora, Wolverine Hall: Imperial Shrine, (-320.000000, -224.000000, 32.000000)), (Sadrith Mora, Wolverine Hall, (2560.000000, 4064.000000, 14240.000000)), (Sadrith Mora, Wolverine Hall: Mage's Guild, (448.000000, 192.000000, 160.000000)), (Sadrith Mora, Wolverine Hall: Mage's Guild, (-70.134480, 434.521700, 65.990490)), (Balmora, Guild of Mages, (-755.896600, -1002.733000, -644.627900)), (Balmora, [-3,-2], (-22130.610000, -8582.789000, 889.572800)), (Hlormaren, [-6,-1], (-43200.000000, -3448.000000, 3072.000000)), (Hlormaren, Dome, (320.000000, -256.000000, 402.000000)), (Hlormaren, Dome, (384.000000, -408.000000, 384.000000))] There's a disadvantage here in that we don't actually see the method of travel to get between nodes and so this travel plan takes some game knowledge to decipher. Basically, we want to use a Divine Intervention spell to go to the Wolverine Hall Fort, then enter the Imperial Shrine, unceremoniously walk through it into the Fort interior, enter the Mage's (sic) guild, get ourselves teleported to Balmora and then walk/fly from there to Hlormaren. How about getting to Sarys Ancestral Tomb, which is located on a remote island on the southwest corner of the map? Easy. (Vivec, Guild of Mages, (3.520470, 1391.325000, -385.853300)), (Ebonheart, [1,-13], (8703.056000, -100602.000000, 1383.638000)), (Bitter Coast Region, [-5,-9], (-37659.390000, -69956.550000, 322.489000)), (Sarys Ancestral Tomb, (7028.375000, 4415.659000, 15001.790000))] We want to again go to the Sadrith Mora Guild and get teleported, this time to Vivec. Then we cast Divine Intervention one more time and end up in Ebonheart, which is a swim away from the island on which the tomb is located. Next time on project Morrowind, we'll try to make the planner's advice slightly more readable by plotting it on the game map. And maybe plot other things on the map. There might even be some source code! Today on project Morrowind, we will start turning some horrible binaries into beautiful data structures in the memory space of a Python interpreter. They are still technically binary, but let's not dwell on it too much. Otherwise we will realise we're all made of atoms and will have an existential crisis and that wouldn't be very nice. I…I don't even see the code. All I see is tree, rock, marshmerrow... Exposition dump Elder Scrolls games made by Bethesda Softworks, including Morrowind and its successors (Oblivion, Skyrim and that peculiarly also kind of includes Fallout 3 and 4) store their core game data (that is, maps and locations of various objects, but not textures/audio/meshes) in the ESM (Elder Scrolls Master) format. It's been evolving ever since Morrowind as the Bethesda developers have been adding more and more features to it, but its main idea remains the same: these files are a collection of records of different types. For example, we can have an NPC_ record, defining a character in the game, which will contain entries for the character's gender, race, AI behaviour etc. It can also have references to other records, for example, the inventory of a character, which refer to ARMO and WEAP records. CELL records describe in-game cells (actual locations) and contain references to, well, everything that is located in that cell, like NPC_, ARMO, WEAP or CONT (containers, e.g. chests). The actual binary format for Morrowind is described very well here and every release of a new Bethesda game promises players lots of fun in reverse engineering their ever so slightly minor alterations to the game data file format. One clever idea that Bethesda had was making game save files an overlay on the game data files in this format. For example, if you were to kill someone in a certain location (pretty much what usually happens in Elder Scrolls games), your save file would have a redefinition of the CELL record that would list the NPC in question as perished. Sadly, this idea has no relevance to this project, just like lots of other clever ideas, but it's interesting nonetheless. There are more complications though: cells can be exterior or interior. Exterior cells are square-shaped and are joined together edge-to-edge to create the actual great (dubious) outdoors of Morrowind. With interior cells, all bets are off - each of them resides in its own little reality and is joined to other cells by doors which basically function as teleports in this case. A small house in the exterior cell often is quite a bit larger from the inside, which means that you can't reliably judge where the player actually is when they're indoors. So if we want to reconstruct a graph of how you can travel around in Morrowind, we have to take care of doors, amongst all other means of movement. With regards to the Almsivi/Divine Intervention spells, there are special marker objects in every Temple and Imperial fort - this is how the game determines where to teleport the player when they cast a particular spell. It's again easy with the exterior cells (as all markers are located outside), but gets more complicated with interiors. Some people claim Morrowind uses the last exterior cell you've been to (which has some pathological cases - say you use a Guild Teleport that teleports you from the indoors to the indoors again, so casting an Intervention spell will warp you to the closest marker to the first Guild, not the second one) and OpenMW, an open-source reimplementation of the Morrowind engine, tries to fix that by using the closest exterior to you as a reference. My copy of Morrowind behaves the correct way for some reason, so I'll emulate that. In much better news, if NPCs offer travel services (be it silt strider, boat or Guild teleport), it will be encoded in their record. All in all, it seems like we want to scrape the hell out of all CELL and NPC_ records, as they contain everything we need for now. Scraping the hell out of all CELL and NPC_ records Now, as much as I thought it would be feasible and fun to decode the binary data according to that excellent spec, I still decided to cheat and used Morrowind Enchanted Editor, a low-level editor for ESM files. In particular, I used the "Dump to Text File" function, which turned the unreadable binary mess into a readable ASCII mess. Meet Todd's Super Tester Guy, presumably made by Todd Howard himself. This is something we can work with: each entry in the record is on a separate line and is clearly keyed by the subrecord (e.g. FNAM is the full name, RNAM is the race name etc). As a good starting point, we can easily extract just the NPC_ and CELL records and tokenize the data by just converting it into a stream of key-value pairs (so a line NPC_ NAME todd would get turned to a tuple (NAME, todd) since we already know it belongs to an NPC_ record). (I was going to put source code and explain it, block-by-block, here, but WordPress decided to not be on my side today. I'll post it on GitHub later, promise. I mean, seriously, who the hell converts > to > after a save cycle and then again to &gt?) In the end, we get something like this: In [6]: cells[:10] [('NAME', ''), ('DATA', '\x02\x00'), ('DATA', '23'), ('DATA', '7'), ('RGNN', "Azura's Coast Region"), ('NAME', ''), ('RGNN', "Azura's Coast Region")] npcs[:10] [('NAME', 'player'), ('FNAM', 'player'), ('RNAM', 'Dark Elf'), ('CNAM', 'Acrobat'), ('ANAM', ''), ('BNAM', 'b_n_dark elf_m_head_01'), ('KNAM', 'b_n_dark elf_m_hair_01'), ('NPDT', '1'), ('NPDT', ''), ('NPDT', '')] Parsing the stream of NPC_ records into a list of NPCs isn't that difficult. I found the neatest way was to pass the stream to a class constructor and allow it to consume as much from it as it needs to initialize itself. But keep in mind that we need to stop parsing when we see the next NPC's NAME subrecord and if we've already consumed that, it's too late, so we need to define an iterator that allows us to peek at the next item without consuming it. Parsing the list of destinations, one of the Holy Grails that we're looking for, is easy too - just look at this example (which is one of the places that Todd's Super Tester Guy can take us): NPC_ DODT 1822.641 NPC_ DODT -231.5323 NPC_ DODT 0 NPC_ DODT 0.5 NPC_ DNAM ToddTest We literally get a list of 6 numbers: the x, y, z coordinates and the angle (which we don't really care about). Sometimes there's also a DNAM subrecord if we're in an interior cell. Add a repr method and we can see a list of actual NPCs! [NPC (player, player, Dark Elf, Acrobat), NPC (todd, Todd's Super Tester Guy, Dark Elf, Guard), NPC (Imperial Guard, Guard, Imperial, Guard), NPC (agronian guy, Tarhiel, Wood Elf, Enchanter), NPC (murberius harmevus, Murberius Harmevus, Imperial, Warrior), NPC (madres navur, Madres Navur, Dark Elf, Acrobat), NPC (farusea salas, Farusea Salas, Dark Elf, Commoner), NPC (erval, Erval, Wood Elf, Commoner), NPC (Dralas Gilu, Dralas Gilu, Dark Elf, Rogue), NPC (uulernil, Uulernil, High Elf, Smith)] npcs[1].inventory [('steel battle axe', 1), ('glass war axe', 1), ('steel mace', 1), ('chitin guantlet - right', 1), ('chitin guantlet - left', 1), ('chitin boots', 1), ('chitin greaves', 1), ('chitin pauldron - right', 1), ('chitin pauldron - left', 1), ('chitin cuirass', 1)] (Interestingly, there are three problems with the "agronian guy" named Tarhiel over there. Firstly, that race name is spelled Argonian. Secondly, he's not an Argonian, he's a Wood Elf. And finally, he has some mental issues but also talents. Next time on project Morrowind, we'll move on to trying to decode CELL data, which has some more peculiarities (like the fact that it contains most of what the player can perceive). But now that we've gotten through the background and the boring bits, we will start moving faster and might even get around to constructing an actual travel graph! You should play Morrowind. (warning: lots of skippable praise for Morrowind here, scroll down for the meat of the post) At the beginning of Morrowind, you're a chump who just got off a prison ship with 87 gold pieces (one loaf of bread costs 1 gold piece in this world, so that's conveniently about £35 - that's how much you would pay for 87 packs of Tesco Everyday Value Sliced White Bread). Your first assignment is to take a parcel to a guy in a different city, and you either have to take the silt strider (a massive insect with long legs piloted by a possibly drunk creepy guy, not unlike London buses) or walk there through the wilderness, fighting off hordes of oversized carnivorous birds with the iron dagger you had just stolen from the Census office, except the dagger always misses because, see, Morrowind's combat system is inspired by tabletop roleplaying games and they didn't pay their animators that much, so even if your weapon clearly appears to hit the mushy body of whatever it is you, the player, are aiming at, there's no guarantee at all that you have actually hit. So after ruining a couple of mice with repetitive rage-filled clicks, you decide to quit Morrowind and do something better with your life. Or you keep going and learn about how fatigue affects your chances to hit everything (and on everything), read up on game mechanics, buy a new mouse, make your way to Balmora and get immersed in one of the richest worlds I've ever seen in gaming. You go through a story that raises questions about organized religion, xenophobia, colonialism, tribal legends, prophecies, free will and the priorities of an individual versus the organization that they belong to. And somewhere during that process of discovery, you realise that the swings with your crappy dagger don't miss anymore. In fact, your dagger is no longer crappy. In fact, you don't even use a dagger, instead having found an amazing sword in a dungeon guarded by a couple of possibly too sexualized and extremely dangerous monsters. You decide to murder a God and capture his soul because it has the biggest enchantment capacity. When you need to get somewhere, instead of a long slog through the wasteland you use one amulet to teleport to the nearest Temple, bunny-hop (because that makes you move faster) or levitate your way through whatever town you ended up at, enter the Mages' Guild, use the Guild Teleport, use another amulet and finally fly to your destination. You murder entire cities in drug-fueled rampages just to please yourself and then reload the last save. You pilfer the treasuries of great Houses and steal rare armor and weapons, just to go to a remote island and sell them to someone who just happens to be a massive crab - you say it's because he gives you the best prices, but it's actually because everybody else is scared of you. Just like real life. (skippable praise ends here) I decided to replay Morrowind recently and in the middle of that "high-ranking executive" stage, as I got slightly annoyed by all the fetch quests I had to do to get promoted in some guilds, thought about making myself a journey planner. This is not a completely trivial task because there are so many ways you can get around in Morrowind: Walking (or levitating, because any self-respecting player has already enchanted something with a constant Levitation effect) Taking the silt strider (or the boat) - but note you can't immediately get to your target town and might have to change through one of those bad parts of town. Takes in-game time, but we'll say it's instantaneous as perceived by the player. Guild of Mages Teleport - instantaneous as well. You have to talk to mages, but they are a nice bunch, really. Divine/Almsivi Intervention - this is where it gets interesting. Divine Intervention teleports you to the nearest Imperial fort (Morrowind is part of the Empire and is still quite reluctant about that idea) and Almsivi Intervention teleports you to the nearest Tribunal Temple (which is the official religion of Morrowind that was around way before the Empire). Mark/Recall - two spells, one places a mark and the other one teleports you to that mark. Propylon Indices - long ago, someone decided to build lots of cool-looking strongholds in a circle around the island. Good news: there's a teleport chamber linking them in a round-robin fashion. Bad news: you need a Propylon Mark for each one of those strongholds to use their teleport and those are often tough to find. Also, these strongholds have been overrun by various nasties and generally aren't pleasant to be around. I'll exclude them from my analysis for now. There are minor delays on the Circle Line due to sharks (from http://www.terminally-incoherent.com). So you can see how some interesting ways to get to places can arise by combining these means. For example, you could totally cast Almsivi Intervention to get teleported to the nearest Temple, then Divine Intervention to get teleported to an Imperial Fort, then use a Guild teleport and immediately cast another Almsivi to get to yet another town. But of course it would be boring if I just spent some time reading those Morrowind travel maps, making a graph and running Dijkstra on it. For one, that wouldn't make for a good blog post. In addition, it doesn't help you if you end up somewhere in the wilderness (see that area in the middle, circled by Falasmaryon, Valenvaryon, Rotheran, Indoranyon, Falensarano, Ald'Ruhn and Maar Gan? Yeah, don't go there). Finally, there are quite a few large fan-made add-ons to Morrowind, including Tamriel Rebuilt, because, see, I've been lying to you and that island isn't called Morrowind, it's actually Vvardenfell and Morrowind is the province Vvardenfell is part of. Tamriel Rebuilt tries to recreate this whole province (yes, the whole Morrowind isn't in the game called Morrowind. What's more, Tamriel is the whole Empire of which Morrowind is a part and, yes, Tamriel Rebuilt just tries to recreate Morrowind in-game. In the game called Morrowind). All of this was me trying to convince you that it's a good idea to find a systematic way to scrape this data out of game files to make our lives easier. And imagine the kinds of things we'll learn if we do that! Demographics! Population heatmaps! Graphs! We might even plot property prices and travel times! Next time on project Morrowind, we will battle with confusing binary formats, bizarre conventions, linear algebra, Python and will possibly learn more about the lore of Morrowind and its game mechanics. Stay tuned! Remaining posts in this series...	CommonCrawl
Distance From Vector To Plane Spanned By Two Vectors See full list on euclideanspace. Let Pand Qbe points in R3 with position vectors p~and ~qrespectively. Angle between two planes The angle between two planes is the same as the angle between the normals to the planes. The black vectors are the two displacements through which the Thompsons went to get to the lodge, the blue vector is the shorter, direct path to the lodge ( the resultant vector ). More precisely, if you take the span of two vectors v and w, the result is the plane that goes through the origin as well as the points v and w. But what are scalars and vectors? A scalar is just a regular number. (b) Since the two lines are perpendicular, they must cross. This video is part of a Linear Algebra course taught. Imagine that perpendicular to that vector (and through the origin) passes a plane. Angles between Vectors. 5 Scalar and Vector and Projections. Advanced Math Solutions - Vector Calculator, Simple Vector Arithmetic. Geometrically, the cross product vector u = v×w is orthogonal to the two vectors v and w: v ·(v ×w) = 0 = w ·(v ×w). 1 Vector representation of planes. Also try to draw your vectors to relative. Vector3 vel = GetForceFrom(ball. If you take the cross product of any two of those vectors, you will get a vector perpendicular to the plane. Also, gives. The angle between two vectors is referred to as a single point, known as the shortest angle by which we have to move around one of the two given vectors towards the position of co directional with another vector. SET Two brothers started the business in the US in the 1950s. If is the angle between the two lines, and is the angle between the red. Given two vectors, calculate the resulting area spanned by these vectors. Suppose we are given two vectors ~vand w~. and choose point C so that. Выбери предложения, которое составлено верно * 1 балл don`t two me women understand. Our strategy will be to find two vectors in the plane, take their cross product to find a vector perpendicular to both of them (and thus to the We will do this by finding the vector from #(1,0,1)# to #(0,2,2)# and from #(1,0,1)# to #(3,3,0)#. camera are different, which makes it change signs during computation. Recent advances in developing clinically desirable AAV capsids, optimizing genome designs and harnessing revolutionary biotechnologies have contributed substantially to the. The orthogonal complement S? to S is the set of vectors in V orthogonal to all vectors in S. 2) std::pmr::vector is an alias template that uses a polymorphic allocator. This perpendicular distance can be spanned with support vectors. Vector, полученные из open source проектов. A point an a vector determine a plane. If the axis of rotation is given by two points P1 = (a,b,c) and P2 = (d,e,f), then a direction vector can be obtained. They have several applications, especially in vector functions and applied mathematics, and in electromagn. If you picture the plane as being flat on a table, the question becomes if the resulting vector go up (our "out" of the table, from our perspective) or down (or "into" the table, from our perspective). 2 Two intersecting planes 5. Second, the sum of any two vectors in the plane L remains in the plane. Example # 7: Give a geometric description of. Vector-based methods provide an alternative approach to latitude/longitude geodesy calculations On an ellipsoidal model earth, it will intersect the equatorial plane at an angle equal to the geodetic On a spherical earth model, the great circle distance between two points (the 'inverse geodetic problem'. Suppose, all vectors are multiple to each other then, they make a line within the origin. A plane is a flat surface that extends infinitely in all directions. LerpUnclamped: Linearly interpolates between two vectors. -od: Distance between two groups. Or tail and head. iˆ, jˆ,kˆ unit vectors in positive direction of x,y,z axes a a iˆ a ˆj (3. Under the hood, the above three snippets compute the cosine similarity between the two specified words using word vectors (embeddings) of each. For any $m$ nonzero vectors, the $m$-volume of the parallelepiped they span is nonzero if and only if the vectors are linearly independent (that is, if none of them can be expressed in terms of the others using scalar multiplication and vector addition). A vector is something that behaves like a vector from an algebraic point of view, no points are involved. Vector calculator. The midpoint formula and the distance formula in 3D. Agreed, but a vector has a start point and an endpoint. A vector is similar to a point. Note that if both a and b are unit vectors, then kakkbk= 1, and ab = cos. So ⃗a 1,⃗a 2,⃗a 3 also span the plane P. Also try to draw your vectors to relative. The method relies on Mathematica's capabilities to handle vectors and the angles between them. Finding unit vector perpendicular to two vectors - Examples. If they do not intersect, take a point in one plane and nd a distance to another plane. Recall from the Dot Product section that two orthogonal vectors will have a dot product of zero. Distance from point to plane. (Note that 0 = 0 0. The normal vector of the plane 2x − y + 4z + 4 = 0 is h2,−1,4i. Drawing vectors in two-dimensional Cartesian coordinates. More specifically, that plane is the xz-plane. A 2 = A x 2 + A y 2 + A z 2. This gives an equation that we can solve for x. 2 will give a vector lying in the plane determined or spanned by v 1 and v 2. And it's going to be perpendicular to our normal vector. The image of T, im(T), is the plane (2 dimensional) in R 3 spanned by the vectors of the first two columns of A as displayed in the following diagram. Illustrations. You can make two different vectors from two different points in a plane. 19 Distance Between Plane and Plane d= je dj j~nj where ~nis the vector orthogonal to both planes, eis the constant of one plane, and dis the constant of the other. study these two phenomena next. If a vector starts at 0, then the vector~v = hv1;v2i points to the point hv1;v2i. by summing the products of the corresponding. 2 Two intersecting planes. But, it is very useful for tasks like image recognition and object detection. To do better than guessing, notice that in going from the tail to the head of a the vertical distance increases by 4 while the horizontal distance increases by 4 √ 2. SPICE routines that take planes as input arguments can accept planes created by any of the routines listed above. Now add another vector C to the set. Definition 4. Schwarz inequality. Example: How to define parallel vectors? Two vectors are parallel if they are scalar multiples of one another. The first is the signal that you want to convert, the second is the length of the resulting vector. Find the distance from the tip of Vector C to the plane through the origin spanned by A and B. DeviantArt is the world's largest online social community for artists and art enthusiasts, allowing people to connect through the creation and sharing of art. Direction Vector = [-0. $ Find $(a)$ the scalar product of the two vectors and (b) the magnitude of the vector product $\vec{a} \times \vec{b}. (c) By (a), the dimension of Span(x 1,x 2,x 3) is at most 2; by (b), the dimension of Span(x 1,x 2,x 3) is at least 2. For a line, you need a point and a direction. -od1: If one plane and one vector is given, the distances for each of the atoms from the center of the plane is given separately. copper Identification of Preferred Slip Planes. You have three points in the plane, so you can find several vectors in the plane joining those points. Eigen offers matrix/vector arithmetic operations either through overloads of common C++ arithmetic operators such as +, -, *, or through special methods For the Matrix class (matrices and vectors), operators are only overloaded to support linear-algebraic operations. this PolygonMatrix minus all the faces that are not visible to the view. -od: Distance between two groups. Scalar Product. Distance is taken from the center of one group to the center of the other group. Addition of vectors means finding the resultant of a number of vectors acting on a body. Another way to find the distance is by finding the plane and the line intersection point and then calculate distance between this point and the given point. Using vectors in geometry 6 www. Addition and scaling Definition 4. And it's going to be perpendicular to our normal vector. Any two vectors not scalar multiples of each other are linearly independent, so your vectors form a basis for the plane they span, so it's 2-diminsional. Computes a matrix representing the rotation around the axes normal to two vectors by the angle which is between the two Returns the closest distance between a point and a line segment defined by two end points. The vector spaces are denoted $\mathbb{R}$ because the values are real numbers. (There is no pivot in that column. position,Camera. Properties of vectors: - two vectors are equal if they are equal in both magnitude and direction Vector (where is the positive number) has the same direction as vector , but its length is times is a VECTOR, the magnitude of which is. 2: Subspaces and Bases. Several models were trained on joint Russian Wikipedia and Lenta. Distance Calculator » Need the distances between two places? Driving Directions Finder » Need driving directions to a new place? Flight Time Calculator » Need to calculate the time it takes to get to a city by plane? Time Zones » Need to figure out the time zone in which a city or country is located in?. Subtracts one vector from another. Enter the elapsed time in the format hh:mm:ss to get the average speed. For examples, the following two vectors n and s are combined into a new vector containing elements Value Coercion. The span of two noncollinear vectors is the plane containing the origin and the heads of the vectors. The vector $\color{green}{\vc{n}}$ (in green) is a unit normal vector to the plane. airline tickets and passport passport with boarding passes tickets for traveling by plane. 016 Fall 2012 c W. Solution : Let a vector = i vector + 2j vector + k vector. Since, a vector must have elements of the same type, this function will try and coerce elements to the same type, if they are different. Also, gives. In general, a line or a plane in R 3 is a subspace if and only if it passes through the origin. Using numpy and vectorize function we have seen how to calculate the haversine. If v1 is the normal and v2 is a point of the plane (or the other way around), the plane is well defined also. The plane spanned by any two axes is 1. This perpendicular distance is smaller by a factor cos , where is the angle that the plane is tilted. Cross [{x, y}] gives the perpendicular vector {-y, x}. A unit vector is the equivalent vector of your original vector that has a magnitude of 1. The vector spaces are denoted $\mathbb{R}$ because the values are real numbers. Plane plane = new Plane(Vector3. Search by image. $$ \begin{pmatrix} -1&5\\ 2&3\\ 3&-1\\ \end{pmatrix} $$ is row equivalent to:. 2020 In 264 In 264. Remarks The angle between the two vectors is measured in the plane spanned by them. A resultant is the sum of two (or more) vectors. First, write down two vectors, $\vecs{v}_1$ and $\vecs{v}_2$, that lie along $L_1$ and $L_2$, respectively. which holds if and only if the vector equation holds. Consider the plane : x+ 2y+ z= 3 and the point P o = (1;1;2). For two vectors, if they lie on the same line through the origin, then that line is the set of all their combinations. Plane Plane Line Line 15. 7 are still true for more general vectors spaces. 3 The straight line passing through two given points 8. Vectors of unit length 6 9. These vectors aren't parallel so the planes. In geometric terms, this occurs when either one or both vectors is the zero vector or when the angle between them is ±90° (since cos(±90°) = 0). ▸ Linear Algebra : Let two matrices be , What is A - B ? Correct To multiply the vector x by 2, take each element of x and multiply that element by 2. What is the distance formula for a plane (2-dimensions)? Another way to take the product of two vectors. this PolygonMatrix minus all the faces that are not visible to the view. For example, Euclidean distance between the vectors could be computed as follows. The dot product of two vectors is thus the sum of the products of their parallel components. Plane plane = new Plane(Vector3. This point and this point lie on the plane, so the difference between these two vectors, the whole vector will lie on the plane. Angles ∠1 and ∠2 are supplementary. However, there are only two independent directions in a plane (i. Most countries have been placed in the red category, and for the limited countries that arent, strict measures apply for arrivals. Of course a non-zero scalar multiple of a normal vector n is still perpendicular to the plane. Example: Let V = Span {[0, 0, 1], [2. If v1 is the normal and v2 is a point of the plane (or the other way around), the plane is well defined also. The vector is defined as a sum of two vectors: one is in the local horizontal plane at the origin point directed along the initial geodesic direction connecting two points with magnitude equal to the surface distance along geodesic; the other is along local vertical at the origin point with magnitude defined by the difference in altitudes. The distance between two vectors u and v in Rn is defined as ku − v. • The parallelogram law of vector addition states that if two vectors acting at a point are represented by the sides of a parallelogram drawn from that point, their resultant is represented by the diagonal which passes through that point of the parallelogram. There are a two different ways to calculate the resultant vector. 0 Plan3lover 19 minutes ago. REMARKS: vectors can be drawn everywhere in the plane. It is easy to recognize parallel planes written in the form ax+by+cz=d since a quick comparison of the normal vectors n= can be made. Let x be a basis for the intersection. Returns the sum of all elements Computes batched the p-norm distance between each pair of the two collections of row vectors. From geometric properties of the cross product, is perpendicular to both. As in the direct lattice, the reciprocal lattice is spanned by unit vectors. · If two planes do not intersect, the planes are parallel. Vectors can be added and subtracted. A Translation Vector is a vector that gives the length and direction of a particular translation. The vector z x lies in O; the vectors z 00x, x0, and x are linearly dependent. Let a = (a1, a2, a3) and b = (b1, b2, b3) be vectors parallel to the plane. A 3 dimensional space maps onto a 2 dimensional space with a 1 dimensional kernel. is not a plane when v is a multiple of u or when u is the zero vector When u and v are nonzero vectors, Span{u ,v } contains only the line through u and the line through v and the origin. Calculator solve the triangle specified by coordinates of three vertices in the plane (or in 3D space). Denote the plane by K. That is, Span{}, is the set of all vectors formed by the Linear Combination of. from my calculation the answer is 4/15. Min: Returns a vector that is made from the smallest components of two vectors. Vectors represented by coordinates All that matters is that our angle between two vectors calculator has all possible combinations available to you. Vector Calculus Plane Chart Airplane Aircraft Airplanes. 4k animation of an abstract old science background with earth map outline paint with ink revealing. Every vector is determined by two points. The performance of a Nearest Neighbor classifier that uses L1 distance will not change if (Select all that apply. The vector z x lies in O; the vectors z 00x, x0, and x are linearly dependent. Finding unit vector perpendicular to two vectors - Examples. plane vector. Some important Vectors: Null Vectors: A Vector which magnitude is ZERO Two equal & opposite forces acting on a point 𝐹 + − 𝐹 = 0 If a rope is pulled by two equal forces by 69. The vector (1, 2, 3) is normal to the plane. 1(b) is the xy-plane, but we also say that the two vectors span the xy-plane. You shouldn't have been listening to their private conversation. The vectors do not span R 2. The plane through c spanned by a and b is the set P = {x ∈ Rn: x = c+y , with y ∈ span(a,b)} = {x ∈ Rn: x = c+sa+tb , s,t ∈ R} Examples I The set{(r,s,1)T: r,s ∈ R}is theplane through(0,0,1)T spanned by the vectors (1,0,0)T and (0,1,0)T. Angle pairs formed by parallel lines cut by a transversal. Methods for calculating a Resultant Vector. ‪Vector Addition‬‪Explore 1D‬‪Explore 2D‬‪Lab‬‪Equations‬. In exterior algebra the exterior product of two vectors is a bivector. Distance to plane. That is, Span{}, is the set of all vectors formed by the Linear Combination of. Think of two planes that combine to span 3 space, and intersect in a line. V = {(-2 -4 2 -4); (-1 2 0 1); (1 6 -2 5)} How to solve this problem? The span of a set of vectors V is the set of all possible linear combinations of the vectors of V. For example you can add two velocity vectors together or two acceleration vectors together, but you cannot add a velocity vector with an acceleration vector. The direction of the unit vector U is along the bearing of 30°. Let (a, b) and (c, d) be two points or vectors. Some notation for vectors 3 5. Hint: It is easier to compute bV?, as it is the projection of b onto the line V? spanned by the vector v = (a, b,c). In vector terms, the tip of the blue vector is at a distance from , so that its position vector is , where is a. Find the distance from y to the plane in R3 spanned by u1 and u2. When a set of vectors Span R^n it means that any linear combination of the components of that subset you are given will produce any any vector in R ^ n. Let's Begin!. You can make two different vectors from two different points in a plane. The calculator will find the angle (in radians and degrees) between the two vectors, and will show the work. A cross product has many usages, such as: Calculating distance of a point to a plane. The resultant vector is the vector that 'results' from adding two or more vectors together. How to nd the area of a triangle spanned by two vectors. 0 points tim, with mass 74. Two planes have equations: 3x + y – z = 2 and x – y. Distance(Vector2, Vector2). What will be the magnitude and direction of the plane's velocity if it does not correct for the wind? We calculate the components of the velocity vectors of both the plane and the wind: Plane: p = Wind: w = The velocity vector of the plane affected by the wind is p + w = (283, 451. If a line in the x, y-plane is given by the equation; then and are two points on the line, and so is a direction vector of the line. To derive Eq. For the non-zero vectors u and v shown here draw a line segment from the head of u that is perpendicular to the line containing the vector v. What are the vectors for Vertical and Horizontal plane. I'm not quite sure where to start or how to. Some notation for vectors 3 5. The equation of the plane through the point (x0;y0;z0) and normal to the vector n = Ai+ Bj+ Ck is A(x x0) + B(y y0) + C(z z0) = 0: 16. Zero vector or null vector is a vector with zero magnitude and indeterminate direction and is denoted. -od1: If one plane and one vector is given, the distances for each of the atoms from the center of the plane is given separately. EXAMPLE 6 Find two vectors in R3 whose span is the plane 2x 6y + 5z = 0. You can drag point $\color{red}{P}$ as well as a second point $\vc{Q}$ (in yellow) which is confined to be in the plane. joining two points. Conversely, given a normal vector, one can easily find two other independent vectors The two denominators are the same and only need to be calculated once. Because of this, , where is the angle formed by the two vectors, and from the right-hand rule condition,. Distance of a Point to a Plane. A vector can be computed from any point on the plane by subtracting p 0 from this point which we will call p. Calculating projection of a point. Vector-based methods provide an alternative approach to latitude/longitude geodesy calculations On an ellipsoidal model earth, it will intersect the equatorial plane at an angle equal to the geodetic On a spherical earth model, the great circle distance between two points (the 'inverse geodetic problem'. - Vectors of sorted eigenvalues - Distances (Euclidean, Manhattan) - how to convert to kernels? exp(- distance)? 4. In this tutorial we shall discuss only the scalar or dot product. 1 Plane from vector to Cartesian form 5. angle_to(Vector2 to). Both components of one vector must be in the same ratio to the corresponding components of the parallel vector. Min: Returns a vector that is made from the smallest components of two vectors. The object is to form the right triangle shown. Thus the sum of two vectors and. A position vector gives the position of a point. ) Adding Vectors. A 2 = A x 2 + A y 2 + A z 2. For vectors with complex entries, using the given definition of the dot product would lead to quite different properties. Write y as the sum of a vector in W and a vector orthogonal to W. Cross [{x, y}] gives the perpendicular vector {-y, x}. e) If vector is a multiple of vector , then. Unit vectors, vectors with magnitude = 1, are denoted with a carat over the top of the variable. Parameter(s): iterator position, iterator start_position, iterator end_position - iterator position is the index using iterator of the vector where elements to be added, start_position, iterator end_position are the iterators of another container whose value will be. In three dimensions, vectors have three components. Magnitude of the vector represents the displacement of a quantity from its origin. Dot product of two vectors. A vector in the plane is a directed line segment. 70) The space of a vector determines all the values that can be taken by this vector. On the other hand, if the field vectors are orthogonal to the plane (i. There are no functions that take a range vector and return a range vector, nor is there a way to do any form of subquery (prior to Prometheus 2. Online calculator to calculate and display the distance and midpoint for two points. The distance between two vectors u and v in Rn is defined as ku − v. 4k animation of an abstract minimal icon tree silhouette animation background. Some vectors are said to be linearly dependent if and only if there exist scalars such that and at least one of the scalars is different from zero. At every point during the algorithm, S spans V, so it spans V at the end. Scale: Multiplies two vectors component-wise. Numerically, we add vectors component-by-component. The formula and the explanation can be found below the calculator. Thus, when v and w are linearly independent, their cross product u = v × w 6= 0 defines a normal direction to the plane spanned by v and w. The vector component of these quantities give the direction as well as the magnitude. All vectors are 300-dimensional. Detailed expanation is provided for each operation. Adeno-associated virus (AAV) vectors are the leading platform for gene delivery for the treatment of a variety of human diseases. also d = 0. where is angle between vectors and. Both of those things can be described using vectors. You can convince yourself with the example below: Figure 7: the sum of two vectors The difference between two vectors. The distance of a point to a plane - plane given in general form Let replace in the Hessian formula for the distance d = x 0 · cos a + y 0 · cos b + z 0 · cos g - p , the direction cosines and the length of the normal p , by coefficients of the general form, to obtain. Vector 2 is the sequel to this game Vector, which has been released on 2016. $ Find $(a)$ the scalar product of the two vectors and (b) the magnitude of the vector product $\vec{a} \times \vec{b}. When the run button is pressed, you can watch an animation of the motion of the cars and also see the position vs. is performed by the Triangle Law of addition. distance time. FP3: intersection of planes. Vector orthogonal to. It is clear that the vector is in the plane, so perpendicular to the normal vector, that their dot product is zero. The component vectors whose resultant is to be calculated are independent of each other. Distance From To: Calculate distance between two addresses, cities, states, zipcodes, or locations. But, it is very useful for tasks like image recognition and object detection. There are two different ways in which the positive z axis could be at right angles to the postive x and y axes. for any vector X in plane K there exist numbers c 1 and c 2 such that X = c 1. Remark We emphasize that the first result in Proposition 4. Let's assume that Hand l contain the origin, so that they are linear subspaces. If you are on Mac, copy this airplane ID to the clipboard and press CMD+L while in the designer in SimplePlanes to download this airplane. In exterior algebra the exterior product of two vectors is a bivector. The further away, the better. While it is convenient to think of the vector [latex]u[/latex] [latex]=\langle x,y\rangle [/latex] as an arrow or directed line segment from the origin to the point [latex]\left(x,y\right)[/latex], vectors can be situated anywhere in the plane. Is b in the span of of a 1? A. The distance between non-parallel planes is 0. (2013c) introduced a new evalua-tion scheme based on word analogies that probes the finer structure of the word vector space by ex-. Well i already worked over it and doing it in labs and it seems to be distance vector behaviour. The bivector between two points is anti-commutative, i. It is known that the strength of radio wave radiation decreases with distance. The vector product (also called the cross product) of two vectors $\mathbf{u}$ and $\mathbf{v}$ is the third vector $\mathbf{w}$ whose length is equal to the product of their lengths and the sine of the angle between them, and which is perpendicular to them. -Are they asking for me to find an equation for the plane that contains vectors A and B [basically take the cross product for then normal then have it pass through the origin] and then. In , the upper plane (in blue) is not a vector subspace, since ∉ and + ∉; it is an affine subspace. How to nd a vector perpendicular to two other vectors. A set containing the zero vector is linearly independent. Approximation of planar vectors¶ Suppose we have given a vector $\boldsymbol{f} = (3,5)$ in the $xy$ plane and that we want to approximate this vector by a vector aligned in the direction of the vector $(a,b)$. The magnitude, typically represented as r , is the distance from a starting point, the origin , to the point which is represented. Adding two vectors A and B graphically can be visualized like two successive walks, with the vector sum being the vector distance from the beginning to the end point. No dimensions, no units. Viewgraph 4. Approximation of planar vectors¶ Suppose we have given a vector $\boldsymbol{f} = (3,5)$ in the $xy$ plane and that we want to approximate this vector by a vector aligned in the direction of the vector $(a,b)$. Step-by-step explanation is provided. A unit vector is a vector that has a magnitude of 1 with no units. Those vectors, thus, have this form, where the are scalars. As we are hoping is becoming a habit, let's start by looking again at the case of functions of one variable, and use what we know from our previous. The cross product is mostly used to determine the vector which is perpendicular to the plane surface spanned by two vectors whereas the dot product is used to find the angle between two vectors or the length of the vector. This fact gives the vector equation of the plane: Calculating the dot. I understand V spanning v means that it consists of all the linear combinations where the second and third entries are equal and are twice the value of the first entry. The component form of a vector is the ordered pair that describes the changes in the x- and y-values. The declaration syntax of std::vector is the same as that of std::array, with the difference that we don't need to specify the array length along with the data type as shown. In the example, choose vectors AB and AC. Vectors are used to represent anything that has a direction and magnitude, length. Wingspan is the total distance spanned by both wings. The shortest distance between skew lines is equal to the length of the perpendicular between the two lines. 1 Distance For p and q be two points in R3, Vector addition: Given two vectors ~uand ~vin R3 we form a new vector,. A^B is different than B^A, so too is the trivector A^B^C different than trivector A^C^B, for example, as shown above. That's is why one can identify points P = (a;b) with vectors ~v = ha;bi. The points on the given plane are exactly the points of the form (x,x,z) where x and z are real numbers. Example: How to define parallel vectors? Two vectors are parallel if they are scalar multiples of one another. Distance calculator helps you to find Air distance is the bird fly distance between two locations which is calculated with the great circle formula. Search by image. Vectors on a plane and in space (12. 1 Example 5. Graphs of u;v and. See full list on euclideanspace. It's then normalized. I Magnitude of a vector and unit vectors. To produce an equation of the form (1) for this plane, we need to nd a vector n which is normal to P. De nition 1. In three dimensional space R3 we have three coordinate axes, often called the x, y, and z–axes. The vector product and the scalar product are the two ways of multiplying vectors which see the most application in physics and astronomy. i think the answer is wrong you've considered equation two leaving out equation one. It differs from the dot product in that it must be in R³ and produces a vector not a scalar. which holds if and only if the vector equation holds. Angle between two 3D vectors. Distance to plane. The storage of the vector is handled automatically, being expanded and contracted as needed. Lesson 15: Solving Vector Problems in Two Dimensions We can now start to solve problems involving vectors in 2D. The line has infinitely many points, so you got infinitely many possibilities which direction vector to take. and is the vector is the vector. Either fill in the coefficients of the vector equation, or enter "NONE" if no solution is possible. Make your Flight Plan at SkyVector. Always draw your vectors as arrows with the point in the direction that the vector is going. To do better than guessing, notice that in going from the tail to the head of a the vertical distance increases by 4 while the horizontal distance increases by 4 √ 2. The direction vector of the plane orthogonal to the given lines is collinear or coincides with their direction vectors that is: N = s = ai + b j + ck. ScreenToWorldPoint Following method returns force by calculating distance between given two Following method displays projectile trajectory path. is performed by the Triangle Law of addition. The ordered pair that describes the changes is (x 2 - x 1, y 2 - y 1), in our example (2-0, 5-0) or (2,5). 70) The space of a vector determines all the values that can be taken by this vector. Refer to famous visualisation of 3Blue1Brown's video: Linear combinations, span, and basis vectors R² and R³. Imagine extending the length and width of a table top forever.  Two vector quantities of. The vector $\color{green}{\vc{n}}$ (in green) is a unit normal vector to the plane. Vector \| Unreal Engine Documentation Vector. This dataset is derived under the Cross-Calibrated Multi-Platform (CCMP) project and contains a value-added monthly mean ocean surface wind and pseudostress to approximate a satellite-only climatological data record. The business was set up by two brothers in the US in the 1950s. Hence we can use the vector product to compute the area of a triangle formed by three points A, B and C in space. The vector equation of the line is then ${\bf r} = {\bf e} + s{\bf d}. If the spherical coordinates change with time then this causes the spherical basis vectors to rotate with the following angular velocity. In exterior algebra the exterior product of two vectors is a bivector. Either fill in the coefficients of the vector equation, or enter "NONE" if no solution is possible. Gensim provides a number of helper functions to interact with word vector models. Advanced Math Solutions - Vector Calculator, Simple Vector Arithmetic. The majority of questions you will work on will involve two non-collinear (not in a straight. Two planes are parallel if their normal vectors are parallel (constant multiples of one another). In other words,. The cross product between two vectors and in is defined as the vector whose length is equal to the area of the parallelogram spanned by and and whose direction is in accordance with the right-hand rule. 4 Intersection of a line with a plane 5. Additionally, if both vectors have the same position vector, they are equal. Choose point A so that. The span of three nonzero vectors in can be a line, a plane, or all of , depending on the degree of dependence of the three vectors. These vectors aren't parallel so the planes. The result is how much stronger we've made the original vector (positive, negative, or zero).  Two vector quantities of. Angle pairs formed by parallel lines cut by a transversal. 3 The Dot Product of Two Geometric Vectors. The triple product a(b c) = a1 a2 a3 b1 b2 b3 c1 c2 c3 is the volume of the parallelogram spanned by the three vectors a, b, and c. cross(A,B) or A. Vectors are also. Access quality crowd-sourced study materials tagged to courses at universities all over the world and get homework help from our tutors when you need it. D raw the vector. The cross product is mostly used to determine the vector which is perpendicular to the plane surface spanned by two vectors whereas the dot product is used to find the angle between two vectors or the length of the vector. To add vectors, place the vectors such that the tail of the second vector is placed at the head of the first vector. It takes two arguments, start position of object(ball) and initial velocity of object. There are a two different ways to calculate the resultant vector. Unit vectors, vectors with magnitude = 1, are denoted with a carat over the top of the variable. Direction Vector = [-0. The normal vector of this plane is equal to the direction vetot of l, h0;2;1i. Vectors are directed line segments in which we precisely know which point is the initial point and which one is the terminal point. The std_logic_vector is a composite type, which means that it's a collection of subelements. Subtraction of Vectors: If a vector. As already announced this new generalized approach applying to more general submanifolds even has previously unknown consequences for totally geodesic submanifolds. This perpendicular distance can be spanned with support vectors. Both of those things can be described using vectors. The c() function can also combine two or more vectors and add elements to vectors. For example you can add two velocity vectors together or two acceleration vectors together, but you cannot add a velocity vector with an acceleration vector. Thus U is a plane; an equation may be found by finding a normal vector u × v = (1,2,−1). All window coordinates are counted from the top-left corner, including these. The resulting learned vector is also known as the embeddings. The points are lies on the plane then their vectors are lie on the same plane. Support Vectors and Margin • Support vectors are those nearest patterns at distance b from hyperplane • SVM finds hyperplane with maximum distance (margin distance b) from nearest training patterns Three support vectors are shown as solid dots. i think the answer is wrong you've considered equation two leaving out equation one. i think the answer is wrong you've considered equation two leaving out equation one. SPICE routines that take planes as input arguments can accept planes created by any of the routines listed above. For vectors with complex entries, using the given definition of the dot product would lead to quite different properties. Learning Objectives: Given a vector, determine if that vector is in the span of a list of other vectors. Vector images created using these programs can be scaled indefinitely without losing quality. We will get in nite solutions for any (a;b) 2R2. 2 Two intersecting planes. For example, work is a scalar product of the force vector and the distance vector. We create free stock vectors which designers can use in commercial projects. (a) The points on the plane are and. Intersections of Vectors with the X-Y Plane. Application in coordinate geometry : 1. Vector plane. The further away, the better. This lesson lets you understand the meaning of skew lines and how the shortest distance between them can be calculated. A position vector gives the position of a point. We may consider vectors in Rn as n ⇥ 1 matrices and define the. This line divides each into two half-plane. Now, because $\vec n$ is orthogonal to the plane, it's also orthogonal to any vector that lies in the plane. Visually, think of ܝ and ܞ as lying in a common plane. Unless your definition of span is something else, the mathematical definition of a (linear) span of a set S of vectors, is all vector you get from linear combination of the vectors from S. In other words, ⃗a 3 lies in the plane P. If you want to transform them directly, there are two ways: you can find two points on the plane (values which solve the normal form equation) and use them to span the plane (vectors and ). If you take the cross product of any two of those vectors, you will get a vector perpendicular to the plane. For , and d = -(n · V 0), the equation for the plane is:. If all three are multiples of each other, we have only a line. Distance from point to plane. g v) while vectors are written in boldface ( e. A spanning set of vectors for a finite-dimensional vector space V can be reduced to a basis for V; a linearly independent set of vectors in V can be expanded into a basis. (The resultant vector is also an element of the set V. Reflect: Reflects a vector off the plane defined by a normal. Each index of vector stores a vector which can be traversed and accessed using iterators. how much potential energy does tim gain? answer in units of j. Distance to plane. Adds two vectors together. Note that the variables used are in reference to the triangle shown in the calculator above. Equation of a plane in. To add vectors, place the vectors such that the tail of the second vector is placed at the head of the first vector. The normal vector of this plane is equal to the direction vetot of l, h0;2;1i. Using numpy and vectorize function we have seen how to calculate the haversine. The distance between two vectors u and v in Rn is defined as ku − v. We rotate this vector anticlockwise around the origin by $\beta$ degrees. 3) If then. So let's construct a vector here. Figure formed by two half-planes and the line is called a dihedral Dihedral angle is measured by the linear, ie the angle formed by two beams perpendicular to the edge and corner of their respective faces. The cross product of two vectors is a vector perpendicular to both. It suggests that hands-free sets may be effective in avoiding all the dangers of mobile phones. It differs from the dot product in that it must be in R³ and produces a vector not a scalar. We substitute that x value in one of the line equations (it doesn't matter which) and solve it for y. e) If vector is a multiple of vector , then. 6 The pilot contacted Italian air-traffic control to request permission for an emergency landing. Finding a basis of the space spanned by the set. Hence the components of vector U are given by. You can adjust the initial position, initial velocity, and acceleration of each of the cars. Methods for calculating a Resultant Vector. Program to check whether 4 points in a 3-D plane are Coplanar; Program to find equation of a plane passing through 3 points; Distance between a point and a Plane in 3 D; Shortest distance between a Line and a Point in a 3-D plane; Minimum distance from a point to the line segment using Vectors; Perpendicular distance between a point and a Line. Column Vector: to define a column vector, you can either separate every element with a semi-colon (;), or you can define the vector and use the transpose function, as we will see in the following sections. c) What is its velocity vector, in unit vector notation? d) In what direction is it moving? The moment of inertia of the system about the z axis. To add vectors, place the vectors such that the tail of the second vector is placed at the head of the first vector. It is the distance of the plane to the origin, ie, the spacing (d hkl). The output is a numpy. Distance-vector routing protocols like RIP were fine for networks comprised of equal speed links, but struggled when networks started to be built out The key feature of distance vector protocols is that each router relies on the reachability information advertised by its neighbors to deduce its best route. Get the free "The Span of 2 Vectors" widget for your website, blog, Wordpress, Blogger, or iGoogle. vector::begin() and vector::end() in C++ STL. Magnitude of vector. Figure 1: straight line through the point A (with position vector {\bf a}), parallel to the vector {\bf d} Figure 1 shows the straight line through the point A (with position vector {\bf a}), parallel to the vector {\bf d}. In this article vectors are multiplied by matrices on the vector's left. The magnitude of the product u × v is by definition the area of the parallelogram spanned by u and v when placed tail-to-tail. In particular it's orthogonal to $\vec r - \overrightarrow {{r_0}} $. A vector is similar to a point. An example of this is shown in the illustration, showing the addition of two vectors and to create a third vector. Calculating the specular light. They include addition, subtraction, and three types of multiplication. distance time. On the graph, u is the unit vector (in black) pointing in the same direction as vector OA, and i, j, and k (the unit vectors in the x-, y-and z-directions respectively) are marked in green. The calculator will find the angle (in radians and degrees) between the two vectors, and will show the work. from my calculation the answer is 4/15. Plane Plane Line Line 15. A sum of two subspaces $ U + W $ is said to be a direct sum if \( U \cap W = \left\{ {\bf 0} \right\}. (b) Use the right-hand rule to decide whether the components of a b are positive, negative, or 0. You have three points in the plane, so you can find several vectors in the plane joining those points. Start with basics and ask your doubts. Point A is called the initial point of the vector, and point B is called the terminal point. Vector orthogonal to. 2) I Vectors in R2 and R3. Dot product of two vectors. So ⃗b cannot be written as a linear. We introduce two important unit vectors. vector ~xis the distance of ~xfrom the origin ~0. Это лучшие примеры Python кода для vector. Our strategy will be to find two vectors in the plane, take their cross product to find a vector perpendicular to both of them (and thus to the We will do this by finding the vector from #(1,0,1)# to #(0,2,2)# and from #(1,0,1)# to #(3,3,0)#. Similarity is determined using the cosine distance between two vectors. EXAMPLE 6 Find two vectors in R3 whose span is the plane 2x 6y + 5z = 0. Most word vector methods rely on the distance or angle between pairs of word vectors as the pri-mary method for evaluating the intrinsic quality of such a set of word representations. (b)Find the point on the plane that lies closest to P o. Also, when d = 0, the plane passes through the origin 0 = (0,0,0). Know the definition and main examples of vector spaces with an inner product. Graphically, we can think of adding two vectors together as placing two line segments end-to-end, maintaining distance and direction. Let A and B be any two non-collinear vectors lying in plane K. • First, some language: we can say that the span of the two vectors in Example 8. But how can we make up points on this plane?. Perform basic vector operations (scalar multiplication, addition, subtraction). , three) components. Reflects a vector off the plane defined by a normal. Take one point as the base point, compute the two difference vectors to the other two points (those two span the plane), and take their cross product to get a normal vector. The first operation, called vector addition or simply addition + : V × V → V, takes any two vectors v and w and assigns to them a third vector which is commonly written as v + w, and called the sum of these two vectors. For which of the f. Example: Let V = Span {[0, 0, 1], [2. The dot product has another interesting property with unit vectors. If u = (x1,x2,x3), v = (y1,y2,y3) then their cross product u×v is the vector (x2y3 −y2x3,x3y1 −x1y3,x1y2 −x2y1). 2 A translation matrix. Recent advances in developing clinically desirable AAV capsids, optimizing genome designs and harnessing revolutionary biotechnologies have contributed substantially to the. If you take the cross product of any two of those vectors, you will get a vector perpendicular to the plane. The cross product of two vectors say a × b, is another vector that is at right angles to the both, and it absolutely. if s 1 and s 2 are vectors in S, their sum must also be in S 2. • The parallelogram law of vector addition states that if two vectors acting at a point are represented by the sides of a parallelogram drawn from that point, their resultant is represented by the diagonal which passes through that point of the parallelogram. The lengths of the line segments representing these vectors are proportional to the magnitude of the What is the physical meaning of a zero vector? Consider the position and displacement vectors in a plane as shown in Fig. (a) The points on the plane are and. Mathematical Problems  Differentiate position vector to get velocity and acceleration. A subspace of a vector space V is a non-empty subset W which is closed under addition and scalar. The black vectors are the two displacements through which the Thompsons went to get to the lodge, the blue vector is the shorter, direct path to the lodge ( the resultant vector ). Calculate the dot product of. Search by image. ndarray and which can be imported in a pandas dataframe. "S" polarization is the perpendicular polarization, and it sticks up out of the plane of incidence. You have three points in the plane, so you can find several vectors in the plane joining those points. Transforming plane equations. Let x be a basis for the intersection. (7 problems) For corrections, suggestions, or feedback, please email [email protected] Find the vectors: PQ = [1, 3, –4], PR = [0, 2, –1] Find their cross product: PQ x PR = [5, 1, 2]. A complete de nition of a vector space requires pinning down these ideas and making them less vague. This video is part of a Linear Algebra course taught. In the previous tutorial, we covered how to use the K Nearest Neighbors algorithm via Scikit-Learn to. A point an a vector determine a plane. This perpendicular distance is smaller by a factor cos , where is the angle that the plane is tilted. In general, a line or a plane in R 3 is a subspace if and only if it passes through the origin. Vectors are used to represent anything that has a direction and magnitude, length. Any vector that is perpendicular to a plane is called a normal vector to the plane. Vectors are parallel if they have the same direction. An example of this is shown in the illustration, showing the addition of two vectors and to create a third vector. Distance Calculator » Need the distances between two places? Driving Directions Finder » Need driving directions to a new place? Flight Time Calculator » Need to calculate the time it takes to get to a city by plane? Time Zones » Need to figure out the time zone in which a city or country is located in?. Detailed expanation is provided for each operation. It is easy to recognize parallel planes written in the form ax+by+cz=d since a quick comparison of the normal vectors n= can be made. There are two kinds of tangent lines - oblique (slant) tangents and vertical tangents. It suggests that hands-free sets may be effective in avoiding all the dangers of mobile phones. This calculator finds the angle between two vectors given their coordinates. The transpose linear transformation T T from R 3 to R 3 is defined by. the kinetic energy of that car. Geometrically, the cross product vector u = v×w is orthogonal to the two vectors v and w: v ·(v ×w) = 0 = w ·(v ×w). But how can we make up points on this plane?. XAxis # x-axis vector print plane. 6 If matrix B is obtained from matrix A by an elementary row operation, then the row space of A is the same as the row space of B. The resulting learned vector is also known as the embeddings. preform to answer this question. B = ABcosθ. Any two $m$-volumes can be compared in terms of their ratio. When row reduced, there will not be a pivot in every row. We also introduce one model for Russian conversational language that was trained on Russian Twitter corpus. Let Pand Qbe points in R3 with position vectors p~and ~qrespectively. Vector plane. Let a point in the plane , sor the position vector pointing this point is. two women don't understand me. (2i – 3j + k) = 5. This vector, represented by a directed line segment joining the origin 0 to a point A, is called the position vector of point A. Works on an image which was rendered as a z-depth image, returning the distance from the camera to the pixel (or plane) in question. Unit vectors, vectors with magnitude = 1, are denoted with a carat over the top of the variable. 16 ), let's begin with the cross-product in matrix form as using the first matrix form in the third line of the cross-product definition in Eq. But how can we make up points on this plane?. Draw the 3rd vector to scale, placing its tail at the tip of the second vector and being sure its direction is correct. The orthogonal complement S? to S is the set of vectors in V orthogonal to all vectors in S. These are the only two directions in the two-dimensional plane perpendicular to the given vector. Definition 3. For a line, you need a point and a direction. See full list on euclideanspace. Find the vectors: PQ = [1, 3, –4], PR = [0, 2, –1] Find their cross product: PQ x PR = [5, 1, 2]. Vertical variation of the Constancy of Upper Winds over India. The output is a numpy. Scale: Multiplies two vectors component-wise. Definition A vector in Rn, with n = 2,3, is an ordered pair of points in Rn, denoted as −−−→ P 1P 2, where P 1, P 2 ∈ Rn. The set of all linear combinations of some vectors v1,…,vn is called the span of these vectors and contains always the origin. There are two different ways in which the positive z axis could be at right angles to the postive x and y axes. Vector graphics. The result is how much stronger we've made the original vector (positive, negative, or zero).  Two vector quantities of. Find the distance from the tip of Vector C to the plane through the origin spanned by A and B. All window coordinates are counted from the top-left corner, including these. A vector quantity is a quantity that is fully described by both magnitude and direction. The generalization of the plane to higher dimensions is called a hyperplane. Then (a, b) ⊗ (c, d) returns the z-coordinate of vector product (a, b, 0) ⊗ (c, d, 0) as single number. If a vector starts at 0, then the vector~v = hv1;v2i points to the point hv1;v2i. Since there are clearly vectors in R4 that are not in the plane (for example, 1 0 0 0. a subspace of R 3 as it lies in the plane x + y + z = 3, which does not contain 0. Coercion is from lower to higher types from logical to integer to double to character. Cross products. Properties of vectors: - two vectors are equal if they are equal in both magnitude and direction Vector (where is the positive number) has the same direction as vector , but its length is times is a VECTOR, the magnitude of which is. Lerp: Linearly interpolates between two vectors. This video is part of a Linear Algebra course taught. The first is the signal that you want to convert, the second is the length of the resulting vector. Now, we know that the cross product of two vectors will be orthogonal to both of these vectors. R² means a Real numbers 2D plane. from my calculation the answer is 4/15. ScreenToWorldPoint(Input. Transforming plane equations. Intersections of Vectors with the X-Y Plane. defining z as the vector of the projection onto all support vectors the decision function is a plane in the z-space with this means that • the classifier operates on the span of the support vectors! • the SVM performs feature selection automatically ()T i T i T k z(x) x x , ,x x 1 = L.	CommonCrawl
Physiological activity in calm thermal indoor environments Tsuyoshi Okamoto ORCID: orcid.org/0000-0003-0749-19921,2,3 na1, Kaori Tamura2 na1, Naoyuki Miyamoto4, Shogo Tanaka4 & Takaharu Futaeda4 Scientific Reports volume 7, Article number: 11519 (2017) Cite this article Stress and resilience Indoor environmental comfort has previously been quantified based on the subjective assessment of thermal physical parameters, such as temperature, humidity, and airflow velocity. However, the relationship of these parameters to brain activity remains poorly understood. The objective of this study was to determine the effect of airflow on brain activity using electroencephalograms (EEG) of participants in a living environment under different airflow conditions. Before the recording, the room was set to a standardised air temperature and humidity. During the recording, each participant was required to perform a simple time-perception task that involved pressing buttons after estimating a 10-second interval. Cooling and heating experiments were conducted in summer and winter, respectively. A frequency analysis of the EEGs revealed that gamma and beta activities showed lower amplitudes under conditions without airflow than with airflow, regardless of the season (i.e., cooling or heating). Our results reveal new neurophysiological markers of the response to airflow sensation. Further, based on the literature linking gamma and beta waves to less anxious states in calm environments, we suggest that airflow may alter the feelings of the participants. A comfortable indoor thermal environment can improve the quality of sleep1 and work productivity2,3,4. Previous studies have generated evaluation scales for indoor thermal comfort based on physical and personal factors5,6,7,8,9, with representative physical factors including room temperature, humidity, and airflow velocity5. An international common scale, the Predicted Mean Vote (PMV)6, has been established to summarise and standardise these factors, and it has been widely accepted in many countries5, 7. The PMV and other similar scales (e.g., the Standard New Effective Temperature)8, 9 are based on results from an extensive survey of subjective evaluations. Comfort is a highly subjective feeling and cannot be measured in an objective manner in principle. Although PMV is widely used as a reliable scale, it has not yet been able to fully elucidate the mechanisms underlying this feeling. More specifically, the brain mechanism that perceives and processes the environmental state evaluated by PMV is unclear. The relationship between PMV and neuronal responses should be investigated in order to better understand the mechanisms underlying comfort. Airflow is one of the factors used to calculate PMV, and its sensation and underlying neuronal mechanisms have been investigated by a number of researchers. Although many investigations have shown the unpleasant effects of air velocity and draught by subjective reactions10,11,12,13,14,15, few studies have addressed neurophysiological mechanisms underlying unpleasantness induced by airflow. In addition to using thermal scales, measuring neurophysiological activity could help to determine the brain-intrinsic factors required to understand the mechanism underlying feelings induced by calm environments. In this study, our aim was to determine the effects of airflow sensation in indoor thermal environments by performing electroencephalography (EEG). Neurophysiological studies conducted in experimental laboratories have reported that the amplitudes of gamma and beta oscillations increase during vigilance states (i.e., sustained attention)16, 17 or mental fatigue18, 19. The neuronal mechanisms of airflow sensation may be revealed by analysing these types of oscillation changes using EEG measurements. In order to examine the effects of airflow in indoor environments that mimic daily life, we conducted experiments under two different seasonal conditions (cooling in summer and heating in winter) and two different airflow conditions (an air conditioner with airflow and a radiant cooling and heating system without airflow) in an environment standardised for temperature and humidity (see Methods and Figs 1 and 2). To standardise the mental states of the participants, we introduced a time-counting task. In each session, the participants were asked to press a button after mentally counting for 10 seconds with their eyes closed. This was repeated for up to 60 seconds per session. EEGs were recorded during five sessions, and frequency analysis was carried out. Experimental environment. (a) System summary of the air conditioner and radiant cooling and heating system. (b) Floor plans of the rooms used for our experiments. (c) A participant in each experiment. The left figure shows the conditions for the cooling experiment; the right figure, the conditions for the heating experiment. The room temperature, relative humidity, and wind velocity of the cooling experiment (upper panels) and the heating experiment (lower panels). The asterisks showed the significant differences (*p < 0.001). We hypothesised that changes in brain activity occur in response to different airflow conditions. Our aim was to determine neurophysiological markers of airflow sensation under conditions of both cooling and heating. Common scales for thermal comfort Room temperature and relative humidity were monitored and maintained at the same levels by an experimenter. For confirmation of the condition, we performed statistical analyses of the data measured at the beginning of the experiments. There was no significant difference in room temperature between the air-conditioned (AC) environment and the radiant cooling and heating system (RS) environment (cooling: Z = −1.4, p = 0.16, heating: Z = 0.67, p = 0.50 by Wilcoxon test) (Fig. 2, left panels), and no significant differences in the relative humidity (cooling: Z = −1.9, p = 0.056, heating: Z = −0.088, p = 0.93) (Fig. 2, middle panels). We also compared air velocities in the experiment room (Fig. 2, right panels). There were significant differences in air velocity between the AC and RS conditions. The median (interquartile range) of air velocity in the cooling experiment was 1.1 (0.46) m/s in the AC condition and 0.0033 (0.22) m/s in the RS condition (Z = −4.2, p < 0.001, Wilcoxon test) (Fig. 2, upper right). The median air velocity in the heating experiment was 0.61 (0.18) m/s in the AC condition and 0.071 (0.053) m/s in the RS condition (Z = −4.1, p < 0.001) (Fig. 2, lower right). To compare the EEG results with subjective ratings of thermal comfort and sensation, we used two thermal scales: the PMV and the Predicted Percentage of Dissatisfied (PPD) scales5, 7 (Fig. 3). The PMV is used to express thermal comfort as a sum of scores based on several types of environmental variables, the participant's metabolic rate, and the level of clothing insulation6. The seven-point American Society of Heating, Refrigerating, and Air-Conditioning Engineers (ASHARE) thermal sensation scale is defined by the PMV (−3: cold, −2: cool, −1: slightly cool, 0: neutral, +1: slightly warm, +2: warm, and +3: hot). The thermal comfort zone indicated by the ASHARE Standard 555, 7 ranges from −0.5 to +0.5. PMV and PPD values obtained by collapsing across the sessions in the cooling experiment (upper panels) and the heating experiment (lower panels). The asterisks showed the significant differences (*p < 0.001). The grey areas in the left panels indicate the thermal comfort zone defined by the ASHARE Standard. In the cooling experiment, the median (interquartile range) of the PMV in the AC (with airflow) condition was −2.0 (0.44) and that in the RS (without airflow) condition was −0.10 (0.29). These values were significantly different (Z = 3.5, p < 0.001, Wilcoxon test) (Fig. 3, upper left). PPD, which measures the ratio of the number of people who feel dissatisfied to a parent population, was also significantly different in the conditions with and without airflow (median (interquartile range)) of PPD: 6.0 (4.2)% in RS, 77 (15)% in AC, Z = −3.5, p < 0.001) (Fig. 3, upper right). In the heating experiment, the median PMV in the RS condition was significantly different from that in the AC condition (0.23 (0.23) and 0.84 (0.43), respectively; Z = −3.8, p < 0.001) (Fig. 3, lower left). PPD was also significantly different in the two airflow conditions (median (interquartile range))in AC = 23 (17)%, median (interquartile range) in RS = 6.2 (1.8)%; Z = −4.0, p < 0.001) (Fig. 3, lower right). The median PMV scores and their interquartile ranges in the RS condition were within the range of comfort (from −0.5 to 0.5) in both the cooling and heating experiments. Neurophysiological activity To compare the conditions with and without airflow, changes in EEG amplitudes in each session relative to the first session were calculated for each frequency band. These bands comprised theta (4–8 Hz), alpha (8–14 Hz), beta (14–30 Hz), and gamma (30–55 Hz) oscillations. The locations of the recording electrodes were chosen to enable measurement of responses based on both mental state and sensation (see Methods, EEG analysis). Gamma band amplitudes at temporal and parietal sites (Pz, T3, and T4) had smaller relative changes in the RS condition than in the AC condition in both experiments (Fig. 4). A two-way analysis of variance (ANOVA) indicated a significant main effect of airflow on gamma band amplitudes at each focal electrode in each experiment (cooling, Pz: F(1,72) = 4.4, p = 0.040, T3: F(1,72) = 8.8, p = 0.0040, T4: F(1,72) = 9.1, p = 0.0036; heating, Pz: F(1,72) = 11, p = 0.0016, T3: F(1,72) = 20, p < 0.001, T4: F(1,72) = 16, p < 0.001). A main effect of session was also significant or marginally significant (cooling, Pz: F(4,72) = 5.4, p < 0.001, T3: F(4,72) = 2.9, p = 0.028, T4: F(4,72) = 5.0, p = 0.0013; heating, Pz: F(4,72) = 2.2, p = 0.076, T3: F(4,72) = 4.2, p = 0.0040, T4: F(4,72) = 7.1, p < 0.001). There was no significant interaction between airflow condition and sessions (cooling, Pz: F(4,72) = 1.5, p = 0.20, T3: F(4,72) = 0.85, p = 0.50, T4: F(4,72) = 0.88, p = 0.48; heating, Pz: F(4,72) = 0.83, p = 0.51, T3: F(4,72) = 1.4, p = 0.24, T4: F(4,72) = 1.3, p = 0.30). We confirmed that the PMV value and gamma amplitudes were correlated in both experiments (cooling: r = −0.24, p = 0.031, heating: r = 0.36, p = 0.0031 at T3) (see Figs S1a and S2a in Supplementary Information). Analysis of gamma and PPD also confirmed a marginally significant correlation with cooling (r = 0.21, p = 0.065) and a significant correlation with heating (r = 0.31, p = 0.013 at T3) (Figs S3a and S4a in Supplementary Information). Although these results supported the relationships between gamma and PMV or PPD, the analytic data were measured repeatedly. To solve this problem, we analysed the correlations using data averaged across sessions. However, we could not find any significant correlations. This may be because of the small degree of freedom (Figs S5a–S8a and Tables S1–S4 in Supplementary Information). We introduced a new index of "two-point slope" to investigate the relationship between EEG amplitudes and PMV or PPD in each session (see Supplementary Methods). Median values of the two-point slopes in gamma that were significantly different from zero potentially indicated the presence of some relationship above chance level between PPD and EEG as independent measurements. Two-point slopes calculated from gamma and PMV had significant differences from zero at session 2 and a marginally significant difference at session 3 in cooling (session 2: Z = −16, p = 0.037; session 3: Z = −14, p = 0.065; Fig. S9a and Table S5 in Supplementary Information), as determined using a one-sample Wilcoxon test (one-sided). In heating, there were significant differences from zero at session 4 and marginal significances at sessions 2 and 5 (session 2: Z = 12, p = 0.055; session 4: Z = 14, p = 0.027; session 5, Z = 12, p = 0.055; Fig. S11a and Table S7 in Supplementary Information). We also assessed the two-point slopes between gamma and PPD and found significant differences and marginal significances in cooling (session 2: Z = 16, p = 0.037; session 3: Z = 14, p = 0.065; Fig. S10a and Table S6 in Supplementary Information) and heating (session 2: Z = 12, p = 0.055; session 3: Z = 10, p = 0.098; session 4: Z = 14, p = 0.027; session 5: Z = 12, p = 0.055; Fig. S12a and Table S8 in Supplementary Information). These results indicate that the higher gamma amplitudes may be candidate factors for explaining the subjective evaluations made using the PMV and PPD. The differential gamma amplitudes (mean ± SEM) from the first session. Beta band amplitudes at central sites (C3 and C4) also had smaller relative changes in the RS condition than in the AC condition in both heating and cooling experiments (Fig. 5). An ANOVA indicated a significant main effect of airflow on beta band amplitudes (cooling, C3: F(1,72) = 5.0, p = 0.030, C4: F(1,72) = 6.0, p = 0.017; heating, C3: F(1,72) = 10, p = 0.023, C4: F(1,72) = 8.5, p = 0.0048). Main effects of session were also found at both C3 and C4 in the cooling experiment (C3: F(4,72) = 3.1, p = 0.022, C4: F(4,72) = 4.3, p = 0.0036) and at the C4 site in the heating experiment (C3: F(4,72) = 1.8, p = 0.15, C4: F(4,72) = 3.1, p = 0.021). However, there was no significant interaction between the airflow condition and session (cooling, C3: F(4,72) = 0.33, p = 0.86, C4: F(4,72) = 0.95, p = 0.44; heating, C3: F(4,72) = 0.71, p = 0.59, C4: F(4,72) = 1.0, p = 0.41). Correlation analysis between PMV and beta amplitudes showed a significant correlation in the cooling (r = −0.23, p = 0.041 at C3) (see Fig. S1b in Supplementary Information) and a marginal significant correlation in the heating experiment (r = 0.23, p = 0.062 at C3) (see Fig. S2b in Supplementary Information). Analyses of beta and PPD also confirmed a significant correlation in cooling (r = 0.22, p = 0.049 at C3) but not in heating (r = 0.15, p = 0.24 at C3) (Figs S3b and S4b in Supplementary Information). These results suggest that the beta activity is somewhat correlated with subjective feelings in the cooling state, while there is no correlation in the heating state. We also performed analyses of two-point slopes, as we did for gamma activity, to investigate the relationship between PMV or PPD and beta more deeply (Supplementary Methods). The two-point slopes of PMV did not have significant differences with zero in any of the sessions in the cooling state (p ≥ 0.10, Fig. S9b and Table S5 in Supplementary Information), although there was a marginally significant difference at session 5 in heating (session 5: Z = 10, p = 0.098, Fig. S11b and Table S7 in Supplementary Information), as assessed using a one-sample Wilcoxon test (one-sided). In addition, the two-point slopes of PPD did not have significant differences in cooling and heating (P ≥ 0.10, Fig. S10b and Table S6 in Supplementary Information), although there was a marginal difference at session 5 in heating (session 5: Z = 10, p = 0.098, Fig. S12b and Table S8 in Supplementary Information). Analyses of the two-point slopes provided us with no evidence to support a relationship between beta and thermal scales, PMV, or PPD. The differential beta amplitudes (mean ± SEM) from the first session. Alpha band amplitudes had different patterns in the cooling and heating experiments (Fig. 6). In the cooling experiment, the relative changes in the alpha band did not indicate a main effect of airflow (C3: F(1,72) = 0.67, p = 0.42, C4: F(1,72) = 0.42, p = 0.52). However, a main effect of airflow was observed in the heating experiment (C3: F(1,72) = 13, p < 0.001, C4: F(1,72) = 7.4, p = 0.0080). In addition, there was a main effect of session in the cooling experiment (C3: F(4,72) = 3.8, p = 0.0079, C4: F(4,72) = 3.5, p = 0.011), but not in the heating experiment (C3: F(4,72) = 1.0, p = 0.40, C4: F(4,72) = 1.1, p = 0.37). No interactions between these factors were found (cooling, C3: F(4,72) = 0.54, p = 0.71, C4: F(4,72) = 0.46, p = 0.76; heating, C3: F(4,72) = 1.1, p = 0.36, C4: F(4,72) = 0.80, p = 0.53). The differential alpha amplitudes (mean ± SEM) from the first session. Theta band amplitudes were also analysed, but no main effect of airflow was found (cooling, Fz: F(1,72) = 1.3, p = 0.25; heating, Fz: F(1,72) = 0.081, p = 0.15). A main effect of session was found in both heating and cooling experiments (cooling, Fz: F(4,72) = 9.3, p < 0.001, heating, Fz: F(4,72) = 3.2, p = 0.019), but no significant interaction between airflow and session was found (cooling, Fz: F(4,72) = 0.20, p = 0.93, heating, Fz: F(4,72) = 0.29, p = 0.89). In brief, gamma and beta amplitudes indicated main effects in the airflow conditions in both cooling and heating environments. The gamma and beta activities may therefore reflect the sensation of airflow itself because differences were observed in both experiments regardless of the season. In contrast, alpha amplitudes indicated a main effect of airflow only in the heating experiment. Therefore, the pattern of alpha activity may be affected by differences in thermal sensation. Theta band amplitudes did not indicate any main effects of airflow conditions at the electrode locations of interest. Time-precision task We analysed the total time length (TTL, approximately 60 seconds) of the task period for each participant. The TTL in the RS condition was longer than that in the AC environment in both the cooling and heating experiments (Fig. 7). A main effect of airflow was detected on TTL in both cooling and heating environments (cooling: F(1,70) = 10, p = 0.0027, heating: F(1,56) = 4.4, p = 0.040). These results indicate that the participants estimated time to be longer in RS environments, which lacked airflow, in both experiments. There was no main effect of session on TTL (cooling: F(3,70) = 0.27, p = 0.85, heating: F(3,56) = 0.23, p = 0.87). The differential total time lengths (TTLs, mean ± SEM) from the first session. Thermography data of skin temperature Airflow has been found to directly influence skin temperature15. At the beginning and end of each experiment, the skin temperature of each participant was measured by using thermography (Fig. 8). Skin temperatures (mean ± SEM) in the cooling experiment (a) and the heating experiment (d), and examples of thermography during the cooling (b, c) and heating (e, f) experiments. In the cooling experiment, the measured skin temperatures in the AC condition at the end of the experiment were lower than those at the beginning (t(22) = −6.3, p < 0.001, two-tailed Student's t-test). In contrast, skin temperatures in the RS condition were not different between the first and last sessions (t(22) = 1.1, p = 0.30). In the heating experiment, the measured skin temperatures in the AC condition at the last session was higher than those at the first session (t(16) = 5.9, p < 0.001). In contrast, skin temperatures in the RS condition were not different between the first and last sessions (t(16) = −0.24, p = 0.59). These results confirm that the airflow condition only influences body surface temperatures. We investigated the effects of airflow on brain activity in a living environment. We compared conditions with and without airflow using neurophysiological responses. As expected, the PMV, PPD, and task performance indicated higher subjective comfort in the environment without airflow. Furthermore, several EEG frequency bands showed significant differences between these conditions, even at the same room temperature. These results suggest that the observed neuronal responses are related to airflow in an indoor environment. Here we characterise the properties of indoor airflow sensation, as determined by brain-intrinsic factors underlying feelings associated with calm environments. To our knowledge, this is the first report describing differences in neuronal activity in indoor conditions with and without airflow. We observed differences in gamma band activity between the two airflow conditions. The gamma amplitudes in the AC condition were higher than those in the RS condition, and this difference was identified in both the cooling and heating environments. Gamma synchronization has been shown to be associated with awareness and emotional content20, and especially unpleasant and aversive emotions21,22,23. In addition, a study of patients with an anxiety disorder indicated that they had higher gamma power in the temporoparietal regions than healthy participants24. We used analytic electrodes located at the same positions as those in a previous study24. In line with the previous study, the lower gamma activity may reflect less anxiety and/or less stress. Lower gamma amplitudes were observed in the RS condition, which may therefore indicate less anxiety and/or less stress in this condition. An explanation for why gamma activity is related to anxious state may lie in its relationship with the GABAergic network. Gamma oscillations can be generated in networks of GABAergic interneurons25,26,27. Several studies have reported that the GABAergic network is related to anxiety28,29,30. The subjective common scales from the PMV support this interpretation, as the scales are guaranteed to be in a comfortable state in the environment without airflow. Furthermore, we observed that PMV and PPD values correlate with gamma amplitude changes, as indicated by robust correlations and two-point slopes, indicating that gamma amplitudes are higher when uncomfortable feelings are increased. The correlations indicate that higher gamma activities reflect a state of anxiety in the airflow condition. Based on this perspective, we suggest that a mental state with less anxiety and/or less stress was induced by the airflow condition. This result likely indicates that airflow can influence feelings associated with environmental comfort. Gamma activity has also been associated with attentional processes16, 17, and the synchronization of gamma oscillations is related to sustained attention16, 17, 31 reflective of a heightened vigilance state. Therefore, our results may also indicate the presence of a more relaxed state characterised by lower vigilance under RS conditions. Beta band amplitudes indicated a main effect of airflow, and the differences were observed near the motor cortex at C3 and C4. Several reports have confirmed that beta synchronization results from mental fatigue18, 19 in the primary motor cortex during tasks that require low mental load19, such as that used in our experiment. Differences in the beta band may therefore reflect changes in mental burden in the airflow condition, especially considering the concurrent changes in behavioural performance in the time-perception task. Participants overestimated the length of 1 minute more so in the RS condition than in the AC condition. That is, the relative speed of psychological time to the real time was faster in the RS condition. The change in time sensation under RS conditions may be caused by a decreased mental burden, such as decreased fatigue or boredom. From this perspective, the lower beta amplitudes in the RS condition may reflect a relaxing effect compared to the AC condition. Summarizing these results, we suggest that the airflow environment led to an increased mental burden. The relationships between beta and the thermal scales (PMV or PPD) should be discussed. Although the PMV scores in the RS condition were within the comfort zone in both the cooling and heating experiments, we found significant correlations with PMV or PPD in the cooling experiment only, but not in the heating state. In the analysis of two-point slopes used to study relationships with PMV or PPD, we were unable to find any significant differences with chance levels. In this study, there was little evidence to support an involvement of beta in subjective feelings of thermal comfort. However, our discussion is not intended to reject the idea that the beta band was a candidate for a neurophysiological marker of airflow sensation, as there were significant differences in beta amplitudes between RS and AC, consistent with performance on the time-perception task. Beta band activity in the motor area has been related to motor control and somatosensory sensation32,33,34,35,36,37. In our experiment, the participants were required to press a button with a finger in both conditions, so motor control is unlikely to underlie this difference. Somatosensory sensation seemed to be involved in the beta activity because of the impact of the airflow. In fact, previous studies have revealed that activities of the somatosensory area are reflected as beta rhythm suppression38,39,40,41. We did not observe such beta suppressions in the AC condition. Therefore, changes in the beta amplitudes are probably induced by mental fatigue, rather than somatosensory function. The alpha band had significantly higher amplitudes in the AC condition than in the RC condition in only the heating experiment. Our data from the heating experiment are in agreement with those of previous studies, which have shown that attenuated alpha band amplitudes in the premotor cortex are associated with thermal sensations42,43,44. The attenuated alpha activity in the RS condition may thus reflect more sensitive thermal sensation. The heterogeneous alpha patterns may reflect differences in the effectiveness of the airflow system to alter cooling and heating sensations. In the cooling environment, the AC and RS conditions did not show have differential effectiveness on cooling sensation, while the AC condition led to lower heat sensation than the RS system in the heating environment. The subjective assessments, however, indicate that airflow in a cooling environment is perceived as unacceptable, as it leads to local cooling of the skin, while appropriate air movement in a warm environment creates comfortable feelings15. Our results seem to contradict the above subjective perceptions of airflow. The observed heterogeneous patterns might be due to fundamental differences in the heat transfer systems, as we used far-infrared heating in the RS condition and convection heating in the AC condition. In order to examine the neuronal mechanism underlying airflow sensation in an indoor environment, we compared the seasonal experiments in different airflow conditions using both electrophysiological and psychological approaches. In both the cooling and heating experiments, higher gamma and beta oscillation activities were observed as neurophysiological markers related to airflow sensation. These markers led to the identification of some candidates of brain-intrinsic factors related to feelings associated with different airflow conditions. This is the first report of neuronal evidence of airflow sensation in an indoor environment. The sample size of this study was within a range of the common sense in human EEG studies though the size was smaller than that in healthy science areas including pharmacological studies. In this study, we removed some data as outliers because the current sample size was sensitive to the effect of abnormal values for parametric statistical analyses. The candidates of the outliers were selected automatically by a jackknife outlier analysis based on multivariate statistics. Although this data-driven method enabled to decide criteria of outliers without any arbitrary assumption, the method might not provide rationale to remove the outliers by itself because it could not clarify that the data categorized as outliers in this study were derived from noises or true outliers. In fact, the criteria were not identical between the cooling and heating experiments. This way of handling outliers might not be appropriate and could influence more or less the significance of the results. Nevertheless, there has been few studies about physiological responses under different thermal indoor environments, and any common consensus to eliminate outliers has not been established in the related studies. This study tried to investigate general features of physiological responses by eliminate outliers based on statistics though it let reduce the analytic data. To lead clearer conclusion, further investigations would be necessary with a larger sample size like pharmacological studies after a consensus of elimination data is established. Twelve healthy volunteers participated in each experiment (cooling: 6 females and 6 males, 43–63 years old; heating: 6 females and 6 males, 44–66 years old) after providing written informed consent. The experiments were approved by the local ethics committee of Kyushu University. All methods were performed in accordance with the approved guidelines. The experimental indoor condition with or without airflow was controlled using either a household air conditioner (AC; MSZ-GM560S, Mitsubishi Electric Corp., Tokyo, Japan) or a radiant cooling and heating system (RS; KFT SystemTM, KFT Co., Ltd., Fukuoka, Japan) (Fig. 1a) in a show house, which was used to mimic a typical modern living environment. Participants sat in a chair placed at the designated position (Fig. 1b). The environment was set to the same air temperature (median (interquartile range)), AC: 25 (1.6) °C, RS: 24 (1.0) °C for the cooling experiment; AC: 26 (0.28) °C, RS: 26 (0.50) °C for the heating experiment) and the same relative humidity (AC: 64 (1.8)%, RS: 63 (2.8)% for the cooling experiment; AC: 24 (4.0)%, RS: 24 (3.4)% for the heating experiment) at the beginning of each experiment (Fig. 1b). The room temperature, relative humidity, and wind velocities were measured by an anemometer (AM-101, Kyoto Electronics Manufacturing Co. LTD., Kyoto, Japan), which was placed close to the participant (Fig. 1b). For the real-time monitoring by an experimenter, the room temperature and relative humidity were also measured by a digital hygrothermograph (RTR-53A, T&D Corp., Nagano, Japan), which was placed near the experimenter. The amount of clothing that each participant was wearing was standardised (Fig. 1c). Time-perception task The task consisted of five sessions. In each session, the participants were required to press a button after counting 10 seconds without uttering words and with their eyes closed. In the first session, the participants pressed the button following time signals from a pure tone of 440 Hz every 1 second and of a pure tone of 880 Hz every 10 seconds. In the second through fifth sessions, the participants were required to estimate 10 seconds as exactly as possible and press the button without any signals as prompts. We measured the TTL (~60 seconds each session) that the participants perceived as a psychophysical factor. Before each session, the participants were asked to relax with their eyes closed; after each session, with their eyes opened. Each participant completed five sessions in each the two airflow conditions, AC and RS, in a random order. EEG recording We recorded EEGs across 8 channels (Fz, Cz, Pz, Oz, C3, C4, T3, and T4) using gold active electrodes according to the international 10–20 system. The reference electrodes were placed on the tip of the nose, and the ground electrode was placed on Fpz. Additional two electrodes were placed on A1 and A2. The measurements were performed using a Polymate 2 (AP-216, Digitex Lab. Co. Ltd., Tokyo, Japan) before, during, and after the time-perception task. The EEG was amplified (with a 3-second time constant and low-pass 100 Hz filter) and digitalised at a sampling rate of 1000 Hz. EEG analysis The measured EEG data were re-referenced to the averages of A1 and A2 and separated by the sessions of the task. The data were then transformed using discrete Fourier transform (DFT) with a rectangular window to obtain the DFT coefficients. DFT analysis was performed using the 'fft.m' function in MATLAB (MathWorks, Inc., Natick, USA). Each EEG data during each TTL (~60 seconds) was segmented into 20 time bins (~3 seconds). Amplitudes of every frequency bin calculated from the DFT coefficients were averaged within the following frequency bands: delta (0.5 ≤ f < 4 Hz), theta (4 ≤ f < 8 Hz), alpha (8 ≤ f < 14 Hz), beta (14 ≤ f < 30 Hz), and gamma (30 ≤ f < 55 Hz), where f indicated the frequency. The obtained amplitudes were averaged across 20 time bins in each frequency band. To assess relative changes compared to the first session, the mean amplitudes of each session were subtracted from those of the first session. The subsequent analyses of gamma activities were restricted to the temporoparietal regions (Pz, T3, and T4) to assess the mental state of the participants24. Similarly, the analyses were restricted to two channels (C3 and C4) to study mental burden using beta activity18, 19 and to study differences in thermal sensation using alpha activity42,43,44. Theta activity was only analysed at Fz to assess concentration levels using "Fm-theta", which is mainly observed in frontal regions45. Subjective thermal comfort We calculated the PMV and PPD5, 7 scores based on environmental variables and the parameters measured during the experiments. PPD can be calculated from the PMV, as shown below7: $${\rm{P}}{\rm{P}}{\rm{D}}=100-95\times \exp [-(0.03353\times {{\rm{P}}{\rm{M}}{\rm{V}}}^{4}+0.2179\times {{\rm{P}}{\rm{M}}{\rm{V}}}^{2})]$$ PMV and PPD were used to assess thermal comfort in both airflow conditions. All necessary variables used to obtain PMV were measured during the experiments. PMV, PPD, and related parameters were obtained using a PMV meter (AM-101, Kyoto Electronics Manufacturing Co. Ltd., Kyoto, Japan). For the PMV calculations, we set the amount of clothing to 0.7 (clo), and the metabolic rate to 1.0 (met) because the participants were seated. Thermography data recording Thermography data used to assess skin temperature were measured five times per participant at the conclusion of each session in the cooling experiments, or twice per participant immediately before the first session and immediately after the fifth session in the heating experiments (Neo Thermo TVS-700, Nippon Avionics Co., Ltd., Tokyo, Japan). To assess the time-dependent changes in temperature in response to airflow, the first and last data points were analysed for each experiment. Although the timing of the measurements was different, we were able to compare the time-dependent changes in skin temperature in response to airflow in each experiment independently. Data removal process The data removal process was as follows. First, we removed the data that were obtained with experimental errors from further analyses. Second, we selected the candidates of outliers by a jackknife outlier analysis based on a multivariate analysis using Mahalanobis distance by JMP® 12 (SAS Institute Inc., Cary, NC, USA) for the remaining data. Third, we removed the data that were suspected to be with artifacts from the candidates. The jackknife outlier analysis defined upper-control limits (UCL) distance to detect outliers based on the statistical alpha level (α = 0.05). The UCLs in EEG data in cooling and heating experiments were 4.0; the UCLs in behavioural data of the time-perception task in the cooling and heating experiments were 2.9; the UCLs for PMV or PPD in the cooling and heating experiments were 3.8. If a Mahalanobis distance of a data point was above UCL line, the participant including the data point was treated as candidate of outliers. For statistical analyses of PMV and PPD, two sets of the data from the cooling experiment were removed because of the system trouble of the measurement apparatus for PMV and PPD (i.e., cooling: n = 10, heating: n = 12; Fig. 3). For statistical analyses of EEG data, in the cooling experiment, three participants were removed because of contaminating huge noise in the measurement apparatus for EEG; in the heating experiment, two participants who failed to complete the time-perception task were removed, and another participant was removed because of contaminating huge noise in the apparatus (i.e., cooling: n = 9, heating: n = 9; Figs 4–6). The exclusion criteria were that the mean amplitude of EEG delta band of each session >6.0 μV in cooling experiment or >60 μV in heating experiment. For statistical analyses of TTL from the time-perception task, in the cooling experiment, one participant was removed because of too much earlier responses; in the heating experiment, two participants were removed because they failed to complete the task as instructed, and another participant was removed because of too much later responses (i.e., cooling: n = 11, heating: n = 9; Fig. 7). The exclusion criteria were that the differential TTL from baseline of each session except for the 1st session < −15 seconds in cooling experiment or >95 seconds in heating experiment. For the other data, no outliers were found (i.e., cooling: n = 12, heating: n = 12; Figs 2 and 8). Environmental parameters, such as room temperature, relative humidity, wind velocity, and summarising score (PMV and PPD) were analysed using non-parametric tests for comparisons between the conditions. Within-participant factors (EEG, behaviour, and skin temperature) were analysed using parametric tests. All statistical analyses were conducted by using JMP® 12 (SAS Institute Inc., Cary, NC, USA). The room temperature and relative humidity at the beginning of each experiment were analysed using a Wilcoxon test to compare between the AC and RS conditions. Wind velocities, PMV, and PPD values were averaged across the duration of each task through the five sessions, and a two-tailed Wilcoxon test was performed to compare between the AC and RS conditions. Relative changes in EEG amplitude for each oscillation band between the first session and subsequent sessions were assessed using a two-way ANOVA (AC/RS × Sessions) for each electrode and in each season (cooling/heating). As mentioned above (see EEG analysis), we restricted the analysed electrodes before two-way ANOVA testing to reduce repetitions of post-hoc comparisons. Multiple comparisons were not performed because there were no significant interactions. Relative changes in TTL between the first session and the subsequent sessions were assessed using a two-way ANOVA (AC/RS × Sessions) for each season (cooling/heating). The thermography data were pooled. We performed K-means clustering to separate skin temperatures from background data in each condition and for each experiment (cluster number: 2). After separating the skin temperature data, they were averaged within subjects in each condition and experiment. A two-tailed Student's t-test was performed to compare averaged skin temperatures between the first and fifth sessions, or the beginning and end of the experiment, in each condition. Data and code availability The data and custom computer codes that support the findings of this study are available from the corresponding author upon reasonable request. Lin, Z. & Deng, S. A study on the thermal comfort in sleeping environments in the subtropics—Developing a thermal comfort model for sleeping environments. Build. 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The Modulatory Role of Dopamine in Anxiety-like Behavior. Arch. Iran Med. 18, 591–603 (2015). Clayton, M. S., Yeung, N. & Cohen Kadosh, R. The roles of cortical oscillations in sustained attention. Trends Cogn. Sci. 19, 188–195 (2015). Baker, S. N., Olivier, E. & Lemon, R. N. Coherent oscillations in monkey motor cortex and hand muscle EMG show task-dependent modulation. J. Physiol. 501, 225–241 (1997). Baker, S. N., Kilner, J. M., Pinches, E. M. & Lemon, R. N. The role of synchrony and oscillations in the motor output. Exp. Brain. Res. 128, 109–117 (1999). Classen, J., Gerloff, C., Honda, M. & Hallett, M. Integrative Visuomotor Behavior Is Associated With Interregionally Coherent Oscillations in the Human Brain. J. Neurophysiol. 79, 1567–1573 (1998). Baker, S. N. Oscillatory interactions between sensorimotor cortex and the periphery. Curr. Opin. Nuerobiol. 17, 649–655 (2007). Riddle, C. N. & Baker, S. N. Digit displacement, not object compliance, underlies task dependent modulations in human corticomuscular coherence. NeuroImage 33, 618–627 (2006). Chakarov, V. et al. Beta-Range EEG-EMG Coherence With Isometric Compensation for Increasing Modulated Low-Level Forces. J. Neurophysiol. 102, 1115–1120 (2009). Gaetz, W. & Cheyne, D. Localization of sensorimotor cortical rhythms induced by tactile stimulation using spatially filtered MEG. NeuroImage 30, 899–908 (2006). Cheyne, D. et al. Neuromagnetic imaging of cortical oscillations accompanying tactile stimulation. Cogn. Brain Res. 17, 599–611 (2003). van Ede, F. & Maris, E. Somatosensory Demands Modulate Muscular Beta Oscillations, Independent of Motor Demands. J. Neurosci. 33, 10849–10857 (2013). Kilavik, B. E., Zaepffel, M., Brovelli, A., MacKay, W. A. & Riehle, A. The ups and downs of beta oscillations in sensorimotor cortex. Exp. Neurol. 245, 15–26 (2013). Stančák, A., Mlynář, J., Poláček, H. & Vrána, J. Source imaging of the cortical 10 Hz oscillations during cooling and warming in humans. NeuroImage 33, 660–671 (2006). Stančák, A., Poláček, H., Vrána, J. & Mlynář, J. Cortical oscillatory changes during warming and heating in humans. Neuroscience 147, 842–852 (2007). Chang, P. F., Arendt-Nielsen, L. & Chen, A. C. N. Comparative cerebral responses to non-painful warm vs. cold stimuli in man: EEG power spectra and coherence. Int. J. Psychophysiol. 55, 73–83 (2005). Ishihara, T. & Yoshii, N. Multivariate analytic study of EEG and mental activity in Juvenile delinquents. Electroencephalogr. Clin. Neurophysiol. 33, 71–80 (1972). This work was supported by JSPS KAKENHI Grant Number JP24650470. We would like to thank all participants in our experiments, Emi Tsuruta and Sayaka Matsumoto for experimental assistance, and Eriko Kiriyama for preparing the manuscript. Tsuyoshi Okamoto and Kaori Tamura contributed equally to this work. Faculty of Medical Sciences, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka, 812-8582, Japan Tsuyoshi Okamoto Faculty of Arts and Science, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan Tsuyoshi Okamoto & Kaori Tamura Graduate School of Systems Life Sciences, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan Anny Group, 6-3 Tenya-machi, Hakata-ku, Fukuoka, 812-0025, Japan Naoyuki Miyamoto, Shogo Tanaka & Takaharu Futaeda Kaori Tamura Naoyuki Miyamoto Shogo Tanaka Takaharu Futaeda T.O. and T.F. designed the study. T.O., N.M., and S.T. performed the experiments. T.O. and K.T. analysed the data and wrote the paper. All authors discussed the results. Correspondence to Tsuyoshi Okamoto. Okamoto, T., Tamura, K., Miyamoto, N. et al. Physiological activity in calm thermal indoor environments. Sci Rep 7, 11519 (2017). https://doi.org/10.1038/s41598-017-11755-3	CommonCrawl
Dibucaine Inhibition of Serum Cholinesterase Elamin, Babiker 149 https://doi.org/10.5483/BMBRep.2003.36.2.149 PDF The dibucaine number (DN) was determined for serum cholinesterase (EC 3.1.1.8, SChE) in plasma samples. The ones with a DN of 79-82 were used, because they had the "usual" SChE variant. The enzyme was assayed colorimetrically by the reaction of 5,5'-dithiobis-[2-nitrobenzoic acid] (DTNB) with the free sulfhydryl groups of thiocholine that were produced by the enzyme reaction with butrylthiocholine (BuTch) or acetylthiocholine (AcTch) substrates, and measured at 412 nm. Dibucaine, a quaternary ammonium compound, inhibited SChE to a minimum within 2 min in a reversible manner. The inhibition was very potent. It had an $IC_{50}$ of $5.3\;{\mu}M$ with BuTch or $3.8\;{\mu}M$ with AcTch. The inhibition was competitive with respect to BuTch with a $K_i$ of $1.3\;{\mu}M$ and a linear-mixed type (competitive/noncompetitive) with respect to AcTch with inhibition constants, $K_i$ and $K_I$ of 0.66 and $2.5\;{\mu}M$, respectively. Dibucaine possesses a butoxy side chain that is similar to the butryl group of BuTch and longer by an ethylene group from AcTch. This may account for the difference in inhibition behavior. It may also suggest the existence of an additional binding site, other than the anionic binding site, and of a hydrophobic nature. Investigation into the Distribution of Total, Free, Peptide-bound, Protein-bound, Soluble-and Insoluble-Collagen Hydroxyproline in Various Bovine Tissues Siddiqi, Nikhat J.;Alhomida, Abdullah S. 154 Collagen is a family of proteins which consists of several genetically distinct molecular species and is intimately involved in tissue organization, function, differentiation and development. The purpose of this study was to investigate the concentration of different hydroxyproline (Hyp) fractions viz., total, free, peptide-bound, protein-bound, soluble- and insoluble-collagen hydroxyproline (Hyp) in various bovine tissues. Results showed that liver had the highest concentration of free Hyp followed by kidney, brain, spleen, lungs, muscle and heart. Liver also had the highest concentration of peptide-bound collagen Hyp followed by kidney, heart, spleen, lungs, brain and muscle. The concentration of protein-bound collagen Hyp was highest in the liver, followed by kidney, spleen, lungs, muscle, brain and heart. Total Hyp was highest in the liver, followed by kidney, spleen, brain, heart, muscle and lungs. Liver also had significantly high concentration of collagen as compared to other tissues examined (P<0.001). Spleen had the significantly higher concentration of soluble-collagen Hyp when compared to other tissues (P<0.001). This was followed by heart, muscle, lungs, brain, kidney and liver. Heart had the highest concentration of insoluble-collagen Hyp followed by lungs, kidney, liver, muscle, spleen and brain. The variation among the insoluble-collagen Hyp concentration of heart and muscle, spleen and brain was significant (P<0.001). We speculate that these differences could be due to the variation in turn over of rate of collagen metabolism in this species. Isolation and Properties of Cytoplasmic α-Glycerol 3-Phosphate Dehydrogenase from the Pectoral Muscle of the Fruit Bat, Eidolon helvum Agboola, Femi Kayode;Thomson, Alan;Afolayan, Adeyinka 159 Cytoplasmic $\alpha$-glycerol-3-phosphate dehydrogenase from fruit-bat-breast muscle was purified by ion-exchange and affinity chromatography. The specific activity of the purified enzyme was approximately 120 units/mg of protein. The apparent molecular weight of the native enzyme, as determined by gel filtration on Sephadex G-100 was $59,500{\pm}650$ daltons; its subunit size was estimated to be $35,700{\pm}140$ by SDS-polyacrylamide gel electrophoresis. The true Michaelis-Menten constants for all substrates at pH 7.5 were $3.9{\pm}0.7\;mM$, $0.65{\pm}0.05\;mM$, $0.26{\pm}0.06\;mM$, and $0.005{\pm}0.0004\;mM$ for L-glycerol-3-phosphate, $NAD^+$, DHAP, and NADH, respectively. The true Michaelis-Menten constants at pH 10.0 were $2.30{\pm}0.21\;mM$ and $0.20{\pm}0.01\;mM$ for L-glycerol-3-phosphate and $NAD^+$, respectively. The turnover number, $k_{cat}$, of the forward reaction was $1.9{\pm}0.2{\times}10^4\;s^{-1}$. The treatment of the enzyme with 5,5'-dithiobis-2-nitrobenzoic acid (DTNB) under denaturing conditions indicated that there were a total of eight cysteine residues, while only two of these residues were reactive towards DTNB in the native enzyme. The overall results of the in vitro experiments suggest that $\alpha$-glycerol-3-phosphate dehydrogenase of the fruit bat preferentially catalyses the reduction of dihydroxyacetone phosphate to glycerol-3-phosphate. Conformational Lock and Dissociative Thermal Inactivation of Lentil Seedling Amine Oxidase Moosavi-Nejad, S. Zahra;Moosavi-Movahedi, Ali-Akbar;Rezaei-Tavirani, Mostafa;Floris, Giovanni;Medda, Rosaria 167 The kinetics of thermal inactivation of copper-containing amine oxidase from lentil seedlings were studied in a 100 mM potassium phosphate buffer, pH 7, using putrescine as the substrate. The temperature range was between $47-60^{\circ}C$. The thermal inactivation curves were not linear at 52 and $57^{\circ}C$; three linear phases were shown. The first phase gave some information about the number of dimeric forms of the enzyme that were induced by the higher temperatures using the "conformational lock" pertaining theory to oligomeric enzyme. The "conformational lock" caused two additional dimeric forms of the enzyme when the temperature increased to $57^{\circ}C$. The second and third phases were interpreted according to a dissociative thermal inactivation model. These phases showed that lentil amine oxidase was reversibly-dissociated before the irreversible thermal inactivation. Although lentil amine oxidase is not a thermostable enzyme, its dimeric structure can form "conformational lock," conferring a structural tolerance to the enzyme against heat stress. Detection of Circulating Melanoma Cells by a Two-marker Polymerase Chain Reaction Assay in Relation to Therapy Bitisik, Ozlem;Camlica, Hakan;Duranyildiz, Derya;Tas, Faruk;Kurul, Sidika;Dalay, Nejat 173 Malignant melanoma is one of the most rapidly increasing cancer types, and patients with metastatic disease have a very poor prognosis. Detection of metastatic melanoma cells in circulation may aid the clinician in assessing tumor progression, metastatic potential, and response to therapy. Tyrosinase is a key enzyme in melanine biosynthesis. The gene is actively expressed in melanocytes and melanoma cells. Melan A is a differentiation antigen that is expressed in melanocytes. The presence of these molecules in blood is considered a marker for circulating melanoma cells. In this study, we analyzed the usefulness of this marker combination I evaluating the response to therapy in the blood of 30 patients with malignant melanoma. Circulating cells were detected by a reverse-transcriptase-polymerase-chain reaction. The tyrosinase expression was observed in 9 (30%) patients and Melan A in 19 (63.3%) patients before therapy. Following treatment, the tyrosinase mRNA was detected in only one patient, while Melan A transcripts were still present in 14 patients. We suggest that this molecular assay can identify circulating melanoma cells that express melanoma-associated antigens and may provide an early indication of therapy effectiveness. Direct Deletion Analysis in Two Duchenne Muscular Dystrophy Symptomatic Females Using Polymorphic Dinucleotide (CA)n Loci within the Dystrophin Gene Giliberto, Florencia;Ferreiro, Veronica;Dalamon, Viviana;Surace, Ezequiel;Cotignola, Javier;Esperante, Sebastian;Borelina, Daniel;Baranzini, Sergio;Szijan, Irene 179 Duchenne muscular dystrophy (DMD) is the most common hereditary neuromuscular disease. It is inherited manifestations. In some rare cases, the disease can also be manifested in females. The aim of the present study was to determine the molecular alteration in two cases of nonrelated DMD symptomatic carriers with no previous history of DMD. Multiplex PCR is commonly used to search for deletion in the DMD gene of affected males. This method could not be used in females because the normal X chromosome masks the deletion of the mutated one. Therefor, we used a set of seven highly polymorphic dinucleotide $(CA)_n$ repeat markers that lie within the human dystrophin gene. The deletions were evidenced by hemizygosity of the loci under study. We localized a deletion in the locus 7A (intron 7) on the maternal X chromosome in one case, and a deletion in the region of introns 49 and 50 on the paternal X chromosome in the other. The use of microsatellite genotyping within the DMD gene enables the detection of the mutant allele in female carriers. It is also a useful method to provide DMD families with more accurate genetic counseling. Purification and Characterization of Chitinase from Streptomyces sp. M-20 Kim, Kyoung-Ja;Yang, Yong-Joon;Kim, Jong-Gi 185 Chitinase (EC 3.2.1.14) was isolated from the culture filtrate of Streptomyces sp. M-20 and purified by ammonium sulfate precipitation, DEAE-cellulose ion-exchange chromatography, and Sephadex G-100 gel filtration. No exochitinase activity was found in the culture filtrate. The molecular mass of the purified chitinase was 20 kDa, estimated by a sodium dodecyl sulfate-polyacrylamide gel electrophoresis, and was confirmed by activity staining with Calcofluor White M2R. Chitinase was optimally active at pH of 5.0 and at $30^{\circ}C$. The enzyme was stable from pH 4 to 8, and up to $40^{\circ}C$. Among the metals and inhibitors that were tested, the $Hg^+$, $Hg^{2+}$, and p-chloromercuribenzoic acid completely inhibited the enzyme activity. The chitinase activity was high on colloidal chitin, chitotriose, and chitooligosaccharide. The purified chitinase showed antifungal activity against Botrytis cinerea, and lysozyme activity against the cell wall of Botrytis cinerea. Vitamin E Modulates Radiation-induced Oxidative Damage in Mice Fed a High-Lipid Diet Shin, Sung-Jae 190 The Vitamin E (VE) effect was examined on oxidative damage to DNA, lipids, and protein in mice that were fed various levels of lipid diets after total body irradiation (TBI) with X-rays at 2 Gy. No increase of 8-hydroxydeoxyguanosine (8OHdG) by TBI was observed in the +VE group; however, in the case of the -VE group, a significantly higher 8OHdG level was observed in the high-lipid group than in the low- or basal-lipid group. In the groups with TBI, the concentration of thiobarbituric reactive substances (TBARS) only significantly increased in the high-lipid (-VE) group. These changes in TBARS, due to TBI, were not detected in other groups. The contents of protein carbonyls only increased in the (-VE) group. The contents of protein carbonyls was significantly different between the (+VE) and the (-VE) groups, regardless of the lipid levels. The concentrations of GSH, vitamins C and E in the liver were lower, and the concentration of non-heme iron in the liver was higher in the high-lipid group than in the low- and basal-lipid groups. These concentrations in the high-lipid group were significantly different between the (+VE) and the (-VE) groups. These results strongly suggest that mice that are fed a high-lipid diet are susceptible to TBI-induced oxidative damage. Also, decreases in the GSH levels and an increase in the iron level are involved in the mechanism of this susceptibility. The Effect of pH and Various Cations on the GTP Hydrolysis of Rice Heterotrimeric G-protein α Subunit Expressed in Escherichia Coli Seo, Hak-Soo;Jeong, Jin-Yong;Nahm, Min-Yeop;Kim, Sam-Woong;Lee, Sang-Yeol;Bahk, Jeong-Dong 196 Previously, we reported the biochemical properties of RGA1 that is expressed in Escherichia coli (Seo et al., 1997). The activities of RGA1 that hydrolyzes and binds guanine nucleotide were dependent on the $MgCl_2$ concentration. The steady state rate constant ($k_{cat}$) for GTP hydrolysis of RGA1 at 2 mM $MgCl_2$ was $0.0075{\pm}0.0001\;min^{-1}$. Here, we examined the effects of pH and cations on the GTPase activity. The optimum pH at 2 mM $MgCl_2$ was approximately 6.0; whereas, the pH at 2 mM $NH_4Cl$ was approximately 4.0. The result from the cation dependence on the GTPase (guanosine 5'-triphosphatase) activity of RGA1 under the same condition showed that the GTP hydrolysis rate ($k_{cat}=0.0353\;min^{-1}$) under the condition of 2mM $NH_4Cl$ at pH 4.0 was the highest. It corresponded to about 3.24-fold of the $k_{cat}$ value of $0.0109\;min^{-1}$ in the presence of 2 mM $MgCl_2$ at pH 6.0. Recombination Activating Gene 1 Product Alone Possesses Endonucleolytic Activity Kim, Deok-Ryong 201 Two lymphoid-specific proteins, RAG1 and RAG2, are required for the initiation of the V(D)J recombination in vitro. The V(D)J cleavage that is mediated by RAG proteins at the border between the coding and signal sequences results in the production of a hairpin at the coding end and a double-stranded break at the signal end. Two hairpin coding ends are re-opened, modified, and sealed; whereas, the signal ends are directly ligated. Here I report that only RAG1 can carry out a distinct endonucleolytic activity in vitro using an oligonucleotide substrate that is tethered by a short single-stranded DNA. The purified RAG1 protein alone formed a nick at the near position to the recombination signal sequence. This endonucleolytic activity was eliminated by immunoprecipitation using the RAG1-specific antibody, and required the 3'-hydroxy group. All of the RAG1 mutants that were incapable of the nick and hairpin formation in the V(D)J cleavage analysis also showed this new endonucleolytic activity. This suggests that the nicking activity that was observed might be functionally different from the nick formation in the V(D)J cleavage. A Simple ELISA for Screening Ligands of Peroxisome Proliferator-activated Receptor γ Cho, Min-Chul;Lee, Hae-Sook;Kim, Jae-Hwa;Choe, Yong-Kyung;Hong, Jin-Tae;Paik, Sang-Gi;Yoon, Do-Young 207 Peroxisome proliferator-activated receptors (PPARs) are orphan nuclear hormone receptors that are known to control the expression of genes that are involved in lipid homeostasis and energy balance. PPARs activate gene transcription in response to a variety of compounds, including hypolipidemic drugs. Most of these compounds have high affinity to the ligand-binding domain (LBD) of PPARs and cause a conformational change within PPARs. As a result, the receptor is converted to an activated mode that promotes the recruitment fo co-activators such as the steroid receptor co-activator-1 (SRC-1). Based on the activation mechanism of PPARs (the ligand binding to $PPAR{\gamma}$ induces interactions of the receptor with transcriptional co-activators), we performed Western blot and ELISA. These showed that the indomethacin, a $PPAR{\gamma}$ ligand, increased the binding between $PPAR{\gamma}$ and SRC-1 in a ligand dose-dependent manner. These results suggested that the in vitro conformational change of $PPAR{\gamma}$ by ligands was also induced, and increased the levels of the ligand-dependent interaction with SRC-1. Collectively, we developed a novel and useful ELISA system for the mass screening of $PPAR{\gamma}$ ligands. This screening system (based on the interaction between $PPAR{\gamma}$ and SRC-1) may be a promising system in the development of drugs for metabolic disorders. A Lectin with Mycelia Differentiation and Antiphytovirus Activities from the Edible Mushroom Agrocybe aegerita Sun, Hui;Zhao, Chen Guang;Tong, Xin;Qi, Yi Peng 214 A lectin named AAL has been purified from the fruiting bodies of the edible mushroom Agrocybe aegerita. AAL consisted of two identical subunits of 15.8 kDa, its pI was about 3.8 determined by isoelectric focusing, and no carbohydrate was discerned. Being treated by pyrogultamate aminopeptidase, the blocked N-terminus of AAL was sequenced as QGVNIYNI. AAL agglutinated human and animal erythrocytes regardless of blood type or animal species. Its hemagglutinating activity was unaffected by acid or alkali treatment and demetalization or addition of divalent metals $Mg^{2+}$, $Ca^{2+}$ and $Zn^{2+}$. AAL was toxic to mice: its LD50 was 15.85 mg per kilogram body weight by intraperitoneal injection. In this study, two novel activities of AAL were proved. It showed inhibition activity to infection of tobacco mosaic virus on Nicotiana glutinosa. The result of IEF suggested that AAL attached to TMV particles. Mycelia differentiation promotion was the other interesting activity. AAL promoted the differentiation of fruit body primordia from the mycelia of Agrocybe aegerita and Auricularia polytricha. AAL antiserum was prepared and immunologically cross-reactived with several proteins from five other kinds of mushrooms. These results suggested that AAL probably was a representative of a large protein family, which plays important physiological roles in mushroom. Suppression of Human Prostate Cancer Cell Growth by β-Lapachone via Down-regulation of pRB Phosphorylation and Induction of Cdk Inhibitor p21WAF1/CIP1 Choi, Yung-Hyun;Kang, Ho-Sung;Yoo, Mi-Ae 223 The product of a tree (Tabebuia avellanedae) from South America, $\beta$-lapachone, is known to exhibit various pharmacological properties, the mechanisms of which are poorly understood. The aim of the present study was to further elucidate the possible mechanisms by which $\beta$-lapachone exerts its anti-proliferative action in cultured human prostate cancer cells. We observed that the proliferation-inhibitory effect of $\beta$-lapachone was due to the induction of apoptosis, which was confirmed by observing the morphological changes and cleavage of the poly(ADP-ribose) polymerase protein. A DNA flow cytometric analysis also revealed that $\beta$-lapachone arrested the cell cycle progression at the G1 phase. The effects were associated with the down-regulation of the phosphorylation of the retinoblastoma protein (pRB) as well as the enhanced binding of pRB and the transcription factor E2F-1. Also, $\beta$-lapachone suppressed the cyclindependent kinases (Cdks) and cyclin E-associated kinase activity without changing their expressions. Furthermore, this compound induced the levels of the Cdk inhibitor $p21^{WAF1/CIP1}$ expression in a p53-independent manner, and the p21 proteins that were induced by $\beta$-lapachone were associated with Cdk2. $\beta$-lapachone also activated the reporter construct of a p21 promoter. Overall, our results demonstrate a combined mechanism that involves the inhibition of pRB phosphorylation and induction of p21 as targets for $\beta$-lapachone. This may explain some of its anticancer effects. Purification and Characterization of Complement-activating Acidic Polysaccharides from the Fruits of Capsicum annuum Paik, Soon-Young;Ra, Kyung-Soo;Chang, In-Seop;Park, Yoon-Chang;Park, Hee-Sung;Baik, Hyung-Suk;Yun, Jong-Won;Choi, Jang-Won 230 Hot water-soluble crude polysaccharide (HCAP-0) that was obtained from the fruits of Capsicum annuum showed potent anti-complementary activity. The activity was unchanged by pronase digestion, but decreased by periodate oxidation. The HCAP-0 was fractionated by DEAE ion-exchange chromatography to give two major fractions, HCAP-II and III. These two fractions were finally purified by gel filtration to give HCAP-IIa, HCAP-IIIa1, and IIIa2 fractions that had high anti-complementary activities. The HCAP-IIIa1 and IIIa2 consisted of homogeneous polysaccharides. The anti-complementary activities were unaffected by treatment with polymyxin B, indicating that the modes of complement activation were not due to preexisting lipopolysaccharide. The molecular weight and sugar content of HCAP-IIIa2 had potent anti-complementary activity. The highest yields were 55 kDa and 75.9%, and the molar ratio of galactose (Ara:Gal, 1.0:4.6) was higher than other sugars. The crossed immuno-electrophoresis showed that both classical and alternative pathways were activated by HCAP-IIIa2. Hepatic Lipase C514T Polymorphism and its Relationship with Plasma HDL-C Levels and Coronary Artery Disease in Koreans Park, Kyung-Woo;Choi, Jin-Ho;Chae, In-Ho;Cho, Hyun-Jai;Oh, Se-Il;Kim, Hyo-Soo;Lee, Myoung-Mook;Park, Young-Bae;Choi, Yun-Shik 237 Hepatic lipase is a key enzyme that is involved in HDL-C metabolism. The goal of this study was to find out the frequency of the hepatic lipase C514T polymorphism, and evaluate its relationship with plasma HDL-C levels and coronary artery disease (CAD) in Koreans. Two hundred and twenty four subjects with no previous history of lipid-lowering therapy, 118 patients with significant CAD, and 106 controls were examined with respect to their genotypes, lipid profiles, and other risk factors for CAD. The frequency of the -514T allele was 0.37 in men and 0.35 in women, which were higher than the frequency that was reported in Caucasians, but lower than the frequency that was reported in African-Americans. The -514T allele was associated with significantly higher HDL-C levels in women. After controlling for age, gender, BMI, DM, and smoking, the non-CC genotype was significantly associated with HDL-C levels, and explained 6% of the HDL-C variation in this study. When the genotypes-distribution was compared between the CAD and non-CAD patients, the hepatic lipase C-514T polymorphism was not associated with the presence of CAD. Koreans have a higher frequency of the hepatic lipase gene 514T allele than Caucasians, and the -514T allele is associated with higher plasma HDL-C levels in Korean women, and perhaps non-smoking men. However, our data does not suggest an association between the polymorphism and an increased risk of CAD.	CommonCrawl
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up. Lions/diPerna type commutator estimates for differential operator in Fokker-Planck type equation I have a question about a particular commutator estimate as it occurs in the study of Fokker-Planck equations with low regularity data, see e.g. [1,2]. Denote by $\rho_\varepsilon$ some usual regularizing kernel (mollifier) family and let $1 < r < 2$ be given and fixed. We have functions $$\sigma \in W^{1,\infty}_{loc}(\mathbb{R}^N)^{N \times K} \quad\text{and}\quad p \in L^\infty(0,T;L^r(\mathbb{R}^N)) \quad \text{with} \quad \sigma^\top \nabla p \in L^2(0,T;L^r(\mathbb{R}^N))$$ at hand. (No info on $\nabla p$ itself.) Let $p_\varepsilon := \rho_\varepsilon \star p$ be the regularized $p$. Define the mollification-commutator $[\rho_\varepsilon,D](f) := \rho_\varepsilon \star (Df) - D(\rho_\varepsilon \star f)$ for some function $f$ and a differential operator $D$. Let $\gamma \in C^2(\mathbb{R})$ with bounded first and second derivative and let $\varphi$ be a test function on $[0,T) \times \mathbb{R}^N$. Main problem: I want to show that $$\int_0^T\int_{\mathbb{R}^N} \varphi \, \gamma'(p_\varepsilon) \, r_\varepsilon \longrightarrow 0 \quad \text{as}~\varepsilon \to 0,\tag{1}$$ where $$r_\varepsilon := \rho_\varepsilon \star \partial_i(\sigma_{ik}\sigma_{jk}\partial_j p) - \partial_i(\sigma_{ik}\sigma_{jk}\partial_j p_\varepsilon) = \partial_i \bigl([\rho_\varepsilon,\sigma_{ik}\sigma_{jk}\partial_j](p)\bigr). $$ In [1,2] the case $r=2$ is considered where this indeed works out. They rewrite $r_\varepsilon$ further into \begin{align}r_\varepsilon &= \partial_i \bigl(\sigma_{ik}[\rho_\varepsilon,\sigma_{jk}\partial_j](p)\bigr) + [\rho_\varepsilon,\partial_i\sigma_{ik}](\sigma_{jk}\partial_j p) + [\rho_\varepsilon,\sigma_{ik}\partial_i](\sigma_{jk}\partial_j p) \\ &:= \partial_i (\sigma_{ik}R_\varepsilon) + S_\varepsilon + T_\varepsilon.\end{align} These commutators are then shown to converge to zero suitably by the commutator lemma (see below) which transfers to (1) by dominated convergence. However I am unable to derive suitable convergence for the term with a derivative on the commutator $\partial_i (\sigma_{ik}R_\varepsilon)$ in my setting. One needs to integrate by parts for this term in (1), resulting in the critical term $$\int_0^T \int_{\mathbb{R}^N} \varphi \, \gamma''(p_\varepsilon) \, \sigma^\top \nabla p_\varepsilon \cdot R_\varepsilon$$ where $\sigma^\top \nabla p_\varepsilon$ is bounded in $L^r(\mathbb{R}^N)$, but also $R_\varepsilon \to 0$ only in $L^r_{loc}(\mathbb{R}^N)$. So this works exactly for $r=2$. The idea: I had suspected (hoped) that with a second derivative on $\sigma$ one could show that $\partial_i R_\varepsilon \to 0$ in $L^1_{loc}(\mathbb{R}^N)$ directly; that would give a positive proof for (1). (Ignoring temporal integrability for the moment.) From calculating the derivative, a commutator of the form $[\rho_\varepsilon, \sigma_{jk}\partial_i\partial_j](p)$ becomes the object of interest. However the proof of the commutator lemma seems to use a quite nice cancellation property which seems to work only for the first order cases, so I did not manage to prove convergence to zero of this term. (At least not without the assumption that $\nabla p$ is integrable, then it is easy from the commutator lemma as below.) Hence a second, more specific question: Subproblem: In the situation described, does the modified commutator estimate $$[\rho_\varepsilon, \sigma_{jk}\partial_i\partial_j](p) \to 0 \quad\text{in}~L^1_{loc}(\mathbb{R}^N)$$ hold true? I am willing to assume more or less any regularity on $\sigma$. As hinted above, I would like to avoid $\sigma\sigma^\top$ being uniformly positive definite as an assumption. (In this case, $\nabla p \in L^{r}(\mathbb{R}^N)$ and the "second order" commutator estimate is good.) The motivation is to consider an inhomogeneous Fokker-Planck equation with data comparable to the cited works [1,2]. Any hints would be welcome. Lemma (Commutator lemma, [3, Lemma II.1]). Let $1/\beta = 1/\alpha + 1/s$ and $g \in L^{\alpha}_{loc}(\mathbb{R}^N)$ and $f_1 \in L^s_{loc}(\mathbb{R}^N)$, and $c \in W^{1,\alpha}_{loc}(\mathbb{R}^N)$ and $f_2 \in L^s_{loc}(\mathbb{R}^N)$. Then $$[\rho_\varepsilon,g](f_1) \to 0 \quad \text{and} \quad [\rho_\varepsilon,c \partial_i](f_2) \to 0, \quad\text{each in}~L^\beta_{loc}(\mathbb{R}^N).$$ [1] Le Bris, C.; Lions, P.-L., Existence and uniqueness of solutions to Fokker-Planck type equations with irregular coefficients, Commun. Partial Differ. Equations 33, No. 7, 1272-1317 (2008). ZBL1157.35301. [2] Luo, De Jun, Fokker-Planck type equations with Sobolev diffusion coefficients and BV drift coefficients, Acta Math. Sin., Engl. Ser. 29, No. 2, 303-314 (2013). ZBL1318.35130. [3] DiPerna, R. J.; Lions, P. L., Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98, No. 3, 511-547 (1989). ZBL0696.34049. ap.analysis-of-pdes HannesHannes Know someone who can answer? Share a link to this question via email, Twitter, or Facebook. Thanks for contributing an answer to MathOverflow! Regularity for transport equation? Regularity of the Maxwell equations properties of frequency-uniform decomposition operator $\square_{k}^{\sigma}$ Regularity of solution to Fokker Planck equation Unexpected regularity of the distance from a $C^2$ submanifold Interior elliptic regularity in W^{k,1} spaces Fokker-Planck equation for a truncated process Modified energy method for transformed Fokker-Planck equation (tricky integration by parts…)	CommonCrawl
Efficient growth of Kluyveromyces marxianus biomass used as a biocatalyst in the sustainable production of ethyl acetate Christian Löser1, Thanet Urit1,2, Erik Gruner1 & Thomas Bley1 Whey is just turning from a waste of milk processing to a renewable raw material in biotechnology for producing single-cell protein, bio-ethanol, or ethyl acetate as an economic alternative. Conversion of whey-borne sugar into ethyl acetate requires yeast biomass as a biocatalyst. A high cell concentration results in a quick ester synthesis, but biomass growth means consumption of sugar at the expense of ester production. Efficient and cost-saving biomass production is thus a practical requirement. Whey is poor in nitrogen and has therefore to be supplemented with a bioavailable N source. Several aerobic growth tests were performed with Kluyveromyces marxianus DSM 5422 as a potent producer of ethyl acetate in whey-borne media supplemented with various N sources. Preliminary tests were done in shake flasks while detailed studies were performed in a stirred bioreactor. Ammonium sulfate resulted in strong acidification due to remaining sulfate, but costly pH control increases the salt load, being inhibitory to yeasts and causing environmental impacts. Ammonium carbonate lessened acidification, but its supplement increased the initial pH to 7.5 and delayed growth. Urea as an alternative N source was easily assimilated by the studied yeast and avoided strong acidification (much less base was required for pH control). Urea was assimilated intracellularly rather than hydrolyzed extracellularly by urease. Conversion of urea to ammonium and usage of formed ammonium for biomass production occurred with a similar rate so that the amount of excreted ammonium was small. Ammonium hydroxide as another N source was successfully added by the pH controller during the growth of K. marxianus DSM 5422, but the medium had to be supplemented with some ammonium sulfate to avoid sulfur limitation and to initiate acidification. Non-limited growth resulted in 82 mg N per g of biomass, but N-limited growth diminished the N content. K. marxianus could be efficiently produced by supplementing the whey with nitrogen. Urea and ammonia were the favored N sources due to the proton neutrality at assimilation which lessened the salt load and reduced the supply of alkali for pH control or made this even needless. Sustainable and environmentally compatible development requires successive substitution of fossil resources by renewable raw materials. This applies to the energy sector but is also true for production of industrial bulk materials. Such a bulk chemical is ethyl acetate with an annual world production of 1.7 million tons [1]. Ethyl acetate is an organic solvent of moderate polarity with versatile industrial applications. Another prospective application is the biodiesel production from vegetable oil; here, triglycerides are transformed to fatty acid ethyl esters in a lipase-catalyzed transesterification reaction with ethyl acetate as an acyl acceptor instead of methanol [2-5]. Although being an irritant and intoxicant at higher concentrations, ethyl acetate is less toxic to humans compared to many other solvents. Ethyl acetate is an environmentally friendly compound since the ester is easily degraded by bacteria [6-8] and is regarded as a non-persistent pollutant of the atmosphere [9]. Synthesis of ethyl acetate currently proceeds by petrochemical processes, which are based on crude oil constituents or natural gas, run at elevated temperature and pressure and commonly require catalysts [9]. The reactions are often incomplete, and the recovery of ethyl acetate and residual precursors needs a high input of energy. Microbial production of ethyl acetate from renewables could become an interesting alternative. Various yeast species can synthesize ethyl acetate (reviewed by Löser et al. [9]), but only Pichia anomala, Candida utilis, and Kluyveromyces marxianus produce this ester in larger amounts. K. marxianus is the most promising candidate for large-scale ester production since this dairy yeast with GRAS status grows quickly, converts sugar directly into ethyl acetate without ethanol as an essential intermediate, and produces the ester with a high rate and yield [9-17]. The ester synthesis in K. marxianus is easy to control by the level of iron [11,13,16-18]. K. marxianus exhibits a distinct thermal tolerance which allows cultivation at an elevated temperature [14,19,20] which in turn accelerates the ester stripping and advances its process-integrated recovery. The outstanding capability of K. marxianus for lactose utilization offers the chance for using whey as a resource of ester synthesis. K. marxianus converts whey-borne lactose with a high yield into ethyl acetate [9], but its ability for sucrose and glucose assimilation [19-21] enables production of ethyl acetate with this yeast from renewables like sugarcane, grain, and corn. Ethanol is another product of microbial sugar conversion, but several factors favor microbial ester over ethanol production [22]: the higher market price of the ester, a reduced number of process stages, a faster process, and a cost-saving product recovery. Conversion of sugar into ethyl acetate requires yeast biomass as a biocatalyst. A high biomass concentration results in a quick process, but the production of this biomass, on the other hand, is connected with sugar consumption which reduces the portion of sugar available for ester production (as demonstrated in pilot-scale experiments [13]). The right balance between yeast growth and ester synthesis or, in other words, a compromise between a quick process and a high ester yield is of practical importance. This balance can be controlled by the available iron [13,16,23]. An efficient production of the required yeast biomass is an important factor for the economy of the total process of ester and ethanol production. At whey-based bio-ethanol production, the biomass is often considered as a gift and sugar utilization for biomass production is ignored. Such an 'out-sourcing' of biomass processing only seemingly improves the economy. Much research was done in the field of whey-based K. marxianus cultivation for single-cell protein production [24-28]. The results refer to some problems at cultivation of K. marxianus in whey-based media; whey is poor in bioavailable nitrogen so that nitrogen can limit yeast growth [26-29]. Nitrogen-limited growth can even deregulate yeast metabolism and provoke ethanol formation at aerobic conditions [30]. Whey was often supplemented with ammonium as a source of nitrogen to stimulate growth of K. marxianus [10-14,16,27,29,31-37]. Added ammonium increased the yield of biomass [27,32,35] or was without significant effect [29,31,36]. Ammonium is usually supplemented in the form of ammonium sulfate where ammonium is intensively consumed while most of the sulfate remains in the medium and causes an ionic imbalance and acidification [15,38-41]. Such acidification can be inhibitory to K. marxianus since its growth rate is distinctly reduced at pH ≤3.5 [22,28,42,43]. Supplementation of whey with (NH4)2SO4 or NH4Cl requires cost-intensive pH correction with NaOH or KOH which in turn increases the salt load and thus inhibits yeast growth [31,42] and creates waste-water problems. Urea is an alternative N source since growth with urea exhibits proton neutrality without significant pH changes [38-40]. Assimilation of urea by yeasts is not an exception but the rule; 122 of 123 tested yeasts were able to metabolize urea [44]. There are several potential advantages of urea [25,28,39]: a high amount of nitrogen per unit weight, a low price, and a reduced or even omitted supply of pH correctives. K. marxianus definitely metabolizes urea, and whey was repeatedly supplemented with urea as an N source for this yeast [28,31,32,37,45-47]. However, the effect of added urea on growth was often not described [37,45,46], or the published results were contradictory. Yadav et al. [28] observed an increased biomass yield, Kar and Misra [32] found no positive effect, Mahmoud and Kosikowski [31] described slight inhibition by added urea, and Rech et al. [47] even detected strong inhibition of growth which had been attributed to alkalinization. These inconsistent results require clarification by more detailed studies on this subject. The first objective of this work was testing the effect of (NH4)2SO4, (NH4)2CO3, or urea as sources of nitrogen at aerobic growth of K. marxianus DSM 5422 in whey-borne medium with special attention on yeast growth and acidification. When using (NH4)2SO4, sulfate remains in the medium and causes proton imbalance and acidification but, when using (NH4)2CO3, carbonate disappears in form of CO2 during cultivation which possibly avoids acidification. The second objective was studying the growth of K. marxianus DSM 5422 in whey-borne medium with urea in detail at defined conditions to get a deeper insight into the urea metabolism. The third objective was testing the pH-controlled feed of ammonia during aerobic growth of K. marxianus DSM 5422 in whey-borne medium. Ammonia as the cheapest source of nitrogen is interesting for large-scale processes. K. marxianus DSM 5422 from the Deutsche Sammlung von Mikroorganismen und Zellkulturen GmbH (Braunschweig, Germany) was maintained with the Cryoinstant preservation system (Lomb Scientific Pty Ltd, Vienna, Austria), cultivated on yeast-glucose-chloramphenicol agar (Roth GmbH, Karlsruhe, Germany) for 2 days at 32°C, and then used as an inoculum. Non-supplemented DW medium All media originate from concentrated and partially demineralized sweet whey. Sweet whey was ultrafiltrated, concentrated by reverse osmosis, and then demineralized by slight alkalinization and moderate heating to yield the used whey permeate (thus processed in the Sachsenmilch Leppersdorf GmbH, Leppersdorf, Germany). Non-supplemented DW medium was prepared in batches of 1 L by mixing 0.5 L whey permeate with the same volume water. This mixture was autoclaved in a sealed 1-L Schott bottle for 15 min at 121°C. Precipitated minerals were allowed to settle overnight before the upper phase was withdrawn for cultivation experiments. Non-supplemented DW medium should not be confused with DW basic medium (as used in [11-14,16]) which contains 10 g/L (NH4)2SO4. Shake-flask cultivation In a first series of shake-flask experiments, various media were prepared like the just-described non-supplemented DW medium with the modification that various sources of nitrogen (10 g/L (NH4)2SO4, 10 g/L (NH4)2CO3, or 5 g/L urea) were added before medium sterilization. The media handling (autoclaving, settlement, withdrawal) occurred as in the above-described manner. These media were supplemented with 2 mL/L autoclaved trace-element solution (preparation as described in [10]) and diluted with water to 1/20 for reducing the content of sugar to 3.9 g/L and, thus, to avoid oxygen-limited growth at a low oxygen-transfer rate in shake flasks. Several 500-mL conical flasks with cotton plugs were filled each with 50 mL medium, inoculated with an agar-plate culture as described in [14], and shaken with 250 rpm at 32°C. After 14 h of pre-cultivation, the process was followed by regular analysis of the optical density (OD) and the pH value over a period of at least 10 h. After a total of 40 h of cultivation, the OD and pH were measured and the residual sugar and formed biomass were analyzed. A second series of shake-flask experiments was based on autoclaved non-supplemented DW medium. Portions of this medium were supplemented with 2 mL/L sterile trace-element solution and separately autoclaved aqueous stock solutions of (NH4)2SO4, (NH4)2CO3, or urea. The pH was then adjusted to 6.5 with 0.1 M HCl or KOH. These media were diluted with water to reduce the sugar content to 3.9 g/L like in the first series. Discrete sterilization of whey and N sources in this second series avoided unwanted interaction between whey constituents and N compounds such as the Maillard reaction. Inoculation, cultivation, and analyses occurred as in the first series. Bioreactor cultivation One reference experiment was done with DW basic medium (DW medium with 10 g/L (NH4)2SO4) and described in detail in [11] while all other presented bioreactor processes were based on non-supplemented DW medium. The sterile 1-L stirred bioreactor with 0.6 mL Antifoam A (Fluka, Sigma Aldrich, St. Louis, USA) was filled with 0.6 L DW medium and 1.2 mL trace-element solution (the latter described in [10]). Further supplements such as (NH4)2SO4, urea, and Na2SO4 were put into 100-mL Schott bottles, autoclaved for 15 min at 121°C, and then transferred to the bioreactor as follows: the bottle was connected with the bioreactor, some culture medium was pumped to the bottle, and, after complete dissolution of the substance, transported back to the reactor. Separate autoclaving avoided unwanted interaction such as the Maillard reaction and sulfate precipitation. The cultivation occurred as usual [10-12,14]: the medium was inoculated with five loops of biomass, and the reactor was operated at 1,200 rpm and 32°C and gassed with 50 L/h dry and CO2-free air (given for 0°C and 101,325 Pa). The pH was controlled to ≥5 with 2 M KOH or 2 M ammonia solution. All processes lasted at least 36 h. Sampling and sample preparation were performed as usual [10]. Test for urea assimilation K. marxianus DSM 5422 was cultivated in diluted DW medium with urea (3.9 g/L sugars, 0.25 g/L urea) as described for the second series of shake-flask experiments. After depletion of the sugar, the cell suspension was separated into biomass and supernatant by centrifugation. The biomass was suspended in 50-mM phosphate buffer at pH 6 containing 0.25 g/L urea to yield an initial biomass concentration of 2 g/L, and the supernatant was supplemented with urea to give a concentration of 0.25 g/L. Both mixtures were then shaken with 250 rpm at 32°C. Sampling occurred at the beginning and after 24 h of incubation. The samples were analyzed regarding urea and ammonium. The optical density of cell suspensions was measured photometrically at 600 nm (after pre-dilution to OD <0.4 if required). The biomass dry weight was determined by separating the yeasts via centrifugation, washing the pellet twice, and drying at 103°C. Sugar was quantified by a modified 3,5-dinitrosalicylic-acid method [48] with lactose as a standard. Ammonium, nitrate, nitrite, sulfate, and phosphate were measured by the LCK303, LCK339, LCK342, LCK153, and LCK049 cuvette tests (Hach Lange GmbH, Düsseldorf, Germany). The total dissolved nitrogen was analyzed by the Kjeldahl method (German DIN 38409 H11). Ethanol was quantified by gas chromatography [10]. Urea was measured in the style of Rahmatullah and Boyde [49] with some modifications. This method had been approved for quantifying urea in wine [50] being a matrix similar to culture liquids. Two reagents were prepared: a mixture of 300 mL sulfuric acid (95% to 98%, ρ = 1,840 g/L), 100 mL phosphoric acid (85%, ρ = 1,670 g/L), and 100 mL water; and a solution of 500 mg butane-2,3-dione monoxime (diacetyl monoxime) and 10 mg thiosemicarbazide in 100 mL water. The analysis reagent was prepared from 40 mL acid mixture and 20 mL of the second solution and used immediately. A volume of 0.1 mL sample was mixed with 3 mL analysis reagent. In the case of colored samples, this mixture was measured photometrically at 525 nm as a blind. Then, the mixture was put in a 25-mL test tube with plastic cap and incubated for 20 min in boiling water. After cooling and short mixing, the absorbance was measured at 525 nm. The blind was subtracted, and the obtained ΔA525nm value was interpreted as a urea concentration by a non-linear calibration curve prepared for several solutions of urea in water (from 0 to 500 mg/L): C Urea,L = a · (ΔA525nm)b with a = 520 mg/L and b = 1.37. The O2 consumption, CO2 formation, and the respiratory quotient (RQ) were calculated as usual [11]. The time-dependent specific growth rate was calculated from masses of formed CO2 assuming a correlation between yeast growth and CO2 formation which only applies to respiratory processes without significant maintenance: μ(t) ≈ Δln(m CO2(t))/Δt. The overall biomass yield (Y X/S) is the ratio between the mass of yeasts grown and the mass of sugar consumed; determination of these masses took losses by sampling and changes of the liquid volume into account. The pH-controlled feeding of 2 M KOH is given as a specific volume, related to the initial liquid volume of the culture. The mass of fed KOH was related to the formed biomass (given as gKOH/gX). The fed 2 M ammonia solution is also expressed as a specific volume and as the mass of supplied ammonia-N. The mass of bioavailable nitrogen was calculated as the sum of initial ammonium-N and urea-N plus the mass of ammonia-N supplied till a given time: $ {m}_{\mathrm{N}}(t)={V}_{\mathrm{L}}\left({t}_0\right)\cdot \left({C}_{{\mathrm{N}\mathrm{H}}_4-\mathrm{N}}\left({t}_0\right)+{\mathrm{C}}_{\mathrm{Urea}\hbox{-} \mathrm{N}}\left({t}_0\right)\right)+{m}_{{\mathrm{N}\mathrm{H}}_4\mathrm{O}\mathrm{H}\hbox{-} \mathrm{N}}(t) $. The consumed nitrogen is this m N(t) value minus the nitrogen not yet used or lost by sampling: $ \Delta {m}_{\mathrm{N}}(t)\kern0.5em =\kern0.5em {m}_{\mathrm{N}}(t)\kern0.5em -\kern0.5em {V}_{\mathrm{L}}(t)\kern0.5em \cdot \left({C}_{{\mathrm{N}\mathrm{H}}_4\hbox{-} \mathrm{N}}(t)+{C}_{\mathrm{Urea}\hbox{-} \mathrm{N}}(t)\right)\kern0.5em -\kern0.5em \varSigma {m}_{\mathrm{N}}\left(\mathrm{sampling}\right) $. These Δm N(t) values were used for calculating biomass-specific consumption rates (r N as mgN/gX/h). The overall biomass yield for nitrogen (Y X/N) is the ratio between the mass of yeasts totally formed and the mass of N altogether consumed. The final N content of the biomass (x N) is the reciprocal of this overall Y X/N value. Nitrogen in non-supplemented DW medium The composition of whey depends on many factors such as origin of milk (cow, goat, or sheep), technology of curd production, and whey processing (e.g., [51,52]). Casein protein is coagulated by acidification (mineral or organic acids directly added or lactic acid produced in the processed milk by bacteria) and/or by using chymosin. Whey processing modifies the composition of whey as well: whey protein is separated by ultrafiltration, solutes are concentrated by reverse osmosis, and/or minerals are partially removed by alkalinization. Preparation of whey-borne culture media also changes the composition by dilution, adding supplements, and heat sterilization. This explains why published compositions of whey-borne media highly fluctuate. Several batches of non-supplemented DW medium were analyzed regarding potential sources of nitrogen and some other parameters (Table 1). The medium is rich in \sugar and thus exhibits a high potential for biomass growth. An amount of 78 g/L sugar allows formation of 28 g/L K. marxianus biomass assuming Y X/S = 0.36 g/g (as observed at aerobic cultivation in DW basic medium with trace elements [11]). These 28 g/L biomass can only develop when yeast growth is not limited by any other resource than sugar. K. marxianus DSM 5422 grown under such conditions exhibited the following content of minerals (in milligrams of the addressed element per gram dry biomass): x N = 78…79 mg/g [10,11], x P = 10 mg/g, x S = 4 mg/g, and x K = 2 mg/g (unpublished results). These data are similar to published compositions of K. marxianus [45,53-55] and Saccharomyces cerevisiae [40]. Multiplying these x values with the cell concentration of 28 g/L gives the required concentration of the respective element in the culture medium to allow non-limited growth: 2,200 mg/L N, 280 mg/L P, 112 mg/L S, and 56 mg/L K. Nitrogen and sulfur are lacking in non-supplemented DW medium while the phosphorous and potassium content covers the demand (Table 1). Table 1 Composition of non-supplemented DW medium DW medium owns 403 mg/L Kjeldahl-N (Table 1). Detailed analysis of five batches of non-supplemented DW medium gave 89 to 130 mg/L ammonium-N (106 mg/L on an average, σn−1 = 15 mg/L), 38.4 to 45.9 mg/L urea-N (43 mg/L on an average, σn−1 = 2.6 mg/L), 4 mg/L nitrate-N, and <1 mg/L nitrite-N. The Kjeldahl-N minus the urea-N and inorganic N gives a proteinogenic N of 250 mg/L which corresponds to ca. 1.5 g/L proteins (Table 1). Utilization of whey proteins by K. marxianus is discussed controversially. Raw cheese whey owns 7 g/L protein comprising 50% β-lactoglobulin, 20% α-lactalbumin, 15% glycomacropeptide, and 15% minor protein/peptide components [51]. Their microbial hydrolysis requires excretion of proteases. Decomposition of whey proteins by K. marxianus has been repeatedly studied; the results varied from absent hydrolysis [26], over 20% to 33% [28,29,56], up to 80% hydrolysis [33]. Recent studies confirmed an extracellular serine protease for K. marxianus [57], and Yadav et al. [28] proved modification of whey proteins by K. marxianus via electrophoresis. Indigenous proteases in milk [58] and the proteolytic activity of lactobacilli [56] could also contribute some to protein modification during milk processing. Pre-treatment of whey protein with added proteases resulted in peptides <1 kDa which were efficiently assimilated by K. marxianus [59]. Some yeasts and fungi assimilate nitrate by intracellular reduction to ammonium [60]. K. marxianus seems to be unable for nitrate assimilation; at least several tested strains were negative [61]. This explains why nitrate added to whey did not improve growth of K. marxianus [32]. Some growth of K. marxianus in NaNO3-supplemented medium was possibly caused by the added yeast extract [62]. K. marxianus DSM 5422 proved to be unable to assimilate nitrate. Due to the uncertainty of whey-protein assimilation by K. marxianus, it is assumed that whey proteins do not contribute to assimilable nitrogen. The utilizable nitrogen in non-supplemented DW medium of ca. 150 mg/L (ammonium-N plus urea-N) is thus much smaller than the calculated demand. Supplementation of DW medium with nitrogen is essentially required. K. marxianus DSM 5422 grows well with ammonium [10,11], but its growth with urea has not yet been tested. Yeasts generally assimilate urea [44] which should also apply to the studied strain. A low amount of iron, zinc, and copper in DW medium limits growth of K. marxianus DSM 5422 [11]. Here, the medium was ever supplemented with trace-element solution to avoid such limitation. Test of several sources of nitrogen without previous pH adjustment This preliminary test for assimilation of diverse sources of nitrogen by K. marxianus DSM 5422 was performed in shake flasks. Non-supplemented DW medium was spiked with several N sources (Table 2): no supplement as a reference, (NH4)2SO4 as the usual N supplement, (NH4)2CO3 as an alternative ammonium resource, and urea as another N compound. The DW medium contributed ca. 7 mg/L N (5 mg/L NH4-N and 2 mg/L urea-N) to the assimilable N in each culture. The initial pH value was influenced by the added N source: (NH4)2SO4 did not change the pH while urea and (NH4)2CO3 alkalinized the medium (Table 2). All shake flasks were inoculated and pre-cultivated for 14 h before the process was followed by repeated OD and pH measurements (Figure 1). Table 2 Parameters at aerobic growth of K. marxianus DSM 5422 in media with various sources of nitrogen without previous pH adjustment Aerobic batch cultivation of K. marxianus DSM 5422 without pH adjustment. Aerobic batch cultivation of K. marxianus DSM 5422 in media with various sources of nitrogen without previous pH adjustment. Concentrated and partially demineralized sweet whey was diluted with the same volume of water, supplemented with various sources of nitrogen, and autoclaved; the clear upper phase was supplemented with trace elements and diluted again with water resulting in media with 3.9 g/L sugar; the media were inoculated and cultivated in conical flasks at 250 rpm and 32°C. The process without a supplement was at first similar to the process with (NH4)2SO4 (Figure 1), but later, nitrogen became a limiting factor so that growth and medium acidification slowed down and nearly stopped after 24 h. The N-limited growth resulted in some residual sugar (Table 2). With a supplement of (NH4)2SO4, K. marxianus DSM 5422 grew at first with μ = 0.57 h−1 as usual in diluted DW medium [12,14], but then, the growth slowed down due to medium acidification (Figure 1). A pH <3.5 impairs growth of K. marxianus [28,42,43]. This acidification was caused by consumption of ammonium without an equivalent uptake of sulfate. The use of ammonium sulfate as an N source calls for buffered medium (in shake-flask experiments [12,14]) or for pH control (in bioreactor experiments [10,11,13,16,22]). The supplement of (NH4)2CO3 at first alkalinized the medium. The initial pH of 7.5 impacted growth of K. marxianus DSM 5422 and caused a highly retarded process (Figure 1). Vivier et al. [42] and Antoce et al. [43] found that a pH >7 is adverse for growth of K. marxianus. Continued growth gradually reduced the pH and accelerated yeast growth so that all sugar had been consumed after 40 h. Carbonate as an exchangeable anion can leave the medium in the form of carbon dioxide which counteracted acidification (medium with (NH4)2CO3) while sulfate as a permanent ion remains and resulted in unfavorable acidification (medium with (NH4)2SO4). The supplement of urea also alkalinized the medium to some degree (initial pH = 7.18) which is, at the first view, surprising since urea reacts neutral in aqueous solution. Autoclaving the medium together with urea maybe caused some hydrolysis of urea to form alkaline ammonium carbonate. This slight alkalinization slowed down yeast growth and retarded the process a little at the beginning, but the yeast metabolism lowered the pH so that the growth rate approached a normal value during pre-cultivation (Table 2). After 21 h, the medium acidification stopped and then the pH increased to a final pH of 7.1 (i.e., only temporary decrease in pH). Absence of enduring pH changes confirms the earlier postulated proton neutrality at growth with urea [38-40]. Test of several sources of nitrogen with previous pH adjustment The just-described shake-flask experiments were repeated with two modifications: all sources of nitrogen were autoclaved separately to eliminate unwanted interaction between the N sources and medium constituents, and the initial pH value was adjusted to 6.5 for avoiding alkaline conditions. The convenient initial pH of 6.5 produced a uniformly high specific growth rate of μ = 0.59 h−1 (Table 3) resulting in very similar cell densities at the beginning of the observation period (Figure 2A). This μ value was identical with the growth rate of K. marxianus DSM 5422 in highly diluted and phosphate-buffered DW basic medium [12,14]. Table 3 Parameters at aerobic growth of K. marxianus DSM 5422 in media with various sources of nitrogen with initial pH adjustment Aerobic batch cultivation of K. marxianus DSM 5422 with initial pH adjustment. Aerobic batch cultivation of K. marxianus DSM 5422 in media with various sources of nitrogen with initial pH adjustment. Non-supplemented DW medium was supplemented with various sources of nitrogen and trace elements, the pH was adjusted to 6.5 by HCl or KOH, and these media were diluted with water resulting in 3.9 g/L sugar; the media were inoculated and cultivated in conical flasks at 250 rpm and 32°C. The culture without a supplement of nitrogen exhibited N-limited growth (Figure 2A), only moderate acidification owing to restricted growth (Figure 2B), a low biomass formation, and some residual sugar after 40 h of cultivation (Table 3). Supplementation with (NH4)2SO4 or (NH4)2CO3 resulted in a nearly identical growth behavior and similar final pH values and biomass yields (Table 2); the pH was suboptimal in both cases which caused impaired growth compared to the process in phosphate-buffered medium [12,14]. A reduced biomass yield for K. marxianus in whey at a low pH has also been described by Yadav et al. [28] and interpreted as diversion of lactose from anabolism (growth) toward catabolism (maintenance). The use of (NH4)2CO3 instead of (NH4)2SO4 was without advantage since the initial pH adjustment of (NH4)2CO3-supplemented medium with hydrochloric acid caused substitution of exchangeable by permanent ions (carbonate replaced by chloride). (NH4)2CO3 is thus not a useful alternative since a high initial pH inhibits yeast growth while preceding pH adjustment with acids eliminates the buffering effect of carbonate. Separate autoclaving of the N source and initial pH adjustment caused good growth in the urea-supplemented medium from the beginning; then, the growth became somewhat retarded (at 18 to 22 h; Figure 2A), but afterward, the growth accelerated again (at t >22 h) and even exceeded growth with (NH4)2SO4 (Table 3). Quick growth in the first period was possibly based on whey-borne ammonium while the temporal slowdown of growth in the second period perhaps came about through the adaptation of yeast metabolism to urea assimilation after NH4-N depletion. The quite high biomass yield with urea is certainly attributed to an appropriate pH value over the whole growth period (compare [39,62]). Urea is thus a promising source of nitrogen for K. marxianus. The acidification with urea was only of temporal nature; the pH increased again to give a final value being nearly identical with the initial pH (due to proton neutrality at assimilation of urea [38-40]). Assimilation of urea by K. marxianus DSM 5422 Ammonium is utilized by all common yeasts directly while urea is either hydrolyzed by urease to form ammonium or it is assimilated via the urea amydolyase pathway [25,38]. Urease acts extracellularly while the amydolyase pathway works intracellularly. K. marxianus is regarded as a urease-negative yeast [40] and should metabolize urea only in the latter way being a two-step process [44,60,63]; urea reacts with hydrocarbonate in an energy-consuming process to form allophanate which, in turn, is hydrolyzed to release ammonium: $$ \begin{array}{l}{\mathrm{NH}}_2\hbox{-} \kern0.1em \mathrm{C}\mathrm{O}\kern0.1em \hbox{-} \kern0.1em {\mathrm{NH}}_2+\kern0.5em {{\mathrm{H}\mathrm{C}\mathrm{O}}_3}^{\hbox{--} }+\mathrm{A}\mathrm{T}\mathrm{P}\kern5em \to \kern5em {\mathrm{NH}}_2\hbox{-} \kern0.1em \mathrm{C}\mathrm{O}\kern0.1em \hbox{-} \kern0.1em \mathrm{N}\mathrm{H}\kern0.1em \hbox{-} \kern0.1em {\mathrm{COO}}^{\hbox{--}}\kern0.5em +\\ {}{\mathrm{H}}_2\mathrm{O}+\mathrm{A}\mathrm{D}\mathrm{P}+{\mathrm{P}}_{\mathrm{i}}\end{array} $$ $$ {\mathrm{NH}}_2\kern0.1em \hbox{-} \kern0.1em \mathrm{C}\mathrm{O}\kern0.1em \hbox{-} \kern0.1em \mathrm{N}\mathrm{H}\kern0.1em \hbox{-} \kern0.1em {\mathrm{COO}}^{\hbox{--}}\kern0.5em +\kern0.5em 3\kern0.3em {\mathrm{H}}_2\mathrm{O}+{\mathrm{H}}^{+}\kern3.5em \to \kern5em 2\kern0.3em {\mathrm{NH}}_4^{+}+{{2\kern0.3em \mathrm{H}\mathrm{C}\mathrm{O}}_3}^{\hbox{--} } $$ These two reactions are catalyzed by urea carboxylase and allophanate hydrolase [44,60,63]. The produced ammonium is then metabolized in the same manner as ammonium taken up directly. An experiment was done for clarifying the way of urea assimilation in K. marxianus DSM 5422. The yeast was cultivated in diluted DW medium with urea, and the obtained culture was then used in an above-described test. K. marxianus DSM 5422 did not excrete urease into the medium since urea added to the cell-free aqueous fraction of this culture was not hydrolyzed at all. This is in accordance with Nahvi and Moeini [61] who found all tested K. marxianus and K. lactis strains being urease negative. These findings argue for assimilation of urea via the amydolyase pathway. The grown yeast biomass was incubated with urea in a phosphate buffer but only a bit urea was reacted to ammonium (average reaction rate 0.25 mg urea/gX/h). Absent sugar obviously suppressed transfer of urea into ammonium which refers to an amydolyase pathway being under transcriptive control. Bioreactor cultivation with the addition of urea The shake-flask experiments clearly demonstrated the capability of K. marxianus DSM 5422 for urea assimilation. Urea is a promising source of nitrogen due to the proton neutrality at its consumption during yeast growth [38-40], avoiding strong acidification as happening at growth with (NH4)2SO4. Urea has been repeatedly used at growth of K. marxianus, but the obtained results were inconsistent [28,31,41,47,62]. Hensing et al. [39] referred to the potential risk of an imbalance between release and assimilation of ammonium; the medium could alkalinize when ammonium is quicker released from urea than is incorporated into biomass. Such an alkalinization was observed during cultivation of K. marxianus in urea-supplemented whey [47]. In the above-described experiments, the pH temporally decreased rather than increased. This phenomenon has not yet been understood and requires clarification in a bioreactor experiment. K. marxianus DSM 5422 was cultivated in a stirred reactor at well-defined conditions (32°C, pO2 ≥30% air saturation, pH ≥5) in DW medium which was supplemented with urea, Na2SO4, and trace-element solution to avoid limitation of growth by nitrogen, sulfur or microelements. Another bioreactor experiment performed with DW medium containing 10 g/L (NH4)2SO4 and trace elements was taken from [11] and used here as a reference. These two processes are depicted in Figure 3, and characteristic parameters are summarized in Table 4. Aerobic batch cultivation of K. marxianus DSM 5422 in stirred bioreactors using ammonium or urea. Aerobic batch cultivation of K. marxianus DSM 5422 in a stirred bioreactor using ammonium (white symbols) or urea (grey symbols) as a source of nitrogen. DW medium with 2 mL/L trace-element solution was supplemented with (NH4)2SO4 or urea plus Na2SO4 (white symbols = 10 g/L (NH4)2SO4; grey symbols = 5 g/L urea and 0.4 g/L Na2SO4); the cultivation occurred in an 1-L stirred reactor at 1,200 rpm, 32°C, and aeration with 50 L/h; the pH was controlled to ≥5 with 2 M KOH; the given growth rate was derived from measured CO2 data. Table 4 Parameters at aerobic growth of K. marxianus DSM 5422 in media with various sources of nitrogen in a stirred bioreactor The courses of yeast growth, sugar consumption, and marginal ethanol formation were very similar for (NH4)2SO4 or urea as the added N sources (Figure 3A). The only marked difference was the amount of formed biomass which was apparently higher with urea (Table 4). This observation is in accordance with Hensing et al. [39] and Rajoka et al. [62]. From the energetic point of view, growth with urea should be less effective compared to growth with ammonium since assimilation of urea via the amydolyase pathway requires ATP [44,60,63]. Cultivation with urea should therefore result in a lower rather than a higher biomass yield. In case of Hensing et al. [39] and Rajoka et al. [62], the observed low growth with ammonium was possibly caused by inhibitory acidification due to absent pH control at shake-flask cultivation. Such an inhibitory acidification was prevented by controlling the pH during bioreactor cultivation (Figure 3B); here, the diverging biomass yields were presumably caused by slightly different amounts of bioavailable nitrogen (1.49 g N in medium with 5 g/L urea, and 1.30 g N in medium with 10 g/L (NH4)2SO4). Nearly all bioavailable nitrogen was assimilated in both processes (only 20 or 30 mg/L residual NH4-N in the culture broth; Table 4) which refers to a slight deficit of nitrogen, and this deficit was more striking with (NH4)2SO4. This argumentation is supported by a higher N content in the biomass grown with urea (Table 4). In urea-supplemented medium, K. marxianus DSM 5422 grew at first quickly; but later, the growth slowed down more and more (Figure 3D), although sufficient O, N, P, S, K, and trace elements should allow non-limited growth over an extended period. This behavior could be explained with a lack of vitamins in whey [27,29] or with inhibition by whey-borne minerals [31]. Supplementing whey with yeast extract [27,29] or vitamins [29,32,47] stimulated the growth of K. marxianus. The source of nitrogen distinctly influenced the pH(t) course (Figure 3B). With (NH4)2SO4, the pH decreased due to ammonium consumption until the pH was controlled to pH 5; 82 mL/L 2 M KOH were supplied which corresponds to a specific dosage of 0.34 g KOH per g of produced biomass. The strong acidification with (NH4)2SO4 is explained by a proton imbalance [38-40]: ammonium was consumed while most of the sulfate remained in the medium. With urea, the pH at first a little decreased, then sharply rose to pH 6.8 and reduced again to pH 5 where the pH controller avoided further acidification; the KOH dosage was in fact much smaller (only 10 mL/L 2 M KOH or 0.04 g KOH per g of produced biomass; Table 4). Hensing et al. [39] cultivated K. lactis in galactose medium with (NH4)2SO4 or urea; the acidification was strong and permanent with (NH4)2SO4, while the acidification was moderate and only temporary with urea. During cultivation of K. marxianus DSM 5422 in urea-supplemented DW medium, the dissolved ammonium-N and urea-N were repeatedly measured and used for calculating the N consumption (Figure 3C). Intracellular conversion of urea to ammonium and usage of this ammonium for biomass growth occurred with nearly the same rate since ammonium excretion was only marginal (some NH4-N originated from the used whey). The N consumption correlated well with the yeast growth (compare Figure 3A and C) and, thus, the courses of the N consumption rate and the specific growth rate were similar (Figure 3D). The quotient of these rates represents a momentary Y X/N value. The small transient NH4-N accumulation (Figure 3C) partially correlated with the temporary increase in pH. Hensing et al. [39] already referred to the danger of alkalinization when ammonium release exceeds ammonium assimilation. Such an alkalization to pH 8.5 was observed by Rech et al. [47] at cultivation of K. marxianus in urea-supplemented whey causing severe growth inhibition. Here, such an inhibition did not occur (only moderate rise of pH to 6.8). Bioreactor cultivation at a pH-controlled feed of ammonia Feeding the required nitrogen in form of ammonia could be a cost-saving alternative. Ammonia was repeatedly used as an N source at cultivation of K. marxianus in whey or other media [34,64-67] but dissolved ammonium or N consumption has not been paid much attention, with exception of Hack and Marchant [65] who depicted the time-dependent supply of ammonia. In another series of bioreactor experiments, K. marxianus DSM 5422 was cultivated in DW medium as before but 2 M NH4OH was used as the predominating N source which was supplied by the pH controller at pH <5. Three experiments were performed with a varied mass of (NH4)2SO4 which was added as a pure substance to the autoclaved DW medium (0, 0.6, or 1.2 g). These processes were limited neither by oxygen (pO2 always >10%) nor by sulfur (proven by residual sulfate). In DW medium without an (NH4)2SO4 supplement (Figure 4; white symbols), K. marxianus DSM 5422 grew on whey-borne nitrogen (0.13 g/L NH4-N and 0.04 g/L urea-N), but this nitrogen was quickly depleted (Figure 4C) and the growth became N limited (Figure 4A). The pH temporally rose (Figure 4B) which seemingly correlated with urea consumption (Figure 4C). After depletion of all bioavailable N, the pH decreased only slowly due to a low metabolic activity (look at the sugar concentration in Figure 4A). Later, the pH stagnated above pH 5 and ammonia was thus not dosed (Figure 4B). The low availability of nitrogen (Figure 4D) caused restricted yeast growth (Figure 4A). The total N consumption and the N consumption rate were accordingly low (Figure 4E,F). Aerobic batch cultivation of K. marxianus DSM 5422 in stirred bioreactors using (NH 4 ) 2 SO 4 and NH 4 OH. Aerobic batch cultivation of K. marxianus DSM 5422 in a stirred bioreactor using various amounts of (NH4)2SO4 and NH4OH as sources of nitrogen. DW medium with 2 mL/L trace-element solution was supplemented with (NH4)2SO4 or Na2SO4 (white symbols = 0.4 g/L Na2SO4; grey symbols = 1 g/L (NH4)2SO4; black symbols = 2 g/L (NH4)2SO4); the cultivation occurred in an 1-L stirred reactor at 1,200 rpm, 32°C, and aeration with 50 L/h; the pH was controlled to ≥5 with 2 M NH4OH; the given growth rates were derived from measured CO2 data. A supplement of 1 g/L (NH4)2SO4 in the second experiment (Figure 4; grey symbols) increased the bioavailable N (Figure 4D) and allowed better yeast growth due to the higher initial NH4-N which let the pH quickly decrease (Figure 4B). After depletion of this nitrogen, the pH stagnated at 5.05 for a while and then dropped below 5 where the pH controller started dosage of ammonia (Figure 4B). The added ammonia was assimilated immediately, and no ammonium accumulated in the medium (Figure 4C). That is, the yeast growth continued but at N-limited conditions as becoming visible from the low rates of ammonia dosage and N consumption (Figure 4D,F). This deficit of nitrogen slowed down growth and diminished the formed biomass (Figure 4A, Table 4). In the stationary period, some ammonium was released into the medium (Figure 4C) which was also observed by Ghaly and Kamal [26] at the cultivation of K. marxianus in whey and interpreted as decomposition of yeast biomass with release of NH4-N into the medium. A supplement of 2 g/L (NH4)2SO4 in the third experiment (Figure 4; black symbols) increased the bioavailable N most (Figure 4D) and resulted in fast yeast growth and quick acidification. The feed of ammonia at pH <5 started before the initially added NH4-N had been depleted (Figure 4C). The early start of ammonia dosage prevented limitation of yeast growth by nitrogen (NH4-N always >100 mg/L), and the supply and uptake of nitrogen were well balanced (Figure 4C). The high rate of ammonia dosage corresponded with an accordingly fast growth and intensive N consumption (Figure 4D,E). The rate of N consumption became gradually smaller which is explained by the gently declining growth rate (possible reasons for this fading growth were discussed above). Urea was assimilated co-metabolically with the ammonium (Figure 4C). The process with a supplement of 2 g/L (NH4)2SO4 and ammonia dosage ran very similar to the process with 10 g/L (NH4)2SO4; the final cell concentrations, formed biomasses, and the overall Y X/S values were nearly identical in both processes (Table 4) which demonstrates effective cultivation of K. marxianus with a pH-controlled feed of ammonia. Supplementing the medium with some (NH4)2SO4 was however required for a quick acidification and for initiation of ammonia dosage. The amount of added (NH4)2SO4 could be reduced by changing the setpoint of the pH controller (e.g., to pH 5.5) so that dosage of ammonia starts earlier and avoids N-limited conditions even at a reduced (NH4)2SO4 supplement, but some (NH4)2SO4 is needed to cover the requirement for sulfur. Nitrogen in biomass The content of nitrogen in biomass grown at cultivation in the stirred bioreactor (Figures 3 and 4) is the inverse of the overall biomass yield for nitrogen: x N = 1/Y X/N. The overall Y X/N values were calculated from the produced biomass and the consumed nitrogen, assuming that only ammonium and urea were assimilated (Table 4). This calculation ignores that K. marxianus possibly hydrolyzes some whey-borne proteins and assimilates thus-formed peptides and amino acids. The N content of biomass depended on the extent of N limitation (Table 4): cultivation with enough nitrogen (process with 5 g/L urea and process with 2 g/L (NH4)2SO4 plus dosed ammonia) gave x N values of 81 and 83 mg/g, a slight deficit of nitrogen during the late growth stage (process with 10 g/L (NH4)2SO4) resulted in x N = 76 mg/g, distinct N limitation (process with 1 g/L (NH4)2SO4 plus ammonia) yielded x N = 67 mg/g, while severe N limitation (process without any N supplement) produced an x N value of only 24 mg/g. A diminished N content of K. marxianus was also observed at limitation of growth by trace elements [10,11]. A decreased N content can be explained by a lowered portion of active biomass owing to intracellular storage of polysaccharides (details in [10,11]). The N content can also be derived from the elemental composition of biomass. Several authors measured the cell composition for K. marxianus by elemental analyzers and transformed these data into biomass formulae: CH1.78O0.75 N0.16 [45], CH1.776O0.575 N0.159 [53], CH1.63O0.54 N0.16 [54], CH1.94O0.76 N0.17 [55]. These formulae represent an N content of 88, 80, 91, or 83 mg/g. The fluctuations originate from measuring errors and from a variable cell composition depending on growth conditions [68]. Stoichiometry of yeast growth Stoichiometric equations for describing the growth of K. marxianus has been derived here by using the method of Hensing et al. [39] and Mazutti et al. [69]. Such balancing requires a sum formula for biomass. The above-given formulae for K. marxianus biomass are restricted to C, H, O, and N as the predominating elements (derived from elemental analyses [45,53-55]). Here, the elements P, S, and K are included for more precision. The C, H, and O content was taken from the above-given biomass formulae (as averages), the N content of 82 mg/g was taken from own measurements at non-limited yeast growth, and the P, S, and K content was assumed with 10, 4, and 2 mg/g (own assimilation measurements). Combination of these data gives CH1.78O0.66 N0.158P0.009S0.0035K0.0015 (yielding a molar mass of 27.027 g/mol). Individual stoichiometric balance equations were derived for ammonium, urea, or ammonia as an N source, assuming respiratory growth (without formation of ethanol or ethyl acetate) of K. marxianus DSM 5422 with lactose as a substrate. The included stoichiometry coefficients were determined by balancing each element: seven balance equations were obtained containing nine unknown stoichiometric coefficients. This uncertain algebraic system was dissolved following Hensing et al. [39] by adding a proton balance and introducing the yield coefficient (Y X/S informs about the relation of assimilatory to dissimilatory substrate utilization and allows to establish the mass ratio between formed biomass and consumed lactose). Y X/S = 0.36 g/g was used here uniformly for all balances as found at non-limited growth with ammonium or ammonia (Table 4). Phosphate and sulfate were consumed in form of HPO4 2− and SO4 2− at the prevailing pH. Three equations were obtained for ammonium, ammonium hydroxide, or urea as an N source: $$ \begin{array}{l}{\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}+\kern0.5em 0.0410\kern0.5em {\mathrm{H}\mathrm{PO}}_4^{2\hbox{-} }+\kern0.5em 0.0160\kern0.5em {\mathrm{S}\mathrm{O}}_4^{2\hbox{-} }+\kern0.5em 0.0068{\mathrm{K}}^{+}+\kern0.5em 7.3790\kern0.5em {\mathrm{O}}_2+\kern0.5em 0.7205\kern0.5em {\mathrm{N}\mathrm{H}}_4^{+}\kern1em \to \\ {}\kern2.5em 4.5600\kern0.5em {\mathrm{C}\mathrm{H}}_{1.78}{\mathrm{O}}_{0.66}{\mathrm{N}}_{0.158}{\mathrm{P}}_{0.009}{\mathrm{S}}_{0.0035}{\mathrm{K}}_{0.0015}+\kern0.5em 7.4400\kern0.5em {\mathrm{C}\mathrm{O}}_2+\kern0.5em 8.0963\kern0.5em {\mathrm{H}}_2\mathrm{O}\kern0.5em +\kern0.5em 0.6133{\mathrm{H}}^{+}\end{array} $$ $$ \begin{array}{l}{\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}+\kern0.5em 0.0410\kern0.5em {\mathrm{H}\mathrm{PO}}_4^{2\hbox{-} }+\kern0.5em 0.0160\kern0.5em {\mathrm{S}\mathrm{O}}_4^{2\hbox{-} }+\kern0.5em 0.0068{\mathrm{K}}^{+}+\kern0.5em 7.3790\kern0.5em {\mathrm{O}}_2+\kern0.5em 0.7205\kern0.5em {\mathrm{N}\mathrm{H}}_4\mathrm{O}\mathrm{H}\kern1em \to \\ {}\kern2.5em 4.5600\kern0.5em {\mathrm{C}\mathrm{H}}_{1.78}{\mathrm{O}}_{0.66}{\mathrm{N}}_{0.158}{\mathrm{P}}_{0.009}{\mathrm{S}}_{0.0035}{\mathrm{K}}_{0.0015}+\kern0.5em 7.4400\kern0.5em {\mathrm{C}\mathrm{O}}_2+\kern0.5em 8.7095\kern0.5em {\mathrm{H}}_2\mathrm{O}\kern0.5em +\kern0.5em 0.1072\kern0.5em {\mathrm{O}\mathrm{H}}^{\hbox{-}}\end{array} $$ $$ \begin{array}{l}{\mathrm{C}}_{12}{\mathrm{H}}_{22}{\mathrm{O}}_{11}+\kern0.5em 0.0410\kern0.5em {\mathrm{H}\mathrm{PO}}_4^{2\hbox{-} }+\kern0.5em 0.0160\kern0.5em {\mathrm{S}\mathrm{O}}_4^{2\hbox{-} }+\kern0.5em 0.0068{\mathrm{K}}^{+}+\kern0.5em 7.9189\kern0.5em {\mathrm{O}}_2+\kern0.5em 0.7205\kern0.5em {\mathrm{N}\mathrm{H}}_2{\mathrm{C}\mathrm{O}\mathrm{NH}}_2\kern1em \to \\ {}\kern2.5em 4.5600\kern0.5em {\mathrm{C}\mathrm{H}}_{1.78}{\mathrm{O}}_{0.66}{\mathrm{N}}_{0.158}{\mathrm{P}}_{0.009}{\mathrm{S}}_{0.0035}{\mathrm{K}}_{0.0015}+\kern0.5em 8.1600\kern0.5em {\mathrm{C}\mathrm{O}}_2+\kern0.5em 8.3495\kern0.5em {\mathrm{H}}_2\mathrm{O}\kern0.5em +\kern0.5em 0.1072\kern0.5em {\mathrm{O}\mathrm{H}}^{\hbox{-}}\end{array} $$ Protons are only formed during growth with ammonium which explains the observed substantial consumption of KOH by the pH controller with ammonium sulfate; the proton release equates to 0.28 g consumed KOH per g grown biomass and hence somewhat deviates from the measured KOH consumption (0.34 gKOH/gX). With NH4OH or urea (Equations 4 and 5), the balances predict a slight alkalinization since OH− ions are formed. The consumption of some KOH with urea as an N source is contradictory to this finding, but it should be kept in mind that the final pH was higher than the initial pH (Figure 3B); synthesis of organic acids (acetate, pyruvate, 2-oxoglutarate, and succinate were by-products of aerobic sugar metabolism of K. marxianus [16,68,70,71]) presumably caused KOH consumption, and consumption of these acidic metabolites after depletion of sugar alkalinized the medium. But such temporary metabolite accumulation was not considered at balancing. Another interfering effect originates from whey-borne lactate (ca. 4 g/L in DW medium [10]) whose microbial utilization also causes some alkalinization. The balance equations allow to compare calculated with measured masses of consumed oxygen and formed carbon dioxide. The expected masses were calculated from the masses of utilized sugar. The measured masses (Table 4) were 1% to 20% smaller than predicted for unknown reason, but the ratio between formed CO2 and consumed oxygen (the average RQ values) was ca. 1.02 mol/mol (Table 4) and agreed well with the predicted values (1.01 to 1.03 mol/mol). Whey is poor in nitrogen and requires supplementation with an N source for effective production of yeast biomass. Ammonium sulfate, as usually applied for this reason, causes medium acidification by residual sulfate which requires pH control by alkaline substances to avoid growth inhibition. Application of ammonium carbonate instead of ammonium sulfate is not helpful since added (NH4)2CO3 elevates the pH to inhibitory levels. K. marxianus DSM 5422 assimilates urea as an alternative N source. Consumption of urea means proton neutrality, medium acidification is minor, and only a little pH corrective is required. Moreover, the use of urea reduces the salt load (less inhibition, diminished environmental impact). 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This publication is dedicated to Prof. Dr. Andreas Zehnsdorf on the occasion of his 50th birthday. Institute of Food Technology and Bioprocess Engineering, TU Dresden, 01062, Dresden, Germany Christian Löser, Thanet Urit, Erik Gruner & Thomas Bley Department of Biology and Biotechnology, Faculty of Science and Technology, Nakhon Sawan Rajabhat University, 60000, Nakhon Sawan, Thailand Thanet Urit Christian Löser Erik Gruner Thomas Bley Correspondence to Christian Löser. CL and TU conceived of the study. EG, CL, and TU explored relevant literature. CL and TU designed the experiments. EG and TU conducted the experiments. CL performed data analysis. CL and TB drafted the manuscript. All authors read and approved the final manuscript. Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (https://creativecommons.org/licenses/by/4.0), which permits use, duplication, adaptation, distribution, and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. Löser, C., Urit, T., Gruner, E. et al. Efficient growth of Kluyveromyces marxianus biomass used as a biocatalyst in the sustainable production of ethyl acetate. Energ Sustain Soc 5, 2 (2015). https://doi.org/10.1186/s13705-014-0028-2 Kluyveromyces marxianus Andreas Zehnsdorf @ 50: A tribute	CommonCrawl
From conservative to dissipative non-linear differential systems. An application to the cardio-respiratory regulation Bifurcation and stability analysis for a nutrient-phytoplankton model with toxic effects A priori estimates for elliptic problems via Liouville type theorems Laura Baldelli 1, and Roberta Filippucci 2,, Department of Mathematics, University of Firenze, viale Morgagni 40-44, 50134 Firenze, Italy Department of Mathematics, University of Perugia, via Vanvitelli 1, 06123 Perugia, Italy * Corresponding author: Roberta Filippucci Dedicated to Professor Patrizia Pucci on the occasion of her 65th birthday, with deep gratitude, esteem and affection Received November 2018 Revised November 2018 Published November 2019 In this paper we prove a priori estimates for positive solutions of elliptic equations of the $ p $-Laplacian type on arbitrary domains of $ \mathbb {R}^N $, when a nonlinearity depending on the gradient is considered. Also the case of systems with very general nonlinearities is considered. Our main theorems extend previous results by Polacik, Quitter and Souplet in [26] in which either the case $ p = 2 $ with a nonlinearity depending on the gradient or the $ p $-Laplacian case with a nonlinearity not depending on the gradient is treated. The technique is based on the use of a method developed in [26] whose main tools are rescaling arguments combined with a key "doubling" property, which is different from the celebrated blow up technique due to Gidas and Spruck in [16]. A discussion on the sharpness of the main result in the scalar case is presented. Keywords: A priori estimates, elliptic problems, $ p $-$ q $-Laplacian systems. Mathematics Subject Classification: Primary: 35J92, 35J70; Secondary: 35J47. Citation: Laura Baldelli, Roberta Filippucci. A priori estimates for elliptic problems via Liouville type theorems. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020148 C. 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The Leap Blog Law \| Economics \| Policy Search interesting materials Can India leapfrog into decentralised energy? by Ajay Shah. India woke up to telecommunications through the reforms of the late 1990s: the power of DOT was curtailed, VSNL was privatised, private and foreign companies were permitted, new methods of working were permitted. At the time, wired lines were mainstream and wireless communications was novel. However, setting up wire lines in India is very hard. India leapfrogged, and jumped into the mobile revolution for both voice and data. The concept of not having a land line at home was exotic in the US when it was normal in India. In similar fashion, India was an early adopter of electronic order matching for financial trading, and of second generation pension reforms: these things became mainstream in the world after they were done in India. Could similar leapfrogging take place in the field of electricity? An important milestone in this story will come about with the announcement by Tesla Motors on Thursday the 30th of April, 2015. The problem of electricity, worldwide Electricity consumption fluctuates quite a bit within the day. More electricity is purchased when establishments are open (i.e. daytime), when it's too hot or too cold, and when humans are awake in the dark. The electricity system has to adjust its production to ensure that instantaneous consumption equals instantaneous generation. If producers are inflexible and consumers are inflexible then generation will not equal consumption. The puzzle lies in creating mechanisms through which both sides adjust to the problems of the other in a way that minimises costs at a system level. For producers, it is not easy to continually modify production to cater to changing demand. The two most important technologies -- coal and nuclear -- are most efficient in large scale plants which run round the clock. It may take as much as a day to switch off, or switch on, a plant. These plants are used to produce the `base load': the amount of electricity that is required in the deep of the night. Other technologies and modified plant designs are required to achieve flexibility of production within the day. This flexibility comes at a cost. Suppose the lowest demand of the day is $L$ and the highest is $H$. For the electricity system as a whole, a given level of average production is costlier when $H/L$ is higher. The cheapest electricity system is one where $H/L=1$; this runs base load all the time. Matters have been made more complicated by renewables. Solar energy is only available when it's light, while peak demand of the day is generally in the late evening. Electricity generation from windmills is variable. Further, the planning and despatch management of the grid is made complicated when there is small scale production taking place at thousands of locations, as opposed to the few big generation plants of the old days. There are thus a large number of decisions: how to produce, how much to produce and when, how much to consume and when. Economic efficiency is achieved by putting a market in between buyers and sellers, where the price of spot electricity continuously fluctuates. The electricity industry, organised around this price, becomes a self-organising system where a large number of players make uncoordinated decisions about how much and when to consume, how to produce, and how much and when to produce. The price in this market is the summary statistic of `the problem of electricity, worldwide' as articulated above. Here's an example (source) of the key patterns, from PJM Interconnect, the biggest power market of the world: Figure 1: Demand and price of electricity at the PJM Interconnection The orange line shows consumption. This was lowest on Saturday night at around 70 GW. It peaked in the evening of Thursday at around 160 GW. This was $H/L> 2$! This gave huge fluctuations in the price, which is the blue line in the graph above. Base load production has no flexibility and was probably configured at 70 GW. When demand was 70 GW, the price was near zero, given the inelasticity of base load production. The price went all the way up to 450 \$/MWh at the Thursday peak. From the viewpoint of both consumers and producers, these massive price fluctuations beg the question: How can we do things differently in order to fare better? The question for consumers is: How can purchase of electricity from the grid be moved from peak time to off-peak time? The question for producers is: How can more production be achieved at peak time? Unique features in India All this is true of electricity worldwide. Turning to India, there are two key differences. The first issue is that ubiquitous and reliable electricity from the grid has not been achieved. The mains power supply in India is unreliable. The euphemism `intermittent supply' is used in describing the electricity supplied by the grid in India. Households and firms are incurring significant expenses in dealing with intermittent supply (example). Intermittent power imposes costs including batteries, inverters, down time, burned out equipment, diesel generators, diesel, etc. Diesel generation seems to come at a cost of \$0.45/kWh. When power can be purchased from the grid, it isn't cheap, as a few buyers are cross-subsidising many others. In large parts of India, the grid has just not been built out. There are numerous places where it would be very costly to scale out the conventional grid. There are places in India where calculations show that a large diesel generator in a village has strengths over the centralised system. There are small towns in Uttar Pradesh where private persons have illegally installed large generators and are selling electricity through the (non-functioning) grid, in connivance with the local utility staff. Global discussions of energy systems talk about base load and peak load. In India, the existing generation capacity is not adequate even at base load! The apparent $H/L$ in the data is wrong; demand at the peak is much greater than $H$ -- we just get power cuts. Every little addition to capacity helps. There has been a large scale policy failure on the main energy system. Perhaps more decentralised solutions can help solve problems by being more immune to the mistakes of policy makers. The second interesting difference is high insolation with high predictability of sunlight. India is much better off when compared with countries in the temperate zone. Arunachal Pradesh and Sikkim get more sunlight than Scotland. Innovations in renewables Substantial technological progress is taking place in wind and in solar photovoltaics (SPV). Wind energy is enjoying incremental gains through maturation of engineering, and also the gains from real time reconfiguration of systems using cheap CPUs and statistical analysis of historical data from sensors. The price of crystalline silicon PV cells has dropped from \$77/watt in 1977 to \$0.77/watt in 2013: this is a decline at 13% per year, or a halving each 5 years, for 36 years. This is giving a huge surge in installed capacity (albeit a highly subsidised surge in most places). For decades, renewables have been a part of science fiction. Now, for the first time, massive scale renewable generation has started happening. The present pace of installation is, indeed, the child of subsidy programs, but the calculations now yield reasonable values even without subsidies. If and when the world gets going with some kind of carbon taxation, that will generate a new government-induced push in favour of renewables, which could replace the existing subsidies in terms of reshaping incentives. Innovations in storage Electricity generation using renewables is variable (wind) or peaks at the wrong times (solar). In addition, wind and solar production is naturally distributed; it is not amenable to a single 100 acre facility that makes 2000 MW. These problems hamper the use of renewables in the traditional centralised grid architecture. These problems would be solved if only we could have distributed storage. What would a world with low cost storage look like? Imagine a group of houses who put PV on their roofs and run one or two small windmills. Imagine that these sources feed a local storage system. The renewable generation would take place all through the day. When electricity prices on the grid are at their intra-day peak, electricity would be drawn from the storage system. For the centralised system, the cost of delivering electricity at a certain $(x,y,t)$ can be quite high: perhaps households at certain $(x,y,t)$ can sell electricity back to the grid. This is the best of all worlds for everyone. The grid would get a reduced $H/L$ ratio and would be able to do what the grid does best -- highly efficient large-scale base load technologies. The grid would be able to deliver electricity to remote customers at lower cost. Consumers would be better off, as payments for expensive peak load electricity would be reduced. This scenario requires low cost storage. For many years, we were stuck on the problem of storage. In recent years, important breakthroughs have come in scaling up lithium-ion batteries, which were traditionally very expensive and only used in portable electronics. Lithium Ion batteries have 2.3 times the storage per unit volume, and 3.1 times the storage per unit mass, when compared with the lead acid batteries being used with inverters in India today. Tesla Motors is an American car company. They have established a very large scale contract with Panasonic to buy Lithium Ion batteries. Nobody quite knows, but their internal cost for Lithium Ion batteries is estimated to be between \$200/kWh and \$400/kWh. On Thursday (30 April 2015), they are likely to announce a 10 kWh battery for use in homes. It's cost is likely to between \$2000 and \$4000 for the battery part, yielding a somewhat higher price as there will also be a non-battery part. (It is not yet certain that the part they announce will be 10 kWh. There are many stories which suggest this will cost \$13,000, which are likely to be wrong). A 10 kWh battery can run for 10 hours at a load of 1000 Watts. Note that Tesla is only pushing innovations in manufacturing; they are not improving battery technology. Many others are on the chase for better battery technology. Stupendous progress has happened with batteries in the last 20 years. Only two years ago, this price/performance was quite out of reach. It is a whole new game, to get a Lithium-Ion battery at between \$200 to \$400 per kWh. Suddenly, all sorts of design possibilities open up. Further, this is only the beginning. Experts in this field in the US believe that when Lithium Ion batteries are below \$150/kWh, they will be fully ready for applications in the electricity industry in the US. These experts believe this number will be reached in 5 to 10 years. The rise of storage links up to the rise of electric cars in two ways. First, electric cars are driving up demand for lithium-ion batteries and giving economies of scale in that industry. Second, a home which has an electric car has that battery! The present technology in electric cars -- Tesla's Model S -- has a 85 kWh battery, which is good capacity when compared with the requirements of a home. Renewables have generated excitement among science geeks for a long time, but have disappointed in terms of their real world impact. Scientific progress in renewables, and in batteries, are coming together to the point of real world impact. Storage is one method for coping with the intermittent generation from renewables. The other method is to make demand more flexible. As an example, a smart water heater or a smart air conditioner could do more when electricity is cheap, and vice versa. This would make consumption more price elastic. Leapfrogging in India? The Indian environment with expensive and intermittent electricity from the grid is an ideal environment for renewables + batteries. Distributed generation and distributed storage are seen as ambitious cutting edge technology in (say) Germany. Perhaps the natural use case for this is in India. In Germany, the grid works -- there is no problem with achieving high availability. In Germany, there isn't that much sun. In India, every customer of electricity suffers increased costs in getting up to high availability, and there is plentiful sunlight. A weird thing that we do in India is to charge high prices for the biggest customers of electricity. For these customers, roof-top PV systems are already cheaper. Problems in the fuel supply have given a steep rise in base load prices, and have pushed the shift to renewables. In the US, the cost of power varies between 7 and 20 cents/kWh. In this environment, grid parity requires that Lithium Ion batteries achieve \$150/kWh. In India, the break even point is much higher. The announcement on Thursday may yield a price that is viable for many applications in India. At a campus scale in India, a small electricity system could be constructed with the following elements: The roofs are covered with PV. There are a few windmills. Large-scale adoption would require windmill designs which cater to aesthetic sense and not just technical efficiency. It would make sense to add one diesel generator into the mix, with the advantage that it would run at top efficiency as it would only be used to feed the battery. (This is similar to the efficiencies of running the engine in a hybrid car). The campus would buy electricity from the grid when it's available and when it's cheap, and use this to charge the battery. Electricity from the grid, the renewables and the disel generator would feed the battery. All consumption would happen from the battery. Users inside the campus would experience 100% uptime. Electric cars and motorcycles could augment the battery capacity at the campus scale. Cheap CPUs would give the intelligence required to seamlessly orchestrate this system, in real time, all the time. As an example, the picture below is a pretty windmill, 3m diameter and 5m high, which has a nameplate rating of 6500 watts. The output would vary with the wind, but under normal circumstances in India, we might get average production of 1500 watts from this. Figure 4: A windmill with aesthetic qualities Sprinkling a few of these devices on a campus would be quite elegant. Here is another example, a device that is 1.5m wide, and costs 4000 Euro or Rs.260,000. A large number of installations of this nature would change the elasticity of demand for electricity. When there is peaking load, and the price of electricity is high, these installations would switch to using their batteries. This would reduce the $H/L$ ratio and thus bring down the capital cost of the centralised electricity system. A related development is taking place with rural mobile towers in India. These must grapple with the problem of intermittent electricity, and are starting to do distributed electricity generation for surrounding households. They are also pushing into new storage technologies. Scenario 1: Hunky dory Scenario 1 is where all this happens. For this, five things have to happen: Higher oil prices, ideally a carbon tax worldwide. In industrial countries: continued government support for R&D and adoption of renewables and electric cars. Continued worldwide scientific progress with batteries. Sustained low interest rates, globally, for a long time. Electricity policy in India which gives time-of-day pricing all the way to each household, and sets up an API through which a CPU at the household can query the price. Ideally, a mechanism for distributed producers to sell back to the grid at a cost which reflects the cost faced by the grid in delivering electricity at that location. If these five things happen, then we're pretty much on our way to a new world of distributed generation and distributed storage, in India and in the world outside. One interesting consequence of this scenario would be a sustained decline in crude oil prices. This would finally yield the outcome envisaged by Sheik Zaki Yamani who said in 1973: The stone age did not end because the world ran out of stones. Scenario 2: This shapes up as a mainstream technology for difficult areas only In an alternative scenario, these five things do not quite work out okay, and distributed generation + distributed storage do not shape up as the mainstream technology for every day use in the first world. However, this could still be compatible with the possibility that these are good technologies for a place like India where grid supply is untrusted and there is plenty of sunlight. An Indian public policy perspective The malleability of a late starter. In the US, where the grid is well established, these new developments threaten the business model of the existing electricity industry where vast investments are already in place [example]. In India, high availability grid power has not yet come about; the grid is far from meeting the requirements of the people. Hence, there is greater malleability and an opportunity to change course, in a direction that favours decentralisation and reduced carbon. Disrupting a broken system. If a lot of buyers in India defect from the excessive prices charged by the grid (owing to the cross subsidisation and theft), this will generate financial difficulties for the grid. As an example, see this submission in Maharashtra by the Prayas, Energy Group, and their response on the proposed amendments to the Electricity Act. Allocative decisions for the capital that goes into distributed energy. On the scale of the country, capital would shift from centralised production of electricity to distributed production + distributed storage. In the Indian public policy environment, it's always better to have self-interested households and firms making distributed choices about capital expenditures, rather than capital being placed in the hands of regulated firms. Industrial policy is not required. This article is not a call for industrial policy. We don't need to launch subsidy programs, or force car manufacturers to switch to electric, or force mobile phone towers to switch to renewables, etc. The Indian State has poor capacity on thinking and executing industrial policy. As a general principle, in public policy thinking in India, it's best to eschew industrial policy or planning, and just focus on getting the basics right. No industrial policy was required in getting to the ubiquitous water tanks on every roof in India -- it came from private choices responding to the failures of public policy on water. The invisible hand is amply at work. Indian car manufacturers exported 542,000 cars in 2014-15. Hence, these firms have ample incentive to figure out electric cars. Unreliable and expensive electricity is giving ample incentive to customers to find better solutions. Indian software services and IT product companies have ample incentive to tune into this space, and build the software end of this emerging global environment. New technological possibilities will be rapidly taken up. India should fix the grid. There are major economies of scale in making centralised electricity generation work. But we should see that we are coming at this from the opposite direction. In the West, we start from 100% centralised energy and will perhaps head towards 66% centralised energy. We in India may first overshoot to 40% centralised energy and then go up to 66% centralised energy through gradual improvements in public policy on centralised electricity. Compare and contrast this with how we see water tanks on roofs. These water tanks are the physical manifestation of the failure of public policy in the field of water. When sound water utilities come up, they will do centralised production of 24 hour water pressure, and the water tanks will go away. On one hand, the failures of public policy on electricity in India are exactly like the failures of public policy in water in India. Once it becomes possible to opt out of public systems to a greater extent, with generation and storage under the control of a campus, people will take to this. This will overshoot, going beyond what's technically sound. In the long run, when the policy frameworks on electricity become better, the share of centralised energy will go up. But there is good sense in distributed energy and it's not just a coping strategy. Even deep in the future, when policy failures are absent, there's a big role for distributed energy while there is no role for distributed water storage. For an analogy, the wireless revolution came first to Indian telecom. But now that this is established, we know that there laying fibre to the home is required in order to get good bandwidth. We will asymptotically endup converging on what's seen in the West, we'll just come at it from a different direction. India has yet to reap the efficiencies of centralised generation, transmission and distribution. We need to end subsidies and combat theft. This is the slow process of improving policy frameworks in electricity. The main point of this article is that along the difficult journey to this destination, we'll first have an upsurge of Sintex water tanks on roofs. Sound pricing rules are required. From an Indian public policy point of view, the key action point required is that moment to moment, supply and demand should clear, the spot price should fluctuate, buyers of electricity should be fully exposed to these fluctuating prices, and the spot price at all points of time should be made visible to each buyer through an API. This is not insuperably difficult. Even the present bad arrangement -- unpredictable grid outage where the price goes to $\infty$ -- is actually pushing private persons in the right direction. The market failure: externalities. Knowledge spillovers benefit society at large, and self-interest favours under-investment in knowledge. In the face of this market failure (i.e. positive externalities), perhaps the government can fund a few research labs [example] so as to grow skills in this emerging landscape. See Rangan Banerjee's article at page 38 of the December 2014 issue of Energy Next which talks about renewables R&D and manufacturing in India. It would help if there was a large number of pilot projects which aim to build towards campus-scale adoption, so as to have a precise sense of how well things work, solve local problems, and diffuse knowledge. The gap in knowledge in India on batteries is large. But it is feasible for India to get into manufacturing power units, solar cells, etc. We need to study the steps taken by Japan and China to build up their capabilities in this field. The importance of the cost of capital. Renewables involve high capital cost and near-zero running cost. The use case is critically about the cost of capital. Successful inflation targeting, and capital account openness, will give lower rates of return for equity and debt, which is required for the adoption of these technologies. There is no market failure in energy conservation. When customers are given high prices of electricity, they have ample incentive to adopt energy-efficient technologies. India is in good shape on pricing in some areas (electricity, petrol) though not in some others (kerosene, LPG). Once the price of energy is correct, the next price that shapes adoption of energy efficient technology is the cost of capital. The failures of monetary policy and finance in India are giving a high cost of capital. Once these are solved, there is no market failure in the adoption of demand side innovations. Low interest rates and low required rates of return on equity will shift the private sector calculation in favour of energy efficient technology. Implications for the private sector If this scenario unfolds as described in India, there will be a loss of momentum in centralised energy, and sharp growth in distributed production and storage of energy. Perhaps we will get a surge in imports of Lithium Ion batteries and slow growth of lead-acid battery production in India. Brijesh Vyas helped me in understanding the issues and in getting the calculations right. He recommends that we read Linden's Handbook of batteries. I also thank Sanjay Arte, Ashwini Chitnis, Ashwin Gambhir, Sanjeev Gupta, Gopal Jain, Rajeev Kapoor and Anand Pai for useful discussions. All errors are, of course, mine. Sowmya Rao Friday, 1 May 2015 at 10:22:00 GMT+5:30 Dear Ajay, I learnt a lot from reading this piece, and it put Elon Musk's /Tesla's keynote re the battery banks in context. When he said "leapfrogging like mobile phones and landlines", I was nodding along, because I'd already understood it through your article. Thanks for writing this piece. I'm keen to see what policy modifications / incentives we need here in India to similarly leapfrog. Exciting times ahead. Sowmya Rao Mayank Jha Monday, 11 May 2015 at 19:23:00 GMT+5:30 Very well written! Saw Musk's keynote earlier but your blog was extremely helpful in putting it in the Indian context and in understanding the various factors that are at play here. 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Problem statement There is a mismatch between the growth of the mutual fund industry ve... Bringing gender equality in the Hindu Succession Act: An overdue reform by Devendra Damle and Ajay Shah. One element of the gender problem in India is the Hindu Succession Act, 1956 (HSA). This law governs inte... Review of "The Rise of the BJP: The Making of the World's Largest Political Party" by Bhupender Yadav and Ila Patnaik by Ajay Shah. The INC emerged as the dominant party after independence. A similar phenomenon was seen in other countries, e.g. the PRI in ... Sophisticated clustered standard errors using recent R tools by Dhananjay Ghei Many blog articles have demonstrated clustered standard errors, in R, either by writing a function or manually adjusting t... Resolving municipal distress in India by Adam Feibelman and Bhargavi Zaveri-Shah . In recent years, municipal bodies in India have been increasingly accessing the public debt... 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How Finance SEZs can matter Brand names versus reality Financial reforms -- a meeting at the BSE tomorrow Making monetary policy more potent	CommonCrawl
… and the Secret of the 90s Back in 2008, when the hype around Usain Bolt started during the Beijing Olympics, I saw the progression of world records in 100m sprint and found it most curious. For me, it looked like the rate at which world records were achieved had increased in the 90s and I wondered about the reasons behind that. My discussion of these reasons is still valid today, but given that quite some time has passed (2018) and I was a bit sloppy in my initial statistical analysis, I have divided this post into two parts: A) the original discussion from 2008 and B) a more detailed statistical inquiry of my hypothesis that there were suspiciously large improvements in world records starting from the 90s. A) Intuitions in 2008 During the run-up to the 100m finals in the 2008 Olympics in Beijing the media expressed doubt about the cleanness of the competition (with respect to doping, e.g. [1], [2]). This certainly wasn't helped by Bolt's seemingly effortless win which resulted in a new world record on the 100m track [3]. Then I saw a list showing the development of the world records over the 100m from 1912 to now and thought that there are suspiciously many in recent years. So I took that list and made a graph of it: World records in men's 100m sprint as a function of the year in that they were first achieved. World records of men who were proven to be stimulated by illegal drugs at the time of the record are not shown. (Scroll to the end of this post to see an updated, interactive version of this figure.) If you look on the development of the world records only until the 80s, it seems that it is following a principle which may be close to the one depicted as a red line. Certainly we can see that the fall of the world record times slowed down. This makes sense, if you assume that there is a natural limit of what a human body can achieve. The red line also suggests that this limit has roughly been hit at the end of the 80s. But what happened then? In the 90s the world record began to fall further and this development has even picked up since then. Now the world record is falling as quickly as it did in the first half of the 20th century again. So how do we interpret this development? Here are some possible explanations: Just a period of slow development in 70s/80s: Between 1936 and 1956 the time for the 100m didn't decrease much either. Maybe it was the same during the 70s and 80s leading us wrongly to believe that we already hit a limit there. Then we have to ask us why there was no development during that time. Was there no interest in the sport, so not enough new talent came through? New training methods: With the help of ever improving training equipment and computer aided analysis based on newest scientific results it is possible to identify and develop athletes' strengths better than ever before. The question is whether this is enough to explain the drop in world record times. How much of a difference in milliseconds can perfect training methods make? Ultimately it is still the athlete's body restricting how fast he eventually can run. Better development in smaller countries: Maybe new support for sports in non-traditional 100m countries has led to the new fall of world records since the 90s. To some extent the genetics of an athlete determines how fast he can run. That's what people usually call talent. It seems, for example, that Africans are predestined for long-distance runs. However, as long as there is no proper sports development in the right countries, the talent might stay unrecognised. Jamaica might be one of the countries where new support has created great athletes, but this still doesn't explain the development in the 90s, because almost all record holders then were American. Doping: Finally, what do you do when you have got the talent and excellent training methods and still can't run any faster, because your body is at its limits? You have to move these limits. Maybe by using substances which increase the level of red blood cells over your natural limit, or let muscles grow stronger than what can be achieved just with training. In this context the plot above suggests that around 1990 athletes started to use doping to push their body limits (and are successful with it) which roughly coincides with when the first doping scandal hit the competition [1]. I know far too little about the development of the sport to make a final judgement about what happened since the 90s. I am convinced that something happened, though, and maybe somebody out there can take it up and clarify more. I certainly believe that there is a limit to how fast a human can run. With doping you might be able to push that limit a bit further. I wonder how far you can eventually go, but I wouldn't want to test it out. Who knows what happens to your muscles when you have pushed them artificially just a little bit too far? Maybe we should ask one of the record holders in 20 years. B) Improved statistics in 2018 All of the above discussion was based on the intuition that from about 1970 to 1990 world records in 100m sprint appeared to have converged on a minimum time while from the 90s new world records were produced again. Is it actually possible to find robust statistical support for this hypothesis? This turns out to be a difficult question, because the world record times are only indirect observations of a complicated process. Here I try to characterise this process, I will build a statistical model for it and then evaluate the statistical evidence for my hypothesis. The statistical analysis will demonstrate the use of Gaussian process dynamics in a hierarchical model with censored observations. All analysis code and data is available in my 100m Github repository. Hidden progression of world performance My intuition is about a virtual construct that cannot be observed directly: the progression of something I call "world performance" that describes the collective performance across the top athletes at a given time. Even more specifically, I only mean the top performances of the top athletes that are needed to achieve world records. The purpose of my statistical model is to infer this world performance progression from world record times of individual athletes. The basic idea is that the performance of an athlete is a combination of world performance with individual ability and that world records are outstanding top performances of those athletes. I will below go through the corresponding components of the statistical model, but start with a brief description of the data. World record data I got the official world records in 100 m sprint from the corresponding Wikipedia page which links to the official results from the IAAF. A complication in the data is that early records were only manually timed with a resolution of 0.1 seconds while from the 1970s more precise automatic timing was introduced. There were 4 automatically timed world records in an overlapping period in which manual and automatic timing co-existed. I rounded these 4 world records down to the nearest .1 second to be compatible with manual times. Often athletes try to reach their top performance at one major event in a year, e.g., the Olympics. I, therefore, bin world records in yearly bins, but maintain the natural order of world records in the analysis as described below. World performance dynamics The crucial part of my analysis was to describe the hidden progression of world performance also in years in which no world records were achieved. Because I didn't want to make unnecessary assumptions about how world performance changes as a function of time, I assumed that world performance follows a Gaussian process. This states that world performances $\mathbb{w} = [w_1, \dots, w_n]^T$ at years $\mathbb{y} = [y_1, \dots, y_n]^T$ are Gaussian distributed $$\mathbb{w} \sim \mathcal{N}(\mathbb{0}, \Sigma)$$ where $\Sigma$ is computed by applying a covariance function to the years $\mathbb{y}$. Conceptually a Gaussian process describes a probability distribution over functions, here a function from years $y$ to world performance $w$. The mentioned covariance function determines the type of functions that can be generated from the Gaussian process. For example, a parameter of the covariance function can determine how smooth the generated functions are. These parameters were inferred together with the world performances $w$ at all years from 1912 to 2017 in the full model. Performance of individual athletes While I assumed that world performance progresses across years, I modeled variability in 100 m times of individual athletes as independent draws from a Gaussian distribution. The mean of that distribution, however, reflects the current world performance in addition to an athlete's ability in relation to the world performance. In equations: $$t(a, y) \sim \mathcal{N}\left(w(y) + b_a, \sigma_a\right)$$ where $a$ identifies an athlete, $y$ is the current year, $t(a, y)$ is a 100 m time of athlete $a$ in year $y$, $b_a$ is the athlete's (mean) ability relative to world performance $w(y)$ in that year and $\sigma_a$ is that athlete's individual variability in performance. The athlete-specific parameters of this distribution, i.e., $b_a$ and $\sigma_a$ needed to be inferred from the world record times of each athlete. It could be that the Gaussian distribution is not the best choice to describe the variability in 100 m times of an athlete, but it was a good start and has limited width of its tails which made it easier to infer the underlying world performance progression. Also, the model I used here targets the virtual entity of world performance that does not really exist and just helps to describe the progression of 100 m world records. It is not crucial for that to find the exact distribution of 100 m times of each athlete. This would also be impossible, because I only tried to model the distribution of only the absolute top of performances in major events for which too few data exist to infer any distribution with high certainty. Censored data Data input to the model were the world record times together with their year of achievement and the athlete who achieved it. To get a data point in every year I filled up the data set with data points for each year that had no world record with the last world record time and no athlete. This way the model knew that no athlete achieved a world record in that year. Every data point tells us that all except the associated athlete did not achieve a world record at the same time, i.e., they only achieved a time that was slower than the time given by the data point (or didn't compete). This is an instance of censored data and means that the likelihood defined for the data is either based on the probability density of the Gaussian (for the athlete that achieved the world record) or it is based on the cumulative distribution function of the Gaussian (for all other athletes). This is also described in the Stan manual. Selection of athletes and length of careers Athletes only perform at their best for a limited period of time. So it is clear that I should not infer anything about Bobby Morrow's top performances in the 1950s from his inability to achieve a world record in the 1980s. To account for that I limited the influence of individual data points on an athlete's performance by only including athlete-specific likelihood terms for a limited period of years – the career of an athlete. For all athletes with a world record I defined their career to include all years from 2 years before the year of the first world record to the 6 years after their first world record. Furthermore, I defined the top athletes in a year to be the 8 athletes that are competing in a typical Olympics final. Because in most years less than 8 world record holders had an overlapping career, I filled up the remaining top athlete spots with anonymous athletes who also had a 9-year long career. I implemented the model and data described above in the probabilistic programming language Stan. Bayesian inference in the model is then approximated with Markov chain Monte Carlo sampling. To get inference in this model running reliably was a bit tricky. Because of the many unknowns and little data, priors had to be chosen suitably to allow the sampler to consistently explore the complicated posterior distribution. Results below are based on 2000 samples from the posterior. Details can be found in the Github repository. The plot below shows the world records of individual athletes as green dots (move the mouse pointer over the points to find out the details of the record). The grey line depicts the progression of the estimated world performance together with a 95% posterior probability interval indicating the posterior uncertainty. Clearly, the (average) top world performance is above the world records which are extreme events in the model. More importantly, the world performance roughly follows my intuition from above: The line has a roughly linear drop until about 1970, then flattens out to be almost constant and then starts to drop slightly again from 1990. The absence of world records after 2009 again leads to a flattening of the curve that even ends in a small rise from 2016 to 2017. Note that this is expected to happen in long periods without world records, because even for constant world performance world records as extreme events should occur sooner or later. So, if world records do not occur over a long period of time, this is an indicator that the underlying average performance has worsened. One thought on "100m World Records" jobia says: your red line fit is arbitrary and implausible in the first place, you can see it curving up at the end which is goofy. An exponential decay is more reasonable than a parabola	CommonCrawl
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Nonlinear Schrödinger equations on a finite interval with point dissipation MCRF Home Application of the boundary control method to partial data Borg-Levinson inverse spectral problem June 2019, 9(2): 313-350. doi: 10.3934/mcrf.2019016 The generalised singular perturbation approximation for bounded real and positive real control systems Chris Guiver *, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, UK Received June 2017 Published December 2018 The generalised singular perturbation approximation (GSPA) is considered as a model reduction scheme for bounded real and positive real linear control systems. The GSPA is a state-space approach to truncation with the defining property that the transfer function of the approximation interpolates the original transfer function at a prescribed point in the closed right half complex plane. Both familiar balanced truncation and singular perturbation approximation are known to be special cases of the GSPA, interpolating at infinity and at zero, respectively. Suitably modified, we show that the GSPA preserves classical dissipativity properties of the truncations, and existing a priori error bounds for these balanced truncation schemes are satisfied as well. Keywords: Balanced truncation, dissipative system, linear system, model reduction, rational interpolation, singular perturbation approximation. Mathematics Subject Classification: Primary: 34K07, 34K26, 93B11, 93C05, 93C70. Citation: Chris Guiver. The generalised singular perturbation approximation for bounded real and positive real control systems. Mathematical Control & Related Fields, 2019, 9 (2) : 313-350. doi: 10.3934/mcrf.2019016 U. M. Al-Saggaf and G. F. Franklin, Model reduction via balanced realizations: An extension and frequency weighting techniques, IEEE Trans. Automat. 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The lines numbered 1-4 correspond to $ \xi_1 = 0.1 $, $ \xi_2 = 1 $, $ \xi_3 = 10 $ and $ \xi_4 = 100 $, respectively. Note the interpolation properties (2.7) and (3.7) hold and are highlighted with vertical dotted lines. The dashed dotted line is the error bound (3.3) Figure 5.3. Plots of errors on the imaginary axis for the bounded real GSPA from Example 5.1, with $ r = 1 $ and $ r = 2 $ in panels (a) and (b), respectively. The lines numbered 1-4 correspond to $ \xi_1 = 0.1 $, $ \xi_2 = 1 $, $ \xi_3 = 10 $ and $ \xi_4 = 100 $, respectively, and are symmetric around $ \omega = 0 $. The dashed dotted lines are the bounds (3.3) Figure 5.4. Semi-log plot of combined errors on the real axis for the positive real GSPA from Example 5.2, with $ \xi = 10 $. The lines numbered 1-3 correspond to $ r \in \{1, 2, 3\} $ respectively. Note the interpolation property (2.7) holds Figure 5.5. Semi-log plot of gap metric error $ \hat \delta( \mathbf G , \mathbf G _r^\xi) $ (crosses) and error bounds (4.4) (circles) for extended circuit model from Example 5.2. Here $ \xi = 10 $ Belinda A. Batten, Hesam Shoori, John R. Singler, Madhuka H. Weerasinghe. Balanced truncation model reduction of a nonlinear cable-mass PDE system with interior damping. Discrete & Continuous Dynamical Systems - B, 2019, 24 (1) : 83-107. doi: 10.3934/dcdsb.2018162 Xin Du, M. Monir Uddin, A. Mostakim Fony, Md. Tanzim Hossain, Md. Nazmul Islam Shuzan. Iterative Rational Krylov Algorithms for model reduction of a class of constrained structural dynamic system with Engineering applications. Numerical Algebra, Control & Optimization, 2021 doi: 10.3934/naco.2021016 Martin Redmann, Melina A. Freitag. Balanced model order reduction for linear random dynamical systems driven by Lévy noise. Journal of Computational Dynamics, 2018, 5 (1&2) : 33-59. doi: 10.3934/jcd.2018002 Gengsheng Wang, Guojie Zheng. The optimal control to restore the periodic property of a linear evolution system with small perturbation. Discrete & Continuous Dynamical Systems - B, 2010, 14 (4) : 1621-1639. doi: 10.3934/dcdsb.2010.14.1621 Stefano Scrobogna. Derivation of limit equations for a singular perturbation of a 3D periodic Boussinesq system. Discrete & Continuous Dynamical Systems, 2017, 37 (12) : 5979-6034. doi: 10.3934/dcds.2017259 Jann-Long Chern, Zhi-You Chen, Yong-Li Tang. Structure of solutions to a singular Liouville system arising from modeling dissipative stationary plasmas. Discrete & Continuous Dynamical Systems, 2013, 33 (6) : 2299-2318. doi: 10.3934/dcds.2013.33.2299 Chris Guiver, Mark R. Opmeer. Bounded real and positive real balanced truncation for infinite-dimensional systems. Mathematical Control & Related Fields, 2013, 3 (1) : 83-119. doi: 10.3934/mcrf.2013.3.83 Ilona Gucwa, Peter Szmolyan. Geometric singular perturbation analysis of an autocatalator model. Discrete & Continuous Dynamical Systems - S, 2009, 2 (4) : 783-806. doi: 10.3934/dcdss.2009.2.783 Charles Fefferman. Interpolation by linear programming I. Discrete & Continuous Dynamical Systems, 2011, 30 (2) : 477-492. doi: 10.3934/dcds.2011.30.477 Marc Massot. Singular perturbation analysis for the reduction of complex chemistry in gaseous mixtures using the entropic structure. Discrete & Continuous Dynamical Systems - B, 2002, 2 (3) : 433-456. doi: 10.3934/dcdsb.2002.2.433 Zuowei Cai, Jianhua Huang, Liu Yang, Lihong Huang. Periodicity and stabilization control of the delayed Filippov system with perturbation. Discrete & Continuous Dynamical Systems - B, 2020, 25 (4) : 1439-1467. doi: 10.3934/dcdsb.2019235 Martin Redmann, Peter Benner. Approximation and model order reduction for second order systems with Levy-noise. Conference Publications, 2015, 2015 (special) : 945-953. doi: 10.3934/proc.2015.0945 Purnima Pandit. Fuzzy system of linear equations. Conference Publications, 2013, 2013 (special) : 619-627. doi: 10.3934/proc.2013.2013.619 A. Lehikoinen, S. Finsterle, A Voutilainen, L. M. Heikkinen, M. Vauhkonen, J. P. Kaipio. Approximation errors and truncation of computational domains with application to geophysical tomography. Inverse Problems & Imaging, 2007, 1 (2) : 371-389. doi: 10.3934/ipi.2007.1.371 Chunyan Ji, Daqing Jiang. Persistence and non-persistence of a mutualism system with stochastic perturbation. Discrete & Continuous Dynamical Systems, 2012, 32 (3) : 867-889. doi: 10.3934/dcds.2012.32.867 Robert T. Glassey, Walter A. Strauss. Perturbation of essential spectra of evolution operators and the Vlasov-Poisson-Boltzmann system. Discrete & Continuous Dynamical Systems, 1999, 5 (3) : 457-472. doi: 10.3934/dcds.1999.5.457 P.E. Kloeden, Victor S. Kozyakin. The perturbation of attractors of skew-product flows with a shadowing driving system. Discrete & Continuous Dynamical Systems, 2001, 7 (4) : 883-893. doi: 10.3934/dcds.2001.7.883 Rogério Martins. One-dimensional attractor for a dissipative system with a cylindrical phase space. Discrete & Continuous Dynamical Systems, 2006, 14 (3) : 533-547. doi: 10.3934/dcds.2006.14.533 George J. Bautista, Ademir F. Pazoto. Decay of solutions for a dissipative higher-order Boussinesq system on a periodic domain. Communications on Pure & Applied Analysis, 2020, 19 (2) : 747-769. doi: 10.3934/cpaa.2020035 Eduard Feireisl, Antonin Novotny, Yongzhong Sun. Dissipative solutions and the incompressible inviscid limits of the compressible magnetohydrodynamic system in unbounded domains. Discrete & Continuous Dynamical Systems, 2014, 34 (1) : 121-143. doi: 10.3934/dcds.2014.34.121 Chris Guiver	CommonCrawl
•https://doi.org/10.1364/OL.444226 Detachable head-mounted photoacoustic microscope in freely moving mice Heng Guo, Qian Chen, Wei Qin, Weizhi Qi, and Lei Xi Heng Guo,1,2,† Qian Chen,1,2,† Wei Qin,2 Weizhi Qi,2 and Lei Xi1,2,* 1School of Physics, University of Electronic Science and Technology of China, Chengdu, Sichuan 611731, China 2Department of Biomedical Engineering, Southern University of Science and Technology, Shenzhen, Guangdong 518055, China †These authors contributed equally to this Letter. *Corresponding author: xilei@sustech.edu.cn Lei Xi https://orcid.org/0000-0002-2598-6801 H Guo Q Chen W Qin W Qi L Xi Heng Guo, Qian Chen, Wei Qin, Weizhi Qi, and Lei Xi, "Detachable head-mounted photoacoustic microscope in freely moving mice," Opt. Lett. 46, 6055-6058 (2021) Spotlight Summary Spotlight Summary by Jürgen Sawinski Absorption of light generates heat and by modulating the light intensity, a sound wave can be generated. This effect, first described by A.G. Bell in 1880 (Am. J. Sci. 20 (118), 305 (1880)) and now known as the photoacoustic effect, has spurred plenty of engineers and scientists over decades. The effect is now well-used in medicine and neuroscience in the form of photoacoustic tomography (PAT) and microscopy (PAM), among other subtypes, with resolutions down to optical resolution, capable of revealing oxygen metabolism, gene expression, vasculature and specific biomarkers (L. Li, J. Yao, L.V. Wang, "Photoacoustic Tomography of Neural Systems" in Neural Engineering, 3rd ed. (Springer, 2020). In this work, Guo et al. present a remarkable down scaling of their previous head-mounted microscope (targeted at rats) to a total weight of 1.8 g suitable for imaging in freely moving mice. It promises to be a valuable tool for long-term hemodynamic studies over days and possibly weeks, and supplement the wide range of brain activity related detection tools. Opt. Lett. 46(24) 6055-6058 (2021) View: Abstract \| HTML \| PDF You must log in to add comments. Ultracompact high-resolution photoacoustic microscopy Qian Chen, et al. Dual-model wearable photoacoustic microscopy and electroencephalograph: study of neurovascular... Biomed. Opt. Express 12(10) 6614-6628 (2021) Multi-modality photoacoustic/ultrasound imaging based on a commercial ultrasound platform Zhan Pang, et al. Laser imaging Optical imaging Original Manuscript: September 30, 2021 Revised Manuscript: October 29, 2021 Manuscript Accepted: October 29, 2021 January 4, 2022 Spotlight on Optics Optical resolution photoacoustic microscopy (ORPAM) is a promising tool for investigating anatomical and functional dynamics in the cerebral cortex. However, observation in freely moving mice has been a longstanding challenge for ORPAM. In this Letter, we extended ORPAM from anesthetized, head-restrained to awake, freely moving mice by using a detachable head-mounted ORPAM probe. We used a micro-electro-mechanical-system scanner and a miniaturized piezoelectric ultrasonic detector to scan the excitation laser beam and detect generated photoacoustic signals, respectively. The probe weighs 1.8 g and has a large field of view of ${\sim}{3}\;{\rm mm} \times {3}\;{\rm mm}$. We evaluated the performance of the probe by carrying out phantom experiments and the imaging of vascular networks in a mouse cerebral cortex. The results suggest that the ORPAM probe is capable of providing stable and high-quality ORPAM images in freely moving mice. © 2021 Optica Publishing Group As an important tool in investigating neural activities, brain imaging allows us to directly observe in vivo psychological processes and cognitive activities [1]. In most experiments, the use of anesthetized and head-restrained animals is common and mature, but inevitably affected by neural inhibition and restricted behavior [2–4]. Hence, carrying out brain imaging in freely moving animals is a promising solution. Miniaturization of imaging devices is an absolute prerequisite for brain studies using freely moving animals. Prior investigations have fully explored the miniaturization of various optical imaging modalities, such as two-photon microscopy [5,6], fluorescence microscopy [7,8], laser speckle imaging [9,10], etc. [11,12]. These miniaturized probes have provided a number of fundamental insights into the truth of cellular activity and how neuronal subpopulations operate during behaviors. Besides cellular and neural activities, hemodynamics is also vital in the investigation of brain activities [13]. In comparison with pure optical imaging techniques, optical resolution photoacoustic microscopy (ORPAM) is a more powerful tool for investigating hemodynamics [14–16]. Owning to its unique working principle based on label free imaging of optical absorption, both structural and functional information of vascular networks can be revealed [17–19]. Unlike conventional optical microscopes, in ORPAM, the low-scattered ultrasonic wave is excited and detected instead of the high-scattered optical photon in biological tissues to guarantee a deeper penetration depth. To excite and record the acoustic wave, separation and integration of acoustic and optical paths are commonly required, making it more difficult to be miniaturized compared with pure optical imaging modalities. In our previous study, we have successfully achieved a wearable photoacoustic (PA) microscope in freely moving rats [20]. However, the weight and size of the ORPAM probe for rats are still unacceptable for mice. In addition, to avoid motion artifacts and achieve stable image quality, the probe was permanently fixed on the rat brain, preventing it from use in long-term brain studies. Among mammalian species, the mouse is a pre-eminent animal model for biomedical studies due to its various pathological and genetic features. Thus, developing an ultralight miniaturized ORPAM probe capable of long-term imaging in freely moving mice is of particular importance. In this Letter, we extended our work from freely moving rats to mice. A miniaturized ORPAM probe consisting of an optical fiber, a miniaturized optical scanner, and a small piezoelectric ultrasonic transducer was presented. Compared with previous wearable imaging probes for rats, we reduce the weight from 8 g to 1.8 g and increase the field of view (FOV) from ${1.2}\;{\rm mm} \times {1.2}\;{\rm mm}$ to ${3}\;{\rm mm} \times {3}\;{\rm mm}$. In addition, the current imaging probe is detachable, making it accessible to longitudinal monitoring of the mouse. Through in vivo experiments, we prove the feasibility of long-term, stable, and high-quality imaging in freely moving mice using this probe. Figure 1(a) shows the configuration of the ORPAM imaging system. The excitation laser beam is emitted from a 532 nm pulsed laser (GLPM-10, IPG, USA) with a repetition rate of 50 kHz, a single pulse energy of 20 µJ, and a duration of 2 ns. Before being coupled into the single mode fiber (SMF), the laser beam is reshaped through an iris (ID12, Thorlabs, USA) and filtered via a customized spatial optical filter consisting of two lenses and a 25 µm high-power pinhole (P25, Thorlabs, USA). A customized optical and electrical rotatory joint is employed to prevent extensive twisting of the optical fiber and electrical wires during the experiment. The imaging probe contains miniaturized optical components for collimation and focusing, a micro-electro-mechanical-system (MEMS) scanner for raster scanning, and a customized small piezoelectric ultrasonic detector for PA signal detection. Fig. 1. Configuration of the ORPAM system and schematic of the miniaturized imaging probe for brain imaging in freely moving mice. (a) The setup of the imaging system. Obj, objective lens; SMF, single mode fiber; RJ, optical and electrical rotatory joint; C, cable; Amp, amplifier; FG, functional generator. (b) The detailed configuration of the probe. CG, cover glass. (c) The probe 3D rendering. (d) Photographs of a well assembled imaging probe and a C57 mouse wearing the imaging probe. The inserted photo shows the weight of the probe. See Visualization 1. Figure 1(b) shows the detailed internal structure of the probe. The fiber tip is fixed in a 1.25 mm diameter ceramic ferrule. An aspheric lens (#83-616, Edmund, USA) collimates the laser beam emitted from the fiber tip. A plano-convex lens (#45-272, Edmund, USA) with a focal length of 12 mm focuses the collimated laser beam. A ${3}\;{\rm mm} \times {3}\;{\rm mm} \times {3}\;{\rm mm}$ prism reflects the focused laser beam to the MEMS scanner with a mirror diameter of 1 mm. It can achieve the maximal optical scanning angle of $\pm {10}^\circ$ with the maximal driving voltage of 4 V. The MEMS scanner then reflects and scans the laser beam to propagate through a water cube with a thin cover glass tilted with an angle of 45° to illuminate the tissue surface. The cube allows the full transmission of the laser beam and partial reflection of the generated acoustic waves [21]. Scanning control is implemented by a function generator (FG) card (PCI-6733, National instruments, USA). By changing the driving voltages of four actuators, the MEMS mirror can achieve a two-dimensional raster scanning of the laser beam on the tissue surface. The induced PA signals are reflected by the 45° tilted cover glass and detected by a customized ultrasonic transducer with a center frequency of 10 MHz, a bandwidth of 80%, and an aperture size of 3 mm in diameter. The signals are amplified with a gain of ${\sim}{66}\;{\rm dB}$ and acquired by a high-speed data acquisition (DAQ) card (ATS9350, Alazartech, Canada) at a sampling rate of ${\sim}{125}\;{\rm MS/s}$. In the study, we used a laser power of 20 mW at a repetition rate of 50 kHz, resulting in single pulse energy of 400 nJ, to perform the in vivo experiments. All of the experimental results showed that there was no obvious damage to the mouse brain after long-term continuous recording. Figure 1(c) shows the three-dimensional (3D) rendering of the image probe. In order to realize the detachable feature of the probe from the mouse head smoothly and accurately, we designed three feet outside the shell of the probe. Three magnets are attached to the tips of the feet. A mounting base is also designed, with three magnets corresponding to the feet on the probe. The mounting base is attached to the mouse skull by tissue adhesive and dental powder to position and immobilize the probe. The outer size of the probe is ${12}\;{\rm mm} \times {6}\;{\rm mm} \times {20}\;{\rm mm}$. Figure 1(d) exhibits the photograph of a well assembled imaging probe and a C57 mouse wearing this probe. The inserted photo shows that the weight of the probe is less than 1.8 g, which is light enough for an adult mouse. Besides, Visualization 1 shows the behavior of the mouse wearing this probe. We first evaluated the key parameters of this probe, including FOV and lateral and axial resolutions. To measure the FOV of this probe, we successively scanned the cerebral cortex of a C57 mouse using the proposed probe and a previously reported rotatory scanning ORPAM (RS-ORPAM) system [22]. With a known FOV of the RS-ORPAM system, we can estimate the FOV of this probe. The maximum amplitude projection (MAP) images of the mouse brain acquired by the probe and the RS-ORPAM system are shown in Figs. 2(a) and 2(b), respectively. The FOV of the RS-ORPAM system is a 10 mm diameter circular area, and the corresponding FOV of the probe is illustrated by a dashed box. Comparing these two MAP images, we may estimate the FOV of this probe to be ${\sim}{3}\;{\rm mm} \times {3}\;{\rm mm}$. To evaluate the lateral resolution, we imaged a sharp edge of a surgical blade and obtained the edge spread function (ESF) curve, as shown in Fig. 2(c). The black dots and curve in Fig. 2(c) represent the normalized raw and fitted cross sectional profiles, respectively. The red curve in Fig. 2(c) shows the derived line spread function (LSF) with an estimated lateral resolution of 2.8 µm. Theoretically, the lateral resolution is approximately 2.5 µm with a numerical aperture (NA) of 0.13, which is slightly better than the experimental value. The major reason for this discrepancy is probably caused by the mismatch of the optical index inside the water cube. To evaluate the axial resolution of the probe, we derived the envelope of a PA signal generated by a single carbon fiber. The envelope is obtained by calculating the absolute value of the Hilbert-transformed PA signal waveform, as shown in Fig. 2(d). By measuring the full width at half-maximum (FWHM) of the Hilbert-transformed PA signals, the axial resolution of the system is estimated to be 165 µm and agrees well with the theoretical value. Fig. 2. Performance of the miniaturized imaging probe. (a) The MAP image of a C57 mouse brain acquired by the miniaturized probe. (b) The MAP image of the same C57 mouse brain acquired by the previously reported RS-ORPAM system with a circular FOV of 10 mm in diameter. (c) The ESF and derived LSF of a sharp surgical blade. The inserted image is the MAP image of the surgical blade. The position of the profile is denoted by an orange dashed line. (d) The original PA signal of a single carbon fiber and its Hilbert-transformed waveform before and after Gaussian fitting. The inserted image is the MAP image of carbon fibers buried in agar phantom. The scale bar is 1 mm. We then conducted in vivo experiments as a further evaluation of this probe. We first anesthetized and maintained a C57 mouse by using the isoflurane (concentration: 2% Vol; gas velocity: 0.4 L/min), then depilated its brain to avoid the influence of hair. After that, we removed the scalp while keeping the skull intact and carefully attached the mounting base to its skull by using tissue adhesive and dental powder. The imaging probe was then fixed on the mounting base by magnets. To ensure ultrasonic transmission, the gap between the imaging probe and the mounting base was filled with medical ultrasonic gel. After the mouse was fully awake, we started our experiment to record a series of cortical images of the mouse in a large transparent polymethyl methacrylate (PMMA) barrel. All of the experimental procedures were approved by the ethics committee at the Southern University of Science and Technology (SUSTech), and all animals were sacrificed using the SUSTech-approved standard procedure after the experiment. We carried out longitudinal imaging of the cerebral cortex in a freely moving mouse for 40 min to test the short-term stability of this probe. Considering the tradeoff between scanning speed and FOV of the MEMS mirror, we adjusted the scanning parameters to balance the acquisition time and image quality. In this experiment, we acquired 500 A-lines within a B-scan and a total number of 500 B-scans to form a MAP image with a size of ${500} \times {500}$ pixels that takes 5 s. Figure 3(a) shows the MAP images acquired at the 0th min. Figure 3(b) represents the overlapped MAP in the 0th and 40th min. The result demonstrates that there are only a few discrepancies, which are marked by the white dashed boxes. In the remaining part, the first and last images have a perfect match, and no obvious differences are observed. The curve in Fig. 3(c) quantifies the correlation of these MAP images over the entire acquisition time. We can see that the correlation of the entire acquisition series is higher than 90% and has a correlation variation of ${\lt} {10}\%$, which demonstrates that the miniaturized probe acquires high-quality ORPAM images with high stability and spatial resolution in the brain of freely moving mice. Visualization 2 displays these MAP images during the acquisition time. Fig. 3. In vivo short-term freely moving imaging experimental results of C57 mice. (a) The MAP image of the continuous scanning experiment at the 0 min. (b) The overlapped first and last MAP image of the acquisition series. The white dashed boxes mark the slight discrepancies between them. (c) The correlation of the MAP images over the entire course of the experiment. (d) The MAP images of the entire imaging domain and four arbitrarily selected areas within the original FOV. See Visualization 2. Besides, we applied different initial bias voltages to four independent actuators of the MEMS mirror to achieve region-of-interest imaging within the original FOV. This scanning mechanism is beneficial for focusing on areas of interest for different experimental models. Figure 3(d) represents both MAP and four sub-images of select areas in a mouse brain. We reduced the number of A-lines and B-scans to 200 for the sub-image with a suppressed FOV of ${1.2}\;{\rm mm} \times {1.2}\;{\rm mm}$. The time cost is thus reduced to about 0.8 s, resulting in an increased volume rate of 1.25 volume/s. To illustrate the detachable feature of the probe, we also performed long-term monitoring experiments on a C57 mouse brain for 7 days. We first fixed the mounting base on the mouse skull by using tissue adhesive and dental powder. Each day, the probe is attached onto the mounting base and immobilized through three magnets. We maintained the skull moisture with another homemade holder and filled the holder with medical ultrasonic gel after daily experiments. Figure 4 presents the imaging results in the 1st, 3rd, 5th, and 7th days. All images clearly show an intact vasculature with large and small vessels and capillaries. However, there are still some slight changes in vascular morphology. Figure 4(b) shows the relative vascular ratio of the area marked by the white dashed box. The statistical result shows that the number of blood vessels slightly decreases over time due to the long-term exposure of the skull. Although we filled the ultrasonic gel on the skull after daily experiment, it became dry in next day, and some marginal small vessels disappeared. Besides, the removal of the mouse scalp might induce inflammation of the tissue and physiological reactions of the mouse. Hence, the diameters of vessels such as V1 and V2 marked in day 1 show a significant increase, and the imaging of the sagittal sinus was varied in the next few days [Fig. 4(c)]. The quantitative parameters in Figs. 4(b) and 4(c) were normalized, and the day 1 data served as the baseline. Fig. 4. (a) Long-term freely moving imaging results of a C57 mouse brain. (b) The relative vascular ratio of the area marked by the white dashed box. (c) The relative diameter changes of V1 and V2 marked by orange lines. In this Letter, we presented a miniaturized ORPAM probe and demonstrated that it is suitable for investigating brain hemodynamics in freely moving mice. The probe contains the optical fiber, two lenses, one prism, one MEMS scanner, and one miniaturized ultrasonic transducer. The outer size of this probe is ${12}\;{\rm mm} \times {6}\;{\rm mm} \times {20}\;{\rm mm}$, and it weighs ${\sim}{1.8}\;{\rm g}$, which is less than 10% of an adult mouse. Both the size and weight of this probe are suitable for adult mice to wear. The lateral resolution of this probe is measured to be 2.8 µm, which is sufficient to resolve most capillaries in the cerebral cortex. The maximum FOV of this probe is estimated to be ${\sim}{3}\;{\rm mm} \times {3}\;{\rm mm}$, which is large enough to cover several key brain regions in reaction and motion control. Besides, a random and adjustable area scanning mechanism allows for observing the interested area for specific animal model with the requirement of a fast imaging speed. The imaging quality and stability of this probe are evaluated by short- and long-term in vivo experiments. In short-term experiments, the correlation variation of the MAP images acquired is always under 10%, indicating a high stability of this probe. As for long-term experiments, the detachable design of this probe also makes it convenient. A C57 mouse is imaged every day within a week. The performance of this probe in long-term experiments is not as good as its performance in short-term experiments. We observed slight displacements and lateral shifts that might be caused by the relative movements of the brain to the skull. From these results, we may conclude that our probe will be a promising tool for investigating mice brain activities in freely moving conditions. National Natural Science Foundation of China (61528401, 61775028, 62022037, 81571722); Guangdong Science and Technology Department (2019ZT08Y191, SZBL2020090501013); Shenzhen Scientific and Technological Foundation (KQTD20190929172743294); Southern University of Science and Technology (PDJH2021C008). 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Liu, C. Liu, Q. Lovenberg, T. Lu, H. Lu, Y. Maslov, K. Miao, P. Mohajerani, M. Molodtsov, M. Mukamel, E. Navabi, Z. Nazari, M. Nimmerjahn, A. Ning, B. Nobauer, T. Otte, S. Pathak, A. Qi, W. Qin, W. Radhakrishnan, H. Rajendran, V. Rong, H. Rong, J. Ruvinskaya, S. Rynes, M. Schnitzer, M. Senarathna, J. Skocek, O. Sun, N. Surinach, D. Thakor, N. Thakur, K. Tong, S. Traub, F. Tu, R. Tyler, B. Vaziri, A. Wang, A. Wang, H. Wang, L. Wang, T. Wang, Y. Weilguny, L. Wong, T. Wu, D. Wu, H. Wu, R. Wu, W. Xi, L. Xia, C. Xie, H. Xu, Y. Yamagata, M. Yang, L. Yao, J. Yu, H. Zhang, J. Zhang, Y. Zhao, Z. Zhou, J. Zhou, Y. Zhou, Z. Ziv, Y. Zong, W. Zou, A. Zuo, Z. J. Biomed. Opt. (1) J. Biophoton. (6) Nat. Commun. (1) Photoacoustics (2) Visualization 1 The behavior of the C57 mouse wearing the probe. Visualization 2 MAP images during the acquisition time.	CommonCrawl
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Epidemiology & Infection Data and methods Analysis of the early COVID-19 epidemic curve in Germany by regression models with change points Published online by Cambridge University Press: 11 March 2021 Helmut Küchenhoff [Opens in a new window] , Felix Günther [Opens in a new window] , Michael Höhle [Opens in a new window] and Andreas Bender [Opens in a new window] Helmut Küchenhoff* Statistical Consulting Unit StaBLab, LMU Munich, Germany Felix Günther Statistical Consulting Unit StaBLab, LMU Munich, Germany Department of Genetic Epidemiology, University of Regensburg, Germany Michael Höhle Department of Mathematics, Stockholm University, Sweden Andreas Bender Author for correspondence: Helmut Küchenhoff, E-mail: kuechenhoff@stat.uni-muenchen.de Save PDF (0.31 mb) View PDF[Opens in a new window] Save to Google Drive Save to Kindle We analysed the coronavirus disease 2019 epidemic curve from March to the end of April 2020 in Germany. We use statistical models to estimate the number of cases with disease onset on a given day and use back-projection techniques to obtain the number of new infections per day. The respective time series are analysed by a trend regression model with change points. The change points are estimated directly from the data. We carry out the analysis for the whole of Germany and the federal state of Bavaria, where we have more detailed data. Both analyses show a major change between 9 and 13 March for the time series of infections: from a strong increase to a decrease. Another change was found between 25 March and 29 March, where the decline intensified. Furthermore, we perform an analysis stratified by age. A main result is a delayed course of the pandemic for the age group 80 + resulting in a turning point at the end of March. Our results differ from those by other authors as we take into account the reporting delay, which turned out to be time dependent and therefore changes the structure of the epidemic curve compared to the curve of newly reported cases. Change pointCOVID-19epidemiology Epidemiology & Infection , Volume 149 , 2021 , e68 DOI: https://doi.org/10.1017/S0950268821000558[Opens in a new window] This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright © The Author(s), 2021. Published by Cambridge University Press The first phase of the coronavirus disease 2019 (COVID-19) pandemic in Germany was managed relatively successfully in comparison to other countries in Europe. Therefore, it is worth taking a closer look at the course of the pandemic in Germany, which has already led to controversial discussions in the public. This particularly concerns the important question about the effectiveness of various control measures. Several publications discuss the effects of control measures in different countries, see, e.g., [Reference Flaxman1–Reference Li3]. As [Reference Floyd and Endowed4] point out, however, many of such studies are undermined by unreliable data on incidence. Many papers use data provided by the Johns Hopkins University (JHU) [Reference Dong, Du and Gardner5]. These data are based on cumulative registered cases in different countries, which induces several problems, particularly the fact that not all cases are reported and that there is delay between the day of infection and the reporting day. Furthermore, the systems of reporting vary between countries, which makes comparisons between countries difficult. In a recent paper on Germany [Reference Dehning6], the authors use a complex Bayesian modelling approach based on the daily registrations in the JHU data for Germany. An important claim in [Reference Dehning6] is that the lock-down-like measures on 23 March were necessary to stop exponential growth. However, this claim is contradicted for example by results from the RKI [7]. Furthermore, these approaches were critically questioned by [Reference Bryant and Elofsson8, Reference Wieland9], where the latter emphasised the importance of taking into account the delay by reporting and incubation time, when analysing the possible effect of non-pharmaceutical interventions. In our analysis we focus on the curve of infection at two geographical levels: the federal state of Bavaria and all of Germany and on four age-strata. The paper is organised as follows. In section 'Data and methods', we present the data and the strategy of estimating the relevant daily counts. Then the segmented regression model, which is the basis for further analyses, is presented. The penultimate section presents the results followed by a discussion. Estimation of diseases onset For the analysis of the Bavarian data, we use the COVID-19 reporting data of the Bavarian State Office for Health and Food Safety (LGL) that is collected within the framework of the German Infection Control Act (IfSG). At the case level, these data include the reporting date (the date at which the case was reported to the LGL) as well as the time of disease onset (here: symptom onset). However, the latter is not always known: partly because it could not be determined and partly because the case did not (yet) have any symptoms at the time of entry into the database. A procedure for imputation of missing values regarding the disease onset has been developed by [Reference Günther10], using a flexible generalised additive model for location, scale and shape (GAMLSS; [Reference Stasinopoulos11]), assuming a Weibull distribution for the time period between disease onset and reporting date. The model includes gender, age, as well as calendar time and day of the week of reporting as covariates. We estimate the delay time distribution from data with disease onset and impute missing disease onsets based on this model. For the German data, no individual case data were available, so instead we used publicly available aggregated case reporting data published on a daily basis by the RKI [12]. These data contain aggregated numbers of reported cases for all observed combinations of disease onset date and reporting date at local health authorities as well as the numbers of reported cases per day without information on disease onset date. Information is aggregated on district level in different age and sex groups. Based on this aggregated data, we estimated a similar model as described above for the imputation of missing disease onset dates, replacing the smooth associations of age and reporting delay by a categorical effect of the age group of the cases. To account for differences in reporting behaviour in the different federal states, the model was estimated separately for each state and daily onset counts were aggregated after imputation. We estimated the imputation model for the German data based on all cases reported up until 1 June. The percentage of imputed values was 37% for the Bavarian data and 28% for the German data. Since this percentage is rather high, we performed a sensitivity analysis using (1) only data with a documented disease onset and (2) utilising the reporting date of cases as disease onset date when the actual onset date is unknown. Back-projection To interpret the course of the pandemic and possible effects of interventions, case-based data on time of infection is essential. However, as such data are generally not available, one simple approach is to shift the curve of disease onsets to the past by the average incubation period. The average incubation period for COVID-19 is about five days [Reference Lauer13]. A more sophisticated approach, however, is to use the incubation period distribution as part of an inverse convolution, also known as back-projection, in order to estimate the number of infections per day from the time series of disease onsets [Reference Becker, Watson and Carlin14, Reference Werber15]. We assume a log-normal distribution for the incubation time with a median of 5.1 days and a 97.5% percentile at 11.5 days [Reference Lauer13]. These are the same values as used by [Reference Dehning6]. For our calculation, we use the back-projection procedure implemented in the R package surveillance [Reference Salmon, Schumacher and Höhle16]. The segmented regression model To analyse the temporal course of the infection, we use the following regression model and change points (see [Reference Muggeo17, Reference Muggeo, Sottile and Porcu18]): (1)$$E\lpar {{\rm log}\lpar {Y_t} \rpar } \rpar = \beta _0 + \beta _1t + \mathop \sum \limits_{k = 1}^K \gamma _k\lpar {t-CP_k} \rpar _ + \comma \;$$ where Yt is the number of detected COVID-19 cases by time t of infection, K is the number of change points and x + = max(x, 0) is the positive part of x. The change points CPk, k = 1, …, K are used to partition the epidemic curve Yt into K + 1 phases. These are characterised by different growth parameters. In the phase before the first change point CP 1 the growth is characterised by the parameter β 1, in the 2nd phase between CP 1 and CP 2 by β 2 = β 1 + γ 1. The next change is then at time CP 2. In the 3rd phase between CP 2 and CP 3 the growth parameter is given by β 3 = β 1 + γ 1 + γ 2. This applies accordingly until the last phase after CPK. The quantities exp(βj), j = 1, …, K + 1 can be interpreted as daily growth factors. Since we use estimated, non-integer values Yt from the back-projection procedure as outcome, we assume a (conditional) Gaussian distribution for log(Yt). Furthermore, we assume an AR(1) error term for the regression model, since serial correlation occurs due to smoothing in the backprojection procedure. Since model (1) is a generalised linear model given the change points, the parameters of the model (including the change points) can be estimated by minimising the respective likelihood function. However, due to the estimation of the change points, the numerical optimisation problem is not straightforward. For the estimation of the model we use the R package segmented, see [Reference Muggeo19]. The starting values are partly estimated by discrete optimisation. The number of change points K is increased from K = 1 up to a maximum of K = 6. It is examined whether the increase of the number of change points leads to a lower value of the Bayesian information criterion (BIC). Since the considered time series consist of only 61 data points, we exclude models with more than 6 change points, since they are hardly interpretable and the danger of overfitting is high. We apply the segmented regression model to time series of the estimated daily counts of infections for detected COVID-19 cases in Bavaria and all of Germany. Since the back-projection algorithm yields an estimate for the expected values of the number of daily infections and does so by inducing a smoothing effect, as a sensitivity analysis for the location of the breakpoints, we also apply a regression model to the time series of the daily counts of disease onsets. The results of this sensitivity analysis are presented in the supplementary material. Furthermore, as a more detailed analysis, we apply our procedure to data stratified by age groups. A special focus is on the age group 80 + , as this group has the highest risk for a critical course of the disease. In Figure 1, the three different time series of daily case counts (newly reported, disease onset and estimated infection date) are presented. The time delay between the three time series for Bavaria and Germany is evident. Furthermore, the curves do not just differ by a constant shift on the x-axis, instead there is also a notable change in the structure of the curves. The curve relating to the date of infection is clearly smoothed due to the back-projection procedure (cf. Section 2.2) and has a clear maximum both for Bavaria and Germany. Fig. 1. Comparison of time series of daily reported cases (7 day average and daily reported numbers, light grey), disease onsets (reported and imputed, grey) and backprojection (derived number of infections, dark grey) for Bavaria (left panel) and Germany (right panel). Bavarian data The overall Bavarian model includes five change points. The result can be seen in Figure 2 (left panel) and in Table 1. Fig. 2. Segmented regression models for Bavaria. The left panel shows results for all reported cases from Bavaria. The solid line is the fitted curve ac cording to the segmented regression model (1) with five change points (K = 5) selected based on BIC. The bars are the expected numbers of detected COVID- 19 cases by time of infection (cf. Section 2.2). Dashed lines and surrounding shaded ribbons indicate estimated change points and respective, approximate 95% confidence intervals. The right panel shows results of the segmented regression in four age groups based on the back-projected number of infections per 100 000 individuals. The back-projection and segmented regression was estimated in each age group separately and the selected number of change points varies between groups. Table 1. Summary table of the segmented regression model for the expected number of daily infections in Bavaria with five change points The dates of the estimated change points and the corresponding 95% confidence intervals are given. For the date of the lower/upper limit of the confidence intervals, the values were rounded up or down to the more extreme value. In the second part of the table the estimated multiplication factors of the number of cases per day with the confidence intervals for the six phases are given The resulting six phases are: 1st phase: There is a substantial increase in new infections with a high daily multiplication factor of 1.25. The first phase ends on 6th March. 2nd phase: The increase slows down to a daily multiplication factor of 1.17. This phase lasts to the 10th of March. 3rd phase: For a short time the multiplication factor further goes down to 1.06 4th phase: The change point on 12th March marks a clearly visible change in the course of the pandemic. It is the turning point of the curve (change of the multiplication factor to 0.97). 5th phase: A further change point is found around 26th March. There is an accelerated decrease in the infections with a daily factor of 0.94. 6th phase: On 25th April the estimated number of infections of reported cases is rather low and there is no further decrease after this change point (multiplication factor close to 1). The age-stratified analysis gives some interesting further insights about the course of the pandemic, see Figure 2 (right panel) and Table S1 in the supplementary material. The age groups 15–59 and 60–79 years show a similar pattern as the overall analysis. However, in the 80 + age group there are clear differences compared to the other groups. There, the turning point of the pandemic is considerably later on 22nd March. Furthermore, the number of estimated infections per 100 000 is higher than in the other groups. The age group 0–14 years has a much lower number of reported infections, and change points similar to the overall analysis. German data The results for the German data are presented in Figure 3 and in Table 2. The model for Germany has four change points inducing five phases: Fig. 3. Segmented regression models for Germany. The left panel shows results for all reported cases. The solid line is the fitted curve according to the segmented regression model (1) with three change points (K = 3) selected based on BIC. The bars are the expected numbers of detected COVID-19 cases by time of infection (cf. Section 2.2). Dashed lines and surrounding shaded ribbons indicate estimated change points and respective, approximate 95% confidence intervals. The right panel shows results of the segmented regression in four age groups based on the back-projected number of infections per 100 000 individuals. The back-projection and segmented regression was estimated in each age-group separately and the selected number of change points varies between groups. Table 2. Summary table of the segmented regression model for the expected number of daily infections in Germany with four change points The dates of the estimated change points and the corresponding 95% confidence intervals are given. For the date of the lower/upper limit of the confidence intervals, the values were rounded up or down to the more extreme value. In the second part of the table the estimated multiplication factors of the number of cases per day with the confidence intervals for the 5 phases are given. 1st phase: There is a strong increase (multiplication factor 1.32 per day) in new infections in the beginning of the pandemic until 5th March, where the increase decreases. 2nd phase: From 5th March to 10th March there is still a substantial increase of infections with a daily multiplication factor around 1.1. 3rd phase: After the change point on 10th March, there is a clearly visible change in the course of the pandemic. There is change from an increasing to a decreasing curve with a daily multiplication factor of about 0.98. This phase lasts until 27th March. 4th phase: An acceleration of the decrease can be seen from 27th March onward. The daily multiplication factor is 0.94. 5th phase After 21st April, the number of infections is rather low with a slow decrease. The results of the age stratified analysis are similar to the results for Bavaria (cf. Figure 3, right panel and Supplement Table S2). The age group 80 + once again differs substantially from the other age groups. The turning point for the 80 + group is on 25th March. The other age groups show a structure similar to the overall analysis. The current analysis is a retrospective, exploratory analysis of the German and Bavarian COVID-19 reporting data during Mar–Apr 2020. The analysis only includes reported cases. If the proportion of undetected cases changes over time, e.g., due to different test criterion, this can distort the curve and thus the determination of the change points. Therefore, additional data on daily deaths and hospital admissions and the number of tests performed should be considered. Furthermore, it is possible to estimate the proportion of undetected cases with the help of representative studies such as the one currently conducted in Munich, see [Reference Radon20]. In a recent paper [Reference Schneble21] performed a time-varying estimation of the case detection ratio (CDR) for different age groups. They find a linear decreasing CDR from 2 March until 12 April in the main age groups. The CDR was only half as large at the end of the period as it was at the beginning. This can only partly explain the curve, where we observe a much higher increase. Our analysis is based to a considerable extent on imputed data, see [Reference Günther10], which is a result of missing data w.r.t. the disease onset. We have performed a sensitivity analysis using only cases with available disease onset date and based on imputing missing disease onset dates by the reporting date of the cases (Figure S2 in the supplementary material). The back-projection procedure is based on an assumption of the distribution of the incubation time. There are some recent papers showing some evidence for a longer incubation time in elderly cases, see [Reference Dai, Yang and Zhao22, Reference Tan23]. There-fore, we performed an additional sensitivity analysis comparing the results for the 80 + age group for different assumptions about the incubation time distribution, see supplementary material Figure S3. We find in this sensitivity analysis that the curve of the new infections is shifted to the left by about 2–3 days. However, the structure of the curve does not change considerably. Altogether, the much later peak in the 80 + compared to the other population strata cannot only be due to a different incubation time. Furthermore, our estimation of the change points and the corresponding confidence intervals is based on the estimated curve of the number of detected COVID-19 cases by time of infection. Due to the additional uncertainty of the curve induced by imputation, back-projection and model selection, the confidence intervals for the change points might not reflect the full extent of uncertainty in our modelling. However, even somewhat wider confidence intervals would not fundamentally change the interpretation of our results. Since changes in behaviour do not occur abruptly, the assumption of change points is also problematic in itself. Therefore, the interpretation of change points should always be done in conjunction with a direct observation of the epidemic curve. Interpretation of results Our analysis is based on the onset of the disease (more precisely: the onset of symptoms) and a back-projection to the date of infections, and therefore, despite its limitations, is better suited to describe the course of the pandemic than the more common analysis of daily or cumulative reported case numbers. In the analysis of the Bavarian and the German data our main result is the change point, where the exponential growth was stopped: this clearly happened already between 9 and 13 March. The timing of this change point coincides with the implementation of the first control measures: the partial ban of mass events with more than 1000 people. Furthermore, in a press conference on March 11th chancellor Merkel and the president of the RKI appealed to self-enforced social distancing [24]. Furthermore, the extended media coverage from Bergamo, Italy, as well as the voluntary transition to home-office work could be related to this essential change in the course of the pandemic. In Bavaria and in Germany, the change point at 26/27th March of the infection date is apparent. This change point is associated with different measures taken in March (closing of schools and stores on 16th March and the shut- down including contact ban on 22nd March in Germany including Bavaria). Other measures were similar in timing in Bavaria and all over Germany. In Bavaria, some measures were implemented a little earlier. Since there were many measures administered simultaneously and since – as described above – other factors beyond the measures itself contributed, we do not think is not possible to quantify the effect of individual measures to the development of the epidemic curve. The results for the 80 + age group indicate an infection curve which is delayed by about one week compared to the other age groups. This is possibly due to the fact that the disease was first introduced into Germany by younger holiday makers and business travellers. Hence, it likely took some additional generations of transmission before the infections mitigated into the 80 + group. Furthermore, many infections in the age group 80 + are due to outbreaks in nursing homes and homes for the elderly, where very different mechanisms of contact occur compared to the rest of the population. Many of the restrictions were targeted at the younger age groups (school closings, mobility restrictions), hence, the effect of these interventions is only indirect for the 80 + group and thus the impact is delayed. This underlines the need for more direct measures for this group. For the age group of 0–14 the breakpoints are similar to the other age groups. The much lower infection rate could be partly due to lower case detection ratio, since infected children show less symptoms, see e.g. [Reference Ludvigsson25]. The claim by Dehning et al. [Reference Dehning6], that the shutdown on 21st March was necessary to stop the growth of the pandemic is not supported by our analysis. There is a change point in the epidemic curve after that date, but the major change from an exponential growth to a decrease was before the shutdown. The difference in results can be explained by the different data bases used for the respective analyses. While Dehning et al. [Reference Dehning6] used data bases on daily registered cases, in our analysis, data on disease onset are included. As can be seen from Figure 1 and from the results of our data analysis, the delay distribution of the time between disease onset and reporting day changed over time. This makes a crucial difference. In a recent technical addendum [Reference Dehning26] the authors re-fit their model on more appropriate data. These analysis – in our opinion – clearly show that the effective reproduction number decreased earlier than in their initial analysis, however, they attribute the decrease to a SIR model peculiarity, where a linear decrease in the contact rate can lead to the incidence curve dropping despite R(t) > 1. The above discussions illustrate how complex the interpretation of even simple SIR models is and the question is, if such SIR modelling is not too simple to really allow for questions to be answered model based (no age structure, no time-varying reporting delay, no incubation period). In contrast, our approach is more data driven with a minimum of modelling assumptions and without the need to include strong prior information about the change points. Directly using a segmented curve with exponential growth (decline) is in line with common models of infectious diseases in its early stages, where the limitation of the spread by immune persons plays no role. The problem of using complex models with many parameters for the evaluation of governmental measures has also been highlighted by [Reference Bryant and Elofsson8]. Our approach is similar to that of [Reference Wieland9] who performs a change point analysis for the cumulative reported numbers as well as the estimated R(t). The use of the time-varying reproduction number R(t), a standard measure to describe the course of an epidemic is challenging, as different definitions have been proposed in the literature that also imply different interpretations (see [Reference Cori27, Reference Lipsitch, Joshi and Cobey28]). However, the analysis of R(t) as a relative measure can be useful, when one wants to analyse data from different countries with non-comparable reporting systems, see [Reference Li3]. Altogether, the effect of governmental measures as a whole is clearly documented in the literature, see, e.g., [Reference Flaxman1] and [Reference Islam2]. Our results are in line with that of [Reference Wood29], where a stop of exponential growth in Great Britain was also observed before the lockdown. Our result on a possible effect of the ban of mass events is also in line with the results of [Reference Li3]. The temporal connection between the change points in our analysis and various control measures should be interpreted as an association, rather than a direct causal relationship. In the end many other explanations exists and from a simple time-series analysis it is not possible to say to what extent the population already had changed their behaviour voluntarily, as for example observed in mobility data [Reference Bryant and Elofsson30, Reference Schlosser31], and in what way the measures contributed to this. More speculative alternative explanations would include the possibility of a seasonal effect on coronavirus activity (e.g. related to temperature) or changes in test capacity or the case detection ratio. However, given the re-emergence of the pandemic in the fall of 2020 at high test capacity and at relatively high temperatures shows that contact behaviour is the major explanatory factor for virus activity. Nevertheless, any analysis of observational Time-series data including only a limited amount of explanatory factors has to be interpreted with care and with respect to the many uncertainties which remain regarding COVID-19 [Reference Davey Smith, Blastland and Munafò32]. Despite the limitations of the approach, we argue that it is advantageous and important to directly interpret the epidemic curve and the absolute number of cases, rather than indirect measures like the R(t). Furthermore, the reproduction rate does not contain information about how many people are currently affected, or whether the infected persons belong to risk groups. The course of the time-varying reproduction number calculated by us for Bavaria fits well with the change point analysis [Reference Günther10]. A value of R(t) > 1 corresponds to a rate of increase >1, noting that the time delays in the interpretation of R(t) must be kept in mind. It should be noted, that the presented analysis is retrospective. Control measures have to be decided based on a completely different level of information than what the retrospectively established epidemic curve suggests. The simple observation of the course of the reported case numbers by reporting date is also problematic because this course is strongly influenced by the reporting behaviour and the methods and capacities of the test laboratories. Typically, substantially fewer cases are reported at weekends than during the week. Therefore, the estimation proposed by Günther et al. [Reference Günther10] is an important step to estimate the better interpretable curve of new cases, but is limited by assumptions and limitations itself, that need to be considered when interpreting the results. Since the impact of the measures also depends on how they are implemented by the population (compliance), the results cannot be directly transferred to the future. Nevertheless, it remains a remarkable result that the clear turning point of the early COVID-19 infection data in Germany is associated with non-drastic measures (no shutdown) and strong appeals by politicians. The supplementary material for this article can be found at https://doi.org/10.1017/S0950268821000558 We would like to thank Katharina Katz and Manfred Wildner from the Bavarian State Office for Health and Food Safety (LGL) for providing the data and for useful discussions. We also thank Nadja Sauter and Daniel Schlichting for help with visualisations. We thank two reviewers whose comments helped to improve the work significantly. Data and code availability Data used for the analyses and all code to reproduce the models, figures and tables in the manuscript are openly and freely available from [Reference Günther33]. All analyses were performed using the R programming language [34]. Flaxman, S et al. 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Cross Validated Cross Validated Meta Cross Validated is a question and answer site for people interested in statistics, machine learning, data analysis, data mining, and data visualization. Join them; it only takes a minute: What does Theta mean? I am a newbie to statistics and found this. In statistics, θ, the lowercase Greek letter 'theta', is the usual name for a (vector of) parameter(s) of some general probability distribution. A common problem is to find the value(s) of theta. Notice that there isn't any meaning in naming a parameter this way. We might as well call it anything else. In fact, a lot of distributions have parameters which are usually given other names. For example, it is common use to name the mean and deviation of the normal distribution μ (read: 'mu') and deviation σ ('sigma'), respectively. But I still don't know what that means in plain English? gui11aume Kamilski81Kamilski81 $\begingroup$ $\theta$ is just a mathematical symbol and means different things in different contexts. Sometimes $\theta$ is used to refer to a parameter to be estimated but there is no real answer to the question "What is $\theta$?". That's like asking "What is the letter A?". Your link even hints at this when it says "Notice that there isn't any meaning in naming a parameter this way. We might as well call it anything else.". $\endgroup$ – Macro Aug 22 '12 at 22:39 $\begingroup$ Its just a way to name a statistical parameter(which defines the distribution of the quantity associated with this 'parameter') with a special letter (other than English letters). $\endgroup$ – Stat-R Aug 22 '12 at 23:01 $\begingroup$ Most of us would take this quotation to be extremely plain English, indeed, but to make any progress we have to accept that the question is not about how to read English. What, then, could it be about? I submit that it is asking us to explain the technical terms in the quotation: the ones with which we are so familiar that we no longer see how strange they might be to the statistically uninitiated. This calls for us to address the meanings of distribution and parameters (of a distribution that is; not of a fitted curve or other deterministic model). $\endgroup$ – whuber♦ Aug 23 '12 at 13:01 It is not a convention, but quite often $\theta$ stands for the set of parameters of a distribution. That was it for plain English, let's show examples instead. Example 1. You want to study the throw of an old fashioned thumbtack (the ones with a big circular bottom). You assume that the probability that it falls point down is an unknown value that you call $\theta$. You could call a random variable $X$ and say that $X=1$ when the thumbtack falls point down and $X=0$ when it falls point up. You would write the model $$P(X = 1) = \theta \\ P(X = 0) = 1-\theta,$$ and you would be interested in estimating $\theta$ (here, the proability that the thumbtack falls point down). Example 2. You want to study the disintegration of a radioactive atom. Based on the literature, you know that the amount of radioactivity decreases exponentially, so you decide to model the time to disintegration with an exponential distribution. If $t$ is the time to disintegration, the model is $$f(t) = \theta e^{-\theta t}.$$ Here $f(t)$ is a probability density, which means that the probability that the atom disintegrates in the time interval $(t, t+dt)$ is $f(t)dt$. Again, you will be interested in estimating $\theta$ (here, the disintegration rate). Example 3. You want to study the precision of a weighing instrument. Based on the literature, you know that the measurement are Gaussian so you decide to model the weighing of a standard 1 kg object as $$f(x) = \frac{1}{\sigma \sqrt{2\pi}} \exp \left\{ -\left( \frac{x-\mu}{2\sigma} \right)^2\right\}.$$ Here $x$ is the measure given by the scale, $f(x)$ is the density of probability, and the parameters are $\mu$ and $\sigma$, so $\theta = (\mu, \sigma)$. The paramter $\mu$ is the target weight (the scale is biased if $\mu \neq 1$), and $\sigma$ is the standard deviation of the measure every time you weigh the object. Again, you will be interested in estimating $\theta$ (here, the bias and the imprecision of the scale). gui11aumegui11aume $\begingroup$ +1 FWIW, I recently posted a worked example along the same lines at stats.stackexchange.com/a/34894. Although it would be misleading to construe it as "plain English"--it does not shy from using technical terms--I made an effort to explain as clearly and briefly as possible what is going on, what assumptions are made, and how one works with a parameterized family of distributions to produce an estimate based on data. For some, this might be an informative adjunct to your answer here. $\endgroup$ – whuber♦ Aug 23 '12 at 22:20 $\begingroup$ Great answer! I am confused when you state the scale is biased if mu != 1, though. In fact, upon "normalizing", the standard normal distribution becomes x ~ N(0, 1). Or, in English, the mu = 0 and the variance = 1. See e.g., en.wikipedia.org/wiki/… $\endgroup$ – Mike Williamson Jan 7 '15 at 20:15 $\begingroup$ I just mean that the instrument has a bias if it indicates something else than 1 kg when it measures a 1 kg object. Perhaps the word "scale" is confusing. Here it just designates the instrument. $\endgroup$ – gui11aume Jan 8 '15 at 2:42 What $\theta$ refers to depends on what model you are working with. For example, in ordinary least squares regression, you model a dependent variable (usually called Y) as a linear combination of one or more independent variables (usually called X), getting something like $Y_i = b_0 + b_1x_1 + b_2x_2 + ... + b_px_p$ where p is the number of independent variables. The parameters to be estimated here are the $\beta s$ and $\theta$ is a name for all the $\beta s$. But $\theta$ is more general can apply to any parameters we want to estimate. Peter Flom♦Peter Flom $\begingroup$ Peter, although you didn't say this exactly, I'm afraid this answer may give a novice the incorrect impression that the symbol $\theta$ will always refer to a parameter vector and, conversely, that this is the only way to refer to a parameter value. As my comment above indicates, I think the answer is nothing more than "$\theta$ is a mathematical symbol", making it not really a statistical question. $\endgroup$ – Macro Aug 22 '12 at 22:42 $\begingroup$ @Macro I think, in this context, it's clear that this is the meaning of $\theta$ that Kamilski wanted. Sure, any symbol can refer to anything. But in this paragraph, Macro means you, and not a course in Economics or a part of SAS or whatnot. $\endgroup$ – Peter Flom♦ Aug 22 '12 at 22:46 $\begingroup$ ok well I don't think that analogy is really apt but I will take it as an attempt at hyperbole. In any case, I'm really referring to something very basic which is that mathematical novices often mistake notation as something inherently meaningful and as something other than what it is - simply a label. My point was that this answer (I think unintentionally) does nothing to dispel that idea. As you know, $\theta$ can refer to other things a statistician may encounter. For example, angles are often denoted by $\theta$. $\endgroup$ – Macro Aug 22 '12 at 23:03 $\begingroup$ This explanation, although it is clear and technically correct, does not explicitly involve any distributions whatsoever, and thus appears not to be relevant to the quotation in the question. $\endgroup$ – whuber♦ Aug 23 '12 at 13:03 In plain English: Statistical distribution is a mathematical function $f$ that tells you what is the probability of different values of your random variable $X$ that has the distribution $f$, i.e. $f(x)$ outputs a probability of $x$. There are different such a functions, but for now let consider $f$ as some kind of "general" function. However, for $f$ to be universal, that is, one that is possible to apply to different data (that share similar properties), it needs parameters that change its shape so that it fits different data. A simple example of such a parameter is $\mu$ in normal distribution that tells where is the center (mean) of this distribution and so it can describe random variables with different mean values. Normal distribution has another parameter $\sigma$ and other distributions also have at least one such a parameters. The parameters are often called $\theta$, where for normal distribution $\theta$ is a shorthand for both $\mu$ and $\sigma$ (i.e. is a vector of the two values). Why is $\theta$ important? Statistical distributions are used to approximate the empirical distributions of data. Say you have dataset of ages of a group of people and on average they are 50 years old and you want to approximate the distribution of their ages using a normal distribution. If normal distribution didn't allow for different values of $\mu$ (e.g. had a fixed value of this parameter, say $\mu=0$), then it would be useless for this data. However, since $\mu$ is not fixed, normal distribution could use different values of $\mu$, with $\mu=50$ being one of them. This is a simple example, but there are more complicated cases where the values of $\theta$ parameters are not so clear and so you have to use statistical tools for estimating (finding the most appropriate) $\theta$ values. So you could say that statistics is about finding the best $\theta$ values given the data (Bayesians would say: given the data and priors). Tim♦Tim Thanks for contributing an answer to Cross Validated! Not the answer you're looking for? Browse other questions tagged terminology or ask your own question. How to estimate the third quartile of binned data? meaning of metric vs. statistic vs. parameter What exactly does it mean to 'pool data'? What does "curvilinear" mean? What does mAP mean? What does "orthogonalize" mean? What does "probability distribution" mean? What does 'vector-valued' mean? What does "marginal" mean as a noun? What does "vanilla" mean? What does scale exactly mean? Naming of mathematical elements in GMM?	CommonCrawl
Siyao Zhu and Jinliang Wang School of Mathematical Science, Heilongjiang University, Harbin 150080, China In this paper, we investigate a diffusive SIS epidemic model with spontaneous infection and a linear source in spatially heterogeneous environment. We first prove that the solution of the model is bounded when the susceptible and infected individuals have same or distinct dispersal rates. The global stability of the constant endemic equilibrium is proved by constructing suitable Lyapunov functionals when all parameters are positive constants. We employ the topological degree argument to show the existence of positive steady state. Most importantly, we have also investigated the asymptotic profiles of the positive steady state as the dispersal rate of susceptible or infected individuals tends to zero or infinity. 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Discrete & Continuous Dynamical Systems - B, 2017, 22 (2) : 507-536. doi: 10.3934/dcdsb.2017025 Jian-Wen Sun, Wan-Tong Li, Zhi-Cheng Wang. A nonlocal dispersal logistic equation with spatial degeneracy. Discrete & Continuous Dynamical Systems - A, 2015, 35 (7) : 3217-3238. doi: 10.3934/dcds.2015.35.3217 Roger M. Nisbet, Kurt E. Anderson, Edward McCauley, Mark A. Lewis. Response of equilibrium states to spatial environmental heterogeneity in advective systems. Mathematical Biosciences & Engineering, 2007, 4 (1) : 1-13. doi: 10.3934/mbe.2007.4.1 Stephen Pankavich, Christian Parkinson. Mathematical analysis of an in-host model of viral dynamics with spatial heterogeneity. Discrete & Continuous Dynamical Systems - B, 2016, 21 (4) : 1237-1257. doi: 10.3934/dcdsb.2016.21.1237 Qingyan Shi, Junping Shi, Yongli Song. Hopf bifurcation and pattern formation in a delayed diffusive logistic model with spatial heterogeneity. Discrete & Continuous Dynamical Systems - B, 2019, 24 (2) : 467-486. doi: 10.3934/dcdsb.2018182 Yoji Otani, Tsuyoshi Kajiwara, Toru Sasaki. Lyapunov functionals for virus-immune models with infinite delay. Discrete & Continuous Dynamical Systems - B, 2015, 20 (9) : 3093-3114. doi: 10.3934/dcdsb.2015.20.3093 Wilhelm Schlag. Regularity and convergence rates for the Lyapunov exponents of linear cocycles. Journal of Modern Dynamics, 2013, 7 (4) : 619-637. doi: 10.3934/jmd.2013.7.619 Luis Barreira, Claudia Valls. Quadratic Lyapunov sequences and arbitrary growth rates. Discrete & Continuous Dynamical Systems - A, 2010, 26 (1) : 63-74. doi: 10.3934/dcds.2010.26.63 Rongsong Liu, Jiangping Shuai, Jianhong Wu, Huaiping Zhu. Modeling spatial spread of west nile virus and impact of directional dispersal of birds. Mathematical Biosciences & Engineering, 2006, 3 (1) : 145-160. doi: 10.3934/mbe.2006.3.145 Sergio Grillo, Jerrold E. Marsden, Sujit Nair. Lyapunov constraints and global asymptotic stabilization. Journal of Geometric Mechanics, 2011, 3 (2) : 145-196. doi: 10.3934/jgm.2011.3.145 Linda J. S. Allen, B. M. Bolker, Yuan Lou, A. L. Nevai. Asymptotic profiles of the steady states for an SIS epidemic reaction-diffusion model. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 1-20. doi: 10.3934/dcds.2008.21.1 Kazuhiro Kurata, Tatsuya Watanabe. A remark on asymptotic profiles of radial solutions with a vortex to a nonlinear Schrödinger equation. Communications on Pure & Applied Analysis, 2006, 5 (3) : 597-610. doi: 10.3934/cpaa.2006.5.597 Ryo Ikehata, Marina Soga. Asymptotic profiles for a strongly damped plate equation with lower order perturbation. Communications on Pure & Applied Analysis, 2015, 14 (5) : 1759-1780. doi: 10.3934/cpaa.2015.14.1759 Tohru Wakasa, Shoji Yotsutani. Asymptotic profiles of eigenfunctions for some 1-dimensional linearized eigenvalue problems. Communications on Pure & Applied Analysis, 2010, 9 (2) : 539-561. doi: 10.3934/cpaa.2010.9.539 Siyao Zhu Jinliang Wang	CommonCrawl
Polynomial and rational first integrals for planar quasi--homogeneous polynomial differential systems DCDS Home An equivalent characterization of the summability condition for rational maps October 2013, 33(10): 4549-4566. doi: 10.3934/dcds.2013.33.4549 A Liouville theorem of degenerate elliptic equation and its application Genggeng Huang 1, School of Mathematical Science, Fudan University, Shanghai, 200433, China Received November 2012 Revised February 2013 Published April 2013 In this paper, we apply the moving plane method to the following degenerate elliptic equation arising from isometric embedding,\begin{equation} yu_{yy}+au_y+\Delta_x u+u^\alpha=0\text{ in } \mathbb R^{n+1}_+,n\geq 1. \end{equation} We get a Liouville theorem for subcritical case and classify the solutions for critical case. As an application, we derive the a priori bounds for positive solutions of some semi-linear degenerate elliptic equations. Keywords: blow-up, semi-linear, Liouville theorem, degenerate., moving plane. Mathematics Subject Classification: Primary: 35J61, 35J70; Secondary: 35B53, 35B4. Citation: Genggeng Huang. A Liouville theorem of degenerate elliptic equation and its application. Discrete & Continuous Dynamical Systems - A, 2013, 33 (10) : 4549-4566. doi: 10.3934/dcds.2013.33.4549 A. D. Alexandrov, Uniqueness theorems for surfaces in the large. V.,, Amer. Math. Soc. Transl.(2), 21 (1962), 412. Google Scholar L. Caffarelli, B. Gidas and J. Spruck, Asymptotic symmetry and local behavior of semilinear elliptic with critical Sobolev growth,, Comm. Pure Appl. Math., 42 (1989), 271. doi: 10.1002/cpa.3160420304. Google Scholar W.-X. Chen, C.-M. Li and B. OU, Classification of solutions for an integral equation,, Comm. Pure Appl. Math., 59 (2006), 330. doi: 10.1002/cpa.20116. Google Scholar W.-X. Chen and C.-M. 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Plenum Press, (1973). Google Scholar J. Serrin, A symmetry problem in potential theory,, Arch. Rational Mech. Anal., 43 (1971), 304. Google Scholar J.-C. Wei and X.-W. Xu, Classification of solutions of higher order conformally invariant equations,, Math. Ann., 313 (1999), 207. doi: 10.1007/s002080050258. Google Scholar X.-W. Xu, Classification of solutions of certain fourth-order nonlinear elliptic equations in $\mathbb R^4$,, Pacific J. Math., 225 (2006), 361. doi: 10.2140/pjm.2006.225.361. Google Scholar Hua Chen, Nian Liu. Asymptotic stability and blow-up of solutions for semi-linear edge-degenerate parabolic equations with singular potentials. Discrete & Continuous Dynamical Systems - A, 2016, 36 (2) : 661-682. doi: 10.3934/dcds.2016.36.661 Alberto Bressan, Massimo Fonte. On the blow-up for a discrete Boltzmann equation in the plane. Discrete & Continuous Dynamical Systems - A, 2005, 13 (1) : 1-12. doi: 10.3934/dcds.2005.13.1 Yihong Du, Zongming Guo. The degenerate logistic model and a singularly mixed boundary blow-up problem. Discrete & Continuous Dynamical Systems - A, 2006, 14 (1) : 1-29. doi: 10.3934/dcds.2006.14.1 Shota Sato. Blow-up at space infinity of a solution with a moving singularity for a semilinear parabolic equation. Communications on Pure & Applied Analysis, 2011, 10 (4) : 1225-1237. doi: 10.3934/cpaa.2011.10.1225 Dongho Chae. On the blow-up problem for the Euler equations and the Liouville type results in the fluid equations. Discrete & Continuous Dynamical Systems - S, 2013, 6 (5) : 1139-1150. doi: 10.3934/dcdss.2013.6.1139 Ansgar Jüngel, Oliver Leingang. Blow-up of solutions to semi-discrete parabolic-elliptic Keller-Segel models. Discrete & Continuous Dynamical Systems - B, 2019, 24 (9) : 4755-4782. doi: 10.3934/dcdsb.2019029 Sachiko Ishida, Tomomi Yokota. Blow-up in finite or infinite time for quasilinear degenerate Keller-Segel systems of parabolic-parabolic type. Discrete & Continuous Dynamical Systems - B, 2013, 18 (10) : 2569-2596. doi: 10.3934/dcdsb.2013.18.2569 Tetsuya Ishiwata, Shigetoshi Yazaki. A fast blow-up solution and degenerate pinching arising in an anisotropic crystalline motion. Discrete & Continuous Dynamical Systems - A, 2014, 34 (5) : 2069-2090. doi: 10.3934/dcds.2014.34.2069 Hua Chen, Huiyang Xu. Global existence and blow-up of solutions for infinitely degenerate semilinear pseudo-parabolic equations with logarithmic nonlinearity. Discrete & Continuous Dynamical Systems - A, 2019, 39 (2) : 1185-1203. doi: 10.3934/dcds.2019051 Frédéric Abergel, Jean-Michel Rakotoson. Gradient blow-up in Zygmund spaces for the very weak solution of a linear elliptic equation. Discrete & Continuous Dynamical Systems - A, 2013, 33 (5) : 1809-1818. doi: 10.3934/dcds.2013.33.1809 Min Zhu, Shuanghu Zhang. Blow-up of solutions to the periodic modified Camassa-Holm equation with varying linear dispersion. Discrete & Continuous Dynamical Systems - A, 2016, 36 (12) : 7235-7256. doi: 10.3934/dcds.2016115 Min Zhu, Ying Wang. Blow-up of solutions to the periodic generalized modified Camassa-Holm equation with varying linear dispersion. Discrete & Continuous Dynamical Systems - A, 2017, 37 (1) : 645-661. doi: 10.3934/dcds.2017027 Wenqiang Zhao. Random dynamics of non-autonomous semi-linear degenerate parabolic equations on $\mathbb{R}^N$ driven by an unbounded additive noise. Discrete & Continuous Dynamical Systems - B, 2018, 23 (6) : 2499-2526. doi: 10.3934/dcdsb.2018065 C. Y. Chan. Recent advances in quenching and blow-up of solutions. Conference Publications, 2001, 2001 (Special) : 88-95. doi: 10.3934/proc.2001.2001.88 Marina Chugunova, Chiu-Yen Kao, Sarun Seepun. On the Benilov-Vynnycky blow-up problem. Discrete & Continuous Dynamical Systems - B, 2015, 20 (5) : 1443-1460. doi: 10.3934/dcdsb.2015.20.1443 Marek Fila, Hiroshi Matano. Connecting equilibria by blow-up solutions. Discrete & Continuous Dynamical Systems - A, 2000, 6 (1) : 155-164. doi: 10.3934/dcds.2000.6.155 Victor A. Galaktionov, Juan-Luis Vázquez. The problem Of blow-up in nonlinear parabolic equations. Discrete & Continuous Dynamical Systems - A, 2002, 8 (2) : 399-433. doi: 10.3934/dcds.2002.8.399 W. Edward Olmstead, Colleen M. Kirk, Catherine A. Roberts. Blow-up in a subdiffusive medium with advection. Discrete & Continuous Dynamical Systems - A, 2010, 28 (4) : 1655-1667. doi: 10.3934/dcds.2010.28.1655 Yukihiro Seki. A remark on blow-up at space infinity. Conference Publications, 2009, 2009 (Special) : 691-696. doi: 10.3934/proc.2009.2009.691 Petri Juutinen. Convexity of solutions to boundary blow-up problems. Communications on Pure & Applied Analysis, 2013, 12 (5) : 2267-2275. doi: 10.3934/cpaa.2013.12.2267 2018 Impact Factor: 1.143 PDF downloads (9) HTML views (0) on AIMS Genggeng Huang Export File RIS(for EndNote,Reference Manager,ProCite) Recipient's E-mail* Content*	CommonCrawl
Home \| Ham Radio \| IcomControl Home Page IcomProgrammmer II JRX: Virtual Ham Radio Morse Code PLSDR RadioComm Home Page Sangean ATS-909X Simple 10 MHz Frequency Standard Software-Defined Radios Share This Page A rather nice portable shortwave radio — All content Copyright © 2013, P. Lutus — Message Page — Introduction \| ATS-909X in depth \| Conclusion I don't normally write articles about radios, but I'm going to make an exception. I have two reasons to write this article about the Sangean ATS-909X. One, I think it's a terrific radio. Two, there is a bunch of misinformation circulating about it on discussion boards, and I think I can correct some of that. Disclaimer: I have no connection with Sangean or any vendor of the radio. This is written purely as a technically skilled purchaser. To me, the perfect shortwave radio doesn't exist, but that isn't to say it cannot exist. Since there are amazing radios like the Icom IC-7000 ham transceiver for about US\$1300 at the time of writing (and that I recently acquired), and since it contains within it a first-rate receiver that could exist as a separate product, therefore if only Icom realized there's an unfilled market niche for a really outstanding battery-operated portable receiver for about US\$700, then there really would be a perfect portable radio. Those who live in the industrialized West get the idea that, for every market need, there's a company willing to jump in and try to fill it. But guess what? As to portable radios, there is a conspicuous gap between the relatively new Sangean ATS-909X (which is a nice radio) and high-end products like the Icom IC-7000, which, although meant for a different audience (radio amateurs), makes a terrific receiver when it's not being a transceiver. The reasons for this gap are easy to guess — people don't listen to shortwave radio very much any more, some of that need is being filled by the Internet and smartphones, American kids don't learn to build things any more, so they're less likely to put together a ham shack or even a formal shortwave receiving station with an outside antenna. But you know what? As the Internet has evolved away from being a discussion forum and technical resource and gradually turned into a marketplace, to me at least it has become somewhat boring. I think there are people out there in cyberland who might jump at the chance to do something that doesn't involve being online — just for some variety in their lives. To wrap up this introduction and get on with a discussion of the ATS-909X, here is the market gap I see that a company like Icom could fill if only they realized that the gap exists: Consumer level Empty Chasm Amateur radio level Sangean ATS-909X Shortwave Radio (about US\$220 at time of writing) This is a market niche with no candidate radios, in spite of substantial consumer interest. It could be filled with a radio having some of the qualities of top-end Icom radios, but not a transceiver, more modest power requirements, and retail priced at about US\$700. Icom IC-7000 Ham Transceiver (about US$1300 at time of writing) ATS-909X in depth I've had a lot of radios over the years, including some I've designed, either as a radio amateur or during my time as a NASA engineer. Decades ago it was easier for a manufacturer to find a market for a shortware radio simply because there was more interesting content on the air. Now that the Internet has assumed some of the roles that radio once filled, there are fewer shortwave radio broadcasters that aren't simply emitting propaganda for their home countries. But this isn't to say there's no interesting shortwave radio content — there's plenty, you just have to be patient and know when and where to listen. And it can't hurt if the radio you choose has the widest possible frequency range. I recently decided to shop for a portable radio, something I do from time to time, often more to see what's available than to actually buy one. This time I decided to actually buy an ATS-909X, because it was reasonably priced, many people had good things to say about it online, and my prior portable radio (a crappy Radio Shack model: Grundig G5, not recommended) had given up the ghost. I paid about US$220 for the ATS-909X at Amazon.com, and as I awaited the radio's arrival I tried to keep my expectations down. I've watched the quality of consumer shortwave radios gradually decline over the years, along with the decline in public interest in shortwave reception, so I didn't expect much, especially given the low price. So color me surprised. The radio is actually rather well-built. It charges its own batteries if you install rechargeable ones, it has a large, easy-to-read display, and it has a number of features that put it a cut above its price class. If you select the slow tuning rate, it tunes in 40 Hz steps, small enough steps to allow easy SSB tuning, and another trait that sets this radio apart from others in its class. Also, its filter design is such that you can easily distinguish upper from lower sideband settings, another trait I don't often see in a portable radio. Some online reviewers say this radio isn't very sensitive, but I haven't noticed any serious difficulty in that area. In my ham shack I tuned in some relatively weak amateur stations for comparison, with my hamshack receivers attached to large antennas and tuners, and the Sangean using its whip antenna and an attached power pack, and I was able to copy weaker stations on both radios simultaneously. I'm not saying the sensitivity criticism is without merit, but so far I haven't seen any support for it. Addendum: After several weeks of use, including occasions using the radio outdoors with only the whip antenna and no power connection (therefore no ground path), I have to agree there is some justification for the claim that this radio isn't supremely sensitive when receiving shortwave (but no problems with commercial broadcast AM and FM reception). I can't decide whether the low shortwave sensitivity while using the whip antenna results from the radio's input circuit itself, or a mismatch between the whip antenna and the input circuit. In any case, for outdoor shortwave reception much better results are obtained using the provided wire-on-a-reel antenna than the whip antenna. Again, this is not an issue for AM and FM broadcast reception. Tuning detent Before I acquired this radio, I read all about the tuning detent issue. As delivered, there is a spring enclosed within the radio's dial tuning device that produces some resistance to movement — the tuning dial jumps from one position to another a few degrees away. There is a company that will take this spring out for you, in case you're not confident enough in your soldering skills, and the online opinions expressed about this detent tuning seem universal — it was a design error. I found enough information online to know how to proceed, so shortly after I acquired the radio, I took it apart and delicately unsoldered the dial tuning device from its circuit board, pried it open, and removed the detent spring. Disassembling and reassembling the radio wasn't difficult, but unsoldering, opening, closing and resoldering the dial tuning device was quite difficult, and I don't recommend it to anyone who isn't an expert at soldering and use of small tools, and has all the right equipment at hand. Anyway, now the tuning mechanism is smooth as silk, which really improves the experience of tuning this radio. Friction, not light Because I removed and examined the tuning mechanism, I got a chance to see how it works, and I have a comment. When I see a freely rotating dial on a modern electronic device, I assume it's an optical encoder. Figure 1: Schematic excerpt from page 52 of the ATS-909X service manual This one isn't — it's mechanical. Inside the tuning device are three little mechanical fingers that contact a plate with patterned metal surfaces to encode which direction the user is rotating the tuning knob. I see this as one of the few negatives in this radio — a frequent tuner is eventually going to wear this device out through simple friction. Power source issue My regular visitors know I spend a fair amount of time on my boat or in my RV, so I try to get equipment that runs on 12 volts DC if possible. This radio comes with a 9 volt AC power converter, and I read a few online accounts in which someone apparently technically knowledgeable scolded owners for trying to run the radio on a direct-current power source. Well, I'm a former NASA electronics engineer, responsible for some electronics on the Space Shuttle, so I know my way around electronics, and I will say that this radio is perfectly happy to be powered by 12 volts DC. But rather than wave my hands in the air, let me provide my reasoning. Figure 2: Mathematical model of full-wave bridge rectifier powered by 9VRMS AC Powering the ATS-909X from 12V DC: Click here for the ATS-909X service manual (PDF). Turn to page 52 in the manual — the "Main Schematic Diagram". At the top of the page, you will see a section of the schematic that's also shown on this page (Figure 1, rotated 90°). At the right of the image, you will see the radio's power jack, marked JK4. Those familiar with electronics and schematic diagrams will see that the power jack, which is provocatively marked "DC/IN", is connected to a full-wave bridge rectifier (D16), followed by a 1000 µf 16V capacitor (C155). The power source delivered with the radio is a 9 volt AC, 700 milliamp power pack. The voltage of AC power packs, and AC sources in general, is expressed in RMS (root means squared) units. The peak voltage of an RMS AC source is equal to: $\text{RMS} \times \sqrt{2}$. The radio's bridge rectifier (D16) and filtering capacitor (C155) have the effect of converting the source 9 V RMS AC into a peak voltage of ($9 \times \sqrt{2}$) = 12.72 VDC. The ATS-909X power treatment circuit is mathematically modeled in Figure 2: a full-wave bridge rectifier driven by a 9 VRMS 60 Hz source, a 1000 µf filter capacitor, and a 160 milliampere load (measured). The model demonstrates that the radio's supply voltage averages 12 VDC. Therefore this radio is perfectly happy to be powered by a direct current source, and 12 volts is right in the middle of its acceptance range. I have my ATS-909X right beside me, powered by a normal 12VDC source, and not only is it running correctly, when powered off it charges the NiMH batteries I installed in it. Click here for the ATS-909X owner's manual (PDF). Turn to page 38. Read where it says "External Power Supply: 9V AC 700mA / Negative Polarity Center" First, if the source is AC, it doesn't have a fixed polarity, so why specify that the "negative" pole should be the center conductor? Second, I recommend that people ignore this section of the manual — I personally think it was written by someone who didn't actually understand what they were writing. If you encounter circumstances where you need to run this radio on 12VDC as I do, I recommend that you use the default polarity convention (tip +, ring -), not because the radio cares about the polarity (the bridge rectifier D16 lets it work either way), but because this reduces the chance of a short between the exposed power connector ring and any part of the radio that might have a common path to your 12V source. This is not meant to suggest there's anything wrong with the 9V AC power pack provided by Sangean — it's actually a nice way to minimize the radio noise caused by many AC/DC converter packs with unfiltered diode switching noise. The circuit diagram in Figure 1 shows the Sangean design filters the bridge rectifier to keep it from adding to radio noise (capacitors C54, C85, C147 and C154). Set a timer/alarm First, they're not timers, they're alarms. Just thought I would get that straight. Second, I always have trouble with alarm setting on portable radios — for some reason, I always find the method counterintuitive and hard to remember. It's true once again for the ATS-909X, and this note is as much for me as it is for you, dear reader. To set a timer: Press one of the three timer buttons. The timer indicator at the upper right will flash. To toggle between an alarm sound and a radio alarm, press the SSB key. The present state will show at the upper right — either a bell symbol (alarm) or a musical note (radio). Use the numeric keys to enter a time of day for the alarm to activate, and press Enter. That completes the alarm setting, but not the radio station selection. Now tune the radio to the desired frequency and mode for the radio alarm. Once tuned, press the memory key followed by the desired timer key. This associates the radio frequency and mode with the timer. To cancel a timer, press a timer button followed by the "C" cancel key. After several days with this radio, I'm still impressed, perhaps even more so. It's a lot of radio for the price. I didn't set out to write a fully detailed review (many others have done that), only to give an overall impression and address some technical issues. I think the company that built this radio has a pretty good sense of its audience, and I think they've met most people's expectations — they've certainly exceeded mine. And even though I like this radio, I still think a company like Icom should show a little foresight and build a truly outstanding portable radio to fill what right now is a perfect market vacuum and opportunity.	CommonCrawl
Home > Journals > Ann. Statist. > Volume 17 > Issue 3 > Article September, 1989 Asymptotic Analysis of Minimax Strategies in Survey Sampling Horst Stenger Ann. Statist. 17(3): 1301-1314 (September, 1989). DOI: 10.1214/aos/1176347270 Suppose that real numbers $y_i$ are associated with the units $i = 1, 2, \ldots, N$ of a population $U$ and that the vector $y = (y_1, y_2, \ldots, y_N)$ is known to be an element of the parameter space $\Theta$. The statistician has to select a sample $s \subset U$ of $n$ units and to employ $y_i, i \in s,$ to estimate $\bar{y} = \sum y_i/N.$ We propose to base this decision on an asymptotic version of the minimax principle. The asymptotically minimax principle is applied to three parameter spaces, including the parameter space considered by Scott and Smith and a space discussed by Cheng and Li. It turns out that stratified sampling is asymptotically minimax if the allocation is adapted to the parameter space. In addition we show that the commonly used ratio strategy [i.e., simple random sampling (srs) together with ratio estimation] and the RHC-strategy (see Rao, Hartley and Cochran) are asymptotically minimax with respect to parameter spaces chosen appropriately. Horst Stenger. "Asymptotic Analysis of Minimax Strategies in Survey Sampling." Ann. Statist. 17 (3) 1301 - 1314, September, 1989. https://doi.org/10.1214/aos/1176347270 Published: September, 1989 Digital Object Identifier: 10.1214/aos/1176347270 Primary: 62D05 Secondary: 62C20 Keywords: asymptotic analysis, Invariance, minimax strategies, Rao-Hartley-Cochran strategy, ratio strategy, sample surveys Ann. Statist. Vol.17 • No. 3 • September, 1989 Horst Stenger "Asymptotic Analysis of Minimax Strategies in Survey Sampling," The Annals of Statistics, Ann. Statist. 17(3), 1301-1314, (September, 1989)	CommonCrawl
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. Join them; it only takes a minute: Why the Moon does not change its orbit from Earth to an another planet? I know that Earths gravity pulls down the Moon towards the Earths center and Moon is falling on Earth, but because of its change in velocity it never fall on Earth but orbits around Earth. Now I don't understand why the Moon can not change its orbit around the Earth to some other planets. As a planet comes near to Moon where the new planets gravity is more than Earths gravity. And the Same situation's why not applying on other planets like Mars and Earth when they are Perihelion point, change it's orbits and orbiting each other or one orbit to another. newtonian-mechanics newtonian-gravity orbital-motion planets moon Communisty Imran KhanImran Khan $\begingroup$ The short answer is "they do". All the bodies in the solar system (and the wider universe for that matter) are affecting each other gravitationally. In fact, the gravity of other planets does have a subtle effect on the Earth's orbit, but these effects are relatively weak. The planets never come close enough to each other for it to have any serious effect. The Earth's gravitational effect on the moon is always far stronger than any other planet simply because the moon is much closer to the Earth. $\endgroup$ – JeneralJames Nov 30 '16 at 11:05 $\begingroup$ If they do affecting each other (with weak gravitational force), so then why not it change the speed, velocity or force of other planet. $\endgroup$ – Imran Khan Nov 30 '16 at 13:58 $\begingroup$ @Imran: what makes you think it hasn't changed speed, velocity or force of another planet? $\endgroup$ – Kyle Kanos Nov 30 '16 at 14:21 $\begingroup$ @Imran: that's the thing, there are affects, but because our lifetimes are incredibly short compared to planetary orbits, you'd never notice it. The forces are just too small to stop a planet, as you could do some math using Newton's gravitational law between earth and, say, Jupiter. $\endgroup$ – Kyle Kanos Nov 30 '16 at 14:59 $\begingroup$ Similar to this physics.stackexchange.com/q/295569 but with its own particularities. Since gravity decreases with the inverse square law, distance between objects is of paramount importance. $\endgroup$ – J. Manuel Nov 30 '16 at 16:09 The higher the mass/distance-between-objects-squared the higher their mutual influence under gravity. In solar system (excluding the earth) the planet having bigger mass/distance-to-moon-squared is Jupiter. So, let's consider Jupiter-to-Moon Vs Earth-to-Moon influence only. The closest distance between earth (moon) and Júpiter is $5.9×10^8 km$. Considering also $m_{earth}=6×10^{24} kg$; $m_{jupiter}=1.9×10^{27} kg$; $d_{earth-moon}=3.8×10^{5} km$; $d_{jupiter-moon}=6.3×10^{8} km$; Now, if α is the ratio between Earth and Jupiter's gravitational influence, then $$\rm α= \frac{M_{earth}}{M_{jupiter}}(\frac{d_{jupiter-moon}}{d_{earth-moon}})^2=7.4×10^{3}$$ Therefore, Earth exerts a force ten thousands times stronger than any other planet into Moon, so we are not going to lose her soon (though we may lose her as Lawrence B. Crowell said). PS: Every object in solar system (I'm avoiding using the universe), do act on others making slight changes in orbit, speed, velocity depending on how strong the interaction is, as a matter of fact, Neptune (and then Pluto) was predicted before observation just because of the anomalies it caused in the obit of Uranus. J. ManuelJ. Manuel In effect this will happen in a way at least in theory. The orbital angular momentum of the Earth's rotation is being transferred to the moon. This is due to tidal interaction between the Earth and the moon. The orbit of the moon is being nudged outwards. Think of a line from the center of the sun through the Earth. The moon crosses this line twice in its orbit around the Earth. However, once the moon is sufficiently far out that its velocity is equal or lower than this line then it is effectively free of the Earth. This will happen in 50 billion years, which means it will be interrupted by the sun in its red giant phase where it will likely swallow up Earth and moon. There are these libration points where centripetal forces and gravitation of many body systems balance. These Lagrange points can be stable or saddle points that are unstable in one direction and stable in the other. In the solar system the planets have their Lagrange points which perburb each other as they come close. It is then possible for a mass to hop from one to the other and move around the solar system this way. This is the interplanetary transport network which has been proposed as a way to get spaceprobes to perform long term explorations. It is possible that over a long period of time that trojan asteroids as Lagrange points might migrate around the solar system, and in the early solar system this may have involved larger bodies comparable to moons around some of the planets. Lawrence B. CrowellLawrence B. Crowell $\begingroup$ I don't think the rotational angular momentum of the earth is sufficient to unbind the moon. $\endgroup$ – DilithiumMatrix Nov 30 '16 at 18:21 $\begingroup$ You might be right. I wrote the $50$ billion years based on memory of this. It might be instead that in $50$ billion years the Earth-moon system might be completely tidally locked and the moon migrates out to its maximal distance. $\endgroup$ – Lawrence B. Crowell Dec 1 '16 at 11:02 I think it is because we are literally closer World WalkerWorld Walker $\begingroup$ This seems like an answer to me, not a comment. Although brief, it does answer the actual question (as does J Manuel's comment, which is an fact an answer) without beating about the bush. $\endgroup$ – sammy gerbil Dec 1 '16 at 3:10 protected by Qmechanic♦ Dec 1 '16 at 12:51 Not the answer you're looking for? Browse other questions tagged newtonian-mechanics newtonian-gravity orbital-motion planets moon or ask your own question. How come the Sun's gravity can hold distant planets in orbit, but cannot rip humans off Earth? The theory of moon creation when a Mars size planet hit Earth Is the Moon freely falling towards the Earth? Why doesn't the moon crash into the Earth? What is the outward force on the Moon that makes it go in orbit rather that falling straight to the Earth? Based on measurements of a moon's orbit with respect to the planet, what can one calculate? Would it be possible to pull Mars and Earth closer each other? If Earth orbit around the sun was closer would it change the shape of its orbit into a dented 104 node ellipse? Is the Moon in a "Freefall" Around the Earth? What orbit does a planet have to have to be a planet? Is there a maximum distance from a planet that a moon can orbit?	CommonCrawl
Models, code, and papers for "H": Game Information System Spits Warnars H. L. H In this Information system age many organizations consider information system as their weapon to compete or gain competitive advantage or give the best services for non profit organizations. Game Information System as combining Information System and game is breakthrough to achieve organizations' performance. The Game Information System will run the Information System with game and how game can be implemented to run the Information System. Game is not only for fun and entertainment, but will be a challenge to combine fun and entertainment with Information System. The Challenge to run the information system with entertainment, deliver the entertainment with information system all at once. Game information system can be implemented in many sectors as like the information system itself but in difference's view. A view of game which people can joy and happy and do their transaction as a fun things. * International Journal of Computer Science and Information Technology 2.3 (2010) 135-148 Detecting Vietnamese Opinion Spam T. H. H Duong, T. D. Vu, V. M. Ngo Recently, Vietnamese Natural Language Processing has been researched by experts in academic and business. However, the existing papers have been focused only on information classification or extraction from documents. Nowadays, with quickly development of the e-commerce websites, forums and social networks, the products, people, organizations or wonders are targeted of comments or reviews of the network communities. Many people often use that reviews to make their decision on something. Whereas, there are many people or organizations use the reviews to mislead readers. Therefore, it is so necessary to detect those bad behaviors in reviews. In this paper, we research this problem and propose an appropriate method for detecting Vietnamese reviews being spam or non-spam. The accuracy of our method is up to 90%. * ICTFIT 2012 * 6 pages, in Vietnamese Consistency Analysis for the Doubly Stochastic Dirichlet Process Xing Sun, Nelson H. C. Yung, Edmund Y. Lam, Hayden K. -H. So This technical report proves components consistency for the Doubly Stochastic Dirichlet Process with exponential convergence of posterior probability. We also present the fundamental properties for DSDP as well as inference algorithms. Simulation toy experiment and real-world experiment results for single and multi-cluster also support the consistency proof. This report is also a support document for the paper "Computationally Efficient Hyperspectral Data Learning Based on the Doubly Stochastic Dirichlet Process". Generalized Statistical Tests for mRNA and Protein Subcellular Spatial Patterning against Complete Spatial Randomness Jonathan H. Warrell, Anca F. Savulescu, Robyn Brackin, Musa M. Mhlanga We derive generalized estimators for a number of spatial statistics that have been used in the analysis of spatially resolved omics data, such as Ripley's K, H and L functions, clustering index, and degree of clustering, which allow these statistics to be calculated on data modelled by arbitrary random measures (RMs). Our estimators generalize those typically used to calculate these statistics on point process data, allowing them to be calculated on RMs which assign continuous values to spatial regions, for instance to model protein intensity. The clustering index (H) compares Ripley's H function calculated empirically to its distribution under complete spatial randomness (CSR), leading us to consider CSR null hypotheses for RMs which are not point-processes when generalizing this statistic. We thus consider restricted classes of completely random measures which can be simulated directly (Gamma processes and Marked Poisson Processes), as well as the general class of all CSR RMs, for which we derive an exact permutation-based H estimator. We establish several properties of the estimators, including bounds on the accuracy of our general Ripley K estimator, its relationship to a previous estimator for the cross-correlation measure, and the relationship of our generalized H* estimator to previous statistics. To test the ability of our approach to identify spatial patterning, we use Fluorescent In Situ Hybridization (FISH) and Immunofluorescence (IF) data to probe for mRNA and protein subcellular localization patterns respectively in polarizing mouse fibroblasts on micropattened cells. We observe correlated patterns of clustering over time for corresponding mRNAs and proteins, suggesting a deterministic effect of mRNA localization on protein localization for several pairs tested, including one case in which spatial patterning at the mRNA level has not been previously demonstrated. Dyna-H: a heuristic planning reinforcement learning algorithm applied to role-playing-game strategy decision systems Matilde Santos, Jose Antonio Martin H., Victoria Lopez, Guillermo Botella In a Role-Playing Game, finding optimal trajectories is one of the most important tasks. In fact, the strategy decision system becomes a key component of a game engine. Determining the way in which decisions are taken (online, batch or simulated) and the consumed resources in decision making (e.g. execution time, memory) will influence, in mayor degree, the game performance. When classical search algorithms such as A* can be used, they are the very first option. Nevertheless, such methods rely on precise and complete models of the search space, and there are many interesting scenarios where their application is not possible. Then, model free methods for sequential decision making under uncertainty are the best choice. In this paper, we propose a heuristic planning strategy to incorporate the ability of heuristic-search in path-finding into a Dyna agent. The proposed Dyna-H algorithm, as A* does, selects branches more likely to produce outcomes than other branches. Besides, it has the advantages of being a model-free online reinforcement learning algorithm. The proposal was evaluated against the one-step Q-Learning and Dyna-Q algorithms obtaining excellent experimental results: Dyna-H significantly overcomes both methods in all experiments. We suggest also, a functional analogy between the proposed sampling from worst trajectories heuristic and the role of dreams (e.g. nightmares) in human behavior. A Fingerprint-based Access Control using Principal Component Analysis and Edge Detection E. F. Melo, H. M. de Oliveira This paper presents a novel approach for deciding on the appropriateness or not of an acquired fingerprint image into a given database. The process begins with the assembly of a training base in an image space constructed by combining Principal Component Analysis (PCA) and edge detection. Then, the parameter H, a new feature that helps in the decision making about the relevance of a fingerprint image in databases, is derived from a relationship between Euclidean and Mahalanobian distances. This procedure ends with the lifting of the curve of the Receiver Operating Characteristic (ROC), where the thresholds defined on the parameter H are chosen according to the acceptable rates of false positives and false negatives. * 5 pages, 9 figures. SBrT/IEEE International Telecommunication Symposium, ITS 2010, Manaus, AM, Brazil SLAMBench2: Multi-Objective Head-to-Head Benchmarking for Visual SLAM Bruno Bodin, Harry Wagstaff, Sajad Saeedi, Luigi Nardi, Emanuele Vespa, John H Mayer, Andy Nisbet, Mikel Luján, Steve Furber, Andrew J Davison, Paul H. J. Kelly, Michael O'Boyle SLAM is becoming a key component of robotics and augmented reality (AR) systems. While a large number of SLAM algorithms have been presented, there has been little effort to unify the interface of such algorithms, or to perform a holistic comparison of their capabilities. This is a problem since different SLAM applications can have different functional and non-functional requirements. For example, a mobile phonebased AR application has a tight energy budget, while a UAV navigation system usually requires high accuracy. SLAMBench2 is a benchmarking framework to evaluate existing and future SLAM systems, both open and close source, over an extensible list of datasets, while using a comparable and clearly specified list of performance metrics. A wide variety of existing SLAM algorithms and datasets is supported, e.g. ElasticFusion, InfiniTAM, ORB-SLAM2, OKVIS, and integrating new ones is straightforward and clearly specified by the framework. SLAMBench2 is a publicly-available software framework which represents a starting point for quantitative, comparable and validatable experimental research to investigate trade-offs across SLAM systems. * 2018 IEEE International Conference on Robotics and Automation (ICRA'18) Dreem Open Datasets: Multi-Scored Sleep Datasets to compare Human and Automated sleep staging Antoine Guillot, Fabien Sauvet, Emmanuel H During, Valentin Thorey Sleep stage classification constitutes an important element of sleep disorder diagnosis. It relies on the visual inspection of polysomnography records by trained sleep technologists. Automated approaches have been designed to alleviate this resource-intensive task. However, such approaches are usually compared to a single human scorer annotation despite an inter-rater agreement of about 85 % only. The present study introduces two publicly-available datasets, DOD-H including 25 healthy volunteers and DOD-O including 55 patients suffering from obstructive sleep apnea (OSA). Both datasets have been scored by 5 sleep technologists from different sleep centers. We developed a framework to compare automated approaches to a consensus of multiple human scorers. Using this framework, we benchmarked and compared the main literature approaches. We also developed and benchmarked a new deep learning method, SimpleSleepNet, inspired by current state-of-the-art. We demonstrated that many methods can reach human-level performance on both datasets. SimpleSleepNet achieved an F1 of 89.9 % vs 86.8 % on average for human scorers on DOD-H, and an F1 of 88.3 % vs 84.8 % on DOD-O. Our study highlights that using state-of-the-art automated sleep staging outperforms human scorers performance for healthy volunteers and patients suffering from OSA. Consideration could be made to use automated approaches in the clinical setting. * 10 pages, journal submitted Optimal Query Complexity for Reconstructing Hypergraphs Nader H. Bshouty, Hanna Mazzawi In this paper we consider the problem of reconstructing a hidden weighted hypergraph of constant rank using additive queries. We prove the following: Let $G$ be a weighted hidden hypergraph of constant rank with n vertices and $m$ hyperedges. For any $m$ there exists a non-adaptive algorithm that finds the edges of the graph and their weights using $$ O(\frac{m\log n}{\log m}) $$ additive queries. This solves the open problem in [S. Choi, J. H. Kim. Optimal Query Complexity Bounds for Finding Graphs. {\em STOC}, 749--758,~2008]. When the weights of the hypergraph are integers that are less than $O(poly(n^d/m))$ where $d$ is the rank of the hypergraph (and therefore for unweighted hypergraphs) there exists a non-adaptive algorithm that finds the edges of the graph and their weights using $$ O(\frac{m\log \frac{n^d}{m}}{\log m}). $$ additive queries. Using the information theoretic bound the above query complexities are tight. Deep Features for Tissue-Fold Detection in Histopathology Images Morteza Babaie, H. R. Tizhoosh Whole slide imaging (WSI) refers to the digitization of a tissue specimen which enables pathologists to explore high-resolution images on a monitor rather than through a microscope. The formation of tissue folds occur during tissue processing. Their presence may not only cause out-of-focus digitization but can also negatively affect the diagnosis in some cases. In this paper, we have compared five pre-trained convolutional neural networks (CNNs) of different depths as feature extractors to characterize tissue folds. We have also explored common classifiers to discriminate folded tissue against the normal tissue in hematoxylin and eosin (H\&E) stained biopsy samples. In our experiments, we manually select the folded area in roughly 2.5mm $\times$ 2.5mm patches at $20$x magnification level as the training data. The ``DenseNet'' with 201 layers alongside an SVM classifier outperformed all other configurations. Based on the leave-one-out validation strategy, we achieved $96.3\%$ accuracy, whereas with augmentation the accuracy increased to $97.2\%$. We have tested the generalization of our method with five unseen WSIs from the NIH (National Cancer Institute) dataset. The accuracy for patch-wise detection was $81\%$. One folded patch within an image suffices to flag the entire specimen for visual inspection. * Accepted for publication in the 15th European Congress on Digital Pathology (ECDP 2019), University of Warwick, UK PDDL 2.1: Representation vs. Computation H. A. Geffner I comment on the PDDL 2.1 language and its use in the planning competition, focusing on the choices made for accommodating time and concurrency. I also discuss some methodological issues that have to do with the move toward more expressive planning languages and the balance needed in planning research between semantics and computation. * Journal Of Artificial Intelligence Research, Volume 20, pages 139-144, 2003 Gene Expression Data Knowledge Discovery using Global and Local Clustering Swathi. H To understand complex biological systems, the research community has produced huge corpus of gene expression data. A large number of clustering approaches have been proposed for the analysis of gene expression data. However, extracting important biological knowledge is still harder. To address this task, clustering techniques are used. In this paper, hybrid Hierarchical k-Means algorithm is used for clustering and biclustering gene expression data is used. To discover both local and global clustering structure biclustering and clustering algorithms are utilized. A validation technique, Figure of Merit is used to determine the quality of clustering results. Appropriate knowledge is mined from the clusters by embedding a BLAST similarity search program into the clustering and biclustering process. To discover both local and global clustering structure biclustering and clustering algorithms are utilized. To determine the quality of clustering results, a validation technique, Figure of Merit is used. Appropriate knowledge is mined from the clusters by embedding a BLAST similarity search program into the clustering and biclustering process. * Journal of Computing, Volume 2, Issue 3, March 2010, https://sites.google.com/site/journalofcomputing/ Rock mechanics modeling based on soft granulation theory H. Owladeghaffari This paper describes application of information granulation theory, on the design of rock engineering flowcharts. Firstly, an overall flowchart, based on information granulation theory has been highlighted. Information granulation theory, in crisp (non-fuzzy) or fuzzy format, can take into account engineering experiences (especially in fuzzy shape-incomplete information or superfluous), or engineering judgments, in each step of designing procedure, while the suitable instruments modeling are employed. In this manner and to extension of soft modeling instruments, using three combinations of Self Organizing Map (SOM), Neuro-Fuzzy Inference System (NFIS), and Rough Set Theory (RST) crisp and fuzzy granules, from monitored data sets are obtained. The main underlined core of our algorithms are balancing of crisp(rough or non-fuzzy) granules and sub fuzzy granules, within non fuzzy information (initial granulation) upon the open-close iterations. Using different criteria on balancing best granules (information pockets), are obtained. Validations of our proposed methods, on the data set of in-situ permeability in rock masses in Shivashan dam, Iran have been highlighted. Toward Fuzzy block theory This study, fundamentals of fuzzy block theory, and its application in assessment of stability in underground openings, has surveyed. Using fuzzy topics and inserting them in to key block theory, in two ways, fundamentals of fuzzy block theory has been presented. In indirect combining, by coupling of adaptive Neuro Fuzzy Inference System (NFIS) and classic block theory, we could extract possible damage parts around a tunnel. In direct solution, some principles of block theory, by means of different fuzzy facets theory, were rewritten. * 8 PAGES,7 FIGURES Contact state analysis using NFIS and SOM This paper reports application of neuro- fuzzy inference system (NFIS) and self organizing feature map neural networks (SOM) on detection of contact state in a block system. In this manner, on a simple system, the evolution of contact states, by parallelization of DDA, has been investigated. So, a comparison between NFIS and SOM results has been presented. The results show applicability of the proposed methods, by different accuracy, on detection of contact's distribution. * Proc. International Symposium on Computational Mechanics (ISCM2007), Yao ZH & Yuan MW (eds.), Beijing: Tsinghua University Press & Springer, July 30-August 1, 2007, Beijing, China, Partial Recovery of Erdős-Rényi Graph Alignment via $k$-Core Alignment Daniel Cullina, Negar Kiyavash, Prateek Mittal, H. Vincent Poor We determine information theoretic conditions under which it is possible to partially recover the alignment used to generate a pair of sparse, correlated Erd\H{o}s-R\'enyi graphs. To prove our achievability result, we introduce the $k$-core alignment estimator. This estimator searches for an alignment in which the intersection of the correlated graphs using this alignment has a minimum degree of $k$. We prove a matching converse bound. As the number of vertices grows, recovery of the alignment for a fraction of the vertices tending to one is possible when the average degree of the intersection of the graph pair tends to infinity. It was previously known that exact alignment is possible when this average degree grows faster than the logarithm of the number of vertices. Individualized Time-Series Segmentation for Mining Mobile Phone User Behavior Iqbal H. Sarker, Alan Colman, MA Kabir, Jun Han Mobile phones can record individual's daily behavioral data as a time-series. In this paper, we present an effective time-series segmentation technique that extracts optimal time segments of individual's similar behavioral characteristics utilizing their mobile phone data. One of the determinants of an individual's behavior is the various activities undertaken at various times-of-the-day and days-of-the-week. In many cases, such behavior will follow temporal patterns. Currently, researchers use either equal or unequal interval-based segmentation of time for mining mobile phone users' behavior. Most of them take into account static temporal coverage of 24-h-a-day and few of them take into account the number of incidences in time-series data. However, such segmentations do not necessarily map to the patterns of individual user activity and subsequent behavior because of not taking into account the diverse behaviors of individuals over time-of-the-week. Therefore, we propose a behavior-oriented time segmentation (BOTS) technique that takes into account not only the temporal coverage of the week but also the number of incidences of diverse behaviors dynamically for producing similar behavioral time segments over the week utilizing time-series data. Experiments on the real mobile phone datasets show that our proposed segmentation technique better captures the user's dominant behavior at various times-of-the-day and days-of-the-week enabling the generation of high confidence temporal rules in order to mine individual mobile phone users' behavior. * The Computer Journal, Section C: Computational Intelligence, Machine Learning and Data Analytics, Publisher: Oxford University, UK, 2017 Scalable Training of Artificial Neural Networks with Adaptive Sparse Connectivity inspired by Network Science Decebal Constantin Mocanu, Elena Mocanu, Peter Stone, Phuong H. Nguyen, Madeleine Gibescu, Antonio Liotta Through the success of deep learning in various domains, artificial neural networks are currently among the most used artificial intelligence methods. Taking inspiration from the network properties of biological neural networks (e.g. sparsity, scale-freeness), we argue that (contrary to general practice) artificial neural networks, too, should not have fully-connected layers. Here we propose sparse evolutionary training of artificial neural networks, an algorithm which evolves an initial sparse topology (Erd\H{o}s-R\'enyi random graph) of two consecutive layers of neurons into a scale-free topology, during learning. Our method replaces artificial neural networks fully-connected layers with sparse ones before training, reducing quadratically the number of parameters, with no decrease in accuracy. We demonstrate our claims on restricted Boltzmann machines, multi-layer perceptrons, and convolutional neural networks for unsupervised and supervised learning on 15 datasets. Our approach has the potential to enable artificial neural networks to scale up beyond what is currently possible. * Nature Communications, 2018 Deep learning-based assessment of tumor-associated stroma for diagnosing breast cancer in histopathology images Babak Ehteshami Bejnordi, Jimmy Linz, Ben Glass, Maeve Mullooly, Gretchen L Gierach, Mark E Sherman, Nico Karssemeijer, Jeroen van der Laak, Andrew H Beck Diagnosis of breast carcinomas has so far been limited to the morphological interpretation of epithelial cells and the assessment of epithelial tissue architecture. Consequently, most of the automated systems have focused on characterizing the epithelial regions of the breast to detect cancer. In this paper, we propose a system for classification of hematoxylin and eosin (H&E) stained breast specimens based on convolutional neural networks that primarily targets the assessment of tumor-associated stroma to diagnose breast cancer patients. We evaluate the performance of our proposed system using a large cohort containing 646 breast tissue biopsies. Our evaluations show that the proposed system achieves an area under ROC of 0.92, demonstrating the discriminative power of previously neglected tumor-associated stroma as a diagnostic biomarker. * 5 pages, 2 figures, ISBI 2017 Submission Minimum entropy production in multipartite processes due to neighborhood constraints David H Wolpert It is known that the minimal total entropy production (EP) generated during the discrete-time evolution of a composite system is nonzero if its subsystems are isolated from one another. Minimal EP is also nonzero if the subsystems jointly implement a specified Bayes net. Here I extend these discrete-time results to continuous time, and to allow all subsystems to be simultaneously interacting. To do this I model the composite system as a multipartite process, subject to constraints on the overlaps among the "neighborhoods" of the rate matrices of the subsystems. I derive two information-theoretic lower bounds on the minimal achievable EP rate expressed in terms of those neighborhood overlaps. The first bound is based on applying the inclusion-exclusion principle to the eighborhood overlaps. The second is based on constructing counterfactual rate matrices, in which all subsystems outside of a particular neighborhood are held fixed while those inside the neighborhood are allowed to evolve. This second bound involves quantities related to the "learning rate" of stationary bipartite systems, or more generally to the "information flow".	CommonCrawl
Quantitative visualization of photosynthetic pigments in tea leaves based on Raman spectroscopy and calibration model transfer Jianjun Zeng1, Wen Ping1, Alireza Sanaeifar2, Xiao Xu1, Wei Luo1, Junjing Sha2, Zhenxiong Huang2, Yifeng Huang3, Xuemei Liu3, Baishao Zhan1, Hailiang Zhang1 & Xiaoli Li ORCID: orcid.org/0000-0001-9689-90542 Photosynthetic pigments participating in the absorption, transformation and transfer of light energy play a very important role in plant growth. While, the spatial distribution of foliar pigments is an important indicator of environmental stress, such as pests, diseases and heavy metal stress. In this paper, in situ quantitative visualization of chlorophyll and carotenoid was realized by combining the Raman spectroscopy with calibration model transfer, and a laboratory Raman spectral model was successfully extended to a portable field spectral measurement. Firstly, a nondestructive and fast model for determination of chlorophyll and carotenoid in tea leaf was established based on confocal micro-Raman spectrometer in the laboratory. Then the spectral model was extended to a real-time foliar map scanning spectra of a field portable Raman spectrometer through calibration model transfer, and the spectral variation between the confocal micro-Raman spectrometer in the laboratory and the portable Raman spectrometer were effectively corrected by the direct standardization (DS) algorithm. The portable map scanning Raman spectra of the tea leaves after the model transfer were got into the established quantitative determination model to predict the concentration of photosynthetic pigments at each pixel of the tea leaves. The predicted photosynthetic pigments concentration of each pixel was imaged to illustrate the distribution map of foliar pigments. Statistical analysis showed that the predicted pigment contents were highly correlated with the real contents. It can be concluded that the Raman spectroscopy was applicable for in situ, non-destructive and rapid quantitative detecting and imaging of photosynthetic pigment concentration in tea leaves, and the spectral detection model established based on the laboratory Raman spectrometer can be applied to a portable field spectrometer for quantitatively imaging of the foliar pigments. Tea is one of the world's three major beverages. The world's tea production exceeds 4 million tons per year and more than 2 billion people consume tea [1]. Tea, which contains high levels of antioxidants and can prevent many diseases including cardiovascular and cancer, has received more and more attention from people [2]. Photosynthesis is the determinant of productivity and the basis of plant growth and development, and an important source of carbon in plants. The photosynthesis of tea leaves is closely related to the quality and yield of tea. Photosynthetic pigments including chlorophyll a (Chl-a), chlorophyll b (Chl-b), and total carotenoids (Car) play a very important role in plant growth. Furthermore, the spatial distribution of foliar pigments is an important indicator of environmental stress, such as pests, diseases and heavy metal stress [3, 4]. In addition, the color and lustre of tea plays an important role in the consumption and production of tea, and the pigment concentration of tea is also an important factor affecting the color of tea. Therefore, developing a method for nondestructive detection and quantitative visualization of foliar photosynthetic pigment content is an important task for plant protection, cultivation and tea processing [5]. Most of the existing imaging studies on photosynthetic pigments concentration are based on visible-near infrared hyperspectral imaging technology. Previous studies have investigated crops such as cucumber leaf [6, 7], spinach [8], pepper leaf [9], tomato [10] and so on, and have achieved good results. Zhao et al. [11] used visible-near infrared hyperspectral technology to extract the corresponding feature parameters and built models based on 7 algorithms. The chlorophyll concentration was predicted by the models and the distribution map of chlorophyll concentration was drawn. Raman spectroscopy is a non-destructive analytical technique, which is based on the scattering interaction between light and chemical bond in materials. It can provide detailed information of chemical structure, phase and morphology, crystallinity and molecular interaction of samples. Compared to visible-near infrared hyper-spectrum, Raman spectroscopy has the advantages of high resolution, which can provide more spatial information for pest and heavy metal detection, and help to further study the mechanism of pests and heavy metal stress. There are a lot of studies on the use of Raman spectroscopy to identify and visualize chemical compounds. Schulz et al. [12] used a NIR-FT-Raman spectrometer to detect carotenoid in various fruits and vegetables such as carrot, tomato, and nectarine, and found Raman spectral fingerprint peaks of carotenoid in plants. The characteristic peaks were used to image the carotenoid distribution inside the plants. Qin et al. [13] developed a bench-top point-scan Raman chemical imaging system to detect and visualize the internal distribution of lycopene in postharvest tomato, and established a Raman chemical image to visualize the spatial distribution of lycopene at different stages of maturity. Yang et al. [14] used a custom row-scan Raman hyperspectral imaging system to detect and display the main chemical components of maize seeds. The characteristic peaks associated with corn starch, mixture of oil and starch, zeaxanthin, lignin and oil were found. Each single band image corresponding to the characteristic band successfully represents the spatial distribution of chemical components in seeds. In addition to the above qualitative analysis, Raman spectroscopy also has many applications in quantitative detection. Baranska et al. [15] detected lycopene and carotene in tomato and its products by FT Raman spectroscopy, and its modeling effect was better than that of near infrared spectrum but slightly lower than that of infrared spectrum. Bhosale et al. [16] and Dane et al. [17] detected the carotenoid concentration in kinds of fruits and vegetables (such as tomato, carrot, mango, etc.) using Raman spectroscopy. The result showed that there was a high correlation between the Raman spectrum signal intensity and the carotenoid concentration, and the correlation coefficient (R) was up to 0.9618. The above researches shows that Raman spectroscopy has great potential for quantitative detection of pigments, but the transferring of the quantitative model of Raman spectroscopy to portable devices, especially the field applicability of the laboratory model, has not been studied so far. In practical applications of spectral determination model, it is often encountered that a multivariate calibration model developed based on one instrument (Master) cannot be used on another instrument (Slave) of the same type as the Master. Or there will be big biases in the prediction result. The poor adaptability of this spectral model greatly limits the application prospect of spectral detection technology, and the spectral models that took a lot of time and money to build in the laboratories are difficult to be used in field or production practice. A strategy of model transfer has been frequently adopted to solve this problem. The essence of model transfer is to overcome the inconsistency between the measured signals (or spectra) of samples on different instruments [18]. Chemometric techniques are used to correct the differences in instrumental response function and then making the existing model transferable [19]. Direct Standardization (DS) is the most widely used method among the calibration standardization methods. The DS method is usually preferred due to its ease of use in correcting the spectra [20]. In this method, the transformation matrix is achieved by modeling two batch spectra of standard samples dataset included on both instruments, and then correction between the new and original calibration datasets is performed, thereby predicting the transformed spectra of the new samples on the second instrument without loss of the accuracy of calibration models [21]. Linking the two instruments through model transfer not only can be applied in actual production, but also make the model more accurate. Ji et al. [22] used a direct standardization (DS) model transfer algorithm to remove the environmental factors from the field spectrum so as to effectively estimate the soil properties. Wang et al. [23] proposed a model transfer algorithm based on genetic algorithm, which makes the partial least squares model of aviation fuel density successfully transferred from one instrument to another, and the accuracy of model prediction result is close to the calibration model and higher than the DS model. Confocal micro-Raman spectrometer has high resolution and precision, and can capture more useful spatial information, but this instrument is too expensive and heavy to be used in field or in vivo plant detection. Portable Raman spectrometer is compact and convenient, and can be used for in vivo or field detection, but it has the disadvantage of low resolution. In regards to field applications, Raman libraries are built and maintained on a more efficient laboratory instrument and then transferred to handheld/portable spectrometers. The need for a successful multivariate calibration model transfer that minimizes prediction error for a Raman spectral library database, such as those available and successfully applied extensively to near infrared (NIR) studies [24,25,26,27] has been a primary goal of the Raman spectroscopy measurements and has been the subject of some researches [28,29,30,31]. For instance, calibration transfer from an at-line to an in-line acquisition of Raman spectra was performed for PLS regression models to predict the concentration levels of two ingredients in a liquid detergent composition [19]. Therefore, further studies are needed to explore the possibility of creating calibration models on a laboratory-based Raman spectroscopy and transferring it to various field instruments. The calibration standardization procedures also provide the possibility for the building of standard free robust models. Nevertheless, little research on the measurement of photosynthetic pigments of tea leaf based on Raman spectroscopy was carried out, and there was no calibration transfer study in spatial distribution of foliar pigments, especially calibration transfer between tea leaf samples with different positions. Good results have been obtained in the previous literatures, but the effect of model transfer method on the variation correction of Raman spectrometers has not been reported. Here we are committed to building a high-precision Raman spectral pigment measurement model based on high-performance instrument in the laboratory, and study the application of this spectral model to the portable field measurement equipment. In order to solve the above problems, this paper aims to study the Raman spectral characteristics of tea leaf and establish an in situ quantitative analysis model between the concentration of photosynthetic pigment and its confocal micro-Raman spectra in tea leaf. On this basis, the portable Raman mapping data after model transfer were brought into the established model, the concentration of each pixel was predicted, and the chemical imaging was carried out to obtain the distribution map of the concentration of photosynthetic pigment in tea leaf at different position. Materials and instruments Material preparation The tea variety is longjing 43 (Camelliasinensis(L.) O.Kuntze). In the summer of 2012, longjing 43 seedlings were obtained from the tea garden in Fuyang, Hangzhou, China. Tea seedlings were planted in pots in the agricultural internet of things exhibition center of college of biosystems engineering and food science, Zhejiang University, receiving natural light and artificial watering. Material 1: in total of 315 leaves including the first four leaves in shoot (as shown in Additional file 1: Fig. S1) were plucked for Raman spectral collection, then all the leaves were stored in the refrigerator within 4 ℃ immediately. Following, approximately 0.1 g of weighed leaf, excluding central vein was taken for reference measurement of concentration of chlorophyll and total carotenoids according to the Reference [8] based on the ultraviolet spectrophotometer with the unit mg·g−1. In detail, 10 mL pigment extraction solution (95% alcohol solution) was added to the cut and ground sample, and stored in a dark room for about 24 h. Material 2: in total of 16 leaves including 4 leaves in each position (as shown in Additional file 1: Fig. S1) were collected for different four tea plants. And the photosynthetic pigment concentration of the 16 leaves was measured in the same method as in the previous section. Master spot scanning: a laser confocal micro-Raman spectrometer (Renishaw, United Kingdom/Via-Reflex 532/XYZ) was used for collecting Raman spectra of the Material 1. Specific parameters were as follow: the excitation wavelength is 532 nm; the spectral collection range is 579–3062 Raman shift/cm−1 with a spectral resolution of 0.2 nm, the laser intensity is 50 mW, the exposure time is 1 s, and the objective lens multiple is 5. Each sample was collected at three points from top to base, and the average spectrum was used as the representative Raman spectrum of the sample. So, a total of 315 spectra were obtained. Slave map scanning: a portable Raman spectrometer (Ocean optics QE Pro, United States) was used for spectral collection of Material 2. Specific parameters were as follow: the excitation wavelength is 532 nm, the spectral collection range is 77–2146 Raman shift/cm−1, the laser intensity is 100 mW, the exposure time is 3 s, and the average time is 2 s. The 16 leaves were map scanned by the Raman spectrometer with horizontal and vertical spatial resolution of 1 mm. In this experiment, the software WIRE 3.3 (Renishaw, United Kingdom) was used to collect and extract Raman spectral data. The pictures in this paper were drawn by Origin 9.0 (Originlab, United States) and Photoshop CS6 (Adobe, United States), and all the preprocessing and modeling methods were performed in Matlab 2013b (MathWorks, United States). Spectral analysis methods Spectral pretreatment The obtained spectral information contains not only the chemical structure information of the sample, but also many background and noise signals from the interference source such as the instrument itself and the experimental operating environment. Therefore, in order to eliminate the influence of the extraneous and interfering signals on the sample signal, the original data can be preprocessed [32]. In this study, five data preprocessing methods were applied including multiplicative scatter correction (MSC), wavelet transform (WT), standard normal variate (SNV), rolling-circle filter (RCF) and adaptive iteratively reweighted penalized least squares (airPLS). The full-band Raman spectrum contains a large amount of redundant information and noise [33]. These interference signal not only affect the prediction performance of the model, but also are not conducive to further detecting the Raman spectral response mechanism of chlorophyll. So, the competitive adaptive re-weighted algorithm (CARS) was used to extract the effective band for spectral measurement of the photosynthetic pigments. Based on the effective bands from CARS, the computational complexity of the spectral modeling can be reduced. Furthermore, the Raman spectral response mechanism of photosynthetic pigment may be discovered based on the assignment of these characteristic bands. Sample division The 315 samples from master spot scanning were divided into a training set and a test set based on 2:1 ratio. First, the samples were arranged in ascending order according to their concentrations of Chl-a, Chl-b and Car, and each three is one set in turn. Then, the second sample in each set is divi3ded into the test set, and the rest are set as the training set. So, 210 training set samples and 105 test set samples were obtained. The statistical information of the sample sets were shown in Table 1. Table 1 The statistical information of the sample set Modeling and evaluation methods Partial least squares regression (PLSR) was adopted to establish a quantitative relationship between the concentration of photosynthetic pigments and Raman spectra of leaf. The PLSR has the advantages of simplicity, accuracy, convenience and wide applicability. It is the most commonly used and most effective multivariate statistical method in chemometric modeling analysis [34]. The performance of the PLSR model was evaluated by the following indicators including coefficient of determination (R2) and root mean square error (RMSE) [35]. In detail, the R2C, R2CV, R2P and RMSEC, RMSECV, RMSEP represent the determination coefficient and root mean square error of calibration, cross validation and prediction, respectively. Considering the subsequent model transfer, the spectral bands of the two instruments need to be unified. The common band range of the two spectrometers is 579–2146 cm−1, but there are obvious high-frequency noise signals at the both ends. So the spectral range of 792–1961 cm−1 was selected for modeling. Model transfer In order to test the prediction result of the model, the sample after the scanning should measure 3 photosynthetic pigments concentration, and compare the actual value with the predicted value. Scanning takes a long time, and if it is detected in vitro, it will inevitably affect the accuracy of photosynthetic pigment concentration. Although the master also has a scanning function, its structure is complicated and impossible to perform living body detection of tea leaves. The slave is small, portable, simple in structure, and can perform scanning without removing the tea leaves. Therefore, the slave is used to scan four leaves of different leaf positions. The direct standardization (DS) method was adopted to improve the adaptability of the spectral model, which is a multivariate full-spectrum model transfer algorithm [36]. The advantage is that the principle is simple, the difference between the standard spectral data and the spectral data to be corrected can be compared, and each wavenumber is sequentially corrected by the full band to realize the transfer of the model [23]. The common spectral range of 579–2146 cm−1 of the two Raman spectrometers was selected, and to remove the high-frequency noise signals at both ends, the range of 792–1961 cm−1 was selected for further model transfer. Since the spectral resolutions of the two spectrometers are different, interpolation processing was performed to form a uniform number of spectral variables. It is important for model transfer to choose representative samples to define the differences between the master and slave instruments. For the slave instrument, the average spectrum of all pixels for each leaf (minus the background) map scanning was taken as the representative spectrum of the leaf, so a total of 16 spectral profiles were obtained. And 4 representative spectra were selected by the Kennard-Stone (KS) algorithm from the 16 spectra. While, for the master instrument, 4 spectra were also selected by KS algorithm from the 315 spectra of master spot scanning. Model transfer was performed by selecting 4 spectra (including all of the leaf positions) from the master and slave instrument. The flow of the DS algorithm is as follow [37, 38]. The spectral matrices of master and slave are Xm, Xs, respectively. Both Xm and Xs have size m × p, where m represents the number of representative transfer spectra (4 in this case) and p represents the number of wavenumbers. $${\mathrm{X}}_{\mathrm{m }}= {\mathrm{X}}_{\mathrm{s}}\times \mathrm{E}+\mathrm{B}$$ where E is the transfer matrix with size p × p of unknown parameter, which accounts for the variation in both Xm and Xs, and B is the background correction matrix [22]. The spectrum Ss of sample to be tested measured on the slave can be used for analysis after conversion: $${\mathrm{S}}_{\mathrm{s},\mathrm{ std}}={\mathrm{S}}_{\mathrm{s}}\times \mathrm{E}+\mathrm{B}$$ The spectral data Ss,std represents the corrected slave spectra through transferred by the DS algorithm, which will be transmitted to the photosynthetic pigments determination model developed by the master. And the prediction accuracy of the model for the slave sample is the performance of model transfer. Establishment of quantitative determination model Raman spectral quantitative determination of photosynthetic pigments in tea leaf As shown in Table 2, different pretreatment methods produced different results referring to the values of R2 and RMSE, indicating that pretreatment has a great influence on the performance of the model. In regard of the Car, model 5 based on the WT preprocessing method is obviously better than model 1 based the original data. In detail, the R2p of the model 1 increased from 0.614 to 0.713 of the model 5, and RMSEp of the model 1 decreased from 0.140 to 0.108 of the model 5. For Chl-a and Chl-b, model 10 and model 16 respectively obtained the best results based on the optimal pretreatment method of RCF. Comparing with the model 7 based on the original data, the R2p of model 10 increased from 0.597 to 0.800, and RMSEp of model 10 decreased from 0.900 to 0.599. While, the R2p and RMSEp of model 16 were respectively 0.734 and 0.330, which were obviously better than the relevant parameters (0.718 and 0.342) of model 13. Furthermore, the difference among calibration, validation and prediction of the model 5, 10 and 16 was also relatively small, which indicates that the stability of these models is improved through pretreatment. Table 2 PLSR modeling results of different pretreatment methods Selecting of characteristic bands for quantitative determination In the present study, WT and RCF pretreatment methods have improved spectral data with higher R2P value and lower RMSEP when compared to other methods (Table 2). The analysis of Raman spectra is usually involved with background problems caused by fluorescence effects. Raman spectroscopy is a weak scattering signal, which intensity is about 1/10 million of that of Rayleigh scattering, that often accompanies it. And it is particularly easily interfered by the background fluorescence of plant tissue, which makes it difficult to directly use the spectrum for reliable quantitative and positional analysis [39]. The background should be deleted because there is no chemical information in it. RCF is an easy-to-use and intuitive filter to eliminate background effects [40]. According to the results reported by [41,42,43], the background with minimum changes in the parameters of the Raman spectra is effectively subtracted by the RCF method. Due to its advantages, this method was widely used and previous research results in the field of Raman spectroscopy proved that RCF is superior to other methods, which is consistent with the results obtained in this work. WT is also a very powerful tool in compressing analytical signals [44, 45]. It transforms the raw data into the wavelet domain, so the information included in raw data can be compressed and explained by a small number of wavelet coefficients. WT was successfully applied and multivariate analytical problems were significantly simplified by this method [46, 47]. Raman spectroscopy provides a wide range of spectral information. In this research, there are 1005 and 1044 spectral variables from the master and the slave instruments respectively. And, there are still remaining 448 spectral variables after intercepting the common wavenumbers and removing the two ends of the spectrum seriously disturbed by noise. The Raman spectra contain not only biological, physiological and structural information related to detection objects, but also redundant information [33]. In order to explore the mechanism of the detection of photosynthetic pigment in tea leaves by Raman spectroscopy, a large number of redundant and interference information were excluded. Furthermore, selecting a small number of effective band can shorten the modeling time and improve the accuracy of the model. The CARS was adopted to extract the effective band for spectral measurement of the photosynthetic pigments based on the spectral data pretreated by the WT and RCF pretreatment, and the models based on the characteristic bands were established, and the modeling results were shown in Table 3. It can be found that the RCF was better than the WT pretreatment for all the three pigments, and the models based on these characteristic bands were better compared with the full-band models (as shown in Table 2). Table 3 PLSR modeling results based on characteristic band The spectral profiles before and after the RCF pretreatment were shown in Fig. 1, it can be found that the RCF method eliminated the fluorescence background and increased the signal-to-noise ratio of spectra, this may be the reason why the RCF pretreatment can improve the performance of the spectral determination models. Oh et al. [48] used RCF pretreatment in real-time estimation of glucose concentration in algae by Raman spectroscopy, and the result was also improved. Raman spectral profiles of tea leaf samples from master instrument. a original spectra; b spectra processed by the RCF Scatter diagram of prediction values and real values of the models (model 19, 21 and 23) for training and test samples were shown in Fig. 2. It can be found that the models based on the characteristic wavenumbers had achieved better result than the model based on the full-band model (as shown in Table 2). In addition, low dimensional input variables of characteristic wavenumbers greatly reduce the complexity of the model and improve the calculation speed of the model. Zhao et al. [11] used hyperspectral imaging technique to build the models to estimate the chlorophyll content in tea and obtained RMSEC, R2C, RMSEP and R2P of Chl-b model with the values of 9.918, 0.711, 8.601, and 0.693, respectively, which is obviously worse than the result of our research. Therefore, the obtained results showed that it is feasible to predict the concentration of photosynthetic pigments based on Raman spectroscopy. PLSR model results achieved from the master instrument based on the CARS characteristic bands selection for a total carotenoids, b chlorophyll a, c chlorophyll b (Val validation set and Pre prediction set) As the Raman spectroscopy can reflect the fingerprints information of the composition and structure of substances, an assignment of these characteristic wavenumbers was implemented to further explore the substance basis of quantitative determination of pigment by Raman spectroscopy. The Raman spectral characteristic bands for pigments detection were selected by the CARS algorithm and the selected wavenumbers were shown in Fig. 3 and Additional file 2: Table S1. There were three distinct peaks in the figure, including the rocking vibration in the CH3 plane at 1008 cm−1, the C–C stretching vibration at 1159 cm−1, and C = C stretching vibration at 1528 cm−1 which are the characteristic peaks of photosynthetic pigment [49, 50]. The assignment of these characteristic wavenumbers was shown in Table 4, and the wavenumbers were connected to the composition and structure of substances based on the references. It can be seen that most of the wavenumbers were related to photosynthetic pigment, which explains the reason why models based on characteristic wavenumbers obtained good results. Distributions of the characteristic wavenumbers selected based on CARS algorithm Table 4 Chemical assignment of Raman characteristic wavenumbers In addition, several characteristic wavenumbers extracted in this study were also related to protein (1651 cm−1) and nucleic acid (1665 cm−1) [56], etc., this may be due to that the concentration of photosynthetic pigments is the percentage of the amount of pigment to the mass of dry matter in tea leaves, in other words, the quantity of other dry matter in tea will also affect the percentage of pigment, so the characteristic peaks of other dry matter in the tea will also be selected. Furthermore, the wavelength selection algorithm based on data mining may also select some bands without specific component assignment as a benchmark for data processing. Calibration model transfer Direct standardization of spectral data from the master and slave instruments The direct standardization (DS) method was adopted to standardize the Raman spectral responses from the slave instrument. It can be seen from the Fig. 1(a) and Fig. 4(a) that the spectral data measured by the two instruments all had distinct fluorescent background, and the trend of the fluorescent background was different due to the different instruments. The spectra after removing the fluorescent background by using RCF was respectively shown in Fig. 1(b) and Fig. 4(b), it can be found that the RCF pretreatment greatly improves the signal to noise ratio of the spectra, which is conducive to the subsequent analysis. Slave spectral after DS was shown in Fig. 4(c). Comparing with Fig. 1(b), it can be found that the spectra of slave instrument (as shown in Fig. 4(c)) after DS was similar to that of the master instrument, indicating that the spectral variation between the master and slave Raman spectrometer can be effectively eliminated. Raman spectral profiles of tea leaf samples from slave instrument. a original spectra; b spectra processed by the RCF; c spectra after DS Imaging photosynthetic pigment in tea leaf based on model transfer Through the above analysis, the quantitative relationship between photosynthetic pigment concentration in fresh leaves and there're master Raman spectroscopy had been verified, and the quantitative determination models of chlorophyll and carotenoid concentration based on characteristic wavenumbers had been established. In order to realize the in situ and non-destructive imaging of chlorophyll and carotenoid concentration in fresh leaves of tea, the slave Raman spectra of material 2 after DS were transported into the established model 19, 21, 23, respectively in pixel-wise order, so the photosynthetic pigment concentration of each pixel in tea leaf was predicted. The predicted photosynthetic pigment concentration was imaged, and the image was subjected to filter filtering to obtain distribution maps of photosynthetic pigments as shown in Fig. 5. Distribution maps of photosynthetic pigment concentration in different leaf positions based on the slave instrument after calibration model transfer By imaging the photosynthetic pigments concentration, it can be found that the pigments concentration in the central vein and margin of the leaf is significantly lower than that in other region, which is related to the maximum efficiency of photosynthesis. These findings are consistent with the results found by [57]. Evaluation of performance of the calibration model transfer After the map scanning spectra of the slave spectrometer were corrected, the spectrum at each pixel was brought into the quantitative determination model to predict the photosynthetic pigment concentration at that pixel. Then the photosynthetic pigment concentration of the foliar pixels was averaged to represent the pigment concentration of the leaf. Furthermore the predicted average value of pigment concentration was compared with the actual value to evaluate the performance of this calibration model transfer, in detail, the R2 and RMSE were shown in Additional file 3: Fig. S2. It can be found that the predicted value of the model for the foliar map scanning spectra is highly correlated with the actual value, which indicates that the pigment determination model based on the master instrument can predict the spectrum of the slave instrument after calibration model transfer. The imaging of foliar pigments results and the correlation analysis proved that the model transfer of the two spectrometers had achieved good results, and this method is feasible. Furthermore, the spectral calibration model constructed in the laboratory (master Raman spectrometer) can be used to measure the distribution of foliar pigment with portable instruments (slave) in the field through model transfer. It is worth noting that the values obtained for the master instrument correspond to point scanning, and only three spectra are taken from each leaf. Although the spatial resolution of the slave instrument is less than that of the master instrument, the slave spectra are obtained by surface scanning, with hundreds or thousands of spectral lines per leaf, so it more closely corresponds to the chlorophyll in the leaf. In addition, slave spectra become very similar to master spectra through data processing methods such as model transfer. As for the DS spectral correction method, a subset of samples that represented the entire experimental dataset well was required to measure the difference in the response of spectra measured under different instruments. Also, too few or too many samples in the transfer set can lead to under or over fitting, this implies that the predictive power of the model has not improved in terms of precision. So, further investigation with more samples in the calibration set or exploring another way to optimize the parameters is necessary for reliable use of the proposed method. The better performance of the slave instrument compared to the master instrument in some of the models transferred is consistent with the previous literature [20, 25, 58]. The mean and variance of the actual and predicted value of photosynthetic pigment in four leaves of the same leaf location were calculated, as shown in Fig. 6. As can be seen from the Fig. 6, the trend of the actual value of photosynthetic pigment increase firstly and then decrease, this is consistent with the finding of Vicente et al. [59]. The concentration of pigments at the first leaf position is low due to poor photosynthesis. The level of photosynthetic pigments increases with an increase in leaf position (age) and growing leaves. The photosynthesis rate reaches the highest value when the leaves are mature (third leaf position), and then decreases substantially during senescence due to weakening in the ability of photosynthetic enzyme expression [9]. The result show that the model established in this paper also has a prospect in the study of the leaf position and leaf age. Line chart of actual and predicted values of photosynthetic pigment concentration achieved from the slave instrument after calibration model transfer In the study, the potential of Raman spectroscopy for in situ, non-destructive and rapid quantitative detection and imaging of photosynthetic pigment concentration in tea leaves was proved. Based on the Raman spectral pretreatment method combined with the CARS characteristic bands selection, the quantitative determination models of chlorophyll and carotenoid concentration were established by regression analysis. By comparison, it can be found that the best pretreatment RCF was most suitable to eliminate the fluorescence interference and other noise in Raman spectrum. And the Raman spectral characteristic bands for pigments detection selected by CARS have been proved to be the Raman-active molecular vibration of pigment components. In addition, model transfer method was applied to the master and slave spectrometers in order to obtain a model that can be available both in vivo or in the field and with high prediction accuracy. This is the first attempt to establish a connection between the two types of instruments, and achieved good results. The foliar map scanning spectra after DS was brought to the pigments determination model established based on master instrument, and the concentration of photosynthetic pigment of each pixel in tea leaves could be predicted. Calculating the R2 between the predicted value and the actual value, the range was in the range of 0.752–0.866. The predicted chlorophyll and carotenoid concentration of each pixel were imaged to obtain the distribution map of photosynthetic pigment in tea leaves, illustrating that the concentration of photosynthetic pigment in the central vein and leaf margin was lower than other parts was obtained, which is consistent with other studies. In the future, this algorithm can be applied to calibration transfer in other plants with different types of samples, different geographical regions, and different varieties to establish more robust models with more physiological and biochemical indexes (e.g., moisture content, mineral elements, dry matter, etc.), which provide a technological basis for the effective detection of the growth and nutrient distribution in plants. Also, further studies will be related to the effect of the data size and optimization sets on the model transferability and comparison of different model transfer algorithms to discuss the results of calibrations. It is worth noting that we have successfully improved the applicability of the Raman spectral model for determination of photosynthetic pigments in tea leaf. Through the calibration model transfer, the tea pigment spectral detection model based on the laboratory spectrometer was successfully applied to the portable quantitative detection of leaf pigment in the field. The model transfer method can effectively eliminate the spectral variation between the master and slave Raman spectrometers and improve the applicability of the spectral model, which will greatly promote the application process of the nondestructive and fast spectra measurement technique. All the seed material and raw imaging data can be obtained from the authors upon request. 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Detection of herbicide effects on pigment composition and PSII photochemistry in Helianthus annuus by Raman spectroscopy and chlorophyll a fluorescence. Spectrochim acta A. 2017;170:234–41. Cai ZL, Zeng HP, Chen M, Larkum AWD. Raman spectroscopy of chlorophyll d from Acaryochloris marina. BBA-Bioenergetics. 2002;1556:89–91. Vrettos JS, Stewart DH, de Paula JC, Brudvig GW. Low-temperature optical and resonance Raman spectra of a carotenoid cation radical in photosystem II. J Phys Chem B. 1999;103:6403–6. Zhang YY, Gao WJ, Cui CJ, Zhang ZZ, He LL, Zheng JK, et al. Development of a method to evaluate the tenderness of fresh tea leaves based on rapid, in-situ Raman spectroscopy scanning for carotenoids. Food Chem. 2020;308. Nicotra AB, Hofmann M, Siebke K, Ball MC. Spatial patterning of pigmentation in evergreen leaves in response to freezing stress. Plant, Cell Environ. 2003;26:1893–904. Qiao L, Lu B, Dong J, Li B, Zhao B, Tang X. Total volatile basic nitrogen content in duck meat of different varieties based on calibration maintenance and transfer by use of a near-infrared spectrometric model. Spectrosc Lett. 2020;53:44–54. Vicente R, Morcuende R, Babiano J. Differences in Rubisco and chlorophyll content among tissues and growth stages in two tomato (LycopersiconesculentumMill) varieties. Agron Res. 2011;9:501–7. No applicable. This research was funded by the National natural science foundation of China (61565005, 41867020, 31771676), Jiangxi provincial department of science and technology project (20181BBF60024, 20181BBF68010, GJJ190315), the National key R & D plan project (Project No: 2018YFD0700501-01), and Zhejiang Province Public Technology Research Program (Project No: 2017C02027). College of Electrical and Automation Engineering, East China Jiaotong University, Nanchang, 330013, China Jianjun Zeng, Wen Ping, Xiao Xu, Wei Luo, Baishao Zhan & Hailiang Zhang College of Biosystems Engineering and Food Science, Zhejiang University, 866 Yuhangtang Road, Hangzhou, 310058, China Alireza Sanaeifar, Junjing Sha, Zhenxiong Huang & Xiaoli Li College of Civil Engineering and Architecture, East China Jiaotong University, Nanchang, 330013, China Yifeng Huang & Xuemei Liu Jianjun Zeng Wen Ping Alireza Sanaeifar Xiao Xu Wei Luo Junjing Sha Zhenxiong Huang Xuemei Liu Baishao Zhan Hailiang Zhang Xiaoli Li XLi and HZ designed the overall scheme, performed the experiment of Raman spectra acquirement, and advised on the initial design of and oversaw the manuscript. JZ, WP and ZH determined the concentration of photosynthetic pigment, XX, WL and JS made major contributions in data processing. AS, YH and XLiu wrote the manuscript. AS and BZ advised on schematic drawings. All authors read and approved the final manuscript. Correspondence to Hailiang Zhang or Xiaoli Li. All authors consent for the publication. Leaf position of tea samples. Characteristic wavenumbers selected by CARS algorithm for photosynthetic pigments in tea leaf. Scatter diagram of actual and predicted values of photosynthetic pigment concentration. Zeng, J., Ping, W., Sanaeifar, A. et al. Quantitative visualization of photosynthetic pigments in tea leaves based on Raman spectroscopy and calibration model transfer. Plant Methods 17, 4 (2021). https://doi.org/10.1186/s13007-020-00704-3 Photosynthetic pigments Concentration distribution imaging	CommonCrawl
arXiv.org > math > arXiv:1408.0668 Mathematics > Geometric Topology arXiv:1408.0668 (math) [Submitted on 4 Aug 2014 (v1), last revised 17 Sep 2017 (this version, v6)] Title:Defining and classifying TQFTs via surgery Authors:András Juhász Abstract: We give a presentation of the $n$-dimensional oriented cobordism category $\text{Cob}_n$ with generators corresponding to diffeomorphisms and surgeries along framed spheres, and a complete set of relations. Hence, given a functor $F$ from the category of smooth oriented manifolds and diffeomorphisms to an arbitrary category $C$, and morphisms induced by surgeries along framed spheres, we obtain a necessary and sufficient set of relations these have to satisfy to extend to a functor from $\text{Cob}_n$ to $C$. If $C$ is symmetric and monoidal, then we also characterize when the extension is a TQFT. This framework is well-suited to defining natural cobordism maps in Heegaard Floer homology. It also allows us to give a short proof of the classical correspondence between (1+1)-dimensional TQFTs and commutative Frobenius algebras. Finally, we use it to classify (2+1)-dimensional TQFTs in terms of J-algebras, a new algebraic structure that consists of a split graded involutive nearly Frobenius algebra endowed with a certain mapping class group representation. This solves a long-standing open problem. As a corollary, we obtain a structure theorem for (2+1)-dimensional TQFTs that assign a vector space of the same dimension to every connected surface. We also note that there are $2^{2^\omega}$ nonequivalent lax monoidal TQFTs over $\mathbb{C}$ that do not extend to (1+1+1)-dimensional ones. Comments: 68 pages, 4 figures, to appear in Quantum Topology Subjects: Geometric Topology (math.GT); Quantum Algebra (math.QA) MSC classes: 57R56 (Primary), 57R65, 57M27 (Secondary) Journal reference: Quantum Topol. 9 (2018), no. 2, 229-321 DOI: 10.4171/QT/108 Cite as: arXiv:1408.0668 [math.GT] (or arXiv:1408.0668v6 [math.GT] for this version) From: Andras Juhasz [view email] [v1] Mon, 4 Aug 2014 13:04:47 UTC (57 KB) [v2] Mon, 17 Nov 2014 18:52:30 UTC (59 KB) [v3] Fri, 23 Jan 2015 15:07:13 UTC (65 KB) [v4] Fri, 2 Oct 2015 17:23:02 UTC (77 KB) [v5] Mon, 20 Jun 2016 14:46:50 UTC (86 KB) [v6] Sun, 17 Sep 2017 20:56:48 UTC (113 KB) math.GT math.QA	CommonCrawl
Evidence of the Berezinskii-Kosterlitz-Thouless phase in a frustrated magnet Ze Hu1 na1, Zhen Ma2,3 na1, Yuan-Da Liao4,5 na1, Han Li6 na1, Chunsheng Ma1, Yi Cui1, Yanyan Shangguan2, Zhentao Huang2, Yang Qi ORCID: orcid.org/0000-0003-0678-97707,8,9, Wei Li ORCID: orcid.org/0000-0003-0474-93376,10, Zi Yang Meng ORCID: orcid.org/0000-0001-9771-74944,11,12, Jinsheng Wen ORCID: orcid.org/0000-0001-5864-14662,9 & Weiqiang Yu1 Nature Communications volume 11, Article number: 5631 (2020) Cite this article Magnetic properties and materials Phase transitions and critical phenomena Topological insulators The Berezinskii-Kosterlitz-Thouless (BKT) mechanism, building upon proliferation of topological defects in 2D systems, is the first example of phase transition beyond the Landau-Ginzburg paradigm of symmetry breaking. Such a topological phase transition has long been sought yet undiscovered directly in magnetic materials. Here, we pin down two transitions that bound a BKT phase in an ideal 2D frustrated magnet TmMgGaO4, via nuclear magnetic resonance under in-plane magnetic fields, which do not disturb the low-energy electronic states and allow BKT fluctuations to be detected sensitively. Moreover, by applying out-of-plane fields, we find a critical scaling behavior of the magnetic susceptibility expected for the BKT transition. The experimental findings can be explained by quantum Monte Carlo simulations applied on an accurate triangular-lattice Ising model of the compound which hosts a BKT phase. These results provide a concrete example for the BKT phase and offer an ideal platform for future investigations on the BKT physics in magnetic materials. Topology plays an increasingly important role in understanding different phases and phase transitions in correlated quantum matters and materials. One prominent example is the Berezinskii–Kosterlitz–Thouless (BKT) mechanism in two-dimensional (2D) systems1,2,3,4,5, which is associated with the binding and unbinding of topological defects. The BKT transition cannot be characterized by conventional order parameters and constitutes the earliest example of phase transition beyond the Landau–Ginzburg paradigm of spontaneous symmetry breaking. Historically, the BKT mechanism was introduced in the XY spin model and long predicted to occur in magnetic thin films1,4. In experiments, signatures of the BKT transition have been observed in superfluid helium films6, as well as in 2D superconducting films7,8 and arrays9. Regarding the original proposal in layered XY-type magnets, despite intensive efforts10,11,12,13,14,15, direct and unambiguous observation of the BKT transition is still lacking. One major obstacle is the three-dimensional (3D) couplings in the magnets, although weak, will inevitably enhance the confining potential of vortices15, leading to 3D ordering that masks the BKT transition. Therefore, it is of fundamental interest to find and identify BKT materials that could overcome the obstacle and study the topology-related low-energy dynamics. Recently, a layered frustrated rare-earth antiferromagnet TmMgGaO416,17,18 was reported to ideally realize the triangular-lattice quantum Ising (TLI) model19. The relatively large interlayer distance of 8.3774 Å along the c axis gives rise to excellent two dimensionality17 and no sign of conventional 3D phase transition was observed in either specific heat or magnetic susceptibility measurements. Nevertheless, it was reported from neutron scattering that TmMgGaO4 ordered below ~1 K into an antiferromagnetic phase with a sixfold symmetry breaking16,18, which closely resembles the ground state of the TLI model originated from an order-by-disorder mechanism20,21. At higher temperatures, the effective XY degrees of freedom emerge and the BKT mechanism is expected to come into play21. In TmMgGaO4, each Tm3+, with a 4f12 electron configuration and a spin–orbit moment J = 6, forms a non-Kramers doublet due to the crystal-electric-field splitting. The doublet is well separated from the rest levels by about 400 K16 and can thus be regarded as an effective spin-1/2. There is further a fine energy splitting within the doublet, induced by the local trigonal crystal field17, acting as an intrinsic "transverse field" applied on the effective spin. From the magnetization measurements16,17,18, one observes that Tm3+ ions contribute highly anisotropic Ising-type moments with Jz = ±6 along the c axis, resulting in an effective out-of-plane g-factor ~ 13.216,19. On the contrary, the effective in-plane g-factor and dipolar moment in the ab plane are negligible. Facilitated by this feature in TmMgGaO4, in this work we employed nuclear magnetic resonance (NMR), a sensitive low-energy probe, to detect the BKT phase. We applied a moderate in-plane field of 3 T, which is adequate to collect the 69Ga NMR signals and, at the same time, hardly disturbs the low-energy electronic states of the material. This is important, as in the TLI model that is believed to accurately model TmMgGaO419, the BKT phase can be fragile against out-of-plane fields22,23,24, thus posing a challenge to NMR measurements. Taking advantage of the fact that in-plane moment in TmMgGaO4 is mostly multipolar16,19, our NMR experiments with in-plane fields, which merely couple to the nuclear spins, can clearly identify the BKT phase in the material. As shown in Fig. 1, from our NMR measurements of the spin-lattice relaxation rate 1/T1, we identify TU ≃ 1.9 K and TL ≃ 0.9 K, which represent the upper- and lower-BKT transitions, where a critical BKT phase resides at zero magnetic field in between the high-T paramagnetic and low-T antiferromagnetic phases. This finding is further substantiated by our scaling analysis of the measured susceptibility data near TL, as well as the simulated NMR and susceptibility data using large-scale quantum Monte Carlo (QMC) calculations. Fig. 1: Phase diagram of TmMgGaO4 under out-of-plane magnetic fields. Under zero field, there are paramagnetic (PM), BKT, and antiferromagnetic (AFM) phases. The TU (TL) is the upper (lower) BKT transition temperature, determined from the plateau structure in the NMR spin-lattice relaxation rate 1/69T1 (see Fig. 2c for details). The BKT phase between TU and TL is illustrated by the solid vertical line, while the AFM regime is indicated by the arrow. The contour background depicts the magnetic specific heat Cm/T at various fields and temperatures, with data adapted from ref. 16 and plotted in logarithmic scale. T* corresponds to the maximum of Cm/T at each field, signifying the position of strong magnetic fluctuations. $T^{\prime}$(T″) denotes the temperature at a specific field where a peak is found in the differential susceptibility dM/dH, shown in Fig. 3b. The Curie–Weiss temperature θCW is obtained from the 1/69T1T (see Supplementary Fig. 1). Remarkably, T, $T^{\prime}$, T″, and θCW all collapse to the same phase boundary between the BKT-like regime and AFM phase. A magnetically ordered phase is supposed to lie below the dome-like boundary. Errors represent 1 SD throughout the paper. NMR probe of the BKT phase The obtained NMR spectra with an in-plane magnetic field μ0H = 3 T are shown in Fig. 2a at representative temperatures. To better resolve the magnetic transition, the hyperfine shifts 69Kn of the spectra were analyzed and plotted in Fig. 2b as a function of temperature. Upon cooling, 69Kn peaks at about 0.8–0.95 K and then starts to drop at lower temperatures. Therefore, the ordering temperature is determined to be TL ≃ 0.9 K, consistent with neutron scattering experiments16,18. In addition, both the second moments (width of the NMR spectra) and the third moments (asymmetry of the spectra) of the spectra change dramatically below ~ 2 K, suggesting the onset of local hyperfine fields enhanced by the static or quasi-static magnetic ordering (Supplementary Fig. 4). These two characteristic temperatures signal the two-step melting of magnetic order through two BKT transitions, suggesting an intermediate floating BKT phase in the system. We suspect that there is some inhomogeneity of the local hyperfine fields, which is very likely caused by the quenched disorder from Mg/Ga site mixing16, although no significant influence on the electronic and more importantly the magnetic properties is seen (see more detailed discussions in Supplementary Note 4). Fig. 2: NMR spectra and spin-lattice relaxation rates of TmMgGaO4. a 69Ga NMR spectra at different temperatures under a 3 T in-plane field, with zero frequency corresponding to γH = 30.692 MHz. Data are shifted vertically for clarity. At high temperatures, the spectra are roughly symmetric, whereas for T ≤ 2 K, a shoulder-like structure can be resolved on the left side of the main peak. b NMR hyperfine shift ${}^{69}{K}_{n}=(\bar{f}/\gamma H-1)\times 100 \%$ as a function of temperature, where $\bar{f}$ is the average frequency of each spectrum. c NMR spin-lattice relaxation rate 1/69T1 vs. temperature measured under in-plane fields of 3 T and 1 T. A plateau-like feature, characterizing strong magnetic fluctuations, is observed between TL ≃ 0.9 K (lower-BKT transition) and TU ≃ 1.9 K (upper BKT transition). d 1/T1 data computed from the dynamical spin–spin correlation function with contributions from all momentum points [c.f., Eq. (3) and see the hyperfine form factor in Supplementary Note 2] in the Brillouin zone (left scale) and from K′ point in the vicinity of the K point (right scale), through large-scale QMC simulations (see "Methods"). The spin-lattice relaxation rate 1/T1 provides a highly sensitive detection of low-energy spin fluctuations25,26,27,28,29, and thus the BKT transition. In Fig. 2c, we show the 1/69T1 obtained under in-plane fields μ0H = 3 T and 1 T, which reflects intrinsic spin fluctuations with zero out-of-plane field. At 3 T, 1/69T1 first decreases upon cooling from 10 K then suddenly increases below TU ≈ 1.9 K, indicating the onset of strong low-energy spin fluctuations. The data at 1 T show similar behaviors. Below TL ≃ 0.9 K, 1/69T1 drops sharply, consistent with the onset of the magnetic ordering as also inferred from the hyperfine shift. Here, 1/69T1 is dominated by the gapped long wavelength excitations in the ordered state. At the magnetic phase transition, a peaked feature in 1/T1 develops, caused by the gapless low-energy spin fluctuations with diverging correlation length. Remarkably, at temperatures between TU ≃ 1.9 K and TL ≃ 0.9 K, 1/69T1 exhibits a plateau-like structure, indicating the emergence of a highly fluctuating phase with diverging spin correlations yet no true long-range order, which is the hallmark of a BKT phase1,2,3,4,5. Therefore, it is for the first time that such a phase is unambiguously observed in a magnetic crystalline material. Our unbiased QMC simulations on the TLI model of the material (see "Methods"), with accurate coupling parameters determined in ref. 19, quantitatively justifies the existence of the BKT phase between TL and TU. We computed 1/T1 and compared with the experiment below. Figure 2d shows the calculated 1/T1 by including fluctuations from all momentum points in the Brillouin zone (cf. Supplementary Fig. 2) and compare to that from K′ (around the K point at the corner of Brillouin zone). The former shows a decrease upon cooling below 4 K and then an upturn above ${T}_{{\rm{U}}}^{ }\simeq 2$ K, followed by a rapid decrease below ${T}_{{\rm{L}}}^{* }\simeq 1$ K. These behaviors are in excellent agreement with the measured 1/69T1. The latter reflects gapless excitations of the XY degrees of freedom emergent in the BKT phase, where the calculated 1/T1 from K′ exhibits an anomalous increase down to ${T}_{{\rm{U}}}^{* }$, below which the increment slows down. The contribution to 1/T1 near the K point reaches a maximum at ${T}_{{\rm{L}}}^{* }$ and drops rapidly below it. The absence of critical spin fluctuations at momentum away from the K point suggests that the measured 1/69T1 below 2 K is mainly contributed by excitations around the K point (see Supplementary Note 3). Overall, the quasi-plateau behaviors in the QMC results and the two characteristic temperature scales are in full consistency with the NMR measurements. This constitutes both strong support for the accurate quantum many-body modeling of the material TmMgGaO4 and also solid proof of the BKT phase therein detected by NMR. Nevertheless, we note that there are still subtle differences between the experimental and numerical data. Needless to say, the real material is always more complicated than our theoretical minimal model. For example, influences from higher crystal-electric-field levels above the non-Kramers doublet, the interlayer couplings not included in our model calculations, and the lack of knowledge on the precise local hyperfine coupling constant, etc., may explain the difference remaining between Fig. 2c, d. Universal magnetic susceptibility scaling Magnetic susceptibility χ measurements were also performed to strengthen the finding of the BKT phase. In Fig. 3a, we show the overall temperature dependence of χ at different out-of-plane fields. For T ≳ 2 K, χ increases monotonically upon cooling and barely changes with fields. However, for T ≲ 2 K, approximately the upper BKT transition TU as obtained from the 1/69T1 measurements, χ increases as the field decreases, suggesting the onset of peculiar magnetic correlations. With further cooling, the susceptibility gets flattened with temperature. The magnetization M(H) was further measured at selected temperatures (data shown in Supplementary Fig. 6), and for the sake of clarity, the differential susceptibility dM/dH is plotted in Fig. 3b. At around 2.5 T, a pronounced peak can be observed at low temperature, indicating the existence of a quantum phase transition, and the phase at lower fields should be a magnetically ordered phase, although its precise nature remains to be uncovered. Besides the high-field feature, for temperatures at 0.8 K and above, a kinked feature is clearly resolved on each dM/dH curve at low fields, whereas at 0.4 K, the low-field kink disappears, which posts a question of whether there is a quantum transition or merely a crossover from the zero-field AFM phase to the finite-field ordered phase under the dome in Fig. 1. The temperature and field values indicated by the down arrows in Fig. 3 are denoted as $T^{\prime}$ and T″ in the phase diagram (Fig. 1). Fig. 3: Uniform magnetic susceptibility of TmMgGaO4 and scaling analysis. a dc susceptibility χ as functions of temperatures under small out-of-plane (H//c) and in-plane (H//ab) fields. The latter is multiplied by a factor of 20 for visualizing purpose. The deviation of data below 2 K indicates the entry to the BKT phase and the field-suppression of magnetic correlations. b The differential susceptibility dM/dH under out-of-plane fields at different temperatures. The kinks at low fields, as denoted by the down arrows, suggest the transition from the BKT-like phase to the ordered phase (under the dome in Fig. 1) with increasing fields. The peaked features at high fields suggests a quantum phase transition to the polarized phase. c Fits of dM/dH to the power-law scaling function dM/dH ~ H−α with α = 2/3 for the 0.4 and 0.8 K data, and α = 0.123 for 2.1 K data in the log-log scale. The 3 K data follow the α = 0 line in the paramagnetic phase. d dM/dH by the QMC calculations in the same field and temperature range as in c, and fits to the power-law function with exponents α, which give consistent results as experiments. Field-theoretical analysis of the TLI model23,24 has predicted that upon applying a small out-of-plane field, the differential susceptibility dM/dH shall exhibit a divergent power-law behavior as dM/dH ~ H−α in proximity to the BKT phase. At TL, α has the value of 2/3, which corresponds to a critical exponent η = 1/9 at the lower-BKT transition and is originated from the sixfold symmetry breaking23. The exponent α gradually decreases as temperature increases, and above an intermediate temperature between TL and TU, α = 0 due to non-universal contributions. This is exactly what we observe in Fig. 3c. We fit the dM/dH with the power-law function at different temperatures, with the fitting regime chosen between 0.6–0.9 T. At 0.8 K, α is very close to the expected value of 2/3 (and thus η = 1/9) at TL, which constitutes a remarkable fingerprint evidence for the BKT transition. At lower temperatures such as 0.4 K, the exponent is also close to 2/3, because the susceptibility saturates with temperature, as shown in Fig. 3a. At high temperatures, α drops rapidly to a small value 0.12 at 2.1 K and becomes effectively zero at 3.0 K. Therefore, the susceptibility scaling gives the lower-BKT transition at about 0.8 K and upper transition probably between 2.1 and 3 K, in good agreement with the TL and TU estimated from NMR. These results are also fully consistent with our QMC calculations on the susceptibility shown in Fig. 3d. At TL or lower, α is 2/3, then decreases to a very small exponent 0.086 at 2.67 K, and above 3 K, becomes zero within numerical uncertainty. Such a power-law behavior in dM/dH again signifies the finite-temperature window of the BKT phase with diverging magnetic correlations, which gives rise to the universal power-law scaling of magnetic susceptibility. We believe the findings in this work are of various fundamental values. Since the original proposal of a BKT phase in magnetic films3,4,5, which also triggered the currently thriving research field of topology in quantum materials, tremendous efforts have been devoted to finding the BKT phase in magnetic crystalline materials, yet hindered by the obstacle outlined in the Introduction. Here, benefiting from NMR as a sensitive low-energy probe, and the nearly zero planar gyromagnetic factor in a TLI magnet TmMgGaO4, we are able to reveal two BKT transitions and a critical BKT phase with an emergent XY symmetry. Together with the power-law behavior of the susceptibility and excellent agreement between our QMC simulation and experiment data, we unambiguously identify the long-sought BKT phase in a magnetic crystalline material. Many intriguing questions are stimulated, based on the phase diagram in Fig. 1 obtained here. First, what is the nature of the ordered phase under finite fields, are there further exotic phases and transitions in the phase diagram, and will there be a field-induced quantum phase transition at the high-field side of the dome—these are all of great interests to be addressed in future studies. Second, it should be noted that the dynamical properties obtained by QMC calculations in Fig. 2 are computed on a large, while finite-size, 36 × 36 lattice, which already produces 1/T1 data in very good agreement with the experimental measurements. Such a great agreement is surprising, given the possible existence of randomness from Ma/Ga site mixing in the material TmMgGaO416, and also the lattice disorder revealed by the large high-temperature second moment of the NMR spectra (Supplementary Note 4). Although the random distribution in intrinsic transverse fields and spin couplings does not seem to alter the low-temperature spin-ordered phase and the sharp spin excitation line shapes18,19, its intriguing effects on the finite-temperature phase diagram of TLI and also the compound TmMgGaO4 call for further studies. Third, in the study of BKT transition in superfluid systems, it has been observed experimentally and understood theoretically that additional dissipations also appear above the transition temperature due to fluctuations of vortices6. Hence, the plateau of 1/T1 we observe may also cover regions slightly above the upper BKT transition temperature. We leave this subtlety to future numerical and experimental efforts. Lastly, in general terms, whether there are other rare-earth magnetic materials in the same family of TmMgGaO4 that, acquire similar 2D competing magnetic interactions from highly anisotropic gyromagnetic factor and unique triangular-lattice structures, and also exhibit the BKT physics, is quite intriguing and calls for future investigations. All these directions are ready to be explored from here. Crystal growth and susceptibility measurements Single crystals were grown by the optical-floating-zone method with an image furnace (IR Image Furnace G2, Quantum Design). The natural cleavage surface of the crystals is the ab plane, which allows us to align the field orientation within an error of 2∘. The dc susceptibility was measured in a PPMS VSM (Quantum Design) for temperatures above 2 K and in a He-3 MPMS (Quantum Design) for temperatures ranging from 0.4 to 2 K. NMR measurements The 69Ga (I = 3/2, γ = 10.219 MHz/T) NMR spectra were collected with the standard spin-echo sequence, with frequency sweep by a 50 kHz step using a topping tuning circuit. The NMR hyperfine shift was obtained by calculating the change of the first moment of the spectra. The spin-lattice relaxation rate 1/69T1 was measured by the inversion-recovery method, where a π/2 pulse was used as the inversion pulse. The NMR data from 1.8 K and above were measured in a variable temperature insert, and the data from 1.8 K and below were measured in a dilution refrigerator. The weak NMR signal at low fields and the rapid decrease of 69T2 upon cooling (Supplementary Note 5) prevented us to measure the 1/69T1 for in-plane fields <3 T, with temperature below 1.8 K. Whereas for in-plane fields of 4 T and higher, the sample could not be held in position because of the large anisotropy in the g-factor and unavoidable sample misalignment (≲2∘). At T = 1.2 K, we did not find any change of 1/69T1 with two different radio frequency excitation levels (14 mT and 24 mT), and with different frequencies across the NMR line, within the error bar. Triangular-lattice Ising model At zero field, the intralayer couplings in TmMgGaO4 can be described by the TLI Hamiltonian, $$H={J}_{1}\sum _{\langle i,j\rangle }{S}_{i}^{z}{S}_{j}^{z}+{J}_{2}\sum _{\langle \langle i,j\rangle \rangle }{S}_{i}^{z}{S}_{j}^{z}+\sum _{i}\Delta {S}_{i}^{x},$$ where J1 and J2 are the superexchange interactions among Tm3+, 〈i, j〉 and 〈〈i, j〉〉 refer to the nearest neighbors and the next-nearest neighbors, respectively, and Δ is the energy splitting within the non-Kramers doublet imposed by the crystal field. We have shown that the parameter set J1 = 0.99 meV, J2/J1 ≈ 0.05 and Δ/J1 ≈ 0.54 reproduces the experimental results of the transition temperatures and the inelastic neutron scattering spectra19. In the TLI model [Eq. (1)], we can define a complex field ψ as a combination of the Ising (Z) components ${m}_{{\rm{A}},{\rm{B}},{\rm{C}}}^{z}$ on three sublattices, i.e., $$\psi ={m}_{{\rm{A}}}^{z}+{{\rm{e}}}^{i2\pi /3}\ {m}_{{\rm{B}}}^{z}+{{\rm{e}}}^{i4\pi /3}\ {m}_{{\rm{C}}}^{z}.$$ Notably, ψ = ∣ψ∣eiθ is a complex order parameter that represents the emergent XY degree of freedom relevant to the BKT physics in the TLI model. QMC calculations QMC simulations were performed in the path integral in the ${S}_{i,\tau }^{z}$ basis with discretization in space and time. The lattice of L × L × Lτ, where L = 36 and Lτ = β/Δτ with Δτ = 0.05 and β = 1/T, were simulated with both local and Wolff-cluster update schemes30,31. The 1/T1 results were obtained by first computing the dynamical spin–spin correlation function $\langle {S}_{i}^{z}(\tau ){S}_{j}^{z}(0)\rangle$ and then acquiring its real-frequency dependence S(q, ω) from the stochastic analytic continuation32. We then determined the 1/T1 either by summing the contributions close to momentum K or over the entire Brillouin zone, as discussed in the Fig. 2d of the main text, $${T}_{1}^{-1}({\bf{q}})=\frac{1}{{L}^{2}}\sum _{{\bf{q}}}\| {A}_{{\rm{hf}}}({\bf{q}}){\| }^{2}S({\bf{q}},\omega \to 0),$$ where Ahf(q) is the hyperfine coupling form factor (see Supplementary Note 2). Similar analyses have been successfully applied to the QMC computation of NMR 1/T1 for the spin-1/2 and spin-1 chains33,34. The data that support the findings of this study are available from the corresponding authors upon reasonable request. Code availability All numerical codes in this paper are available upon request to the corresponding authors. Berezinskii, V. L. Destruction of long-range order in one-dimensional and two-dimensional systems having a continuous symmetry group I. classical systems. JETP 32, 493 (1971). ADS MathSciNet Google Scholar Berezinskii, V. L. 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We acknowledge the supports from the National Key Projects for Research and Development of China through Grant numbers 2016YFA0300502 and 2016YFA0300504, the National Natural Science Foundation of China through Grant numbers 11574359, 11674370, 11822405, 11674157, 11974036, 11834014, 11874115, and 51872328, RGC of Hong Kong SAR China through Grant number 17303019, Natural Science Foundation of Jiangsu Province with Grant number BK20180006, Fundamental Research Funds for the Central Universities with Grant number 020414380117, and the Research Funds of Renmin University of China. We thank the Center for Quantum Simulation Sciences in the Institute of Physics, Chinese Academy of Sciences, the Computational Initiative at the Faculty of Science and the Information Technology Services at the University of Hong Kong, the Platform for Data-Driven Computational Materials Discovery at the Songshan Lake Materials Laboratory, Guangdong, China, and the Tianhe-I, Tianhe-II, and Tianhe-III prototype platforms at the National Supercomputer Centers in Tianjin and Guangzhou for their technical support and generous allocation of CPU time. These authors contributed equally: Ze Hu, Zhen Ma, Yuan-Da Liao, Han Li. Department of Physics and Beijing Key Laboratory of Opto-electronic Functional Materials and Micro-nano Devices, Renmin University of China, Beijing, 100872, China Ze Hu, Chunsheng Ma, Yi Cui & Weiqiang Yu National Laboratory of Solid State Microstructures and Department of Physics, Nanjing University, Nanjing, 210093, China Zhen Ma, Yanyan Shangguan, Zhentao Huang & Jinsheng Wen Institute for Advanced Materials, Hubei Normal University, Huangshi, 435002, China Zhen Ma Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing, 100190, China Yuan-Da Liao & Zi Yang Meng School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, 100190, China Yuan-Da Liao School of Physics, Key Laboratory of Micro-Nano Measurement-Manipulation and Physics (Ministry of Education), Beihang University, Beijing, 100191, China Han Li & Wei Li Center for Field Theory and Particle Physics, Department of Physics, Fudan University, Shanghai, 200433, China Yang Qi State Key Laboratory of Surface Physics, Fudan University, Shanghai, 200433, China Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China Yang Qi & Jinsheng Wen International Research Institute of Multidisciplinary Science, Beihang University, Beijing, 100191, China Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, SAR, China Zi Yang Meng Songshan Lake Materials Laboratory, Dongguan, Guangdong, 523808, China Ze Hu Han Li Chunsheng Ma Yi Cui Yanyan Shangguan Zhentao Huang Jinsheng Wen Weiqiang Yu W.Q.Y. and J.S.W. designed the experiments, with proposals from Y.Q., W.L., and Z.Y.M. Z.M. grew and characterized the single crystals and performed susceptibility measurements and analysis, with help from Y.Y.S.G., Z.T.H., Z.H., and H.L. Z.H., C.S.M., and Y.C. performed NMR measurements and analysis. Y.D.L. and H.L. carried out the large-scale quantum many-body calculations, with the guidance from Y.Q., W.L., and Z.Y.M. W.Q.Y., J.S.W., W.L., Z.Y.M., and Y.Q. wrote the manuscript with comments from all coauthors. Corresponding authors Correspondence to Yang Qi or Wei Li or Zi Yang Meng or Jinsheng Wen or Weiqiang Yu. The authors declare no competing interests. Peer review information Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available. Publisher's note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Peer Review File Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/. Hu, Z., Ma, Z., Liao, YD. et al. Evidence of the Berezinskii-Kosterlitz-Thouless phase in a frustrated magnet. Nat Commun 11, 5631 (2020). https://doi.org/10.1038/s41467-020-19380-x Received: 01 May 2020 Accepted: 13 October 2020 By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate. Editors' Highlights Top Articles of 2019 Nature Communications ISSN 2041-1723 (online)	CommonCrawl
Focus on: All days 28 Jun 2021 29 Jun 2021 30 Jun 2021 1 Jul 2021 All sessions Adaptive Substrates Session Meet the Speakers Poster Session Soft Substrates Session Switchable Substrates Session Wetting Dynamics Session Hide Contributions Dynamical Wetting of flexible, adaptive & switchable substrates (SPP2171) 28 Jun 2021, 09:00 → 1 Jul 2021, 17:00 Europe/Berlin The workshop "Dynamic Wetting of Flexible, Adaptive, and Switchable Substrates" by the SPP 2171 shall give PhD students and young researchers the opportunity to discuss recent subjects related to the themes underlying the Priority Programme 2171. Besides networking and presenting the latest developments in the SPP's field of research, the workshop aims to provide a platform for young researchers to openly discuss the current issues and questions on their scientific work and career. In addition to that, the programme will include tutorial lectures by experts from the across the fields of wetting, surface science and physico-chemical hydrodynamics. The workshop is organized by a group of PhD students of the Priority Programme and is explicitly open to all interested students and young researchers, not restricted to members of the SPP 2171. Amal Kanta Giri Anil Rajak Chirag Hinduja Christian Honnigfort Christopher Henkel Claas-Hendrik Stamp Dirk Peschka Dominic Mokbel Fahimeh Darvish Felix Weißenfeld Frieder Mugele Gissela Constante Hansol Jeon HUGO BELLEZZA Jacco Snoeijer Josua Grawitter Khalil Remini Laura Gallardo Domínguez Lauritz Beck Leon Topp Leonie Schmeller Lucia Wesenberg Lukas Hauer Mirela Encheva Moritz Stieneker Nikolai Kubochkin Niloofar Nekoonam Olivier Vincent Robert Style Simon Hartmann Simon Schubotz Sissi de Beer Thomas Scheel Uwe Thiele Xiaomei Li SPP Manager: Simon Hartmann s.hartmann@uni-muenster.de Monday, 28 June Mon, 28 Jun Tue, 29 Jun Wed, 30 Jun Thu, 1 Jul 09:00 → 10:30 Tutorial Lecture on "Relating the macroscale and mesoscale descriptions of wettability" 1h 30m After spilling some liquid on my desk I will remind you the macroscale description of wettability and capillarity followed by experimental examples illustrating that a more appropriate description on smaller is needed scales. Such a description is provided by a mesoscale theory based on wetting potential/disjoining pressure. At this point I switch to pen and pad to discuss some details of the two formulations and their relation. This includes a derivation of the macroscopic Laplace and Young-Dupre laws and of their mesoscale equivalent. These are then used to (i) relate contact angle and wetting potential, (ii) establish consistency relations for the two levels of description, and (iii) discuss the stability of thin films of partially wetting liquids. Finally, it is briefly explained how the mesoscale description feeds into the gradient dynamics approach as explained in detail in the February 2020 SPP Winter School. If time remains, we discuss how wetting potentials can be obtained from microscale models and dwell on an extension of the approach towards complex liquids (surfactant covered films, or films of mixtures). Speaker: Uwe Thiele (WWU Münster) Scientific Writing Workshop: How to see ghosts and communicate science 4h 15m Every stage of a researcher's career is built on foundations of writing and other forms of communication, yet this topic is rarely taken seriously in European schools and universities. Students who don't master the basic skills will struggle with every paper, crucial applications for jobs and funding, and routine requirements of their jobs. The ability to clearly and effectively communicate science is somehow connected to the quality of a scientist's thinking and research – but why should that be true? And what are the implications? A few years ago, I began a very systematic study of the problems scientists have when communicating in different contexts: with experts from their own field, across disciplinary boundaries, and with the lay public. This work revealed some fascinating patterns. Communication problems have an underlying logic that can be captured in a general model to explain what goes wrong and how they can be fixed. The model has very clear implications for how we teach communication and how we ought to be teaching science. It suggests a way of thinking about writing and giving talks that not only make these tasks a lot easier, but can ultimately improve your research. The workshops I offer are based on the scientific work of the participants; the content comes from texts from your field and your own work. The first (morning) session is a theoretical introduction that use examples to expose problems and give participants a new way to think about communication tasks. Faculty and other guests are welcome to sit in. The afternoon will get practical, providing tools and strategies to apply what we've done to your writing. About the instructor: In over two decades as a science writer, Russ Hodge has witnessed "the good, the bad, and the completely ridiculous" sides of science and its practitioners. Besides being a diplomat trying to negotiate new boundaries between science, humor, and art, Russ is one of Europe's most respected science communicators and teachers. In 1997 he was plucked from a peaceful existence as a writer and musician to launch the Office of Information and Public Affairs at EMBL. He helped shape it into one of the most respected centers of public outreach for molecular biology in the world. He currently works as science writer and communications trainer at the Max Delbrück Center for Molecular Medicine in Berlin. He has written thousands of articles, dozens of book-length journalistic reports for institutes across Europe and the US, and published 8 books on science. He is a co-author on 10 original scientific papers, has written highly successful international grants, and most recently written and illustrated a children's book on evolution. Alongside humorous pieces on his blog, he is carrying out important work on the theory, practice and didactics of science communication. Some of his work can be found at: www.goodsciencewriting. com. His artwork can be seen at russhodge.wordpress.com. His author page at Amazon is: www.amazon.com/Russ-Hodge/e/B0024J8XO0/ Speaker: Russ Hodge (Max Delbrück Center, Berlin) lunch break 1h Tuesday, 29 June Soft Wetting Dynamics 1h 30m Droplet spreading and sliding on soft substrates is typically much slower than on rigid surfaces. This effect is called "viscoelastic braking": it is caused by the motion of the wetting ridge that is transported along with the moving contact line. The moving ridge induces a time-dependent deformation, which causes viscoelastic dissipation inside the substrate. In this talk we quantify the substrate deformation, the dissipation, and show how one can predict the dynamic contact angle on viscoelastic substrates. We also discuss other dynamical soft wetting phenomena such as stick-slip motion and the cheerios effect Speaker: Prof. Jacco Snoeijer (University of Twente) Soft Substrates Session: I Dynamic wetting ridge of soft surface 25m When a liquid droplet is sitting on a soft surface, the capillary forces of liquid deform the soft solid into a sharp wetting ridge. The amplitude of this wetting ridge is determined by the elasto-capillary length. If such droplet moves, a strong viscoelastic dissipation occurs in the soft solid. In this research, we visualise the moving wetting ridge created on a soft surface by water and fluorinated oil and measure the solid and liquid contact angles. We have noticed that the rotation of the wetting ridge follows the dynamic contact angle at slow contact line speed. On the other hand, the rotation angle starts to decrease at high contact line speed. In this talk, we will explain how does this phenomenon can be explained by dynamic solid surface tension. Speaker: Hansol Jeon (Max Planck Institute for Dynamics and Self-Organization) Wetting Ridge Dynamics on Soft Surface Wetting 25m In veins, objects like vesicles adhering to the endothelium (i.e. inner channel walls) can become harmful as they cause high blood pressure or, more severely blood clots. Understanding how such adhering objects interact with soft surfaces is essential to decrease the risk. Liquid droplets are good approximations of vesicles in terms of their wetting behavior. To understand the interaction, we investigate liquid droplets sliding on soft substrates. The substrate can be swollen by another liquid solvent. During sliding, the solvent, the substrate, the droplet, and the ambient do interact via mass and momentum transfer which can be coupled. The contact domain where droplet, surface, and ambient meet (so-called wetting ridge) governs the most important coupling between the involved components. We combine optical methods such as confocal- and interferometric microscopy, which allows us to a) discriminate between components, and b) resolve length scales, much below the wavelength of visible light. Both methods are appropriate to dynamically map the wetting ridge while the droplet while it slides over the surface. A novel force sensor setup facilitates the direct force measurement between droplet and surface during the sliding motion. Speaker: Lukas Hauer (Max Planck Institute for Polymer Research, Mainz) Gradient Dynamics Model for Spreading Drops on soft Substrates 25m The wetting behaviour of liquids on viscoelastic or elastic substrates is of great interest as it is relevant in many applications. Here, we present a simple model for partially or completely wetting liquids on fully compressible elastic substrates. It is shown that the model faithfully captures not only the double transition of steady drops (with increasing softness), but also features of dynamic processes. We focus on the example of a spreading drop on soft substrates and consider the effect of viscoelastic braking, i.e. the increase of dissipation in the substrate with increasing softness. Furthermore we show that the scaling laws of a Kelvin-Voigt material [1] are correctly recovered for partially wetting liquids and indicates that the behaviour crucially changes in the case of complete wetting. [1] S. Karpitschka, S. Das, M. van Gorcum, H. Perrin, B. Andreotti, and J. H. Snoeijer. Droplets move over viscoelastic substrates by surfing a ridge. Nat. Commun., 6:7891, 2015. doi:10.1038/ncomms8891 Speaker: Christopher Henkel (WWU Münster) Meet the Speakers lunch break 45m Soft Substrates Session: II Comparative Study of the Dewetting Dynamics from Elastic to Visco-Elastic Substrates 25m When a thin layer of polystyrene of about 100 nanometres is dewetting from a PDMS layer we observe the appearance of nucleated holes at the surface. The polystyrene that is removed from the dry centre of the hole accumulates at a dewetting rime surrounding the latter. These dewetting rims have characteristic shapes and grow with time accumulating more and more of the dewetted polystyrene. For the dewetting dynamics we can distinguish three regimes according to the elasticities of the PDMS substrates by spanning a range of three orders of magnitude (few MPa to few kPa). The first regime concerns elastic moduli of few MPa to few hundreds kPa where we could observe dewetting velocity decreases for decreasing elastic module. The second regime (from few hundreds kPa to few ten kPa) is a regime where the dewetting velocity is very low (tends to zero); and the last regime concerns elasticities in the range of only a few kPa where we could observe an increasing dewetting velocities for decreasing elastic moduli. A comparison of the rim shapes, heights, and contact angles for these three regimes gives valuable hints about the influencing parameters involved on the dewetting dynamics and therefore would lead for a better theoretical description. In the latter stage of the dewetting process, the dewetting rims coalesce and form a pattern of straight ribbons that decay by Rayleigh-Plateau instability into isolated droplets which are the equilibrium state of dewetting and enable to characterize E-module and size dependent contact angles that can be correlated to the dewetting dynamics in the three different regimes. Our experiments consist of polystyrene 18kg/mol layers with a typical thickness of 120 nm dewetting from PDMS rubber substrates with typical thicknesses of 6-10 microns and variable E-module. The polystyrene layers are prepared in a glassy state and dewetting is started when heating the samples above the glass transition temperature of the polystyrene. When a desired dewetting situation is reached the sample can be quenched down to room temperature and the rim or droplet shape can be obtained by atomic force microscopy. Lifting the glassy polystyrene layer off from the rubber PDMS layer using a UV-curable glue enables additionally to image the formerly buried polystyrene/PDMS interface and thus to obtain the full three dimensional shape of the dewetting morphologies. Speaker: Khalil Remini (Saarland University) Phase field model with nonlinear elasticity 25m To study the dewetting dynamics of thin liquid films from visco-elastic materials we consider intermediate steps. First, the very soft substrate is described with a phase field model accounting for nonlinear elasticity and for the possibility of phase separation. In this talk, I present the components the two-phase system and derive a weak formulation from which we build our 2d code. Secondly, a three phase system including an air, liquid and elastic substrate phase is described using two phase field variables. Here, the choice of system parameters, including the interface size $\varepsilon>0$ and the mobility in the Cahn-Hilliard equation, are crucial for the numerical efficiency of this model. We use an adaptive mesh refinement to facilitate the computations, especially at the three phase contact line. A future step will be to replace the elastic solid phase in the latter model with the two-phase system described at first. Speaker: Leonie Schmeller (WIAS Berlin) Finite Element Methods for Fluids and Dewetting 1h 30m This lecture gives a compact introduction to the use of energetic variational methods for modeling and simulation of wetting flows. Therefore, in the first lecture, I will introduce GENERIC structures for the evolution of thermomechanical systems and motivate the use of weak formulations and finite element methods for the description and discretization of these equations. In the second lecture, I will present examples relevant for "Dynamic Wetting of Flexible, Adaptive, and Switchable Substrates" and their explicit discretization will be discussed interactively using the finite element framework FEniCS and presented using Jupyter notebooks. Speaker: Dirk Peschka (WIAS Berlin) Informal get together 1h 45m Controlling wetting, adhesion and friction using polymer brushes 1h 30m Polymer brushes consist of long polymer that are end-anchored to a surface at a high density. Due to this end-anchoring they can be utilized as versatile coatings under many conditions where regular coatings would normally degrade. In this lecture I will provide a general introduction to polymer brushes and explain, via different examples, how to employ them to control surface or interfacial properties, such as wetting, adherence and friction. Speaker: Prof. Sissi de Beer (University of Twente) Adaptive Substrates Session: Wetting of Polymer Brushes Adaptation of PS/PAA copolymer to water 25m When a droplet is sliding on surfaces, adaptation of the surface leads to changes of the dynamic contact angles [1]. Hereby two adaptation processes play a role: (i) the adaptation of the surface upon bringing in contact to the droplet (wetting) and (ii) the adaptation of the surface after the droplet passed (dewetting). In order to study both processes, we investigated samples made from polystyrene (PS) polyacrylic acid (PAA) random copolymers by using a tilted-plate method and by sum-frequency generation spectroscopy (SFG). For the wetting process, the advancing and receding contact angles of water droplets decrease when PS/PAA surface adapts to water. We measured a relaxation time of ~1 ms for 40 - 100 nm thick PS/PAA films adapting to water by a tilted-plate method [2]. Here, both water diffusion and polymer reorientation play a role in the adaptation process. For the dewetting process, the sliding droplet velocity decreased for subsequent droplets with different droplet intervals. From the drop interval and the drop velocity, we calculated the time that is required for the surface to (re-)adapt to air. While for the wetting process water diffusion and copolymer reorientation played a role, it is not clear to which extend both effects are present during dewetting. Therefore, we performed SFG experiments on PS/PAA surfaces to determine the contribution of both effects. [1] H. J. Butt et al, Langmuir 34 (2018), 11292−11304. [2] X Li et al, Langmuir 37(2021), 1571−1577. Speaker: Xiaomei Li (Max-Planck-Institut für Polymerforschung) Memory effects of PNiPAAm brushes in different atmospheres 25m Some polymer brushes show a co-nonsolvency effect: They collapse in a mixture of two good solvents at some specific mixing ratio. Previous studies focused on the response of brushes which are entirely covered by a liquid. Here, we concentrate on partial wetting of co-nonsolvent polymer brushes, i.e., on the dynamics of a three-phase contact line moving over such brushes. We use Poly(N-isopropylacrylamide) (PNiPAAm) brushes and water and ethanol as good solvents. In water/ethanol mixtures, the brush thickness is a non-monotonous function of the ethanol concentration. The memory seen by consecutively depositing drops at the same position. Previously deposited drops adapt the brush and changes the wetting behavior (advancing contact angle) of subsequent drops [1]. One approach to test for the competition between water and ethanol in the brush, is to measure with a water drop in an ethanol-saturated atmosphere. At the three-phase contact line, the air and probably also the brush will transition from an ethanol-rich state to a water-enriched state. Thus the brush might pass through the regime of the co-nosnsolvency effect. On large time scales the ethanol enriched gas phase and the water drop will become mixtures of ethanol and water. We present strategies to counter this mixing effect. The memory effect shown above cannot be experienced in an ethanol-enriched atmosphere. Schubotz, S., et al., Memory effects in polymer brushes showing co-nonsolvency effects. Advances in Colloid and Interface Science, 2021. 294: p. 102442. Speaker: Simon Schubotz (Leibniz-Institut für Polymerforschung Dresden e.V., 01069 Dresden, Germany; Technische Universität Dresden, 01069 Dresden, Germany) simon_schubotz.png Modeling forced (de-)wetting of adaptive substrates 25m When a liquid drop spreads on an adaptive substrate the latter changes its properties what may result in an intricate coupled dynamics of drop and substrate. In [1] we presented a mesoscale hydrodynamic model for a droplet spreading on a polymer brush as a gradient dynamics on an underlying energy functional. The model accounts for coupled spreading, absorption and wicking dynamics, while the underlying energy functional incorporates capillarity, wettability and brush energy. In this talk, we give a brief recap of the model and provide further insights into the (de)wetting behavior and the dynamics of a moving contact line on polymer brushes that we obtain from numerical simulations. [1] U. Thiele, S. Hartmann "Gradient dynamics model for drops spreading on polymer brushes" EPJ ST, 229, 1819--1832 (2020) Speaker: Simon Hartmann (WWU Münster) Wetting Dynamics Session Droplet Scanning Microscopy 25m Sliding drops on solid surfaces experience lateral adhesion owing to capillary forces. Local capillary forces of drops are of interest for fundamental wetting science and industrial applications such as self-cleaning surfaces or paint spraying. In particular, functional coatings can be stained on purpose or unintentionally as a defect during a coating deposition process. Therefore, techniques are required to map capillary forces over large areas. Attempts have been made by measuring locally the vertical adhesion forces [1] or the roll-off angles. However, both techniques are time-consuming and cannot examine a relatively large area at once. In order to overcome these limitations, we have built a setup that allows us to measure the sliding force of drops over area of 5x2 cm2, with different hydrophobicities, within 1-5 minutes. The drop of 15 μL volume is immobilized by a metal ring, which is attached to a glass capillary. While the drop is sliding over the surface, the lateral deflection of the glass capillary, which is proportional to the sliding force [2], has been recorded in form of a video. The obtained deflection of the glass capillary is multiplied with its spring constant which results in the lateral sliding force. Subsequently, we plot the force values for the respective positions in form of 2D-Heat map. With this technique, we mapped heterogeneous hydrophobic surfaces made from PFOTS and OTS (Figure 1(a)). This scanning technique allows studying the lateral distribution of different hydrophobicities. As our contribution, we will discuss the setup and the origin of forces while water drops are drawn over different hydrophobically stained areas. Our initial experiments reveal that we can detect stained areas smaller than 1/4th fraction of the drop diameter. Speaker: Mr Chirag Hinduja (Max Planck Institute for Polymer Research) Abstract_Chirag_SPP2171.pdf Lattice Boltzmann simulations of liquid lens coalescence 25m The lattice Boltzmann method is an efficient approach to simulate complex fluids and wetting processes. We present results based on the colour gradient method which is particularly designed for multicomponent fluids and is able to obtain thermodynamically consistent results over wide ranges of viscosities and surface tensions. After demonstrating benchmarks to analytically accessible solutions such as the Laplace pressure, Neumann angles, Hagen-Poiseuille velocity profiles or surface tension deducted from drop oscillations, the method is applied to investigate the dynamics of liquid lens coalescence. Thereby the respective asymptotic power-laws obtained from similarity solutions of the thin-film equations are verified in the viscous and inertial limit. Speaker: Thomas Scheel (Forschungszentrum Jülich) Wetting and freezing on soft surfaces 1h 30m Liquids have surface tensions that are widely recognised as playing a crucial role in many aspects of their behaviour. Solids also have a surface tension, but it is typically ignored, as being too small to have an observable affect. However, this is certainly not true for soft solids, where surface tension can completely change wetting behaviour and phenomena like adhesion and composite behaviour. I will mainly talk about two related aspects of this. Firstly, I will talk about how we can measure solid surface tensions, and why this is not easy to do accurately. In particular, I will focus on recent experiments that measure how surface tensions in gels have an unexpectedly large stretch dependence, and discuss why this is, and what its implications for wetting are. Secondly, I will talk about wetting of non-ideal substrates: ones which have extremely large contact-angle hysteresis, or which can be swollen by the wetting liquid. In particular, I will demonstrate a novel technique, with which we can still measure equilibrium properties in such systems. This is strongly tied to concepts of adaptive wetting, as described by the group of Profs. Vollmer and Butt. Finally, if time permits, I will also describe our recent experiments looking at freezing on soft surfaces. I will show how stresses are generated at the contact line that are significantly bigger than anything we see in wetting experiments, and talk about how these stresses are the root cause of damage in soft materials caused by freezing. Speaker: Prof. Robert Style (ETH Zürich) A High-Order Sharp Interface Method with Contact Line Singularities 1h 30m When distinct phases interact, contact lines occur. Characteristically, singularities are observed at the contact lines, e.g. a jump in pressure or varying surface tensions. This offers a significant obstacle for high order methods, where generally smooth functions are required to obtain a high order of convergence. By introducing a flexible discontinuous polynomial ansatz space, we overcome this restriction. We construct an extended discontinuous Galerkin (XDG) method that resolves contact line discontinuities while maintaining a high order of convergence. We will briefly summarize the XDG method, concentrating on one of its pillars: the level set function. The zero isocontour of the level set function implicitly defines the surfaces of the contact lines. We will focus on two central components: first, contact line regularization and evolution and second, quadrature methods for surfaces and volumes with singularities. Speaker: Lauritz Beck (TU Darmstadt) Capillary Statics in Nanowedges 1h 30m Understanding of capillary transport in porous media is beneficial for a manifold of industries and technologies, which can be exemplified by ink-jet printing, oil and gas production, food production, and water resources research. The geometry of porous media is in most cases tremendously complicated and cannot be always represented by interconnected cylindrical capillaries. Instead, the corner-containing geometries can serve as a more realistic representation of the porous media topology. The simplest element of the angle-containing structures is an open wedge (corner). It is well known that when the Concus-Finn condition $\theta+\alpha>\pi/2$ relating the contact angle of the wetting liquid $\theta$ and the wedge opening angle $2\alpha$ is fulfilled, the steady state of liquid in the wedge is possible. Otherwise, the rivulet driven by the curvature-induced pressure is expected to propagate infinitely along the corner. However, at the nanoscale, the wetting behavior is drastically affected by surface forces. To date, the understanding of the nanowetting of the corner geometries is still poor. In the present work, we investigate wetting of the wedge-shaped nanochannels accounting for the surface forces and show that introduction of the latter leads to the appearance of steady state of meniscus in the wedge in the cases for which the Concus-Finn condition is violated. We present and discuss the influence of the surface force parameters as well as the corner geometry on the equilibrium rivulet profile. Speaker: Nikolai Kubochkin (Institute for Technical Thermodynamics, Technische Universität Darmstadt) Impact of salt on sorption isotherms in nanoporous media 1h 30m Salt water is ubiquitous in nature (e.g. geomaterials, soil, clouds formation) and in technology (e.g. desalination, concrete weathering, heritage conservation). In most of these situations, salt water is confined within a porous medium, often with pores down to the nanometer scale: for example, crystallization and dissolution cycles induced by humidity changes are known to induce structural damage to building materials, artwork, etc. And yet, these processes are not well characterized, especially when pores are in the nanometer range. Here, we investigate the response of the salt water confined in several porous silicon samples (average pore diameter from 3 nm to 20 nm) to humidity cycles. We performed sorption isotherms where we monitored optically water content in the porous medium. We systematically characterized how the salt concentration impacts the shape of the isotherms and compared these results to a minimal model coupling solution thermodynamics to capillarity, nucleation and confinement effects. Speaker: Hugo Bellezza (Université Lyon 1-CNRS, Université de Lyon 69622 Villeurbanne, France) Poster_interpores_v15.pdf Spiropyran thin film preparation and photoswitching 1h 30m Wetting is a ubiquitous phenomenon that can be found in everyday situations such as a rain-soaked glass pane or a piece of rotten wood. However, it plays a key role in more sophisticated tasks that our society relies on, such as oil extraction, inject printing or protein adsorption. In order to improve the wetting process and enhance its applications, it is necessary to understand the physicochemical properties of wetting. Surfaces that under external stimuli are able to switch from more hydrophobic to less hydrophobic states constitute a powerful tool to understand at the molecular scale the wetting process. The spiropyran/merocyanine (SP/MC) (Figure 1) pair of molecules are two isomers that can be switched to each other by light. The feature that makes them so interesting is the difference in their dipole moment which happens to take values from 4-6 D for spiropyran to 14-18 D for merocyanine. In this work, we focus on the preparation of SP/MC thin films and study the change in the water contact angle of these films. Speaker: Mirela Encheva Abstract_Mirela_Encheva.pdf Wettability study of smart surfaces with tunable geometry 1h 30m Various living organisms have structured surfaces with specific wettability that allows their efficient adaptation to the environment and improves their survival rate. For example, the rice leaves have micro-and nanoscale structures on their surface that form a superhydrophobic surface for self-cleaning and water repellence[1]. Bioinspiration of these natural surfaces in science can be beneficial for applications in biotechnology, microfluidics, textiles, fabrication of sensors, etc[2]. Addressing these challenging goals requires the development of both materials with tailored properties and methods for the fabrication of structured surfaces. In comparison to previously reported surface patterning techniques, melt-electrowriting (MEW) is a novel and solvent-free technique that is based on 3D printing and electrospinning which allows programmed deposition of polymeric microfibers [3]. Shape memory polymers offer a very interesting combination of properties such as switching of mechanical properties and the capability of stimuli-induced restoration of shape after deformation [4, 5]. In this work, we report the fabrication of surfaces with tunable geometry and mechanical properties with high aspect ratio surface features (50:1) and the investigation of their wetting properties. For the fabrication of the topographical surface, we melt-electrowrite lamellas structure with a thermoplastic polyurethane with shape memory behavior (Polybutylene adipate based TPU). Our smart surfaces were programmed by the use of extra small forces driven by the surface tension of water. The actuation and switching of surface topography occurs in few minutes (below 5 min). This investigation can open the door for further research in the application of micro/millifluidic devices, creating smart locks to allow the passage of fluids by changing the temperature of the set. [1] D.H. Kwon, H.K. Huh, S.J. Lee, Exp. Fluids 55(3) (2014) 1691. [2] Z. Cheng, D. Zhang, X. Luo, H. Lai, Y. Liu, L. Jiang, Adv. Mater. 33(6) (2021) 2001718. [3] P.D. Dalton, Current Opinion in Biomedical Engineering 2 (2017) 49-57. [4] L. Ionov, G. Stoychev, D. Jehnichen, J.U. Sommer, ACS Applied Materials & Interfaces 9(5) (2017) 4873-4881. [5] G. Stoychev, M.J. Razavi, X. Wang, L. Ionov, Macromol. Rapid Commun. 38(18) (2017) 1700213. Speaker: Gissela Constante (Universität Bayreuth) Wettability study of smart surfaces with tunable geometry PhD workshop.docx Thursday, 1 July Electrowetting – how to make drops move 45m Electrowetting is a flexible manner to modify the wettability of droplets of conductive liquids such as water by applying a voltage between the drop and an electrode that is submerged in the substrate under a thin hydrophobic dielectric layer. Electrowetting allows to vary the contact angle locally by more than 90° on a time scale much faster than any hydrodynamic response time of the drop. In this first lecture, I explain the physical principles of electrowetting and illustrate a number of applications including (i) drop actuation for lab-on-a-chip, (ii) controlled trapping and release of drops on inclined planes, (iii) electrowetting-controlled reduction of contact angle hysteresis and (iv) electrowetting-enhanced water condensation. Speaker: Prof. Frieder Mugele (University of Twente) Reverse Electrowetting and other manners to harvest energy from moving drops 45m While conventional electrowetting uses electric actuation to generate mechanical deformation and motion of drops, reverse electrowetting makes use of the inverse process: it makes use of mechanical motion of conductive drops to generate electrical currents by means of electrostatic induction. These currents are fed into electrical circuits and can be used to operate and/or charge low power electric devices. I will discuss the physical principles of a few common approaches and discuss in detail the physical processes involved in harvesting energy from (rain) droplets falling onto electrically charged surfaces in so-called electrical nano-generators. Switchable Substrates Session Time scales in multiscale dynamics of droplets on switchable substrates 22m The dynamics of droplets on switchable substrates is an interplay of multiple time scales calling for a multiscale theoretical modelling. We combine a microscopic Molecular Dynamics model (MD) and a mesoscopic thin film model (TF) to investigate detailed changes in the contact region in the MD model, while simultaneously analyzing long sterm stabilities of pattern analytically in the context of the lubrication approximation described by the TF model. Using the dimensionless version of both models, the time scales can then be determined using experimentally measure quantities like the viscosity or the surface tension. However, for quantitative comparisons such a time scale mapping would not be accurate enough due to the uncertainties of the relevant quantities. Instead we matched the profiles from both MD and TF models and obtained the relation between the time scales. In this talk we introduce this general procedure and discuss the alternative possibility to use measure characteristic times within both models. Speaker: Moritz Stieneker (Institute of Theoretical Physics) The Interplay of Spreading, Imbibition and Evaporation of Water Droplets on Nanoporous Surfaces 22m The study of fluid dynamics in nanoporous materials is nowadays a topic of great interest due to the often significantly modified thermal equilibrium and non-equilibrium properties of extremely spatially confined liquids compared to their bulk counterparts. However, fluid transport in nanoscale geometries plays also an increasing role in functional materials consisting of fluid-infused solids, such as supercapacitors and porous materials with integrated actuation, sensation [1] and adaptive lubrication [2]. Here we present a study on the spreading of water droplets on nanoporous silicon as a function of time. The evolution of the droplet volume is analyzed theoretically and experimentally considering the evaporation and the radial imbibition of the liquid into the porous substrate. The scaling behavior of these quantities are qualitatively in agreement with phenomenological descriptions [3,4], however also substantial deviations compared to Molecular Dynamics simulations on this phenomenology are revealed [5]. Our experiments shall serve as a base for future studies employing electrowetting to control the competition of spreading and imbibition [6]. Speaker: Laura Gallardo Domínguez (Research Group Physics and X-Ray Analytics of Functional Materials, Hamburg University of Technology, Germany ) Molecular Changes and Wetting Dynamics of Arylazopyrazole Monolayers on α-Al₂O₃(0001) 22m There is great interest in smart surfaces that can change their wetting behavior on demand and which have application potential e.g. for self-cleaning surfaces. Using light as a stimulus to change the wetting behavior allows to confine the stimulus both in space and time which renders light as stimulus highly interesting to address dynamic wetting of surfaces. Here we have synthesized a new class of photoswitchable molecules - arylazopyrazole phosphonic acids (butyl-AAP-C₁₈-PA) that can undergo E/Z photoisomerization reactions and are highly useful to decorate aluminum oxide surfaces with photo-responsive monolayers. On an Al₂O₃ substrate, the AAP moieties are irreversibly adsorbed because of strong covalent interactions of the PA head group with the Al₂O₃ substrate surface. Modification of $\alpha$-Al₂O₃(0001) surfaces is done by a Langmuir-Blodgett transfer of butyl-AAP-C₁₈-PA monolayers. The prepared layers with a surface coverage of 4 molecules/nm₂ were shown to exhibit the largest differences in terms of static contact angle change. In particular, we show that with the use of butyl-AAP-C₁₈-PA monolayers the contact angle can be changed reversibly between 84° (E state) and 76° (Z state). While contact angle measurements can quantify the changes in the macroscopic wetting, the application of inherently interface specific sum-frequency generation (SFG) spectroscopy can provide more detailed information on the interfacial molecules as well as on the kinetic changes of AAP monolayers as a function of light irradiation and thus E/Z configuration of butyl-AAP-C₁₈-PA moieties. For instance, we have used time-resolved SFG spectroscopy to study C-H stretching vibrations of the butyl-AAP-C₁₈-PA monolayers under different light irradiations, which is useful to address the switching kinetics on a molecular scale and can be further compared to the macroscopic changes of the contact angle. Using time-resolved SFG spectroscopy, we show that a steep initial decrease in contact angle for E to Z switching (green to UV irradiation) is accompanied by a substantial reduction of aromatic C-H modes and the electronic non-resonant contribution to the SFG spectra. A possible explanation for this might be an order / disorder transition or a change in the net molecular orientation of the molecular groups contributing to the SFG spectra. The time scale of the molecular changes is ~10 s (E to Z) and ~200 s (Z to E) from one equilibrium state to other. For E to Z switching this is comparable to the initial fast change of the contact angle, however, the contact angle shows also subsequent slower changes. Speaker: Christian Honnigfort (WWU Münster) Photoswitchable surface properties of soft and flexible spiropyran-containing photorheological fluids 22m Movement of the droplets induced by changes in surface properties such as wettability has been of great interest for many applications such as microfluidic devices [1], functional coatings [2], transport of chemical species with a droplet [3], etc. Special stimuli-responsive materials with switchable surface properties are capable to offer the possibility of droplet movement in the material or across the surface [2,3]. Spatially controllable and reversible photoswitching of colorless hydrophobic Spiropyran (SP) to magenta hydrophilic Merocyanine (MC) makes this class of molecular switches especially promising for responsive materials. Spiropyran has been already integrated into reverse micellar lecithin/bile salt organogels with highly viscoelastic behavior [4]. It was possible to prove with dynamic rheological measurements that they present photoswitchable rheological properties and go under significant changes of viscosity under UV irradiation after SP addition [4-6]. Such special stimuli-responsive soft materials can be utilized to move a droplet between spots with different softness upon a high-resolution photoswitch on the surface. Herein, we have obtained a few micrometer-resolution for photoswitching of the transparent thin layer of the lecithin-based samples using a maskless stereolithography machine [7]. Also, commonly used volatile solvents for the lecithin-based organogels have been successfully replaced with a non-volatile organic solvent, isopropyl palmitate [8] to stabilize the properties during the application. Next, localized photoswitching of the sample created a softness gradient resulted in the droplet movement into the fluid and later, the concept will be used to induce droplet movement across the surface. [1] H. Gau, S. Herminghaus, P. Lenz, R. Lipowsky, H. Gau, Science, 1999, 283, 46–49 [2] K. Liu, M. Cao, A. Fujishima, and L. Jiang, Chem. Rev. 2014, 114, 10044−10094 [3] L. Florea, K. Wagner, P. Wagner, G. G. Wallace, F. B. Lopez, D. L. Officer, D. Diamond, Adv. Mater. 2014, 26, 7339–7345 [4] H. Y. Lee, K. K. Diehn, K. Sun, T, Chen, and S. R. Raghavan, J. Am. Chem. Soc. 2011, 133, 8461–8463 [5] R. Kumar, A. M. Ketner, and S. R. Raghavan, Langmuir 2010, 26(8), 5405–5411 [6] M. Y. Cho, J.-S. Kim, H. J. Choi, S.-B. Choi and G.W. Kim, Smart Mater. Struct.26 (2017) 054007 [7] A. Waldbaur, B. Waterkotte, K. Schmitz, B. E. Rapp, small 2012, 8, No. 10, 1570–1578 [8] S. H. Tung, Y. E. Huang, and S. R. Raghavan, J. AM. CHEM. SOC. 2006, 128, 5751-5756 Speaker: Niloofar Nekoonam (University of Freiburg) Response of nanoporous media to humidity 1h 30m I will present a variety of responses associated with humidity changes in nanoporous media or micro/nano composites, which we investigated using artificial systems. These phenomena include capillary flows (imbibition, drying), osmotic flows, nucleation (cavitation, precipitation) and self-organized evaporation patterns. Through these examples, I will discuss how the interplay of thermodynamics and transport can result in interesting dynamics that can be triggered using external humidity as a control parameter. Speaker: Olivier Vincent (CNRS)	CommonCrawl
URL: /core/journals/journal-of-fluid-mechanics Focus on Fluids JFM Rapids JFM Perspectives Only show content I have access to (29) Only show open access (26) Last 3 months (17) Last 12 months (54) Last 3 years (54) MathJax MathJax help Close MathJax help MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org. < Back to all volumes Volume 949 - 25 October 2022 Graphical abstract from L'Estimé, M., Duchemin, L., Reyssat, É. & Bico, J. 2022 Fingering instability in adhesion fronts. J. Fluid Mech. 949, A46. doi:10.1017/jfm.2022.789. Direct statistical simulation of the Busse annulus Jeffrey S. Oishi, Keaton J. Burns, J.B. Marston, Steven M. Tobias Published online by Cambridge University Press: 03 October 2022, R1 We consider direct statistical simulation (DSS) of a paradigm system of convection interacting with mean flows. In the Busse annulus model, zonal jets are generated through the interaction of convectively driven turbulence and rotation; non-trivial dynamics including the emergence of multiple jets and bursting 'predator–prey' type dynamics can be found. We formulate the DSS by expanding around the mean flow in terms of equal-time cumulants and arrive at a closed set of equations of motion for the cumulants. Here, we present results using an expansion terminated at the second cumulant (CE2); it is fundamentally a quasilinear theory. We focus on particular cases including bursting and bistable multiple jets and demonstrate that CE2 can reproduce the results of direct numerical simulation if particular attention is given to symmetry considerations. JFM Papers Unsteady convective–diffusive transport in semicircular microchannels with irreversible wall reaction Milad Azari, Arman Sadeghi Published online by Cambridge University Press: 21 September 2022, A1 The unsteady dispersion of a solute band by a steady pressure-driven flow in a semicircular microchannel is theoretically studied via the generalized dispersion model. Considering an irreversible first-order reaction at the curved wall while assuming a no-flux boundary condition at the flat wall, analytical solutions are obtained for the exchange, convection and dispersion coefficients as well as the dimensionless forms of solute concentration and mean solute concentration. The solutions are obtained assuming an initial solute band of arbitrary cross-sectional shape and axial distribution and the results are presented for both circular and semicircular shapes with the uniform distribution being a special case of the latter. Besides the general solutions, special solutions are also derived for uniform velocity and no-reaction cases. In the following, the influences of the initial concentration distribution and the Damköhler number, a measure of the reaction rate, on the transport coefficients and the concentration distribution are investigated in depth. It is demonstrated that the combination of the initial concentration distribution and the Damköhler number specifies the variations of the transport coefficients in the short term but the Damköhler number is the only parameter dominating the long-term values: the exchange and convection coefficients are increasing functions of the Damköhler number whereas the opposite is true for the dispersion coefficient. Moreover, we show that, provided the solute injection is appropriately positioned and shaped, liquid-phase transportation with little dispersion is possible in typical microchannels utilizing semicircular geometry. Unsteady mechanisms in shock wave and boundary layer interactions over a forward-facing step Weibo Hu, Stefan Hickel, Bas W. van Oudheusden The flow over a forward-facing step (FFS) at $Ma_\infty =1.7$ and $Re_{\delta _0}=1.3718\times 10^{4}$ is investigated by well-resolved large-eddy simulation. To investigate effects of upstream flow structures and turbulence on the low-frequency dynamics of the shock wave/boundary layer interaction (SWBLI), two cases are considered: one with a laminar inflow and one with a turbulent inflow. The laminar inflow case shows signs of a rapid transition to turbulence upstream of the step, as inferred from the streamwise variation of $\langle C_f \rangle$ and the evolution of the coherent vortical structures. Nevertheless, the separation length is more than twice as large for the laminar inflow case, and the coalescence of compression waves into a separation shock is observed only for the fully turbulent inflow case. The dynamics at low and medium frequencies is characterized by a spectral analysis, where the lower frequency range is related to the unsteady separation region, and the intermediate one is associated with the shedding of shear layer vortices. For the turbulent inflow case, we furthermore use a three-dimensional dynamic mode decomposition to analyse the individual contributions of selected modes to the unsteadiness of the SWBLI. The separation shock and Görtler-like vortices, which are induced by the centrifugal forces in the separation region, are strongly correlated with the low-frequency unsteadiness in the current FFS case. Similarly as observed previously for the backward-facing steps, we observe a slightly higher non-dimensional frequency (based on the separation length) of the low-frequency mode than for SWBLI in flat plate and ramp configurations. Experimental study of bubble competition and spike competition in Richtmyer–Meshkov flows Yu Liang, Lili Liu, Xisheng Luo Shock-tube experiments on various two-bubble and two-spike interfaces are performed to examine the dependence of bubble competition and spike competition on the initial spectra and density ratio of the interface. The differences in the influences of bubble competition and spike competition on the Richtmyer–Meshkov instability are highlighted for the first time. The bubble-competition effect is mainly dependent on the initial spectra of the two-bubble configuration. In contrast, the spike-competition effect is determined by both the initial spectra and density ratio. The extended buoyancy–drag model is adopted to explain the variation of the drag force imposed on the long-wavelength and short-wavelength structures as the initial conditions change. Based on the spectrum analysis, it is found that the constituent modes of two-bubble and two-spike interfaces have different contributions to the long-wavelength and short-wavelength perturbation growths. A generalised, nonlinear, analytical model is then established to quantify the bubble-competition effect and spike-competition effect considering arbitrary initial spectra and density ratio. The bubble-competition effect is believed to be stronger than the spike-competition effect at a high density ratio because it suppresses the high-frequency perturbation growth more evidently. Control of oblique breakdown in a supersonic boundary layer employing a local cooling strip Teng Zhou, Zaijie Liu, Yuhan Lu, Dake Kang, Chao Yan Oblique breakdown in a Mach 2.0 supersonic boundary layer controlled by a local cooling strip with a temperature jump is investigated using direct numerical simulations and linear stability theory. The effect of temperature on the stability of the fundamental oblique waves is first studied by linear stability theory. It is shown that the growth rate of fundamental oblique waves will decrease monotonically as the temperature decreases. However, the results of the direct numerical simulations indicate that transition reversal will occur as the growth rate of the fundamental oblique waves of cooled case becomes faster compared with that of baseline case downstream of the cooling strip. When the cooling strip is in the linear region, the transition is delayed due to the suppression effect of the cooling strip on the fundamental oblique waves. When the cooling strip is located in the early nonlinear region, the fundamental oblique waves will be suppressed by higher spanwise wavenumber steady modes generated by the mutual and self-interaction between the fundamental oblique waves and harmonic modes, which is first called the self-suppression effect (SSE) in the present study. Further research indicated that the meanflow distortion generated by steady modes plays an important role in the SSE. Compared with the stabilization effect of the cooling strip, the SSE is more effective. Moreover, the SSE might provide a new idea on the instability control, as it is observed that the SSE works three times leading to the growth rate of fundamental oblique waves slowing down at three different regions, respectively. Stability of thermocapillary flow in liquid bridges fully coupled to the gas phase Mario Stojanović, Francesco Romanò, Hendrik C. Kuhlmann The linear stability of the axisymmetric steady thermocapillary flow in a liquid bridge made from 2 cSt silicone oil (Prandtl number 28) is investigated numerically in the framework of the Boussinesq approximation. The flow and temperature fields in the surrounding gas phase (air) are taken into account for a generic cylindrical container hosting the liquid bridge. The flows in the liquid and in the gas are fully coupled across the hydrostatically deformed liquid–gas interface, neglecting dynamic interface deformations. Originating from a common reference case, the linear stability boundary is computed varying the length of the liquid bridge (aspect ratio), its volume and the gravity level, providing accurate critical data. The qualitative dependence of the critical threshold on these parameters is explained in terms of the characteristics of the critical mode. The heat exchange between the ambient gas and the liquid bridge that is fully resolved has an important influence on the critical conditions. Examining capillary dynamics in rectangular and circular conduits subject to unsteady surface tension Martin N. Azese, Jaures J. Engola, Jacques Hona, Emile Jean Yap, Yves C. Mbono Samba The unsteady effects of transitioning surface tension, $\gamma (t)$, on the dynamics of capillary imbibition in channels of arbitrary shape are analytically investigated with a focus on rectangular and circular channels. With proper scaling, two unsteady models for $\gamma (t)$ are defined and used to highlight this transient behaviour. The convoluted dynamics at the flow front are correctly captured in the governing equations, which are rigorously analysed using unsteady eigenfunction expansion. Then, the final solution and data are obtained by employing the Runge–Kutta fourth-order scheme elegantly applied simultaneously to two derived nonlinear ordinary differential equations. Ultimately, the results are more accurate compared with previous studies. Dynamics and kinematic similarity between rectangular and circular channels are investigated and discussed and the conditions for equivalence in both channels are highlighted. Using a small parameter ( $\epsilon$) that stretches the time scale, we successfully use a robust asymptotic analysis to develop and capture the long-time dynamics. Ultimately, we recover the Lucas–Washburn regime analysed in Washburn (Phys. Rev., vol. 17, 1921, pp. 273–283), Lucas (Kolloidn. Z., vol. 23, 1918, pp. 15–22) for steady surface tension where the variations of depth and rate with time result in $h\thicksim t^{1/2}$ and $v \thicksim t^{-1/2}$. In the end, the three forces, namely the inertia, $F_{v}$, the viscous, $F_{\mu }$, and the surface tension, $F_{\gamma }$, are briefly analysed and used to highlight three main distinct regimes. We show that at early times, $F_{v}/F_{\gamma } \thicksim 1$, whereas at a long time, $F_{\mu }/F_{\gamma } \thicksim -1$. Modelling the downstream development of a turbulent boundary layer following a step change of roughness Mogeng Li, Charitha M. de Silva, Daniel Chung, Dale I. Pullin, Ivan Marusic, Nicholas Hutchins In this study, we develop an analytical model to predict the turbulent boundary layer downstream of a step-change in the surface roughness where upstream flow conditions are given. We first revisit the classical model of Elliott (Trans. Am. Geophys. Union, vol. 39, 1958, pp. 1048–1054), who modelled the velocity distribution within and above the internal layer with a simple piecewise logarithmic profile, and evolved the velocity profile using the streamwise momentum equation. Elliott's model was originally developed for an atmospheric surface layer, and to make the model applicable to a spatially developing turbulent boundary layer with finite thickness, we propose a number of more physical refinements, including adding a wake function to the velocity profile, considering the growth of the entire boundary layer in the streamwise direction, and using a more realistic shear stress profile in the momentum equation. In particular, we implement the blending model (Li et al., J. Fluid Mech., vol. 923, 2021, p. A18) to account for the deviation of the mean flow within the internal layer from a canonical velocity profile based on the local wall condition. These refinements lead to improved agreement between the prediction and the measurement, especially in the vicinity of the rough-to-smooth change. Opposing-buoyancy mixed convection through and around arrays of heated cylinders Tingting Tang, Zhiyong Li, Shimin Yu, Jianhui Li, Peng Yu We numerically investigated the opposing-buoyancy mixed convection through and around square arrays of $10\times 10$ heated circular cylinders with the solid fraction ( $\phi$) ranging from 0.0079 to 0.66 and the Richardson number ( $Ri$) varying from 0 to 1 at a fixed Reynolds number ( $Re$) of 100. Our simulations revealed that the large mean recirculation in the far wake can be detached from or connected with the vortex pair in the near wake for different combinations of $Ri$ and $\phi$. Also, it was found that the array with relatively small $\phi$ can significantly promote flow instability even at moderate $Ri$. The instability, which is closely related to the fluctuating heat flux, develops from the lateral sides to the downstream side of the array and gives rise to the large mean recirculation in the far wake. The power spectra density of the array-scale force coefficients demonstrates that the flow undergoes different bifurcation behaviours under various parameter combinations, which reflects the interaction between the near-wake and far-wake vortexes. Interestingly, the Strouhal–Richardson number curves can be collapsed onto the same curve when $Ri$ is increased by a $\phi$-dependent factor. Also, for $\phi \leqslant 0.22$, both the mean drag coefficient and the mean Nusselt number of the array were found to decrease linearly with $Ri$ since the buoyancy within the array becomes prominent in this range of $\phi$. Transient flows and migration in granular suspensions: key role of Reynolds-like dilatancy S. Athani, B. Metzger, Y. Forterre, R. Mari We investigate the transient dynamics of a sheared suspension of neutrally buoyant particles in pressure-imposed rheology configuration, subject to a sudden change in shear rate or external pressure. Discrete element method simulations show that, depending on the flow parameters (particle and system size, initial volume fraction), the early stress response of the suspension may differ strongly from the prediction of the suspension balance model based on the steady-state rheology. We show that a two-phase model incorporating the Reynolds-like dilatancy law of Pailha & Pouliquen (J. Fluid Mech., vol. 633, 2009, pp. 115–135), which prescribes the dilation rate of the suspension over a strain scale $\gamma _0$, captures quantitatively the suspension dilation/compaction over the whole range of parameters investigated. Together with the Darcy flow induced by the pore pressure gradient during dilation or compaction, this Reynolds-like dilatancy implies that the early stress response of the suspension is non-local, with a non-local length scale $\ell$ that scales with the particle size and diverges algebraically at jamming. In regions affected by $\ell$, the stress level is fixed, not by the steady-state rheology, but by the Darcy fluid pressure gradient resulting from the dilation/compaction rate. Our results extend the validity of the Reynolds-like dilatancy flow rule, initially proposed for jammed suspensions, to flowing suspension below the critical volume fraction at which the suspension jams, thereby providing a unified framework to describe dilation and shear-induced migration. They pave the way for understanding more complex unsteady flows of dense suspensions, such as impacts, transient avalanches or the impulsive response of shear-thickening suspensions. The dominant mechanisms for each regime of secondary flows in horizontal particle-laden pipe flows Xinchen Zhang, Graham J. Nathan, Zhao F. Tian, Rey C. Chin Published online by Cambridge University Press: 23 September 2022, A10 Numerical simulations have been conducted to identify the dominant mechanism responsible for driving secondary flow motions in horizontal particle-laden pipe flows, based on an analysis of the forces acting on each phase. A four-way coupling Euler–Lagrangian approach was employed, using direct numerical simulations for the gas phase and Lagrangian particle tracking to account for the drag, gravitational and lift forces, together with the interactions that occur for both particle–wall and inter-particle collisions. The four different flow regimes, which had been identified previously as depending on various combinations of flow parameters and are characterised by the secondary flow structures of both the fluid and particle phases, were identified via varying the mass loading alone from $\varPhi _m=0.4$ to $\varPhi _m=1.8$. The distribution of the divergence of Reynolds stresses was used to help characterise the classes of the secondary fluid flow. This shows that secondary fluid flows of both the first and second kinds can either exist separately or co-exist in such flows. The forces exerted on the fluid phase by the pressure gradient and fluid–particle interactions were examined qualitatively and quantitatively to identify their contribution to the secondary fluid flow motions. A similar study was also applied to the drag, lift and gravitational forces exerted on the particle phase for the secondary particle flow motions. These were found to explain the secondary flows of both the fluid and particle phases with regard to both the flow direction and magnitude, together with the interaction between the two phases. Vertical and torsional vibrations before the collapse of the Tacoma Narrows Bridge in 1940 Daeun Song, Woojin Kim, Oh-Kyoung Kwon, Haecheon Choi We perform a three-dimensional direct numerical simulation of flow over the Tacoma Narrows Bridge to understand the vertical and torsional vibrations that occurred before its collapse in 1940. Real-scale structural parameters of the bridge are used for the simulation. The Reynolds number based on the free-stream velocity and height of the deck fence is lower ( ${Re}=10\ 000$) than the actual one on the day of its collapse ( ${Re}=3.06 \times 10^{6}$), but the magnitude of a fluid property is modified to provide the real-scale aerodynamic force and moment on the deck. The vertical and torsional vibrations are simulated through two-way coupling of the fluid flow and structural motion. The vertical vibration occurs from the frequency lock-in with the vortex shedding, and its wavelength and frequency agree well with the recorded data in 1940. After saturation of the vertical vibration, a torsional vibration resulting from the aeroelastic fluttering grows exponentially in time, with its wavelength and frequency in excellent agreement with the recorded data of the incident. The critical flutter wind speed for the growth of torsional vibration is obtained as $3.56 < U_c / (f_{nat} B) \le 4$, where $U_{c}$ is the critical flutter wind speed, $f_{nat}$ is the natural frequency of the torsional vibration and $B$ is the deck width. Finally, apart from the actual vibration process in 1940, we perform more numerical simulations to investigate the roles of the free-stream velocity and vertical vibration in the growth of the torsional vibration. Global stability analysis and direct numerical simulation of boundary layers with an isolated roughness element Rong Ma, Krishnan Mahesh Global stability analysis and direct numerical simulation (DNS) are used to study boundary layer flows with an isolated roughness element. The aspect ratio of the element ( $\eta$) is small, while the ratio of element height to displacement boundary layer thickness ( $h/\delta ^{}$) is large. Both steady base flows and time-averaged mean flows are able to capture the frequencies of the primary vortical structures and mode shapes. Global stability results highlight that although the varicose instability is dominant for large $h/\delta ^{}$, sinuous instability becomes more pronounced as $Re_h$ increases for the thin geometry ( $\eta =0.5$), due to increased spanwise shear in the near-wake region. Wavemaker results indicate that $\eta$ affects the convective nature of the shear layer more than the type of instability. DNS results show that different instability mechanisms lead to different development and evolution of vortical structures in the transition process. For $\eta =1$, the varicose instability is associated with the periodic shedding of hairpin vortices, and its stronger spatial transient growth indicated by wavemaker results aids the formation of hairpin vortices farther downstream. In contrast, for $\eta =0.5$, the interplay between varicose and sinuous instabilities results in a broader-banded energy spectrum and leads to the sinuous wiggling of hairpin vortices in the near wake when $Re_h$ is sufficiently high. A sinuous mode with a lower frequency captured by dynamic mode decomposition analysis, and associated with the 'wiggling' of streaks, persists far downstream and promotes transition to turbulence. A new regime map is developed to classify and predict instability mechanisms based on $Re_{hh}^{1/2}$ and $d/\delta ^{*}$ using a logistic regression model. Although the mean skin friction demonstrates different evolutions for the two geometries, both of them efficiently trip the flow to turbulence at $Re_h=1100$. An earlier location of a fully-developed turbulent state is established for $\eta =1$ at $x \approx 110h$. Exact solutions of time-dependent oscillations in multipolar spherical vortices A. Viúdez Exact solutions of the time-dependent three-dimensional nonlinear vorticity equation for Euler flows with spherical geometry are provided. The velocity solution is the sum of a multipolar oscillatory function and a rigid cylindrical motion with swirl. The multipolar oscillation is a velocity mode whose radial and angular dependencies are given by the spherical Bessel functions and vector spherical harmonics, respectively. The local frequency of the velocity oscillations equals the angular speed of the rigid flow times the angular azimuthal wavenumber of the oscillating flow. The unsteady motion corresponds to inertial oscillations in multipolar flows with spatial azimuthal waves (non-vanishing azimuthal wavenumber) in the presence of a background flow with constant axial vorticity. In these nonlinear solutions, the curl of the Lamb vector has a linear dependence with the oscillation velocity, a property that makes it possible for the oscillating motion to satisfy different linear wave equations. Based on these inviscid time-dependent velocity modes, new exact solutions to the time-dependent Navier–Stokes equation are also provided. Vorticity amplification in wavy viscoelastic channel flow Jacob Page, Tamer A. Zaki Surface distortions to an otherwise planar channel flow introduce vorticity perturbations. In Newtonian fluids, the vorticity induced by small surface undulations on the lower wall is advected by the background flow and diffuses into the fluid. When the fluid is viscoelastic, we identify new mechanisms by which significant vorticity perturbations can be generated in both inertialess and elasto-inertial channel flows. We focus on the case where the lengthscale of the surface distortion is much longer than the channel depth, where we find significant departure from plane shear (Page & Zaki, J. Fluid Mech., vol. 901, 2016, pp. 392–429) due to the non-monotonic base-flow streamwise-normal elastic stress. In inertialess flows, a purely elastic response results in streamlines deforming to match the bottom topography in the lower half the channel. However, the vanishing stress at the centreline introduces a blocking effect, and the associated $O(1)$ jump in normal velocity is balanced by a large-amplitude streamwise-oscillating 'jet' in a boundary layer, resulting in a localised, chevron-shaped vorticity perturbation field. In elasto-inertial flows, resonance between the frequency of elasto-inertial 'Alfvén' waves and the frequency apparent to an observer moving with the fluid results in vorticity amplification in a pair of critical layers on either side of the channel. The vorticity in both layers is equal in magnitude, to leading order in Weissenberg number, and as such the perturbation vorticity field penetrates the full channel depth even when inertia is dominant. The results demonstrate that long-wave distortions, which are relatively innocuous in Newtonian fluids, can drive a significant flow distortion in viscoelastic fluids for a wide range of parameter values. Width effect on contact angle hysteresis in a patterned heterogeneous microchannel Xiangting Chang, Haibo Huang, Xi-Yun Lu, Jian Hou The width effect on contact angle hysteresis in a microchannel with patterned heterogeneous surfaces is systematically investigated. In the model, identical defects periodically appear on the background surface. To this end, a droplet's evaporation and condensation processes inside the microchannel are studied by theoretical analysis and numerical simulation based on a diffuse-interface lattice Boltzmann method. The microchannel width effect on the system's equilibrium properties is studied. The results demonstrate that the number of equilibrium configurations increases linearly with the microchannel width ( $b$), and has a quadratic relationship with the cosine of the reference contact angle and the heterogeneity strength ( $\varepsilon$). The average most stable contact angle is independent of $b$ and is always equal to the contact angle predicted by the Cassie–Baxter equation. For contact angle hysteresis ( $H$), when the microchannels are narrow and wide, there are individual-effect-dominated hysteresis (IDH) and collective-effect-dominated hysteresis (CDH), respectively. The IDH and CDH are hysteresis modes corresponding to the jumping behaviour of contact lines affected by individual defects and two neighbouring defects, respectively. Based on the graphical force balance approach, we establish a scaling law to quantify the connection between $H$, $b$ and $\varepsilon$. Specifically, in the IDH mode, $H\sim b \varepsilon ^2$, while in the CDH mode, $H$ increases linearly with $\varepsilon$ but nonlinearly with $b$. Spatial and spectral characteristics of information flux between turbulent boundary layers and porous media Wenkang Wang, Adrián Lozano-Durán, Rainer Helmig, Xu Chu The interaction between boundary layer turbulence and a porous layer is the cornerstone of interface engineering. In this study, the spatial and spectral-resolved transfer entropy is used to assess the asymmetry of the causal interaction next to the permeable wall. The analysis is based on pore-resolved direct numerical simulation of turbulent channel flow over cylinder arrays. The spatial map of transfer entropy reveals the information flux between the porous medium and arbitrary nearby positions, and paths connecting locations with maximum information transfer are identified. The paths in the 'top-down' and 'bottom-up' directions, respectively, lean upstream and downstream, demonstrating that the coupling process is directionally dependent. The scale dependence of transfer entropy is inspected with a surrogate data strategy. As wall permeability increases, the active scale range in causal interaction shifts from near-wall vortices to Kelvin–Helmholtz type eddies. In addition, linear stochastic estimation is used to determine the statistical velocity field for a local informative event. In an average sense, the interaction between a convecting sweep or ejection event and the up/down-welling motions at the pore unit is the core mechanism that contributes to the causal coupling. The statistical findings derived from the transfer entropy are then validated using a neural network-based remote sensing model. Drop deformation during diffusiophoresis Brian E. McKenzie, Henry C.W. Chu, Stephen Garoff, Robert D. Tilton, Aditya S. Khair Diffusiophoresis refers to the motion of a colloidal particle in a solute concentration gradient, animated by particle–solute interactions. We present a theoretical analysis of the diffusiophoretic motion of a viscous drop in a gradient of neutral solute at zero Reynolds number. In a spatially uniform gradient, the translational velocity of a spherical drop was found by Anderson et al. (J. Fluid Mech., vol. 117, 1982, pp. 107–121). Here, we show additionally that the drop experiences no tendency to deform, regardless of the magnitude of the interfacial tension at the interface of the drop and suspending fluid. Next, we consider a non-uniform gradient, where the ambient solute concentration takes the form of a quadrupole around the drop centroid. This gradient does not induce drop translation, due to symmetry, but does induce a deformation in the drop shape, which is spheroidal to first order in the capillary number $Ca=\beta k_B T R^2 K/\gamma$, where $\beta$ is the magnitude of the quadrupolar variation in solute concentration, $k_B T$ is the thermal energy, $R$ is the drop radius, $K$ is the Gibbs adsorption length, and $\gamma$ is the interfacial tension. Whether the drop becomes prolate or oblate depends on whether the solute–drop interaction is attractive or repulsive. Therefore, our work shows that in principle, a drop could undergo deformation during diffusiophoresis in a non-uniform solute gradient. Superhydrophobic surface immobilisation by insoluble surfactant Michael D. Mayer, Darren G. Crowdy The effects of insoluble surfactants, satisfying a Langmuir equation of state, on transverse Stokes flow over a superhydrophobic surface of unidirectional grooves with flat menisci are examined. The phenomenon of surface immobilisation, whereby surfactants cause part or all of the Cassie-state menisci to become effectively no-slip zones thereby degrading the slip properties of the surface, is of primary interest. The study employs a combined analytical and numerical approach allowing an exploration of surfactant effects over the full range of surface Péclet numbers, Marangoni numbers and surfactant loads. For small surface Péclet and Marangoni numbers, perturbation theory is used to gain basic insights into the physical mechanisms at work. That analysis also provides checks on a robust numerical scheme, built around a complex variable formulation of the problem, used to compute solutions across a wide range of non-dimensional parameter values. Two distinct mechanisms are found to be responsible for surface immobilisation. In the first, most commonly seen at higher surface Péclet numbers, a stagnant cap forms because swept surfactant immobilises a section of the meniscus before any portion of the meniscus reaches maximum packing. Such a cap exists even for a linear equation of state and grows in length with increasing Marangoni number. A second immobilisation mechanism is associated with the nonlinear equation of state: an immobilised region forms because the surfactant concentration reaches its maximum value near the downstream edge of the meniscus. Immobilisation of the latter form can occur at much lower surface Péclet numbers, even if the Marangoni number is small, as long as there is sufficient surfactant in the system. The study enhances understanding of how insoluble surfactants can degrade slip over superhydrophobic surfaces. Instability of a quantum vortex by twist perturbation Matteo Foresti, Renzo L. Ricca In this paper, we determine the instability effects of a phase twist superposed on a quantum vortex defect governed by the Gross–Pitaevskii equation. For this, we consider the modified form of the equation in two cases: when a uniform phase twist is present everywhere in the condensate, and when the defect is subject to a localized phase twist confined to the defect healing region. In the first case, we show that a secondary, new defect is produced as manifestation of an Aharonov–Bohm type effect. In the second case, we prove that due to energy minimization, the defect changes its configurational energy by converting localized twist to writhe. This mechanism, typical of classical elastic systems, is shown to occur also in quantum defects, and it may find useful applications in science and technology.	CommonCrawl
Curvature effects on phase transitions in chiral magnets Kostiantyn V. Yershov, Volodymyr P. Kravchuk, Denis D. Sheka, Ulrich K. Rößler SciPost Phys. 9, 043 (2020) · published 1 October 2020 \| Periodical equilibrium states of magnetization exist in chiral ferromagnetic films, if the constant of antisymmetric exchange (Dzyaloshinskii-Moriya interaction) exceeds some critical value. Here, we demonstrate that this critical value can be significantly modified in curved film. The competition between symmetric and antisymmetric exchange interactions in a curved film can lead to a new type of domain wall which is inclined with respect to the cylinder axis. The wall structure is intermediate between Bloch and N\'eel ones. The exact analytical solutions for phase boundary curves and the new domain wall are obtained. The influence of spacetime curvature on quantum emission in optical analogues to gravity Maxime J. Jacquet, Friedrich Koenig SciPost Phys. Core 3, 005 (2020) · published 30 September 2020 \| Quantum fluctuations on curved spacetimes cause the emission of pairs of particles from the quantum vacuum, as in the Hawking effect from black holes. We use an optical analogue to gravity to investigate the influence of the curvature on quantum emission. Due to dispersion, the spacetime curvature varies with frequency here. We analytically calculate for all frequencies the particle flux, correlations and entanglement. We find that horizons increase the flux with a characteristic spectral shape. The photon number correlations transition from multi- to two-mode, with close to maximal entanglement. The quantum state is a diagnostic for the mode conversion in laboratory tests of quantum field theory on curved spacetimes. Emergence of generalized hydrodynamics in the non-local Luttinger model Per Moosavi SciPost Phys. 9, 037 (2020) · published 11 September 2020 \| We propose the Luttinger model with finite-range interactions as a simple tractable example in 1+1 dimensions to analytically study the emergence of Euler-scale hydrodynamics in a quantum many-body system. This non-local Luttinger model is an exactly solvable quantum field theory somewhere between conformal and Bethe-ansatz integrable models. Applying the recent proposal of generalized hydrodynamics, we show that the model allows for fully explicit yet non-trivial solutions of the resulting Euler-scale hydrodynamic equations. Comparing with exact analytical non-equilibrium results valid at all time and length scales, we show perfect agreement at the Euler scale when the interactions are short range. A formal proof of the emergence of generalized hydrodynamics in the non-local Luttinger model is also given, and effects of long-range interactions are briefly discussed. Analytic and numerical bootstrap of CFTs with $O(m)\times O(n)$ global symmetry in 3D Johan Henriksson, Stefanos R. Kousvos, Andreas Stergiou Motivated by applications to critical phenomena and open theoretical questions, we study conformal field theories with $O(m)\times O(n)$ global symmetry in $d=3$ spacetime dimensions. We use both analytic and numerical bootstrap techniques. Using the analytic bootstrap, we calculate anomalous dimensions and OPE coefficients as power series in $\varepsilon=4-d$ and in $1/n$, with a method that generalizes to arbitrary global symmetry. Whenever comparison is possible, our results agree with earlier results obtained with diagrammatic methods in the literature. Using the numerical bootstrap, we obtain a wide variety of operator dimension bounds, and we find several islands (isolated allowed regions) in parameter space for $O(2)\times O(n)$ theories for various values of $n$. Some of these islands can be attributed to fixed points predicted by perturbative methods like the $\varepsilon$ and large-$n$ expansions, while others appear to arise due to fixed points that have been claimed to exist in resummations of perturbative beta functions. Heavy operators and hydrodynamic tails Luca V. Delacretaz SciPost Phys. 9, 034 (2020) · published 8 September 2020 \| The late time physics of interacting QFTs at finite temperature is controlled by hydrodynamics. For CFTs this implies that heavy operators -- which are generically expected to create thermal states -- can be studied semiclassically. We show that hydrodynamics universally fixes the OPE coefficients $C_{HH'L}$, on average, of all neutral light operators with two non-identical heavy ones, as a function of the scaling dimension and spin of the operators. These methods can be straightforwardly extended to CFTs with global symmetries, and generalize recent EFT results on large charge operators away from the case of minimal dimension at fixed charge. We also revisit certain aspects of late time thermal correlators in QFT and other diffusive systems. Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions Etienne Granet, Maurizio Fagotti, Fabian H. L. Essler We consider the problems of calculating the dynamical order parameter two-point function at finite temperatures and the one-point function after a quantum quench in the transverse field Ising chain. Both of these can be expressed in terms of form factor sums in the basis of physical excitations of the model. We develop a general framework for carrying out these sums based on a decomposition of form factors into partial fractions, which leads to a factorization of the multiple sums and permits them to be evaluated asymptotically. This naturally leads to systematic low density expansions. At late times these expansions can be summed to all orders by means of a determinant representation. Our method has a natural generalization to semi-local operators in interacting integrable models. Honeycomb rare-earth magnets with anisotropic exchange interactions Zhu-Xi Luo, Gang Chen SciPost Phys. Core 3, 004 (2020) · published 4 September 2020 \| We study the rare-earth magnets on a honeycomb lattice, and are particularly interested in the experimental consequences of the highly anisotropic spin interaction due to the spin-orbit entanglement. We perform a high-temperature series expansion using a generic nearest-neighbor Hamiltonian with anisotropic interactions, and obtain the heat capacity, the parallel and perpendicular spin susceptibilities, and the magnetic torque coefficients. We further examine the electron spin resonance linewidth as an important signature of the anisotropic spin interactions. Due to the small interaction energy scale of the rare-earth moments, it is experimentally feasible to realize the strong-field regime. Therefore, we perform the spin-wave analysis and study the possibility of topological magnons when a strong field is applied to the system. The application and relevance to the rare-earth Kitaev materials are discussed. Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters Jonas Richter, Tjark Heitmann, Robin Steinigeweg We study quantum quenches in the transverse-field Ising model defined on different lattice geometries such as chains, two- and three-leg ladders, and two-dimensional square lattices. Starting from fully polarized initial states, we consider the dynamics of the transverse and the longitudinal magnetization for quenches to weak, strong, and critical values of the transverse field. To this end, we rely on an efficient combination of numerical linked cluster expansions (NLCEs) and a forward propagation of pure states in real time. As a main result, we demonstrate that NLCEs comprising solely rectangular clusters provide a promising approach to study the real-time dynamics of two-dimensional quantum many-body systems directly in the thermodynamic limit. By comparing to existing data from the literature, we unveil that NLCEs yield converged results on time scales which are competitive to other state-of-the-art numerical methods. Lecture notes on Generalised Hydrodynamics Benjamin Doyon These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo Institute of Technology, October 2019. I overview in a pedagogical fashion the main aspects of the theory of generalised hydrodynamics, a hydrodynamic theory for quantum and classical many-body integrable systems. Only very basic knowledge of hydrodynamics and integrable systems is assumed. On the low-energy description for tunnel-coupled one-dimensional Bose gases Yuri D van Nieuwkerk, Fabian H L Essler We consider a model of two tunnel-coupled one-dimensional Bose gases with hard-wall boundary conditions. Bosonizing the model and retaining only the most relevant interactions leads to a decoupled theory consisting of a quantum sine-Gordon model and a free boson, describing respectively the antisymmetric and symmetric combinations of the phase fields. We go beyond this description by retaining the perturbation with the next smallest scaling dimension. This perturbation carries conformal spin and couples the two sectors. We carry out a detailed investigation of the effects of this coupling on the non-equilibrium dynamics of the model. We focus in particular on the role played by spatial inhomogeneities in the initial state in a quantum quench setup.	CommonCrawl
Creating a realistic world map - Countries Borders From previous questions, I made a nice mass of land, which was enriched up until the drawing of precise coastlines. But all that nice lands looks a bit empty. In my world, I want to make it alive, and one of the first step, to complete my map is to draw the borders and define the countries. Is there any alternative, to rewriting the whole of history from prehistoric migrations up until the time where the story takes place? For a given country, I could follow the steps indicated in this question. But if I have a whole continent available? This is part of a series of questions that tries to break down the process of creating a world from initial creation of the landmass through to erosion, weather patterns, biomes and every other related topics. Please restrict answers to this specific topic rather than branching on into other areas as other subjects will be covered by other questions. These questions all assume an earth-like spherical world in orbit in the habitable band. See the other questions in this series here : Creating a realistic world Series geography politics worldbuilding-process Tim B♦ clem steredennclem steredenn $\begingroup$ Sorry, I meant this one: youtube.com/watch?v=gtLxZiiuaXs $\endgroup$ – SJuan76 Aug 31 '15 at 20:17 $\begingroup$ I actually watched that video some time ago. But that's exactly my point. It is not trivial to make those distinctions. And just using rivers and mountains aren't enough. $\endgroup$ – clem steredenn Aug 31 '15 at 20:24 $\begingroup$ But do you need that level of detail? Granted, the last examples are spectacular but affect a tiny percent of the world borders and population; and do not appear in anything else than very detailed maps. I think just a few landlocked countries and enclaves and exclaves should do. $\endgroup$ – SJuan76 Aug 31 '15 at 20:45 $\begingroup$ Let me also just point out that sometimes longitude and latitude are used to form borders. Note the border between Northeast Alaska and Canada, for instance. Other examples include Papua New Guinea's west border, the western US/Mexico border, the western US/Canada border, Libya, Egypt, Sudan, Namibia, Guatemala, and others. This is by no means an exhaustive list, nor a particularly common occurrence, but it may be worth adding a few instances of on your map. $\endgroup$ – Dan Aug 31 '15 at 23:33 $\begingroup$ We didn't always use latitude and longitude to navigate, which pre-dates using them to define borders. Maybe your culture uses circles or points at certain places in the world with radial lines coming off at all angles? The possibilities are endless! $\endgroup$ – CJ Dennis Sep 1 '15 at 8:34 National borders will follow rivers, mountain ranges, large forests, inland lakes and deserts. Mountain ranges, deserts and large forests will all form buffer zones between nations since these biomes are not well suited to (human) habitation. So you may have two major nations separated by a mountain range, but a minor nations inhabiting the mountains themselves (like the Himalayas). So think of major nations separated by buffer nations with the latter inhabiting buffer zones featuring more challenging habitability. Challenging habitability need not mean its impossible or very difficult to live, merely that the population there will be smaller and have to have special skills to live there. Once these factors have been taken into account, we need to add a second level of fine detail that is based on your worldbuilding the historical linguistics of your world. Decide how ancient peoples in your world migrated, and thus determine the patchwork of distinct language zones in your world. You can then draw more national borders that are based on language that will serve to create border lines in areas that do not feature natural obstacles. To see an excellent example of such an imagined history of migration you could do much worse than look at Tolkien's work on the three ages of middle earth - here (http://tolkiengateway.net/wiki/Middle-earth). It covers the creation of elves, men, hobbits and dwarves, and if you scour that site above you will find descriptions of the various migration patterns and how that generated the nations in middle earth at the time of the Lord of the Rings. With specific regard to dutch, it evolved along with various other germanic languages from Low Franconian, which was the language of the Franks. https://en.wikipedia.org/wiki/Low_Franconian_languages Then, where you have a single language zone that spans natural obstacles, you can introduce separate dialects/accents of that language. rumguffrumguff $\begingroup$ This was my starting point, but it isn't necessarily enough. Look at Europe. The Netherlands aren't really bordered by large rivers, mountains, and so on. Germany was split into numerous small territories all practically intependent. And the border between Germany and France follow the Rhine, but only up until one point, and not all the way to the Netherlands. So yes those parameters are certainly important to take into account. But what then? $\endgroup$ – clem steredenn Sep 1 '15 at 12:17 $\begingroup$ Fair point - I have updated my answer... $\endgroup$ – rumguff Sep 1 '15 at 12:49 $\begingroup$ +1 excellent answer. Just want to add that the precise, draw-exact-lines-on-the-map concept of boundaries is very modern, both due to the ability to make and to care about such precise measurements. If there wasn't a clear natural boundary or a reason to care exactly where the boundary was, it could be fuzzy -- claimed by both countries, but without the claim being enforced by either. $\endgroup$ – LindaJeanne Sep 1 '15 at 14:08 $\begingroup$ cheers Linda - and I agree. Tolkien's maps don't feature drawn boundaries at all. $\endgroup$ – rumguff Sep 1 '15 at 16:18 $\begingroup$ Minor rivers often form national borders. Navigable rivers usually form the core of a nation or province unless that region is not well settled. $\endgroup$ – Oldcat Sep 1 '15 at 19:12 It is quite common that borders go along natural features like rivers or mountains (also called "natural borders"). Basically it's a line that naturally is hard to cross. Therefore it's also harder to conquer land beyond that border than if there's no natural border to begin with. Also, if the border is negotiated, those landmarks are easily recognized, and therefore may prevent future disagreement about the position of the border. celtschkceltschk $\begingroup$ That depends a lot of the technology at hand, though. If you look at older European borders, you will find that e.g. lakes are not borders, but rather in the middle of nations, as that is where it's possible to travel and transport, whereas areas with only forests are difficult to get through, and are often border areas. $\endgroup$ – leo Sep 1 '15 at 8:43 Can't believe I missed this question. Prep Steps You need to do these before you really get started, you have some done but I am listing everything for future user reference. You need a map This map should be geographical down to a regional level (local specifics/peculiarities can and should wait, create them as needed) Include major bodies of water, rivers, biomes, mountains etc. This should be the satellite image from orbit level of detail. You need a history Drawing political borders is obviously impossible to do without having some idea of what came before now whenever now happens to be in the story. Like the map this doesn't need to be the nitty gritty. Think of the level of detail you get in elementary education. Egypt, Greek City States, Roman Empire, Byzantium, Medieval, Renaissance...etc etc etc. This should be the broad sweeps of history. Rough out where on the map these major nations/empires covered and overlapped. Setting the now Determine a time period. Pick a socio-technical point in time (or create your own, medieval twitter!...ahem anyway) for your now to exist. Technology level helps define the shape of borders. As mentioned in other posts you are, for example, not going to have longitudinal borders during the Roman Empire...and if they could you know the Romans would, everyone knows the Romans loved math. How much 'open' space is there in your world. For the vast majority of human history much of the world was not part of any political entity, if you're working in the past keep that in mind. Get to it Step 1: So between your time period and geographical map you can start plotting obvious places for civilization to start. We all know (or do now) that the earliest civilizations on planet Earth started along rivers. Regular access to fresh, clean water makes life a whole lot easier. You don't need to name these civs or anything like that (though it may be fun to come back and do it later). Step 2: Apply the rough brushes of history you outlined in the preparation steps (you did do the preparation steps right?). Step 3: Once you arrive at now, stop. If things look a little too planned out at this point that's perfect. Right where we should be. Step 4: Fine tune your map. Review major historical events, people disasters (wars, migrations, famines etc) and modify the map appropriately. While you are doing this write down why the changes makes sense while you are doing this, you will never remember why later. This can cause strange squiggles across what looks like an obvious border, or set the border at a certain landmark, for example mountains or a river, or a particular city. This helps give your map more depth. Always keep in mind that borders are fluid and on a planetary scale they change constantly. James♦James $\begingroup$ +1 for "You need a history". So many borders on Earth aren't in optimal locations, because of various historical events. $\endgroup$ – HDE 226868♦ May 8 '17 at 17:25 Political boundaries are geography plus populations plus as many other things as you want to add. Draw a map of your continent/world/galaxy/universe. Fill in details like terrain, biomes, topography, geology, vulcanology, resources, etc...whatever details you want to include in your story. Make a list of the people's you want to have in your world. Perhaps the benevolent Empire (heh, when are empires ever benevolent?) or a nation of marauding wanderers. Figure out which groups are stronger than the others and why they are stronger. Maybe one group has a mobility advantage while another has a great economy. Place your weakest nations/tribes/groups first and give them the largest possible area that seems reasonable for their size. Don't worry, they won't hold this much territory for long. Now drop in your stronger nations. They will naturally push back on the weaker nations, shrinking their territory. Pushback will extend until a natural barrier is reached such as rivers, oceans, or mountain ranges. You may lose a weaker nation or two. Make adjustments to their strengths till they can hold at least a little territory. Go back and make some weird boundaries that can't be explained by one nation being stronger than the other. These small boundary changes give you, the author, an opportunity to inject some political back-history. Point Roberts on the boundary between Canada and the USA is an example of this kind of political boundary making. Europe is famous for these kinds of boundary shifts. Make a few adjustments to the boundaries to account for resource allocation on the map. Stronger nations will have more resources available to them or very strong trade routes to get those resources. Designate capital cities as meets your needs. Often capitals are centrally located but not always (ex. Moscow or Washington D.C.). Using this method we can retrospectively see why the Mongols gained so much territory as they had a huge mobility advantage over their peers. Every extra "layer" of information added to the map will increase the richness of your world but at the expense of complexity. Add as many layers as you can manage then stop. Just adding terrain, resources and population to your map will be enough for a very rich world. Introduction and assumptions Borders clearly aren't static; they change over years, decades and centuries as countries grow, shrink, and are born and die. As time passes, they may become vague or disputed. Therefore, I'd argue that you do need to create a somewhat detailed history of a region to properly map out where its borders are at a certain time. However, it should be relatively easy to get a decent idea of where a country's borders lie when it is first formed, assuming certain conditions hold. I'm going to suggest a way to build a country's borders from the ground up, starting from a small city-state society with medieval or pre-medieval technology. I want to make a few key assumptions: Power is somewhat centrally located, preferably in a city or military fortification. This is the most secure part of the state, and it is easier to control land closer to this location than land farther away. Territory is contiguous; you should be able to travel from any one point to another via land while remaining in the country. The technology is sufficiently limited such that the above assumptions hold. While naval power may be possible, air travel is not. This should hold for the sort of society we're talking about, assuming there aren't significant magical powers. Neighboring states have relatively similar strengths. I'll address scenarios where this isn't true more at the end. Approximation 1: Voronoi diagrams I'll hypothesize that the original borders of a city-state, according to what I discussed above, can be approximated by creating a Voronoi diagram. Essentially, given a set of $n$ points (cities) in some two-dimensional space, a Voronoi diagram divides that space up into $n$ regions. The region $r_i$ contains all the points closer to point (city) $c_i$. The lines of the diagrams can be interpreted as the borders of these regions. Here's an example: Image courtesy of Wikipedia user Balu.ertl under the Creative Commons Attribution-Share Alike 4.0 International license. Voronoi diagrams have already been used to model the borders of countries and states; see specifically the work of Jason Davies (images copyrighted, by the way). There are certainly many differences from real-life borders (although in certain parts, like North Africa, things seem to work), but again, this is only a first approximation. For large $n$, creating such a diagram becomes a little complicated. Brute-force searches work but are obviously tedious; more sophisticated methods like Fortune's algorithm become useful. For more information, see Easiest algorithm of Voronoi diagram to implement? and How do I derive a Voronoi diagram given its point set and its Delaunay triangulation?. However, I'd like to deal with a much simpler case, where $n=3$. $n=1$ is obviously trivial, and $n=2$ yields precisely one border - namely, the perpendicular bisector of the line segment connecting the two cities. However, $n=3$ is a little more interesting, although it is certainly simple to solve. All we need to do is find the one vertex where all three borders coincide. There are several ways in which we can do this, knowing the locations of three cities and assuming that each one is the center of its own city-state. We could use one of the above algorithms, if we really wanted, but those can be time-consuming to implement. Alternatively, we could use the fact that any Voronoi vertex is the center of a circle containing three points, and therefore, given three points, we could find the center of that circle. However, I'd like to use what I think is the simplest option: Determine perpendicular bisectors of segments connecting any two cities, and find the point where they intersect. Some assumptions (well, just one, for now): The three points are not collinear. If they are, then the borders are just parallel lines, and there is no central vertex. Let's have a set $C$ of three cities, $(c_1(x_1,y_1),c_2(x_2,y_2),c_3(x_3,y_3))$. We choose to find the segments connecting $c_1$ and $c_2$ ($\bar{s_{12}}$) and $c_2$ and $c_3$ ($\bar{s_{13}}$). Given that the $\bar{s_{ij}}$ is the set of points equidistant to both $c_i$ and $c_j$, we can set $$\sqrt{(x-x_i)^2+(y-y_i)^2}=\sqrt{(x-x_j)^2+(y-y_j)^2}\tag{1}$$ Simplifying eventually yields the equation $$y=\frac{x_j-x_i}{y_i-y_j}x+\frac{x_i^2+y_i^2-x_j^2-y_j^2}{2(y_i-y_j)}\tag{2}$$ Clearly, this blows up if $y_i=y_j$, but if that's the case, then the border simply has the equation $$x=\frac{1}{2}(x_j-x_i)$$ which is simple enough. We do the above for all three sets of points. To find the vertex, we simply find the point where all three lines intersect, which is simple, as we can do it for any two of the lines. I wrote a program to do this in Python 3. To simplify things a bit, I've assumed that no two cities have the same $y$-coordinate, as that produces a line with infinite slope in $\text{(2)}$. If, for some reason, your setup includes a case like that, simply rotate the coordinate system a little so that all three points have different $y$-coordinates. Here's an example, with $c_1=(2,1)$, $c_2=(9,5)$ and $c_3=(4,7)$: P1 = [2,1] Set = [P1,P2,P3] def dist(point1,point2): """Returns distance between two points.""" x1 = point1[0] y1 = point1[1] return np.sqrt((x2 - x1)2 + (y2 - y1)2) def perp(point1,point2): """Returns slope and y-intercept of the perpendicular bisector of the segment connecting two cities.""" m = (x2 - x1)/(y1 - y2) b = (x12 + y12 - x22 - y22)/(2(y1 - y2)) return m,b M1 = perp(P1,P2)[0] B1 = perp(P1,P2)[1] def vertex(): """Finds central vertex""" x = (B1 - B2)/(M2 - M1) y = M1x + B1 return x,y This next bit divides each of the lines into a certain number of line segments by adding a number of points onto the lines, and then removes those points in the third city's Voronoi cell. for point1 in Set: if point2 != point1: N = [] delta = 0.001 for i in range(0,10000): N.append(idelta) M = [perp(point1,point2)[0]a + perp(point1,point2)[1] for a in N] Other_point = [a for a in Set if a not in [point1,point2]] while i < len(N): x = N[i] y = M[i] if dist([x,y],point1) > dist([x,y],Other_point[0]): N.remove(x) M.remove(y) plt.plot(N,M,'k') for point in Set: name = 'City at ('+str(point[0])+','+str(point[1])+')' plt.plot(point[0],point[1],'x',label=name) plt.plot(vertex()[0],vertex()[1],'kx') plt.legend(loc='upper left') plt.title('Voronoi cells of three countries') plt.xlim(0,10) plt.ylim(0,10) Here's the output: Approximation 2: Terrain. Voronoi cells are, I think, a decent approximation. However, they completely ignore the landscape and terrain of the area. For instance, if an edge lies in the middle of a valley surrounded by two high mountain ranges, it seems possible that the border may shift to one of those ranges, as they're easier to defend. The same thing goes for rivers, cliffs, etc. I'll assume that the following objects would cause borders to shift: Large bodies of water I think these objects have been sufficiently justified as limitations (see celtschk 's answer). Most of these can be approximated with curves of essentially negligible thickness (lakes and oceans aside). Therefore, let's say that any landform $L$ can be represented as a curve parameterized by a variable $t$: $$\mathbf{L}=\mathbf{x}_L(t)=(x_L(t),y_L(t)),\quad t_0\leq t\leq t_f$$ We can also represent a section of border $B$ as another parameterized curve, given by a parameter $s$: $$\mathbf{B}=\mathbf{x}_B(s)=(x_B(s),y_B(s)),\quad s_0\leq s\leq s_f$$ The challenge, then, is to come up with some iterative algorithm that maps $\mathbf{B}_{n}$ to $\mathbf{B}_{n+1}$. There are probably many options out there. I chose one of the following form: Divide $\mathbf{B}_n$ into $N$ points $\{p_{1,n},p_{2,n},\cdots,p_{N,n}\}$. For each $p_{i,n}(x_p,y_p)$, calculate the distance to all points on $\mathbf{L}$ and choose the point on $\mathbf{L}$ that is closest, $l_{i,n}(x_l,y_l)$. Move $p_{i,n}$ accordingly. I played around with things and decided on a certain formula: $$dx=\frac{x_l-x_p}{1+a\cdot\text{dist}(p_{i,n},l_{i,n})},\quad dy=\frac{y_l-y_p}{1+a\cdot\text{dist}(p_{i,n},l_{i,n})}$$ $$x_{p,n+1}=x_{p,n}+dx,\quad y_{p,n+1}=y_{p,n}+dy$$ where $a$ is some scale factor and $\text{dist}(\mathbf{a},\mathbf{b})$ is the distance between two points $\mathbf{a}$ and $\mathbf{b}$. This can be done as many times as possible. I've found that in many cases, even one iteration can be enough. Here's my implementation of the above, again written in Python 3. I've chosen $a=0.3$: scale = 0.3 RiverPath = np.linspace(0,49,1000) def River(t): x = np.sqrt(t) y = tnp.exp(-t) BorderPath = np.linspace(0,7,1000) def Border(t): x = t y = t/4 def dist(y,x): Returns closest point on the target curve to a given point on the border. Set = [] for loc in RiverPath: dx = x - River(loc)[0] dy = y - River(loc)[1] distance = np.sqrt(dx2 + dy2) Set.append([distance,loc]) Set = sorted(Set, key=lambda S: S[0]) dR = Set[0][0] p = Set[0][1] target = River(p) return target def move(Q): """Moves each point on the border curve parameterized by Q.""" X = [] Y = [] for q in Q: x = Border(q)[0] y = Border(q)[1] point = dist(y,x) point_x = point[0] point_y = point[1] mag = np.sqrt((point_x - x)2 + (point_y - y)2) dx = (point_x - x)/(1 + scalemag) dy = (point_y - y)/(1 + scale*mag) X.append(x + dx) Y.append(y + dy) plt.plot(River(RiverPath)[0],River(RiverPath)[1],'b',label='River') plt.plot(Border(BorderPath)[0],Border(BorderPath)[1],'k',label='Border') plt.plot(move(BorderPath)[0],move(BorderPath)[1],'r') It uses the following parameterizations: $$\mathbf{L}=(\sqrt{t},te^{-t}),\quad0\leq t\leq49,\quad\mathbf{B}_n=(s,s/4),\quad0\leq s\leq7$$ Here's the result: The new border hugs the river near the left, then shifts roughly halfway between the old border and the new border. More iterations might be desirable, but there's currently something of a balance. The formula for $dx$ and $dy$ could use some improvement, but even though it's imperfect right now, I do think it's functional. It can be adapted for multiple perturbing objects (i.e. multiple rivers, mountains, etc.) by calculating all the $dx$s and $dy$s, summing them, and then moving the border, not accounting for one landform at a time. You can vary the scale factor if you want, both in general and for specific landmasses. I haven't yet played around to see how this could affect things. The borders of countries still don't quite match up with these approximations. I'd argue that part of that is because of modern technology. However, a great deal is due to history. Those mountains over there are supposedly uncrossable . . . until a feud between rival kingdoms necessitates a battle, which ends with one king triumphant, ruler of both. Or maybe that river was considered a fairly good border, until holy relics were found on the other side and suddenly the head priest really wants the site inside the country. At this point, I'd say that James' answer becomes invaluable. In the end, it is the people of your world who shape it, often more than you, the god-like figure outside it. You can control that history, of course, but those events can and will change the world. All my suggestions are are simply slightly more detailed slates with which to start building countries. After that, it's up to you. HDE 226868♦HDE 226868 $\begingroup$ I learned about Voronoi diagrams from this post, very interesting. $\endgroup$ – neontapir Jan 18 '18 at 15:08 $\begingroup$ The contiguity assumption has many exceptions in the real world. Ocean transport and the sorts of inheritance laws used by pre-modern Germanic peoples encourage non-contiguous territories. $\endgroup$ – Jasper Oct 8 '18 at 8:08 Don't focus too much on rivers Rivers can sometimes be used to mark borders (the Rio Grande being one of the famous ones). However, it's almost always the case that the border would be there regardless, and they simply adjusted it to fit the river so it would provide them both with a bit of defense, and spare each country the trouble of constantly having to cross it. Here's a map of medieval Europe: There are few things to keep in mind looking at this: 1) Most powerful nations are based around a river, not divided by one. London, Paris, and Rome all have major rivers flowing through them. This provides a major artery of trade, as well as fertile cropland to feed a large population. Over time, the tribes and cities that expand to form kingdoms tend to be ones with large populations. Therefore, most of your kingdoms will have a fertile heartland containing most of the population and usually the capitol. This core territory will then likely hold dominion over a more rugged hinterland with a much smaller population. When two of these kingdoms collide, the border usually changes quite often as they fight each other. Usually the line will settle down somewhere in between the two, usually across rugged or less hospitable land that neither one is that interested in fighting for. If one side was in the midst of conquering, say, a fertile valley, they wouldn't agree to stop and draw a new border until they'd taken the whole thing. The best example of this is Medieval Scotland. The vast majority of Scotland's population lives in the fertile area around Edinburgh, while the Highlands and islands are only lightly populated. In the population map below, notice now the main farming and trading area is packed with people, and formed the core of a kingdom that then expanded outwards. Note that this is a modern map, and the medieval numbers were likely a bit more balanced, albeit with the same general pattern. 2) The map is filled with dependent kingdoms. This was also true in Ancient Roman times. Looking at a map of the Roman Empire makes it seem like one big state, but in reality there were lots of dependent kingdoms within it, who had control over internal affairs, but deferred to Rome in everything else. On the Medieval Europe map above, Bohemia, Croatia, and Moravia fall into this category, along with many others. You may or may not want to include this in your setting, but it was a common historical occurrence. These dependent states often existed on the frontiers of their parent empires, contained a distinct ethnic group, and were used as buffer zones against hostile empires. Late-Medieval Croatia fell into this category. They were ruled by the Austro-Hungarian Empire, but held a lot of autonomy, and were used primarily as a buffer against the Ottoman Empire. These borders will often be very defensible, going along rivers and surrounding rugged of mountainous terrain, as these small dependencies would not be able to hold vulnerable, fertile lands against the encroachment of larger forces. 3) City States are common in areas with large coastlines and rugged terrain. City states simply rule one large city and the surrounding countryside. These states focus largely on trade and rarely build empires in their immediate neighborhood, instead conquering overseas possessions to expand their trade network. The Greeks used this system in the Classical Age, and the Italians had it for most of the Middle Ages. If your world has a rugged/coastal area with rich trade connections, I suspect it would be full of smaller city states, with small (and somewhat unimportant) borders. 4) Undefined Borders are common in vast uninhabited areas. Nobody (except Muammar Qaddafi) cares where a border is drawn across an uninhabited desert. Notice in the Medieval Europe map, how the Eastern European principalities of Kiev, etc, have borders that just sort of fade out into the Steppes. This is common in sparsely populated kingdoms sharing borders with undefined tribal groups. Since the nomadic horsemen will be crossing the border regardless, and the state doesn't have the will or ability to police it, there isn't so much a border as a general understanding that "the stuff over there belongs to them". This also goes for desert borders. Lots of maps of Ancient Egypt show their empire extending out into the Sahara, but it wasn't like you would run into Ancient Egyptian Border Patrol out there. Rather, there was just an understanding that Egypt ruled the Nile Valley, and anybody that came too close would be in trouble. You can draw a defined line for these types of borders, but just know that the reality on the ground would be much more fluid. 5) Disorganized Tribal Groups rule the frontier. In the Medieval Europe map, notice the Cumans, Uzes, and Vlachs in the South East, and the Prussians, Selonians, etc, in the North East. In sparsely populated areas, especially those inhabited by nomads, Kingdoms don't really exist. Instead the area is divided among tribes, clans, and other small entities. On maps these are generally marked together as a single ethnic group (like the Cumans), but are not given a color or borders. Instead, the other borders end, and the white area has the names of said ethnic groups, with the location indicating roughly where they were, and the size of the word often indicating the size of each. So, pre-Genghis Khan, the area north of China would be a blank area with the word Mongols written there, along with a few other nomadic groups. Historically, these groups would often unite and conquer their sedentary neighbors, forming new kingdoms who would be conquered in turn a few hundred years later. The Parthian Empire is a good example of this, as a nomadic horse nation who settled down and was later conquered by the Sassanids, another nomadic horse nation (who were then conquered by Arabs, who were then conquered by Mongols, who were then conquered by Afghans, etc). Bert HaddadBert Haddad Here's what I do when designing a DnD campaign once I have a map: Look for every place that has something that would make people settle there. Minimum would be food and water. Any useful features and resources add bonuses. If the land is recently settled, start at one edge. Otherwise figure that people have been over most of the land (except for areas that you don't want them to be). Make circles (use light pencil). Once you have the settlements, judge based on how much food and resources they have, how big their influence will be (a compass or a pencil on a string will work). Since circles are unrealistic, adjust them for the terrain. If travel is hard, pull it in some and if travel is easy let it out some. Also, if there are natural features (river, cliff, forest edge, desert edge, etc.) near the edge, the edge usually conforms to the natural feature. Overlaps are zones of conflict. The border will generally be within that zone of conflict (often following a natural feature). Assimilation. If one settlement is completely or mostly within the area of influence, decide if it has already been assimilated into the larger power or not. If it has been assimilated, extend the powers influence in that direction by the strength of the assimilated power. If it has not been assimilated, pull the border back in that area. On the first pass, most will be assimilated. Decide which borders might be peaceful and which will have conflict. Neighbors with different resources may be more peaceful toward each other and have trading relationships. Neighbors with similar resources are more likely to come into conflict since they gain less through trade. Adjust for trade or conflict. Widen the borders of powers that have trade agreements and narrow the borders of powers that are in conflict. Repeat 4 through 7 as needed. Some powers may be assimilated and some new zones of conflict may occur. If a border shrinks to "free" a smaller settlement, decide if it breaks away (if not, leave a connection to the larger unit). Fine tune as needed or desired. Back Story. Create as much history describing how things got to the present time as you wish. There are likely many great plot hooks in the evolving map. You are now at the start of the story or campaign. ShadoCatShadoCat How much detail do you need for your story to make sense? As others have noted, national borders tend to run along coastlines, rivers, and mountain ranges. But there are plenty of exceptions, especially when no convenient river or mountain range was available in the general vicinity of where two nations bumped against each other. Sure, you could write a history of the world up to this point to explain how your borders came to be. But is that necessary? If in a story a writer says, "Bob was tall and had red hair", he normally doesn't find it necessary to trace Bob's genetic history back to Noah to explain exactly how he came by this traits. If for some reason you need an unusual national border in your story -- if say, country A is on the west side of the ocean and also control a tiny strip on the east side of the ocean, and country B is then east of that strip -- you might need a couple of sentences of explanation of how that came to be. But if the history isn't relevant to the story, even that probably isn't necessary. If I'm reading a story set in a ficitonal world, or in some part of the world where I'm not familiar with the geography, I don't recall ever wondering, "Hey, wait a minute! How come the border between Foobar and Plughland runs through the Fwacbar Valley? Didn't the author say that there's a river near here? Why isn't the river the border? What's the history behind that?" Unless the story is about geography and politics, I doubt such a question would even come to the mind of 99.9% of readers. Borders are a tricky subject. Though most will end due to natural terrain, like rivers or mountains, most borders are set by expanding kingdoms, only stopping when they meet resistance from another expanding kingdom. Because of this, there's no real formula per se. However, you don't have to write prehistoric histories. Make one kingdom and have fun with. Think about who their enemies are. What do they produce? Maybe they trade with a neighbouring city. Before you know it, you'll have a flourishing kingdom before you. Good luck! RecelicaRecelica Although rivers are mentioned frequently here, the reason we humans have them as borders is due to transportation of goods, both to a political region and from it. Most USA citizens do not realize that our States had shooting wars, with people killed, over rights to the water sources and waterways for transporting goods, for irrigation and drinking water. The same goes for natural oceanside ports (or those on big lakes). Water wars (literally wars) are the primary reason our map has weird bumps and extensions, water access, for both consumption and travel, is critical. Barges are far and away the cheapest form of transportation for goods; far, far cheaper than rail, trucks or horse drawn wagons. Unless a region has a lot of natural lakes, it probably can't grow very much on rainfall alone. Not for agriculture or city life. Find your glaciers or heavy lakes being replenished by rainfall, Trace your rivers through the valleys, rank each river based on how much "good land" it provides access to, how many other rivers it can join (it's network connections), whether it reaches a coast line. You can probably find the "good harbors" based on some surrounding landscape criteria (and how many rivers can reach it). The highest-ranking rivers are borders; those are the ones people fought to keep some other political faction (country, state, whatever) from owning entirely. If those borders produce a country too large, sub-divide it using the highest-ranking river that passes through it, and do that recursively. Amadeus-Reinstate-MonicaAmadeus-Reinstate-Monica One alternative to generating the entire story, is generate stuff using Markov Chains based at current year heightmap/border earth data. First you get an earth height map that has countries borders. If the pixel of the height map is ocean/border you change its color to A, if its ocean/international land, you change its color B, if its ocean/country land you change its type to C, if its not-ocean/border you change it's color to color D, and if its not-ocean/international land you change to E and if its non-ocean/country land you change to F. Some program will then get this modified heightmap and analyze it creating an probability table: The chance of some tile X being border, "international land" or "country land", based at what specific tile type their 8 neighbors are and based too the tile itself you are generating is ocean or non ocean. With that info in your hand, the world map generator program will get a random tile and discover if it is "country land", "international land" or border based at their 8 neighbor tiles and his own type. After find this tile type it will go for the next one and generate it, and then go for the next one, and next one..... until it generate the entire map. Some important things to make sure this works: 1-You must always generate the not-generated tile with most amount of already generated neighbor tiles, if you don't do that, the world will have some patterns based at how you generated it, as some example generating left to right starting from the first line, create something with an X pattern. 2-The markov chain data must be based at ALL 8 neighbors and must be influenced by the direction of the neighbor tile too. 2.1- An example, If at the top of the ocean tile you are generating there is a ocean/border tile, at the bottom of this tile you are generating there is a ocean/border tile too and you didn't generated the other 6 neighbor tiles but they are all ocean. The "question the program will ask" is something like this: "Assuming this tile is a ocean, the top and bottom tile is ocean/border, and all others are ocean tiles, what is the chance of this tile being a border, what is the chance of this tile being 'international land' and what is the chance of this tile being 'country land'? " Then the program will select its tile type (border, country or international) at random weighted by those probabilities. 2.2-If you don't use this method, most of the time you will have a map that is made entirely out of international area, or made entirely of country area. 3-Points 1 and 2 are based at discoveries I found while trying to map makov chain map. You will find some markov chain map generator ideas at internet that assume the markov chain wont work at generating maps (x pattern or whateaver) because they didnt discovered what caused their problems as assumed the use of markov chain itself was the problem. monkeypumonkeypu You can use Geographic Information System tools to make what you want by creating or using existing data, you can use rasters and vectors staticlly or dynamiclly ELMOELMO $\begingroup$ Hi ELMO. Welcome to Worldbuilding SE. It sounds interesting, but could you detail a bit how the tools work? We usually like to have answers a bit more than a link. So that people can evaluate without clicking the link. Links can be modified or disappear and the content of your answer lose its value. $\endgroup$ – clem steredenn Sep 1 '15 at 10:31 Not the answer you're looking for? Browse other questions tagged geography politics worldbuilding-process or ask your own question. 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search filter All ContentElementa: Science of the Anthropocene Special Features & Forums Data Accessibility Statement Research Article\| June 11 2020 On energy sufficiency and the need for new policies to combat growing inequities in the residential energy sector In Special Collection: Eric Daniel Fournier; Eric Daniel Fournier 1The California Center for Sustainable Communities, Institute of the Environment and Sustainability, University of California Los Angeles, Los Angeles, CA, US Robert Cudd; Robert Cudd Felicia Federico; Felicia Federico Stephanie Pincetl Elementa: Science of the Anthropocene (2020) 8: 24. https://doi.org/10.1525/elementa.419 Eric Daniel Fournier, Robert Cudd, Felicia Federico, Stephanie Pincetl; On energy sufficiency and the need for new policies to combat growing inequities in the residential energy sector. Elementa: Science of the Anthropocene 1 January 2020; 8 24. doi: https://doi.org/10.1525/elementa.419 The decreasing cost and increasing availability of new technologies capable of improving household energy efficiency, generating and storing renewable energy, and decarbonizing major end use appliances have begun to significantly transform many residential communities across the U.S. Despite these positive developments however, the degree to which disadvantaged communities (DACs) have been able to participate in and benefit from these transformations remains far from equal. Using historical time series data at the zipcode level within Los Angeles County, we document the scale and extent to which DACs continue to be left behind. These data show per-capita levels of electricity and natural gas consumption within DACs that are, on average, about half of those seen within their more affluent counterparts. We argue that the magnitude of these differences reflect a fundamental departure in the use of energy from purposes of sufficiency to those of excess. We introduce a set of forecasts that show the extent to which current inequities in per-capita energy consumption, rates of vehicle electrification, and adoption of rooftop solar PV are likely to persist under the status quo. In conclusion, we suggest that the redistributive investment of public funds for the purpose of accelerating DAC participation in energy system transformations constitutes a socially optimal investment strategy – one which reflects the dramatically higher marginal utility of units of energy consumed at levels of sufficiency rather than excess. Energy sufficiency, Residential electricity, Energy efficiency, Income, Housing size, Equity Residential Energy Systems in Transition Energy systems are highly complex. Within them, technologies and policies interact with economics and social histories in unexpected ways. Some of these interactions combine to produce large scale systemic transformations while others do not (Grubler, 2012; Rutter and Keirstead, 2012; Cherp et al., 2018). Energy systems are also highly embedded. This statement applies not only to their physical manifestations but also to popular consumer expectations regarding the price-performance role of energy services (Goldthau and Sovacool, 2012; Stefes and Laird, 2012; Wilson, 2014; Edelstein and Kilian, 2009). People, often subconsciously, structure their lives around the expectation that the energy services they use will not change, and will continue to be available more or less indefinitely (DiCicco et al., 2015). These embedded expectations are evident in the layout of our cities, the design of our homes, the types of energy appliances that we own, and the frequency and intensity with which we use them (Banister et al., 1997; Kahn, 2000; Ewing and Rong, 2008). In this way, the impacts of major energy system transformations have the potential to reverberate through every aspect of society. The suite of end-use energy demands supplied within residential buildings have historically been limited to: space heating and cooling, refrigeration, water heating, ventilation, cooking, lighting, laundry, computing and entertainment equipment, and other miscellaneous plug loads (Hirst and Jackson, 1977; Schipper et al., 1982). Over the past several decades, numerous incremental improvements have been made to the efficiency with which many of these services can be rendered (Meyers et al., 2003; Brown et al., 2008). Working in opposition to these trends however, have been other, troubling, developments. These include growth in the size of new residential structures and the penetration levels of the most energy intensive appliances (Isaac and van Vuuren, 2009; Zhou et al., 2014; Fournier et al., 2019). In addition to the changing dynamics within these traditional categories of residential energy end-use, a rapidly expanding market for electric vehicles is causing residential buildings to increasingly function as conduits for the supply of an entirely new sector of energy demand: transportation (Needell et al., 2016; Bunsen et al., 2018). In other instances, the rapid growth in the adoption of distributed renewable energy generation and storage resources, is even causing some residential buildings to intermittently switch from being net consumers to net-suppliers of energy to the electric power grid (Li and Yi, 2014; Janko et al., 2016; Kurdgelashvili et al., 2019). In an effort to combat the destabilizing influence of highly uneven or bi-directional power flows resulting from these changes, utilities and rate-setting bodies are working to develop new default energy tariffs which would more aggressively disincentivize consumption on the basis of time-of-use (TOU) (Alexander, 2007). The equity impacts of these new default TOU rate structures are still not well understood within the U.S. context (Youn and Jin, 2016; George and Bell, 2018; Ozaki, 2018). However, it is likely that residents of low-income DACs will be inherently more limited in terms of their ability to either reduce or shift the timing of their consumption. Consequently, these communities may be more adversely impacted by these new energy pricing schemes. Wealth is a prominent driver of demand for residential energy. Worldwide, wealthier groups lead more materially and energetically intensive lives than the less affluent, consuming in excess of what they require to meet their essential needs (Meyers et al., 2003; Creutzig et al., 2015; Fournier et al., 2019). In the state of California, this relationship between income and the demand for residential energy services has been previously studied – with higher-income groups being found to consume more electricity and gas than lower-income groups (California Energy Commission, 2018). These lower levels of consumption, in many cases, are also paired with a lower standard of energy services due to the inferior thermal performance among the older, lower-quality housing stock, and less efficient household appliances which are common in DACs (Barbose et al., 2018). The Energy Sufficiency Paradigm Domestic energy consumption may be thought to consist of three regimes. The first is the "insufficiency regime" which reflects a state of energy poverty. The second is the "sufficiency regime" which consists of the energy consumed to meet essential needs. Finally, the third is the "regime of excess" which reflects consumption above and beyond what is required to sustain an individual or household in a particular location (Peet, 1992, Princen, 2005). Depending on the operative definition of "essential needs," many possible thresholds between sufficiency and excess are possible, thus the sufficiency-excess threshold will naturally vary by climate zone and other features of the local geographic context. Consumption within the sufficiency regime can be though to encompass all energy end-uses required to maintain a safe, healthful, and decent standard of living in a particular place (Fawcett and Darby, 2018). It therefore includes not only the energy required to meet biological needs, such as food preparation and the maintenance of a safe, thermally comfortable home, but also the energy required to maintain health and participate in a productive economic and social life. The energy consumed for transportation, or to power personal computers and consumer electronics also counts towards the quantity that is considered sufficient. Thus, the quantity of energy sufficient to live decently within a given community is therefore a function of the predominant modes of life in that community, the infrastructural systems that make these modes possible, and the energy intensity of the infrastructure systems (Princen, 2005). Energy sufficiency is not defined with respect to personage; it is independent of wealth and notions of socio-economic status (Fawcett and Darby, 2018). This is because the quantity of energy required for a productive social and economic life is locationally determined. As such, the quantity of energy required for an individual or household to sustain a decent existence in a particular place is unrelated to whether or not one can consume energy in excess of that quantity. The differences between these regimes can be illustrated graphically by the plots contained in Figure 1. Figure 1a. provides a conceptual view of how these regimes of consumption map to a model frequency distribution of per-capita consumption intensities. Figures 1b. and 1c. illustrate how these regimes might be more rigorously defined using empirical data on per capita residential electricity and natural gas usage among zipcodes within Los Angeles County (LAC). Here the sufficiency ranges have been specified, somewhat arbitrarily, as ±1 standard deviation from the mean. Conceptual illustration depicting the relationship between (a.) regimes of energy insufficiency (blue), sufficiency (green), and excess (red) with empirical data on (b.) residential per capita electricity usage [kWh/Capita] and (c.) residential per capita natural gas usage [Therms/Capita] among zipcodes within Los Angeles County as of 2017. DOI: https://doi.org/10.1525/elementa.419.f1 Excess consumption has many causes, but often arises from individuals choosing to meet their needs by inherently more energy intensive means, such as purchasing large, single-family homes, or by overconsumption of energy services, such as leaving the air conditioning on while the home is unoccupied. Distinguishing between consumption regimes is necessary in order to analyze the equity effects of residential electrification, renewable energy, and efficiency programs, and estimate cumulative value society derives from them. DACs and non-DACs differ greatly with respect to socio-demographic characteristics, most significantly income and the age and condition of their housing stock (Hernández et al., 2016). These factors determine the relative burden of energy costs, the proportion of a household's total budget devoted to energy, and the value extracted per unit energy consumed (USDOE, 2018). Thus, the value of the benefits received by program participants depends to a large extent on the exigencies of their individual situations. Current Policy Approaches to the Redress of Energy Inequities Faced with need to reduce the greenhouse gas emissions (GHGs) of their energy consumption, many states, including California, have embarked on courses of market-based ecological modernization (Mol et al., 2009). In the past 20 years, market-based electrification and energy efficiency (EE) initiatives, primarily subsidies and tax credits, have become preferred tools for encouraging adoption of domestic renewable energy systems, electric vehicles, and newer, more efficient appliances (Reames and Stacey, 2019). Rather than curtailing the demand for energy, states have instead sought to reduce the GHG intensity of energy services by increasing the efficiency of residential housing stock and electrifying end-uses currently powered by fossil fuels. Increases in residential efficiency and distributed generation, it is hoped, will decrease demand for energy, with gradual fuel-switching for heating and transportation enabling further de-carbonization (Reames and Stacey, 2019). California has taken steps to reduce the energy intensity of new housing stock, passed measures that require new homes be built to accommodate rooftop PV panels, and implemented building codes requiring continuous improvements in the energy efficiency of building materials and systems. However, by and large, improving energy efficiency and promoting the deployment of renewable generation systems have been the preferred to pursuing actual reductions in residential demand (California Energy Commission, 2018). In parallel, the state has also been working to promote the electrification of fossil fuel dominated end-uses. This included providing rebates for EVs, heat pumps, and various types of household appliances. If successful, these efforts are likely to greatly increase future electricity demand. It is presumed that the environmental impacts of this consumption will be mitigated by transitioning the grid to be powered by 100% renewable sources. However, the timely success of this transition is not guaranteed. Governments and utilities have enthusiastically embraced market-based approaches to incentivizing these transitions because they are simple to implement, do not complicate utility operations, and do not otherwise limit absolute levels of consumption (Tonn and Peretz, 2007). Overall spending on such programs provide a good indication of their popularity – in 2016 at least $2.5 billion dollars on residential EE initiatives, based upon data available from twenty-nine states (Reames and Stacey, 2019). While their ease of implementation and politically inoffensive nature are attractive to policymakers, many of these programs have been found to disproportionately benefit wealthier individuals (Galli-Robertson et al., 2019). Incentive programs, even those that offer more generous payments to applicants that meet low-income requirements, are consistently under-utilized by lower-income and minority cohorts due to financial barriers, limited awareness of such programs, and lower rates of property ownership (Bird and Hernández, 2012; Scavo et al., 2016; Parsons et al., 2018). California has previously experimented with more redistributive policy measures designed to enhance DAC participation in energy transitions (Lukanov and Krieger, 2019). Unfortunately, the scope of the impacts from these programs have thus far been small due to their limited budgets and restrictive eligibility requirements. For example, the California solar initiatives single family affordable solar home (SASH) program, established in 2006 by state assembly bill 2723, has provided qualified low-income homeowners fixed, up-front, capacity-based incentives to help offset the upfront cost of a solar electric system – currently, $3 per watt (California State Assembly, 2006). In order to be eligible for this incentive however, applicants must (1) own and live in their home, (2) have a household income that is 80% or below the area median income, and (3) live in a home defined as "affordable housing" by California Public Utilities Code 2852. Due to these restrictions on eligibility, over its entire lifetime the program has spent $124 million on the construction of 8,228 PV systems representing a total combined capacity of just 26 MW statewide. In addition to SASH there was also a Multi-Family Solar Housing (MASH) program. First initiated in 2008, MASH provides fixed, up front, capacity-based incentives for qualifying solar energy systems (California State Assembly, 2013). The amount of the incentive depends on the chosen application tract. Different tracts reflect different characteristics of the loads intended to be offset by the system. Under the program participating tenant units receive benefits through a virtual net metering scheme which offset a portion of their energy consumption with a portion of the output from the installed system. Despite the potentially transformative power of this virtual net metering concept for renters, the program's reach has been limited. Since its inception just 480 projects have been completed statewide, representing 41.9 MW of installed capacity. Furthermore, at present, the MASH program is closed and is no longer accepting new applications. Assessing Current Status and Future Progress In order to assess the current and likely future effectiveness of the existing suite of policies for promoting equity within the residential energy sector, we analyzed set of historical time series data documenting per-capita levels of energy consumption and energy system transformation engagement. The first component of this analysis focuses on quantifying the current magnitude of the inequities which exist between DACs and non-DACs within LAC, a diverse area home to some 10.2 million people. The second component of this analysis uses recent historical trends observable within these data to develop forecasts of expected future changes. These forecasts are then used to assess whether or not existing levels of inequality are likely to be diminished in the future as a result of currently implemented policy measures. Data on Community Disadvantage The California Office of Environmental Health Hazard Assessment (OEHHA), on behalf of the California Environmental Protection Agency (CalEPA), has developed a quantitative methodology which assigns numerical scores to local geographies based upon their aggregate burden of and vulnerability to various sources of environmental pollutants. This effort is known as the CalEnviroScreen program and is currently on its third iteration. CalEnviroScreen 3.0 (CES) scores are issued at the census tract level for the entire state. Census tracts whose combined CES scores place them above the 75th percentile statewide are technically classified by the California Energy Commission (CEC) as environmentally disadvantaged communities (DACs). This designation qualifies these communities for priority consideration under various state level funding programs and initiatives. The CES program's use of census tract boundaries as a reference geography presents a challenge for this analysis as zipcode geographies are the most common geographic unit for the spatially disaggregated reporting for energy system transformation metrics. In order to reconcile the incongruence between census tract and zipcode geographies we developed a methodology to assign each zipcode with the average scores of all of the census tracts that it spatially intersects. According to this methodology, zipcodes whose mean CES composite scores are still above the 75th percentile DAC threshold were assigned the label majority-DAC zipcodes. A more detailed discussion of this spatial aggregation as well as a map visualization of the spatial correspondence between DAC census tracts and majority-DAC zipcodes are provided in the supplementary material. Data on Residential Electricity and Natural Gas Usage Our research group at the California Center for Sustainable Communities (CCSC), which operates within UCLA's Institute of the Environment and Sustainability, has developed a unique multi-year time series database of electricity consumption data for customers served by the major investor owned utilities (IOUs) and municipally owned utilities (MOUs) operating within LAC (Porse et al., 2016). For the purposes of this analysis, these utilities include Southern California Edison (SCE), the Los Angeles Department of Water and Power (LADWP) and the Southern California Gas Company (SCG). This dataset, which we refer to as the UCLA Energy Atlas, is based upon raw monthly account level billing data obtained under non-disclosure agreements with either the individual utilities themselves, or with the California Public Utilities Commission (CPUC). The full temporal coverage of this dataset spans from 2011 to 2016. Data on Residential Electrification Our approach to quantifying residential electrification involved normalizing total electricity and natural gas consumption data derived from the UCLA Energy Atlas into standardized units [MBtu]. Following from this, for each zipcode, we calculated the fraction of the total volume energy consumed within each zipcode and for each each year that was delivered in the form of electricity. Changes in this fraction over time provide insights into the cumulative effects of of electricity load growth, natural gas usage efficiency improvement, and natural gas appliance electrification between the various zipcode geographies. Data on Alternative Fuel Vehicle Adoption The National Renewable Energy Laboratory (NREL) has developed a time series database of residential light-duty vehicle registrations, disaggregated by vehicle fuel type, for the entire United States. Access to records from this dataset, known as the Alternative Fuel Vehicles Database (AFVD), was obtained for zipcodes within LAC through a representative at the Southern California Association of Governments (SCAG). Records within the AFVD are sourced from state level vehicle registration reporting data. The full temporal coverage of this dataset spans from 1990 to 2017. For this analysis, these records were aggregated to generate annual counts of the total number of vehicles registered within each zipcode, separated by fuel category. These categories include: Conventional Fuel Vehicles (CFVs) – gasoline, gasoline-hybrid, diesel, and diesel-hybrid; Alternative Fuel Vehicles (AFVs) – ethanol, hydrogen fuel-cell, butane, compressed natural gas, methane, and propane; Plug-In Electric Vehicles (PEVs) – battery electric and plug-in hybrid. For the purposes of this analysis we focus only on the PEV category, and disaggregate its entries into EVs and PHEVs subgroups. A more detailed overview of relative proportions of vehicles of different fuel types that are registered within each zipcode is provided in the supplementary material. In urbanized areas such as LAC, active and public transit options can function as important alternatives to personal vehicle ownership. This is particularly true with respect to DAC residents, for whom the costs of personal vehicle ownership are often prohibitively high (Giuliano, 2005). The availability and usage of public transit options (buses, light-rail, subways, etc.) throughout the LAC region is highly uneven. This uneven distribution, to a large extent, reflects the distribution of population density throughout the region. Recent analyses have shown that, despite substantial investments in the expansion and upgrading of the LAC's public transit infrastructure over the past decade, ridership rates have actually declined (Manville et al., 2018). A more detailed discussion of the region's available public transit options and patterns of use is provided in the supplementary material for additional context. Data on Residential Rooftop Solar PV Adoption The CPUC coordinates a statewide, multi-agency effort, to collect and standardize historical data about the location and design characteristics of installed solar generation assets. This database is known as the Distributed Generation Statistics (DG-Stats) database. Records within the DG-Stats database are sourced from a variety of sources including participating IOUs, MOUs, and independent solar installation and development firms. For the purpose of this analysis, records within the DG-Stats database were first filtered on the basis of their rated nameplate capacity to reflect net-metered systems deemed to be of residential scale (<25 kW-AC). They were then aggregated on an annual basis to the zipcode level. The full temporal coverage of this dataset spans from 1990 to 2017. Methods of Forecasting Energy Consumption Developing an understanding of the extent to which current inequities within the energy system are likely to persist, or even grow, in the future is of critical importance. This requires the development of forecasts for future energy system consumption and transformation metrics. Our approach to forecasting future per-capita electricity and natural gas consumption levels is based upon the application of a parametric model of exponential decay to recent historical rates of change observed within the individual zipcode level time series data. This approach reflects the perpetuation of existing policies in a "business as usual" context. According to this model formulation, the growth rate at some future time f(t) can be expressed mathematically as in Equation 1. f(t) = Ce−kt, where:k>0f(t) = C(1−e−kt), where:k<0 \[\begin{array}{l}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,f\left( t \right)\,\, = \,\,C{e^{ - kt}},\,\,where:k > 0\\f\left( t \right)\,\, = \,\,C\left( {1 - {e^{ - kt}}} \right),\,\,where:k < 0\end{array}\] Using a set of numerical libraries written in the Python programming language, estimates for the model parameters (C,k) were generated for each zipcode using a least squares based procedure to statistically fit the model's functional form to its historical per-capita consumption time series. These parameter estimates were then used to generate individualized forecasts, with corresponding escalating uncertainty bounds (0–10%), for each zipcode and for each future year, through the end of a 2030 forecast time horizon. Median values for the groups of majority-DAC and majority non-DAC zipcodes were then computed from the individual zipcode level forecasts. For electricity consumption, the increasing form of the model (k > 0) was used. For natural gas, the decreasing form of the model (k < 0) was used. Methods of Forecasting Energy Transformation Participation Our approach to the problem of forecasting future per-capita EV, PHEV, and rooftop solar PV adoption levels involved a broadly similar process; however, here we made use of a fundamentally different parametric growth model. In order to realistically forecast energy transformation participation, the growth model used must be able to accurately depict the non-linear, saturating growth behavior characterized by consumer adoption decisions that occur as a new product passes through phases from initial release on to full market penetration. For this reason, we chose to use the Bass Diffusion Model. The Bass diffusion model can be expressed mathematically as in Equation 2. A more detailed discussion of the conceptual ideas behind the Bass model's formulation and our justification for its use in this application is provided in the supplementary material. f(t) = (p + qF(t))(1−F(t)) \[f\left( t \right)\,\, = \,\,\left( {p\,\, + \,\,qF\left( t \right)} \right)\left( {1 - F\left( t \right)} \right)\] According to the Bass diffusion model the growth rate at some future point in time f(t) can be expressed as a differential equation comprised of two fixed parameters (p, q) and the current level of adoption at that time F(t). When estimating parameters for any individual Bass diffusion model fit, it is necessary to provide a fixed value which corresponds to the boundary condition of the market's full saturation potential. For the EV and PHEV forecasts, these boundary conditions were chosen to be the total number of vehicles registered within the zipcode in the most recent year in the time series; this assumes static vehicle ownership levels throughout the forecast period. Competition between EVs and PHEVs for a market share was addressed by iteratively constraining the combined adoption levels between the two categories within each successive forecast year. For the rooftop solar PV forecasts, full market saturation potentials were computed for each zipcode using a database of individual building level rooftop solar capacity potentials generated for all structures larger than 400 ft2 within Los Angeles County (Jakubiec and Reinhart, 2012). Similar to the historic analysis, only systems with residential scale solar potential values (<25kW-AC) were included. Current Consumption Status Figure 2 depicts the current status of three key metrics of residential energy system performance at the zipcode level within LAC. These metrics include: (a.) annual total electricity usage per-capita, (b.) annual total natural-gas usage per-capita, and (c.) the ratio of per-capita total electricity to total natural gas usage. Data for of these metrics are shown in map form – with majority-DAC zipcodes outlined in red – as well as in scatterplots – with each zipcode being sorted along the horizontal axis on the basis of its mean CES score and the majority-DAC zipcodes plotted in red. Within each scatterplot, a simple linear trend line has been fit to illustrate the directionality and consistency of the relationships. Zipcodes for which consumption data was not available from the UCLA Energy Atlas or for which CES scores were not generated due to low population densities have been colored in gray within the maps and excluded from the scatterplots. Paired maps and scatterplots depicting (a.) residential electricity usage intensities per-capita [kWh/Capita], (b.) residential natural gas usage intensities per capita [Therms/Capita], and (c.) the fraction of total combined energy use delivered as electricity [Unitless] among Los Angeles County zipcodes as of 2017. Majority-DAC zipcodes are colored in red in both the maps and the plots. DOI: https://doi.org/10.1525/elementa.419.f2 As Figure 2a. and 2b. illustrate, the relationship between community disadvantage status and per-capita energy consumption levels are striking, with a significant degree of separation between the majority-DAC and majority non-DAC groups. The average resident within the majority-DAC zip codes consumes 1,383 kWh/CapitaYear. This is 55% of the 2,487 kWh/CapitaYear consumed, on average, by the residents of the majority non-DAC zip codes. In terms of natural gas usage the differences are similarly stark. The average per capita consumption among the majority DAC zipcodes is 76 Therms/CapitaYear. This amounts to 60% of the 126 Therms/CapitaYear consumed, on average, by residents of the majority non-DAC zipcodes. Results for the computed fractions of total per-capita residential energy use that are being delivered in the form of electricity are depicted in Figure 2. The strength of the correlation between these fractions and each zipcode's mean CES score is significantly weaker than for the previous two metrics and thus, does not provide sufficient evidence for any meaningful conclusions to be drawn. Current Transformation Participation Status Figure 3 depicts the current status of three key metrics of residential energy system transformation participation at the same zipcode level as was used previously. These metrics include: (a.) cumulative total battery electric vehicle registrations (b.) cumulative total plug-in hybrid electric vehicle registrations, (c.) cumulative total installed capacity of residential scale rooftop solar PV systems. Here again, zipcodes for which adoption data was not available or for which CES scores were not generated due to low population densities have been colored in gray within the maps and excluded from the scatterplots. Paired maps and scatterplots depicting recent (a.) battery electric vehicle adoption levels [EVs/1k-Capita], (b.) plug-in hybrid vehicle adoption levels [PHEVs/1k-Capita], and (c.) residential scale distributed rooftop solar installed capacities [MW-AC/1k-Capita among Los Angeles County zipcodes as of 2017. Majority-DAC zipcodes are colored in red in both the maps and the plots. DOI: https://doi.org/10.1525/elementa.419.f3 Across all three metrics plotted within Figure 3 strong and consistent negative relationships between the mean CES score of the zipcode and their levels of transition participation are evident. The maps of EV and PHEV adoption levels, (Figure 3a. and 3b.), show much higher levels in majority non-DAC coastal areas. These differences are also clearly evident in the statistics computed for the two groups, with the average for majority DAC zip codes is 2.52 PHEVs/1k-Capita, which is 65% lower the 7.34 PHEVs/1k-Capita for the majority non-DAC group. The spatial distribution of rooftop solar adoption mapped in Figure 3c. shows the highest rates of adoption within the high desert communities that are located in the Northwestern portion of LAC. These adoption rates reflect the abundant solar resources that are available in this region as well as generous levels of financial compensation that are being provided to customers for their distributed solar generation output under the current feed-in-tariff. This new feed-in-tariff structure was implemented by the recently formed local Community Choice Aggregation (CCA), Lancaster Clean Energy, and differs substantially from the net-metering tariff that was previously available from SCE. Forecasts of Future Energy Consumption Figure 4 depicts the recent historical and projected future rates of change in levels of (a.) annual total electricity consumption per-capita and (b.) annual total natural gas consumption per-capita between majority-DAC and majority non-DAC zipcode groups. These values have been calculated as the median of all the zipcodes contained within each group for each time period. As Figure 4a. illustrates, future forecasts based upon recent historical rates of change in per-capita electricity consumption levels indicate that the current significant differences (+81%) between the majority-DAC and majority non-DAC zipcode groups are likely to persist through the end of the forecast time horizon. This persistence is despite modest growth in median per-capita consumption levels within the majority-DAC group and correspondingly modest declines in the median per-capita consumption levels among majority non-DAC group. Time series plots depicting recent past (solid lines) and forecast future (broken lines) (a.) residential electricity usage intensities per capita [kWh/Capita] and (b.) residential natural gas usage intensities per capita [Therms/Capita] calculated as the median values for each group of majority-DAC and majority non-DAC zipcodes. DOI: https://doi.org/10.1525/elementa.419.f4 Figure 4b. shows how recent historical declines in per-capita gas consumption within both majority-DAC and majority non-DACs are expected to continue on into the future. With these ongoing reductions in per-capita gas usage, existing differences between the majority-DAC and majority non-DAC zipcode groups are forecasted to diminish, but not disappear (+65%), through the end of the forecast time horizon. This is due to the expectation that future reductions in consumption intensity will be proportionally higher within the majority non-DAC group. Forecasts of Future Energy Transformation Participation Figure 5 depicts the recent historical and project future rates of change in levels of (a.) battery electric vehicle adoption per 1k-capita (b.) plug-in-hybrid electric vehicle adoption per 1k-capita, and (c.) residential scale distributed rooftop solar PV adoption per 1k-capita. Across all three categories of energy system transformation, the plots clearly illustrate that we are currently approaching the period where rates of new adoptions are expected to reach their maxima. Time series plots depicting recent past (solid lines) and forecast future (broken lines) (a.) battery electric vehicle adoption levels [EVs/1k-Capita], (b.) plug-in hybrid vehicle adoption levels [PHEVs/1k-Capita], and (c.) residential scale distributed rooftop solar installed capacities [MW-AC/1k-Capita] calculated as the median values for each group of majority-DAC and majority non-DAC zipcodes. DOI: https://doi.org/10.1525/elementa.419.f5 As Figure 5a. and 5b. show, within majority non-DAC communities, the numbers of EVs and PHEVs per 1k-capita are expected to more than double from their current levels by just 2022. By 2024, EV adoption levels within majority non-DAC communities are expected to surpass those for PHEVs and continue climbing. The situation with the majority-DAC communities appears significantly less promising. For EVs, it will take until 2030 for per-capita penetration levels within majority-DAC zipcodes to reach levels already achieved in majority non-DAC areas. The situation is quite similar for the case of PHEVs with future growth in majority-DAC communities stagnating after 2024. Looking at the expected future growth in the adoption of residential scale distributed rooftop PV systems, recent historical trends suggest that both majority-DAC and majority non-DAC groups will experience rapid growth through 2022, after which growth rates will begin to taper off through the end of the 2030. Despite these positive growth trends, the current, substantial, differences in per-capita installed capacities which currently exist between the two groups are expected to significantly increase, through the forecast time horizon. Shortcomings of Existing Market Based Programs Mapping energy consumption and renewable technology adoption by DAC-status reveals stark differences between communities with respect to their participation in the energy transition so far, and the failure of market-based programs to adequately address the equity dimensions of the energy transition. Forecasts of EV/PHEV and rooftop solar adoption also indicate that unless redistributive measures are taken, existing inequities in access to zero-emission energy end-use technologies will persist long into the future. By design, market-based approaches to residential EE, electrification, and renewable generation capacity expansion programs tend to prioritize volume – measured in units of either of estimated energy savings, sales, or installed capacity – over the equitable distribution of program benefits. The tendency of these programs to be over-utilized by the rich and under-utilized by the poor is well-documented. However, this tendency is not always perceived as problematic or even especially undesirable. If the primary objective of market-based incentive programs is GHG abatement, what does it matter if wealthy citizens are the ones who are participating, so long as demand for grid-supplied energy diminishes? This simplistic approach ignores the fact that the marginal benefits enjoyed from the consumption of each additional kilowatt-hour or therm vary between individuals as well as at different levels of consumption. These marginal benefits decline substantially as the volume of consumption increases beyond the sufficiency range. Thus, the cumulative benefits generated from the expenditure of public funds are maximized when programs target households whose levels of consumption are within the sufficiency range. The Need for a Fundamental Change in Approach The time has come to reflect upon the reasons why the current slate of market-based incentive programs continue to produce such inequitable outcomes. We believe that, in many cases, program elements which were assumed to ensure equality of access or opportunity, may be inadvertently responsible for unequal rates of program utilization. This is because DAC members are known to be inherently more limited than their non-DAC counterparts in terms of their available time, attention, and capacity to take advantage of programs which are "generally" available (Scavo et al., 2016). There are myriad examples of specific ways in which well intentioned program designs can produce unintended consequences. Consider, for example, which of the following alternative policy approaches would be more likely to produce equitable outcomes in the future: Continuing to finance EE programs whose measures are most easily implemented during the processes of new construction or major renovations and thus, are disproportionally used by affluent, single family homeowners? OR Creating new EE programs whose measures can be readily implemented in densely occupied, aging, or multi-family structures and which address the renter-owner split incentive barrier? Continuing to subsidize net-metering tariffs which pay the owners of affluent single family homes above market rates to install large PV systems capable of offsetting up to 100% of their total annual consumption? OR Creating new virtual net-metering tariffs which allow for the output of community scale PV systems to be virtually allocated to several multi-family households, partially offsetting a fraction of their annual consumption? Continuing to provide tax rebates for the members of affluent households to purchase multiple, potentially redundant, EV/PHEVs for limited use in satisfying their personal transportation needs? OR Restricting the availability of these rebates to low-income, single vehicle households and ride share fleet operators whose services can, potentially, satisfy the transportation needs of numerous households? The design of residential energy policies determines, in part, who is able to benefit from advances in energy technology. Current and future policy choices will also determine the depth and inclusivity of the energy transition as it progresses. If the renewable energy transition is to both significantly reduce emissions of locally impactful criteria pollutants and globally impactful GHGs as well as alleviate energy insecurity without enabling excessive consumption, current residential energy policies are inadequate. In order for these policies to maximize the social benefits of domestic renewable energy systems, electric vehicles, and energy efficiency programs, they must account for the higher marginal utility of units of energy consumed at or below the level of sufficiency. DAC residents who currently experience energy poverty stand to benefit immensely from such redesign of energy efficiency and residential renewable energy incentives. Inequities in the energy transition are of concern not because DAC members should have EVs, PV systems, and efficient appliances as a matter of fairness in material allocations. Rather, they are of concern because adoption of these goods ensures that individuals and households are not deprived of the full suite of energy services in a renewable future and are not subjected to economic hardship or other indecencies as a result of the energy transition. The results of this study have shown how public policies designed to reduce GHG emissions in California have resulted in a skewed distribution of benefits toward those who utilize the most energy. This is because these affluent consumers have a greater ability to access existing programs and incentives. This inequality of participation amounts to the implicit subsidization of excess consumption, which is being financed by the general energy utility rate payer. Program participation requires extra effort, knowledge and access. The underlying design assumption behind the majority of these policy programs – that equality of availability will necessarily produce equality of participation – is fundamentally flawed. This assumption reflects a modernist ideology that is evident in the design and layout of other major urban infrastructure systems. Current policies do not address the absolute levels of energy consumption, per se, but rather tend to focus on increasing energy efficiency. However, increases in efficiency have largely only been realized at the highest levels of consumption. Low income DAC residents continue to live in less comfortable housing and pay a larger proportion of their income for that discomfort. This problem with efficiency has been known for over a century, and was first described by William Stanley Jevons when observing the introduction of coal in England (Alcott, 2005). He noted that though the efficiency of engines was improving, more and more coal was needed as there was an expansion of its use. It is critical today to understand that efficiency improvements alone are not likely to lead to absolute reductions in energy use. The future need for additional generation capacity is likely to continue, whether it be from fossil or renewable sources. Renewably generated energy constitutes a dramatic improvement over the use of fossil fuels. However, it too has considerable environmental and social impacts – from the extraction of raw materials in production, to habitat loss in deployment, and the need to dispose of electronic waste at end of life. It is likely that the imposition of hard limits on total energy use will ultimately be necessary to mitigate all of the impacts incurred across the breadth of this life cycle. The inequities in the system as it exists today place a larger burden of cost on the least affluent, and, perversely, reward the high consumers with access to incentives. Policy aims need to get beyond efficiency to address absolute levels of consumption and to reflect reasonable need rather than excessive use. If not, efficiencies will continue to chase increased demand with limited effect, and DAC communities will be prevented from improving their well-being, though they use the least energy of all. All data files associated with the manuscript have been uploaded to FigShare and can be accessed here https://doi.org/10.6084/m9.figshare.12206366. The authors would like to acknowledge the work of Dan Cheng, staff database developer, and Hannah Gustafson, staff analyst, for their work in developing the UCLA Energy Atlas as part of the California Center for Sustainable Communities at UCLA. The authors would also like to thank Dr. Jason Sexton for his helpful review and comments during the development of this manuscript. This work was funded by grant #CCRP0057 from the California Strategic Growth Council, Climate Change Research Program. The authors have no competing interests to declare. Eric Daniel Fournier executed the quantitative analyses, generated the figures, and contributed to the development of the manuscript and its arguments. Robert Cudd, Felicia Federico, & Stephanie Pincetl contributed to the development of the manuscript and its arguments. 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Keirstead A brief history and the possible future of urban energy systems Scavo Korosec Doughman Low-Income Barriers Study, Part A: Overcoming Barriers to Energy Efficiency and Renewables for Low-Income Customers and Small Business Contracting Opportunities in Disadvantaged Communities Ketoff International residential energy end use data: Analysis of historical and present day structure and dynamics Stefes Creating Path Dependency: The Divergence of German and U.S. Renewable Energy Policy SSRN Electronic Journal https://doi.org/10.2139/ssrn.1667615 Peretz State-level benefits of energy efficiency . Low-Income Household Energy Burden Varies Among States — Efficiency Can Help In All of Them. Community resilience: Path dependency, lock-in effects and transitional ruptures Journal of Environmental Planning and Management https://doi.org/10.1080/09640568.2012.741519 Youn The effects of progressive pricing on household electricity use Journal of Policy Modeling https://doi.org/10.1016/j.jpolmod.2016.06.001 Dirks Seiple Modeling the effect of climate change on U.S. state-level buildings energy demands in an integrated assessment framework Copyright: © 2020 The Author(s) Supplementary Data- zip file Supplementary Material. Text S1. - pdf file Recipient(s) will receive an email with a link to 'On energy sufficiency and the need for new policies to combat growing inequities in the residential energy sector' and will not need an account to access the content. 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Convective Heat Transfer Assignment 7 — Internal Convection Starting from the energy equation for a constant density fluid in axisymmetric coordinates: $$ \rho \left(\frac{\partial e}{\partial t} + u \frac{\partial e}{\partial x} + v \frac{\partial e}{\partial r} \right) = \frac{\partial }{\partial x}\left(k\frac{\partial T}{\partial x} \right) + \frac{1}{r} \frac{\partial }{\partial r} \left(kr \frac{\partial T}{\partial r} \right) + \mu \left(\frac{\partial u}{\partial x} \right)^2 + \mu \left(\frac{\partial u}{\partial r} \right)^2 + \mu \left(\frac{\partial v}{\partial x} \right)^2 + \mu \left(\frac{\partial v}{\partial r} \right)^2 $$ In the thermally fully-developed region of a pipe of diameter $D$, show that $$ {\rm Nu}_D=\frac{h D}{k}=\frac{48}{11} $$ $$ {h}\equiv \frac{q_{\rm w}^{\prime\prime}}{T_{\rm w}-T_{\rm b}} $$ with $T_{\rm b}$ the bulk temperature. Outline all assumptions. Note: you can make use of the velocity profile in the fully-developed region $u=2 u_{\rm b}(1-r^2/R^2)$ with $u_{\rm b}$ the bulk velocity. Water at $30^\circ$C enters at a rate of 0.25 kg/s a 4-cm-diameter smooth pipe. Over its entire length of $L=6$ m, the pipe is heated on its outside surface by a cross flow of air at a pressure of 1 atm, a temperature of $300^\circ$C, and a speed of 100 m/s. For a pipe of negligible wall thickness (resulting in essentially equal internal and external pipe diameters), calculate the bulk water temperature at the pipe exit. Consider a 30 m long pipe with a diameter of 1 cm and with a smooth interior wall surface. The pipe wall temperature is kept constant at 60$^\circ$C. (a) Some liquid enters the pipe with a temperature of 20$^\circ$C and exits the pipe with a mixing cup (bulk) temperature of 57$^\circ$C. Knowing that the mass flow rate of the liquid is of $0.015$ kg/s, that the liquid density is of 1000 kg/m$^3$, that the friction force exerted on the pipe due to the motion of fluid is equal to 0.144 N, determine the viscosity and the Prandtl number of the liquid. (b) Using the Prandtl number and viscosity found in part (a), estimate the bulk temperature at the exit of the pipe for the same inflow temperature as in (a) but with the mass flow rate increased to 0.15 kg/s. Hint: When the flow in a pipe is fully-developed, the friction factor is equal to: $$f=\frac{(-{\rm d}P/{\rm d}x)D}{\rho u_{\rm b}^2/2}$$ 2. 71.4$^\circ$C. 3. $0.001~{\rm kg/ms}$, $8.88$, $60^\circ{\rm C}$. Due on May 30th at 17:00. Do all questions.	CommonCrawl
Seismic potential around the 2018 Hokkaido Eastern Iburi earthquake assessed considering the viscoelastic relaxation Makiko Ohtani ORCID: orcid.org/0000-0001-5321-502X1 & Kazutoshi Imanishi1 The 2018 Mj 6.7 Hokkaido Eastern Iburi earthquake (Iburi earthquake) occurred near the eastern boundary fault zone of the Ishikari lowlands, which is composed of a northern and southern fault. Aftershock distribution suggests the existence of a previously unknown fault (the Shallow Iburi (SI) fault) at a shallower extension of the Iburi earthquake fault. In the present study, we examined the seismic potential of the northern, southern, and SI faults based on seismological analysis and numerical simulations. The aftershock focal mechanisms infer the present-day stress field that is characterized by an ENE–SWS compression around the target faults. Slip tendency analysis shows that all target faults originally have high slip potential under the estimated stress field. We, therefore, evaluated earthquake occurrence potential on the target faults influenced by the Iburi earthquake based on the Coulomb stress (ΔCFF). We consider postseismic viscoelastic deformation in the viscoelastic medium with a three-dimensional structure. The present paper shows one possible scenario based on a model incorporating information currently available. The most of the entire SI fault was brought closer to rupture just after the earthquake, indicated by the positive ΔCFF, which is consistent with the activation of seismicity in this region. The ΔCFF continues to increase over many years after the earthquake, which may imply a growing risk of seismic hazards along the SI fault. The distribution of the ΔCFF along the southern fault and the southern half of the northern fault is characterized by a similar depth-dependent pattern. The faults were brought closer to rupture just after the earthquake, indicated by the positive ΔCFF, except for mid-depths along the faults. Then, the ΔCFF increases at shallow depths for a few decades after the earthquake, which suggests a continuous build-up of stress. Although the ΔCFF decreases at the deep depths for a few decades after the earthquake, it is insufficient to return the stress level to that before the earthquake. These results suggest that all target faults are in the state of increasing seismic risk after the Iburi earthquake. On September 6, 2018, the Mj 6.7 Hokkaido Eastern Iburi earthquake (hereafter referred to as the Iburi earthquake or mainshock) occurred in Hokkaido, northern Japan (Fig. 1). The earthquake triggered large landslides and caused severe damage to the surrounding area. According to Japan Meteorological Agency (JMA), the Iburi earthquake occurred at a depth of 37 km, which is deep compared with usual activity of inland earthquakes in Japan. This area, including beneath the Hidaka Mountains (Fig. 1), is a region where deep inland earthquakes commonly occur (e.g., Kita et al. 2012). The centroid moment tensor (CMT) solution and aftershock distribution indicate that the mainshock occurred as a reverse faulting along a steeply eastward-dipping plane. On February 21, 2019, there was an Mj 5.8 aftershock that occurred at the northern part of the aftershock area (Japan Meteorological Agency 2019), which was the largest aftershock as of April 2019. Although coseismic slip mainly occurred at depths greater than 16 km (Geospatial Information Authority of Japan 2018; Japan Meteorological Agency 2018), shallower aftershocks were also active. The tectonic structure in the Hokkaido region is characterized by thrust faults and geological units that are almost parallel to N–S direction (Fig. 1). This N–S trending feature indicates the long-term existence of E–W compression, which is a consequence of westward migration of the Kuril Arc sliver and its collision with northeastern Japan due to the oblique subduction of the Pacific plate since the late Miocene (e.g., Kimura 1986). The Iburi earthquake likely occurred under a stress field caused by ongoing arc–arc collisional processes. Map of the Iburi earthquake and the three target faults in the present study, shown with the geological map (see details in GeomapNavi; https://gbank.gsj.jp/geonavi/geonavi.php). The black, blue, and green rectangles indicate the surface projection for the geometry of the three target faults: the northern fault, the southern fault in the Ishikari fault zone, and the SI fault, respectively. The star and gray circles indicate the hypocenter of the mainshock and the 40-day aftershocks based on the earthquake catalog of Japan Meteorological Agency. The "beach ball" represents the centroid moment tensor solution for the mainshock by Japan Meteorological Agency (https://www.data.jma.go.jp/svd/eqev/data/mech/cmt/fig/cmt20180906030759.html. Accessed: January 29, 2019). The red rectangle shows the surface projection of the Iburi earthquake fault estimated by Japan Meteorological Agency (2018). The original fault slip distribution and the modified distribution used in the present study are shown on the left and right of the right lower panel. Red lines indicate active faults after Research Group for Active Faults of Japan (1991). The small green squares represent seismic stations used for analysis. The location of Hidaka Mountains is also indicated. The bottom panel shows the target faults, the mainshock, and the aftershocks projected onto the E–W vertical section An active fault zone near the source region of the Iburi earthquake is known as the eastern boundary fault zone of the Ishikari lowlands (Headquarters for Earthquake Research Promotion 2010) (hereafter referred to as the Ishikari fault zone). On the basis of geological structure distribution patterns, the Ishikari fault zone is divided into northern and southern faults, where eastward-dipping thrust faultings are expected. The average vertical slip rate along the northern fault is estimated to be 0.4 m/1000 years or more. Along this fault, earthquakes with a vertical slip of > 2 m repeatedly occur at an interval of 1000–2000 years with the most recent occurrence between AD 1739 and 1885. On the basis of fault length, the northern fault could potentially produce an earthquake around M7.9. The average vertical slip rate along the southern fault is estimated to be 0.2 m/1000 years or more. Although the history of seismic ruptures along this fault is not well constrained, this fault appears to have the potential to generate an M7.7 earthquake or larger. If an earthquake of this magnitude occurs, it will produce more destructive damage than the Iburi earthquake. Evaluating earthquake potential in the Ishikari fault zone is therefore important. In the present study, we discuss the potential for future ruptures along the northern and southern faults in the Ishikari fault zone. In addition, we also focus on a fault inferred from aftershock distributions of the Iburi earthquake. The fault is a shallower extension of the Iburi earthquake fault as estimated by Japan Meteorological Agency (2018) (Fig. 1); hereafter, we call it as the Shallow Iburi (SI) fault. Details for the three target faults are listed in Table 1. The target faults are located at depths shallower than the mainshock fault, i.e., at depths from 0 to 15 km for the northern and southern faults and from 0 to 20 km for the SI fault. Table 1 Source parameters for the three target faults: the northern, southern, and SI faults (Fig. 1 black, blue, and green rectangles) First, we infer the present-day stress field around the target faults based on aftershock focal mechanism solutions ("Slip tendency of the target faults under the present-day stress field" section). On the basis of the estimated stress field, we evaluate the slip potential for the target faults using a slip tendency analysis. Next, in "Stress change due to the Iburi earthquake in an elastic-viscoelastic medium" section, we calculate the stress change along the target faults due to the Iburi earthquake and derive the Coulomb stress, which is modified by an inelastic strain evolution in a viscoelastic medium with a three-dimensional (3-D) structure. Then, we discuss the long-term effects that the Iburi earthquake has on the target faults. We should note that, at present, no observation data (seismicity or ground surface deformation) exist that are comparable with time-dependent results because only 7 months have passed since the Iburi earthquake as of April 2019. However, a rapid evaluation of the stress change allows a discussion on the potential for a future earthquake. Slip tendency of the target faults under the present-day stress field Prior to evaluating the stress change caused by the Iburi earthquake, we investigate the slip tendency of the target faults based on the present-day stress field. Since shallow seismicity in the area was low before the Iburi earthquake, the stress field there has not been quantitatively estimated (e.g., Yukutake et al. 2015). Shallow aftershocks of the Iburi earthquake provide an opportunity to infer the stress field by a suite of focal mechanism solutions. We focused on 45 shallow aftershocks that occurred between September 6 and November 18, 2018, which had JMA magnitude (Mj) larger than 1.8 and focal depths at less than 22 km. The largest event was Mj 4.3, which occurred at 12:54 (JST) on September 11. Only this event's focal mechanism (reverse faulting type) was routinely determined by JMA and National Research Institute for Earth Science and Disaster Resilience. Data for these analyses derive from regional high-sensitivity seismic stations (Fig. 1). We determined hypocenters of the earthquakes by applying a maximum-likelihood estimation algorithm (Hirata and Matsu'ura 1987) to manually picked arrival times. The velocity model used in the present study (lower right panel in Fig. 2a) is a one-dimensional (1-D) velocity structure that contains low-velocity layer beneath the source region (Iwasaki et al. 2004). We first located the hypocenters for all events without station corrections. We then relocated the hypocenters by introducing station corrections, which were computed by averaging the differences between the observed and theoretical travel times at each station. We repeated the procedure until the reduction in the root mean square (RMS) for the arrival time residuals had converged. After three iterations, the RMS decreased from 0.437 to 0.135 s for the P-wave and from 0.907 to 0.280 s for the S-wave. The average spatial errors calculated using the maximum-likelihood estimation algorithm were 205 m horizontally and 253 m vertically, which are sufficient for the objectives of the present study. The circles in Fig. 2a show the relocated aftershocks, which suggest that they align along the N–S direction and dip eastward at a high angle of about 70°. Compared with the distribution of JMA catalog, the relocated aftershocks clustered, but overall features did not change. a Focal mechanism solutions for the 27 aftershocks determined in this study (lower hemisphere of the equal-area projection) with colors used to differentiate between the reverse (green), strike slip (red), and normal faulting (blue) mechanisms. A triangle diagram (Flohlich 1992) with a color scale is presented at the top right. Open circles indicate relocated hypocenters derived using the velocity model shown in the bottom right. The S-wave velocity is assumed by scaling the P-wave velocity by a factor of $1/\sqrt 3$. b Results of the stress tensor inversion. The top panels show the principal stress axes with their 95% confidence regions plotted on the lower hemisphere stereonets. The middle panel shows the misfit angle for the data with respect to the best stress tensor determined by the stress tensor inversion. Here, the misfit angle represents the angular difference between the tangential traction predicted by the best solution and the observed slip direction on each focal mechanism. The bottom panel shows the frequency of the stress ratio ϕ, which belongs to the 95% confidence region. Inverted triangle represents the stress ratio of the best stress tensor Determination of focal mechanism solutions and stress field We then determined focal mechanism solutions for the aftershocks using absolute P- and SH-wave amplitudes, as well as P-wave polarity (see detail procedures in Imanishi et al. 2011). The 27 focal mechanisms, with at least 10 P-wave polarities and a variance reduction of > 50%, are plotted on the map shown in Fig. 2a. On the basis of definitions by Flohlich (1992), most events are categorized as reverse faulting. Interestingly, the strikes for each of these events slightly deviate from N–S aftershock alignment but are more similar to the strike of the southern fault in the Ishikari fault zone. Using the 27 focal mechanism solutions, we estimated the stress field by applying the inversion method of Michael (1984, 1987). The estimated stress parameters are as follows: the maximum ($\sigma_{1}$), intermediate ($\sigma_{2}$), and minimum ($\sigma_{3}$) compressive principal stresses, as well as the stress ratio ($\phi = \left( {\sigma_{2} - \sigma_{3} } \right)/\left( {\sigma_{1} - \sigma_{3} } \right)$). The result of the stress tensor inversion indicates that this area is characterized by a reverse faulting stress regime with $\sigma_{1}$ oriented to a subhorizontal ENE–SWS direction (Fig. 2b). The stress ratio is greater than 0.5, which suggests that the magnitude of $\sigma_{2}$ is closer to $\sigma_{1}$ than $\sigma_{3}$. The ENE–SWS compressional stress is considered to be a consequence of westward migration of the Kuril Arc sliver and its collision with northeastern Japan. Slip tendency analysis On the basis of fault geometry (Table 1) and the estimated stress field, we can evaluate the slip potential along target faults using a slip tendency analysis. Morris et al. (1996) defined slip tendency (Ts) as the ratio of shear stress (τ) to effective normal stress (σn) that act on the plane of weakness. Following Lisle and Srivastava (2004), we used the normalized slip tendency defined as Ts′ = Ts/max(Ts) = Ts/μ, where μ is the static frictional coefficient. The value of Ts′ is between 0 and 1, where larger values correspond to greater slip potential. We supposed that the frictional sliding envelope is tangential to the $\sigma_{1} - \sigma_{3}$ Mohr circle, which allows us to calculate Ts′ without knowledge of the absolute stress value (Lisle and Srivastava 2004). Collettini and Trippetta (2007) defined favorably oriented planes of slip by 0.5 < Ts′ ≤ 1 and unfavorably oriented planes by 0 ≤ Ts′ ≤ 0.5. Figure 3 shows a histogram of Ts′ values computed from 95% confidence regions of the assumed stress tensor (bars), together with the best stress tensor (inverted triangle). Here, we set the static friction coefficient to 0.6. The results indicate that the present-day stress field is favorably oriented to the faults in the Ishikari fault zone (Fig. 3a, b). Even for the SI fault, which is a high-angle fault, the Ts′ value for the best stress tensor exceeds 0.5. Furthermore, more than half of the Ts′ values computed from the 95% confidence regions also exceed 0.5 (Fig. 3c). Thus, all target faults originally have high slip potential with respect to the present-day stress field, which suggests that we need to evaluate the stress change along the faults caused by the Iburi earthquake. Frequency of the normalized slip tendency computed from the 95% confidence region of the stress tensor in Fig. 2b. The inverted triangles show the normalized slip tendency of the best stress tensor. The gray dotted line indicates the boundary as to whether or not the fault is easy to move under the assumed stress tensor (Collettini and Trippetta 2007). For the case of a northern, b southern, and c SI faults Stress change due to the Iburi earthquake in an elastic–viscoelastic medium Here, we calculate the Coulomb stress change along the target faults caused by the Iburi earthquake. The Coulomb stress estimation has been employed in a number of regions and proved to be an effective method to evaluate earthquake triggering (Stein 1999; King and Cocco 2001). In the present study, we take into account the viscoelastic relaxation in the lower crust to calculate the time-dependent Coulomb stress. Viscoelastic relaxation plays an important role in producing delayed earthquake triggering, such as in the 1992 Landers–1999 Hector Mine earthquakes (Freed 2005). We employ an equivalent body force method to evaluate the stress field produced by an inelastic strain (Barbot and Fialko 2010; Lambert and Barbot 2016). Here we summarize the method. The strain field, εt, is composed of the elastic and inelastic strains, εe and εi. The elastic stress, σ, is noted as σ = C: εe = C: (εt − εi), where C is the elastic constant and (:) denotes the inner product. We can rewrite the continuum equation, i.e., $\nabla {\varvec{\upsigma}} = 0$, using the equivalent body force, ${\mathbf{f}} = - \nabla {\mathbf{m}} = - \nabla \left( {{\mathbf{C}} :{\varvec{\upvarepsilon}}^{i} } \right)$, as follows: $$\nabla \left( {{\mathbf{C}} :{\varvec{\upvarepsilon}}^{t} } \right) - \nabla {\mathbf{m}} = \nabla \left( {{\mathbf{C}} :{\varvec{\upvarepsilon}}^{t} } \right) + {\mathbf{f}} = 0.$$ The displacement field, ${\mathbf{u}}\left( {\mathbf{x}} \right)$, is derived by solving Eq. 1, the inhomogeneous Navier's equation, and we get $${\mathbf{u}}\left( {\mathbf{x}} \right) = \mathop \int \limits_{\Omega }^{{}} {\mathbf{G}}\left( {{\mathbf{x}},{\mathbf{y}}} \right){\mathbf{f}}\left( {\mathbf{y}} \right){\text{d}}{\mathbf{y}},$$ where G (x, y) is the elastic Green's function to a point force at y. When the inelastic strain field is discretized into volumetric cuboid cells with uniform strain and stress, Ωk (k = 1, …, Nv), the displacement field is the sum of displacement produced by inelastic strain in each volumetric cell: $${\mathbf{u}}\left( {\mathbf{x}} \right)\sim\mathop \sum \limits_{k = 1}^{{N_{v} }} {\mathbf{u}}_{k} \left( {\mathbf{x}} \right) = \mathop \sum \limits_{k = 1}^{{N_{v} }} \mathop \int \limits_{{\Omega _{k} }}^{{}} {\mathbf{G}}\left( {{\mathbf{x}},{\mathbf{y}}} \right){\mathbf{f}}_{k} \left( {\mathbf{y}} \right){\text{d}}{\mathbf{y}}.$$ G (x, y) is analytically derived by Barbot et al. (2017). For an inelastic strain field, εi(t), at time t, elastic stress field, σ(x, t), is calculated using only the information at the time; $${\varvec{\upsigma}}\left( {{\mathbf{x}},t} \right) = \mathop \sum \limits_{k = 1}^{{N_{v} }} {\mathbf{K}}_{k}^{v} \left( {\mathbf{x}} \right){\varvec{\upvarepsilon}}_{k}^{i} \left( t \right),$$ written in the form of Green's function K k v (x) multiplied by inelastic strain ${\varvec{\upvarepsilon}}_{k}^{i} \left( t \right)$. K k v (x) is the uk(x) for a unit of strain in Ωk. When no external forces is applied, the time derivatives for the stress and inelastic strain in each volumetric cell are $$\left\{ {\begin{array}{{20}l} {{\dot{\varvec{\upsigma }}}_{k} \left( t \right) = \mathop \sum \nolimits_{k = 1}^{{N_{v} }} {\mathbf{K}}_{kj}^{v} {\dot{\varvec{\upvarepsilon}}}_{j}^{i} \left( t \right)} \hfill \\ {{\dot{\varvec{\upvarepsilon }}}_{k}^{i} \left( t \right) = g\left( {{\varvec{\upsigma}}_{k} \left( t \right)} \right)} \hfill \\ \end{array} } \right.,$$ where g varies depending on the deformation mechanism. In the present study, we assume Maxwell viscoelasticity, and therefore, we denote $g\left( {\varvec{\upsigma}} \right)$ as $g\left( {\varvec{\upsigma}} \right) = {\varvec{\upsigma}}'/\eta$, where σ′ is the deviatoric stress and η is the viscosity. We solve Eq. (5) using a time step adaptive Runge–Kutta method (Hairer et al. 1993). In the present paper, we assume the Iburi earthquake occurs at t = 0. For simplicity, we assume that there is no strain and deviatoric stress before the earthquake. The initial conditions at t = 0 just after the earthquake are as follows: $$\left\{ {\begin{array}{{20}l} {{\varvec{\upsigma}}_{k} \left( 0 \right) = \mathop \sum \nolimits_{j = 1}^{{N_{f} }} {\mathbf{K}}_{kj}^{f} {\mathbf{s}}_{j} } \hfill \\ {{\varvec{\upvarepsilon}}_{k}^{i} \left( 0 \right) = 0 } \hfill \\ \end{array} } \right.,$$ where sj is the slip on the fault cell j (j = 1, …, Nf), and K kj f is the elastic stress response observed at the volumetric cell k due to a unit slip in the slip direction on the fault cell j, which is calculated by the method of Okada (1992). The change in stress Δσ(x, t) from a reference value of just before the earthquake is calculated as the summation of the stress change due to the fault slip (coseismic stress change) and the time-dependent inelastic strain (postseismic stress change): $$\Delta {\varvec{\upsigma}}\left( {{\mathbf{x}}, t} \right) = \mathop \sum \limits_{j = 1}^{{N_{f} }} {\mathbf{K}}_{j}^{f} \left( {\mathbf{x}} \right){\mathbf{s}}_{j} + \mathop \sum \limits_{j = 1}^{{N_{v} }} {\mathbf{K}}_{j}^{v} \left( {\mathbf{x}} \right){\varvec{\upvarepsilon}}_{j}^{i} \left( t \right).$$ Following Reasenberg and Simpson (1992), we calculate the Coulomb stress (ΔCFF) along each target fault as $$\Delta {\text{CFF}}\left( t \right) = \Delta \tau \left( t \right) - \mu^{\prime}\Delta \sigma_{n} \left( t \right),$$ where Δτ(t) is the shear stress change and Δσn(t) is the change in the stress that is normal to the fault (negative if the fault is unclamped), which is calculated from Δσ(x, t). The coefficient μ′ is the effective friction, which ranges from 0 to 1. An increase in the shear stress and a decrease in normal stress increase the Coulomb stress. Faults with a positive ΔCFF value are brought closer to rupture, whereas faults with a negative ΔCFF value are brought farther away. Source model for the Iburi earthquake For the fault slip, s in Eq. (6), we use a finite fault source model for the Iburi earthquake derived from an inversion of near-source strong motion data (Fig. 1; Japan Meteorological Agency 2018). The fault with a strike of 0° and a dip of 70° was divided into Nf = 100 subfaults, where sj (j = 1, …, Nf) was estimated. The fault is characterized by reverse faulting and a maximum slip of 1.65 m. The majority of the coseismic slip occurred at depths between 15 and 40 km, and a seismic moment of 1.5 × 1019 Nm (Mw = 6.7) is released. Although the majority of the slip concentrates along the mid-depths of the assumed fault, there are also minor peaks in the slip at the rims of the fault (left in the lower right panel in Fig. 1), which are possibly less reliable than the middle main slip. Therefore, we set the slip at the rims as 0 m. The slip distribution used in the present study for the fault model is shown at the right of the lower right panel in Fig. 1. The modified model generally explains the displacement from GNSS observation (Geospatial Information Authority of Japan 2018), other than the station closest to the mainshock, whose displacement is in the opposite direction to the observation. For simplicity, we assume that the Iburi earthquake occurs at t = 0 and that the fault produces no slip at t > 0, i.e., sj(t) = 0 at t > 0. There is another available source model, derived from an inversion of geodetic data (Geospatial Information Authority of Japan 2018). The estimated fault plane is slightly offset from the aftershock distribution and a little shallower than that used in the present paper. In spite of this difference, the calculated ΔCFF for the source model by Geospatial Information Authority of Japan (2018) showed similar postseismic change to that by Japan Meteorological Agency (2018), suggesting that the present result is robust with regard to the choice of source model. Crustal model Cho and Kuwahara (2013b) derived the viscoelastic structure beneath the Japanese islands based on a 3-D thermal structure (Cho and Kuwahara 2013a) and flow law of rocks. The model consists of two layers: a shallower elastic layer and a deeper viscoelastic layer. The thickness of the derived elastic layer, defined as depthe(x) in Fig. 4a, varies widely from 10 km to 45 km in the Hokkaido region, and the Iburi earthquake fault is located where the elastic layer is thick, i.e., depthe(x) > 40 km. In the present study, we assume the viscoelastic medium with the 3-D structure and investigate the effects of the structure. For the objectives of the present study, however, the model of Cho and Kuwahara (2013b) has a problem that there are no data for the depthe(x) beneath the Hidaka Mountains (Fig. 1) and oceanic areas. On the basis of the Moho map (Matsubara et al. 2017) and the thickness of the seismogenic layer (Omuralieva et al. 2012), we set the depthe(x) to 45 km under the Hidaka Mountains. For the oceanic area, we determined the depthe(x) by extrapolating the existing data using the "surface" command in the Generic Mapping Tools (Wessel and Smith 1998). We further incorporated the subducting Pacific plate into the model to limit the viscoelastic layer to shallower depths than the subducting plate interface. For the plate interface depth, defined as depthp(x) in Fig. 4a, we used the model estimated in Kita et al. (2010) and Nakajima and Hasegawa (2006). The colored circles in Fig. 4b show the spatial distribution of depthe(x), i.e., the uppermost depth of the viscoelastic layer. For both layers, we assume that the rigidity is 50 GPa and the Poisson's ratio is 0.25. For the viscoelastic layer, we assume that η is 1 × 1019 Pa s, with reference to previous studies in the Hokkaido (Ueda et al. 2003; Itoh and Nishimura 2016) and Tohoku regions (Suito and Hirahara 1999; Ohzono et al. 2012). a Schematic view of the medium with a shallower elastic layer and deeper viscoelastic layer. The viscoelastic layer is limited to depthe(x) < Z < min{depthp(x), 170.0 km}. b Distributions of the discretized viscoelastic cells in the X and Y directions, with the depthe indicated by specific colors. Each dot indicates the location of the subfault midpoint, which is distributed in the X and Y directions, although multiple subfaults in the Z direction are set at each location up to min{depthp(x), 170.0 km}. The red rectangle corresponds to the surface projection of the mainshock fault We embed the Iburi earthquake source model ("Source model for the Iburi earthquake" section) into the crustal model (Fig. 4). Here, we set the X- and Y-axes in the north and east directions and the Z-axis is depth, downward positive. We set the ground surface at Z = 0. We discretize the viscoelastic layer into Nv = 45,700 unequal-sized cuboid cells, in which the horizontal size has a minimum value of 2 km × 1.3 km in the X and Y directions and increases as it goes away from the Iburi earthquake (Fig. 4b). We set the cell size in the Z direction to increase with increasing Z. We set the bottom limit for the viscoelastic layer to be 170.0 km. The viscoelastic region is thus limited to 322 km × 333 km in the X and Y directions and depthe(x) < Z < min{depthp(x), 170.0 km}. Time-dependent ΔCFF We evaluated the time-dependent ΔCFF(t) along the target faults (Table 1) using Eq. (8) and μ′ = 0.4, which value is commonly used in the calculation of ΔCFF to minimize the uncertainty in μ′ (King et al. 1994). First, we show the elastic response in Fig. 5. The top panels show the coseismic Coulomb stress ΔCFF(0) or coseismic ΔCFF with the same meaning, resolved onto each target fault. The bottom panels show cross-sectional views of ΔCFF(0) at X = 18 km for the receiver faults, which have identical fault parameters as each target fault. The SI fault has identical strike and dip as the Iburi earthquake fault, and the ΔCFF(0) distribution is characterized by typical pattern for blind reverse faulting (Fig. 5c bottom; Lin and Stein 2004). The mainshock relieves stress along the slipped fault and generates stress shadows with a negative ΔCFF(0) value. On the other hand, stress concentrated along both ends of the slipped fault and positive ΔCFF(0) values are calculated there, which indicates that the receiver faults there are brought closer to rupture. The SI fault is located at the shallower end of the Iburi earthquake fault, so that the ΔCFF(0) value is mainly positive along the fault plane. The ΔCFF(0) has the value up to 6.14 MPa (Fig. 5c top), which is high because the SI fault partially overlaps with the Iburi earthquake fault. Seeing only the shallower portion of the SI fault than the Iburi fault (Z < 8.8 km), ΔCFF(0) is always positive and has a value of 0.23 MPa at point I1 in Fig. 5c. The northern and southern faults have identical dip angle and comparable strike, which results in similar ΔCFF(0) distributions (Fig. 5a, b). The cross sections indicate that negative-ΔCFF(0) regions in these two cases are narrower than those in the case for the SI fault. However, the northern and southern faults traverse the narrowed negative-ΔCFF(0) regions, such that ΔCFF(0) is negative at mid-depths and positive at deeper and shallower portions along the faults (Fig. 5a, b). The ΔCFF(0) value ranges from − 0.14 to 0.22 MPa along the southern half of the northern fault, whereas the ΔCFF(0) value in the northern half is negligible. Along the southern fault, the ΔCFF(0) ranges from − 0.17 to 0.34 MPa. The magnitude of the ΔCFF(0) is larger along the southern fault compared with the northern fault because the former is closer to the Iburi earthquake fault than the latter. We observe that, in all of the target faults, regions exist along the fault plane where ΔCFF(0) exceeds the earthquake triggering threshold of 0.01 MPa (Stein 1999). Coseismic Coulomb stress (ΔCFF(0)) due to the Iburi earthquake for a the northern, b southern, and c SI faults. For each fault, the top panel shows the ΔCFF(0) resolved onto the target fault. The bottom panel shows the ΔCFF(0) on the receiver faults, which are distributed on the X = 18 km plane (dotted line in the top panels), assumed to have identical source parameters as each target fault. The black, blue, and green rectangles indicate the geometry of the northern, southern, and SI faults, respectively. In each panel, the red rectangle and yellow star show the fault model and hypocenter of the Iburi earthquake, respectively. The black circle in the top panel of c indicates observation point I1 The development of viscoelastic deformation modifies the ΔCFF as time goes. Hereafter we refer to the postseismic change in ΔCFF after the mainshock, ΔCFF(t) − ΔCFF(0), as post-ΔCFF. Figure 6 shows the post-ΔCFF for t = 10 years; ΔCFF(10 year) − ΔCFF(0). Similar to the coseismic ΔCFF distribution, the distribution of the post-ΔCFF along the northern and southern faults show a similar pattern to each other. However, as shown by a comparison of the cross sections (Figs. 5, 6), the sign of the post-ΔCFF tends to be the opposite of the sign of ΔCFF(0) because the postseismic deformation relaxes the imposed coseismic strain in the viscoelastic region (Freed and Lin 1998; Freed 2005). Here, the postseismic stressing source seems to be the inelastic strain in the viscoelastic region (the region deeper than the dotted line in Fig. 6) around the deeper end of the Iburi earthquake fault, i.e., approximately 0 km < X < 40 km and − 10 km < Y < 30 km, where exhibits large post-ΔCFF value. This inelastic strain generates the positive post-ΔCFF in the shallow western part of the Iburi fault and negative post-ΔCFF in the shallow eastern part, in the cross-sectional view (Fig. 6a, b bottom). The northern and southern faults are adjacent to the boundary of the positive/negative post-ΔCFF values. Then, the value of the post-ΔCFF along the northern and southern faults is positive at shallower portions and negative at deeper portions, respectively (Fig. 6a, b top). For the SI fault, the entire fault is located in the positive lobe of the post-ΔCFF (Fig. 6c). Similar to Fig. 5 but shows the post-ΔCFF for 10 years following the Iburi earthquake; ΔCFF(10 year) − ΔCFF(0). Note that the color scale range is smaller than that in Fig. 5 by a factor of 5. In the top panels, the contour lines are shown for every 0.01 MPa. The dotted lines in the lower panels indicate the depth of elastic thickness (depthe). The black circles in the top panels of b, c indicate observation points S1–S3 and I1 In Fig. 7a (solid lines), we show the ΔCFF(t) at three points, S1, S2, and S3, on the southern fault, as indicated in Fig. 6b (black circles). These points are representative of the shallow, middle, and deep portions of the southern fault, respectively. At S3 (deep), the Iburi earthquake gives a positive ΔCFF(0) of 0.3109 MPa, which decreases by 0.0216 MPa (0.0339 MPa) during the 10 years (20 years) following the mainshock. At S1 (shallow), the ΔCFF(0) is 0.0901 MPa and further increases by 0.0122 MPa (0.0194 MPa) during the 10 years (20 years) following the mainshock. At both points, the post-ΔCFF for the 2 decades after the mainshock is one order of magnitude smaller than the coseismic ΔCFF. On the other hand, at S2 (middle), the ΔCFF(0) is − 0.1238 MPa, and ΔCFF does not change substantially after that (increase by only 0.0006 MPa during the 10 years following the mainshock). This negligible post-ΔCFF value is because S2 is located near node points, at which the post-ΔCFF value changes its sign (Fig. 6b bottom). Although we do not show the figure here, a similar Coulomb stress evolution was observed along the southern half of the northern fault. For the SI fault, the value of post-ΔCFF along the entire fault is always positive after the mainshock. The ΔCFF value at point I1 (Fig. 6c black circle) increases by 0.0165 MPa (0.0257 MPa) during the 10 years (20 years) after the coseismic ΔCFF value of 0.2270 MPa (Fig. 7b solid line). Similar to the points on the southern fault, the amount of post-ΔCFF for 2 decades after the mainshock is one order of magnitude smaller than that of coseismic ΔCFF. Time evolution of ΔCFF(t) at three points along the southern fault (S1–S3 in Fig. 6b) and the point along the SI fault (I1 in Fig. 6c). The solid and dashed lines indicate the cases for η = 1019 Pa s and 1020 Pa s, respectively In addition to the case of μ′ = 0.4 shown above, we also have examined the cases of μ′ = 0.1 and 0.7. The resultant distributions of coseismic and postseismic ΔCFF showed similar patterns to those in the case of μ′ = 0.4, and the magnitude of ΔCFF increased with increasing μ′. Variation in viscoelastic structure Prior to discussing the seismic potential of the target faults, we investigate the effect that viscoelastic structure uncertainty has on the computed Coulomb stress. In the previous section, we showed results for η = 1 × 1019 Pa s, though the representative viscosity of the lower crust is not well constrained. Iio et al. (2004) argued that viscosity in the lower crust is high, except for fault zones. Here, we computed the Coulomb stress for a scenarios with high viscosity, η = 1 × 1020 Pa s, to examine how viscosity influences our results. Dashed lines in Fig. 7a show the evolution of ΔCFF at the points S1–S3 on the southern fault. During the 10 years following the mainshock, the ΔCFF changes 0.0015 MPa at S1, − 0.0027 MPa at S2, and − 0.0003 MPa at S3, which amount is one order of magnitude smaller than the case of η = 1 × 1019 Pa s. Then, in the case of η = 1 × 1020 Pa s, the amount of post-ΔCFF for the 2 decades following the mainshock is two orders of magnitude smaller than that of coseismic ΔCFF, which suggests that the postseismic effects of triggering a rupture along the target faults, in the case of η = 1 × 1020 Pa s, will be small. This is the same for the SI fault (Fig. 7b). We note that the sense of the evolution of the ΔCFF does not change regardless of the viscosity value. We also computed ΔCFF(t) by assuming a 1-D viscoelastic structure to examine the effects of the 3-D structure. We specifically aimed to understand how a laterally homogeneous simple-layered model causes a bias in the estimation of the time-dependent Coulomb stress. For the 1-D structure, we set depthe(x) to 40.49 km, i.e., uniform throughout the entire area. We selected a value that is identical to the 3-D structure just below the hypocenter of the mainshock. Here, we ignore the plate subduction. For a scenario using the 1-D structure (1-D case), we set the viscoelastic region to 40.49 km < Z < 170.0 km. Figure 8a shows the post-ΔCFF for 10 years after the Iburi earthquake in the 1-D case. We observe quite similar post-ΔCFF to that in the 3-D case (Fig. 6b). Although we only show the southern fault, this trend is the same for the other target faults. The postseismic stressing source, which seems to locate approximately 0 km < X < 40 km and − 10 km < Y < 30 km, is also identical for the 3-D case. Similar post-ΔCFF distributions between the two cases are due to a comparable elastic thickness depthe of $\sim$ 40 km around the postseismic stressing source (Figs. 4b, 6). a Post-ΔCFF distribution for the southern fault calculated assuming the 1-D viscoelastic structure. See the captions of Figs. 5 and 6 for an explanation of the figure. b Surface deformation in the E–W direction (eastward positive) for 10 years following the Iburi earthquake. The top and bottom left panels show the calculated deformation patterns for the 3-D and 1-D viscoelastic structures, respectively. The right bottom panel also shows the computed E–W deformation assuming the 1-D viscoelastic structure but calculated using methods of Fukahata and Matsu'ura (2005, 2006) Figure 8b shows the postseismic deformation on the ground surface in the E–W direction during the 10 years following the mainshock for the 3-D (Fig. 8b top) and 1-D cases (bottom left). A large amount of deformation is observed above the Iburi earthquake fault and in the east side. The magnitude in the former case is approximately 0.6 times smaller than that in the latter case. However, the location of the area of large deformation does not differ substantially, and the stressing source area around 0 km < X < 40 km and − 10 km < Y < 30 km, same with that in the 3-D case, is also inferred. Then the bias due to assuming the 1-D structure appears small. This result does not assert that the 1-D structure assumption is always reasonable. It just happened that the influence on the target faults in the present study was small. Lastly, we show the results calculated using the method of Fukahata and Matsu'ura (2005, 2006), by assuming the same 1-D structure shown above to validate the results from our numerical code. We should note that the viscoelastic region in our method is set only in the limited region where viscoelastic cuboid cells were assigned. On the other hand, the case using Fukahata and Matsu'ura assumes a viscoelastic layer, which spreads infinitely in X, Y, and Z > depthe = 40.49 km. Therefore, strictly speaking, the viscoelastic structure differs in locations that are far from the mainshock fault. The surface deformation for the case using the method of Fukahata and Matsu'ura (Fig. 8b bottom right) is similar to that in our 1-D case (Fig. 8b bottom left), which demonstrates the validity of our numerical code. This result also indicates that the viscoelastic volumetric cells, set in our model, are sufficient to calculate the post-ΔCFF at least along the target faults. Evaluation of seismic potentials Our results indicate that the ΔCFF distribution varies even along each target fault. Along the southern fault, we observed the positive value of the coseismic ΔCFF in the deeper portion, suggesting that the portion is brought closer to the rupture due to the Iburi earthquake. The increases in the ΔCFF do not always indicate the immediate seismic triggering, even when enough stress for a rupture is imposed on the fault. This is because of a "delayed failure" nature of the rate- and state-dependent friction (Dieterich 1979), which is a more realistic friction than classic Coulomb friction. Though a large earthquake has not happened on the southern fault yet, after the mainshock, the positive value of the coseismic ΔCFF indicates a higher seismic risk for a certain period after the mainshock. Our calculation indicates that postseismic viscoelastic relaxation lowers the ΔCFF from the coseismic value. However, the risk of the delayed trigger of an earthquake remains for a certain period, because the magnitude of the stress decrease is insufficient to return the stress level to that before the Iburi earthquake, at least for a few decades after the Iburi earthquake. The middle portion of the fault was brought away from rupture just after the Iburi earthquake, because the value of the coseismic ΔCFF is negative, and this situation does not change for a few decades due to negligible changes in postseismic stress. The shallower portion of the southern fault has a positive coseismic ΔCFF value, which further increases after the mainshock because of viscoelastic relaxation. Therefore, the shallow portion was brought closer to rupture just after the mainshock, and seismic risk continuously increases for decades after the mainshock. These depth-dependent features are also true for the southern half of the northern fault. The coexistence of positive and negative ΔCFF values along a fault plane may influence the size of future earthquakes, depending on the role that negative stress regions play during dynamic rupture propagation. As previously mentioned in Introduction, the most recent event along the northern fault presumably occurred within a few hundred years or less. By taking into account the 1000–2000 year recurrence interval, Headquarters for Earthquake Research Promotion (2010) evaluated the probability of an earthquake within the next 30 years is nearly 0%. However, the paleoseismic data suggest that the most recent event is restricted to the central part of the northern fault and has not been found on the southern part where the ΔCFF values exceeded the earthquake triggering threshold. If the southern part of the fault remains unbroken, our results suggest that high seismic potential is left there, especially for moderate-sized earthquakes. As for the southern fault, we have no knowledge of an accurate recurrence interval and the elapsed time since the last event, which makes it difficult to evaluate the seismic potential of this fault. Nevertheless, this fault is one of the precaution faults considering that it has a high slip tendency under the present-day stress field (Fig. 3), and furthermore, it received large positive stress change as mentioned above. We conclude that the southern fault, as well as a part of the northern fault, is in a state that seismic risk has increased after the mainshock. In this study, we also focused on a previously unknown fault (SI fault), which was subject to the largest stress increase among the target faults. The most of the fault plane is brought close to failure by the coseismic stress change due to the mainshock, as well as by the postseismic stress change at least for a few decades after the mainshock. The location and geometry of the SI fault derive from aftershock distributions, where background seismicity was low. We note that the calculated ΔCFF is consistent with the activation of seismicity there. The ΔCFF value continues to increase over many years after the mainshock, which may imply a growing risk of seismic hazards along the SI fault. The empirical relationship between the rupture area and moment magnitude (Wells and Coppersmith 1994) indicates that the SI fault has the potential to produce an Mw ~ 7 earthquake. To evaluate the risk of the earthquake hazards in this region, it is necessary to take this previously unknown fault into consideration. Lastly, we comment about the seismic triggering threshold for postseismic stress change. The amount of the post-ΔCFF for 10 years after the mainshock is 0.0122 MPa at point S1 and 0.0165 MPa at point I1, both of which are greater than the seismic trigger threshold shown in Stein (1999), 0.01 MPa. We should note that this threshold is derived for the coseismic stress change. When we consider the rate- and state-dependent friction, if it takes time to increase the stress, the triggering effect will be smaller than that for an instantaneous increase. This is because friction strength can increase during this period via healing mechanisms. Although future studies are required to evaluate the triggering threshold for the postseismic stress change, we believe that the consideration of time-dependent stress change is crucial for evaluating seismic potential and reliable assessments of seismic hazard. We examined the seismic potential for the region around the 2018 Hokkaido Eastern Iburi earthquake (Iburi earthquake) fault, based on seismological analysis and numerical simulations. In the vicinity of the Iburi earthquake, there is an active fault zone known as the eastern boundary fault zone of the Ishikari lowland, which consists of the northern and southern faults. The shallow aftershock distribution also suggests the existence of a previously unknown fault (SI fault) at a shallower extension of the Iburi earthquake fault. In the present study, we focused on the evaluation of seismic potential of the SI fault, together with the northern and southern faults. The seismicity around the target faults was low before the Iburi earthquake. The focal mechanism solutions for the shallow aftershocks of the Iburi earthquake, which are located at a depth around the target faults, provide an opportunity to infer the present-day stress field. We estimated the stress field as ENE–SWS compressional, which is considered to be a consequence of westward migration of the Kuril Arc sliver and its collision with northeastern Japan. Slip tendency analysis indicates that all the target faults originally have high slip potential under the estimated present-day stress field. We then evaluated the potential for earthquake occurrence along the target faults affected by the Iburi earthquake. We calculated the time-dependent Coulomb stress (ΔCFF) due to the Iburi earthquake, taking into account postseismic viscoelastic relaxation with a 3-D viscoelastic structure. Note that the result shown in the present paper provides one possible scenario derived from a model that uses information currently available. After the mainshock, the viscoelastic deformation occurs in the viscoelastic layer around the deeper end of the Iburi earthquake fault to relax the imposed coseismic stress. The elastic thickness is almost uniform around there, so the biases in the estimation of ΔCFF when assuming a 1-D viscoelastic structure were small. The ΔCFF distribution along the southern fault and southern half of the northern fault had a similar depth-dependent pattern. The faults were brought closer to rupture just after the Iburi earthquake, which is indicated by the positive ΔCFF values, except for middle depths along the faults. The ΔCFF value increases in the shallow portion after the Iburi earthquake due to the postseismic process, suggesting a continuous stress build-up for many years following the mainshock. Although the ΔCFF value decreases in the deep portion as time goes on after the mainshock, it is insufficient to return the pre-shock stress level, at least for a few decades. These results suggest that the northern and southern faults are in a state of increasing seismic risk after the mainshock. The most of the SI fault was brought closer to rupture just after the mainshock, indicated by the positive ΔCFF values. This is consistent with the activation of seismicity in this region. The ΔCFF value continues to increase over many years following the mainshock, which may imply a growing seismic risk. It is, therefore, necessary to consider this previously unknown fault when evaluating future seismic risks in this region. All target faults experiences the postseismic positive ΔCFF changes for 2 decades following the Iburi earthquake, which is greater than the seismic triggering threshold (0.01 MPa). This result suggests that time-dependent changes in stress are crucial to evaluate seismic potential and have reliable assessments of seismic hazards, despite the need for more studies on the magnitude of triggering threshold. The seismic datasets used in this article are available on Hi-net (http://www.doi.org/10.17598/NIED.0003) from NIED. 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We used Japan Meteorological Agency (JMA) earthquake catalog. Seismic stations used in this study include permanent stations operated by Hokkaido University, the National Research Institute for Earth Science and Disaster Resilience (Hi-net), and JMA. We used "Slick Package" (http://earthquake.usgs.gov/research/software/) software coded by Andrew Michael for the stress tensor inversion. The figures were drawn using GMT (Wessel and Smith 1998). Geological Survey of Japan, AIST, Central 7, 1-1-1 Higashi, Tsukuba, Ibaraki, Japan Makiko Ohtani & Kazutoshi Imanishi Search for Makiko Ohtani in: Search for Kazutoshi Imanishi in: All authors designed the present study. KI performed stress analysis using seismic data and wrote "Slip tendency of the target faults under the present-day stress field" section of the manuscript. MO calculated the Coulomb stress and drafted the remaining parts of the manuscript. All authors discussed the results and contributed to the final manuscript. Both authors read and approved the final manuscript. This work was supported by JSPS KAKENHI Grant Number JP16K17789. Correspondence to Makiko Ohtani. Ethics declarations Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. 2018 Hokkaido Eastern Iburi earthquake Seismic potential Stress field estimation Time-dependent Coulomb stress Viscoelastic relaxation 4. Seismology The 2018 Hokkaido Eastern Iburi Earthquake and Hidaka arc-arc collision system	CommonCrawl
Selected articles from the IEEE International Conference on Bioinformatics and Biomedicine 2015: genomics Efficient sequential and parallel algorithms for finding edit distance based motifs Soumitra Pal1, Peng Xiao1 & Sanguthevar Rajasekaran2 Motif search is an important step in extracting meaningful patterns from biological data. The general problem of motif search is intractable and there is a pressing need to develop efficient, exact and approximation algorithms to solve this problem. In this paper, we present several novel, exact, sequential and parallel algorithms for solving the (l,d) Edit-distance-based Motif Search (EMS) problem: given two integers l,d and n biological strings, find all strings of length l that appear in each input string with atmost d errors of types substitution, insertion and deletion. One popular technique to solve the problem is to explore for each input string the set of all possible l-mers that belong to the d-neighborhood of any substring of the input string and output those which are common for all input strings. We introduce a novel and provably efficient neighborhood exploration technique. We show that it is enough to consider the candidates in neighborhood which are at a distance exactly d. We compactly represent these candidate motifs using wildcard characters and efficiently explore them with very few repetitions. Our sequential algorithm uses a trie based data structure to efficiently store and sort the candidate motifs. Our parallel algorithm in a multi-core shared memory setting uses arrays for storing and a novel modification of radix-sort for sorting the candidate motifs. The algorithms for EMS are customarily evaluated on several challenging instances such as (8,1), (12,2), (16,3), (20,4), and so on. The best previously known algorithm, EMS1, is sequential and in estimated 3 days solves up to instance (16,3). Our sequential algorithms are more than 20 times faster on (16,3). On other hard instances such as (9,2), (11,3), (13,4), our algorithms are much faster. Our parallel algorithm has more than 600 % scaling performance while using 16 threads. Our algorithms have pushed up the state-of-the-art of EMS solvers and we believe that the techniques introduced in this paper are also applicable to other motif search problems such as Planted Motif Search (PMS) and Simple Motif Search (SMS). Motif search has applications in solving such crucial problems as identification of alternative splicing sites, determination of open reading frames, identification of promoter elements of genes, identification of transcription factors and their binding sites, etc. (see e.g., Nicolae and Rajasekaran [1]). There are many formulations of the motif search problem. A widely studied formulation is known as (l,d)-motif search or Planted Motif Search (PMS) [2]. Given two integers l,d and n biological strings the problem is to find all strings of length l that appear in each of the n input strings with atmost d mismatches. There is a significant amount of work in the literature on PMS (see e.g., [1, 3–5], and so on). PMS considers only point mutations as events of divergence in biological sequences. However, insertions and deletions also play important roles in divergence [2, 6]. Therefore, researchers have also considered a formulation in which the Levenshtein distance (or edit distance), instead of mismatches, is used for measuring the degree of divergence [7, 8]. Given n strings S (1),S (2),…,S (n), each of length m from a fixed alphabet Σ, and integers l,d, the Edit-distance-based Motif Search (EMS) problem is to find all patterns M of length l that occur in atleast one position in each S (i) with an edit distance of atmost d. More formally, M is a motif if and only if ∀i, there exist k∈ [ l−d,l+d],j∈ [ 1,m−k+1] such that for the substring $S^{(i)}_{j,k}$ of length k at position j of S (i), $ED\left (S^{(i)}_{j,k},M\right) \le d$. Here E D(X,Y) stands for the edit distance between two strings X and Y. EMS is also NP-hard since PMS is a special case of EMS and PMS is known to be NP-hard [9]. As a result, any exact algorithm for EMS that finds all the motifs for a given input can be expected to have an exponential (in some of the parameters) worst case runtime. One of the earliest EMS algorithms is due to Rocke and Tompa [7] and is based on Gibbs Sampling which requires repeated searching of the motifs in a constantly evolving collection of aligned strings, and each search pass requires O(n l) time. This is an approximate algorithm. Sagot [8] gave a suffix tree based exact algorithm that takes O(n 2 m l d\|Σ\|d) time and O(n 2 m/w) space where w is the word length of the computer. Adebiyi and Kaufmann [10] proposed an exact algorithm with an expected runtime of O(n m+d(n m)(1+pow(ε)) logn m) where ε=d/l and p o w(ε) is an increasing concave function. The value of p o w(ε) is roughly 0.9 for protein and DNA sequences. Wang and Miao [11] gave an expectation minimization based heuristic genetic algorithm. Rajasekaran et al. [12] proposed a simpler Deterministic Motif Search (DMS) that has the same worst case time complexity as the algorithm by Sagot [8]. The algorithm generates and stores the neighborhood of every substring of length in the range [l−d,l+d] of every input string and using a radix sort based method, outputs the neighbors that are common to atleast one substring of each input string. This algorithm was implemented by Pathak et al. [13]. Following a useful practice for PMS algorithms, Pathak et al. [13] evaluated their algorithm on certain instances that are considered challenging for PMS: (9,2), (11,3), (13,4) and so on [1], and are generated as follows: n=20 random DNA/protein strings of length m=600, and a short random string M of length l are generated according to the independent identically distributed (i.i.d) model. A separate random d-hamming distance neighbor of M is "planted" in each of the n input strings. Such an (l,d) instance is defined to be a challenging instance if l is the largest integer for which the expected number of spurious motifs, i.e., the motifs that would occur in the input by random chance, is atleast 1. The expected number of spurious motifs in EMS are different from those in PMS. Table 1 shows the expected number of spurious motifs for l∈ [ 5,21] and d upto max{l−2,13}, n=20, m=600 and Σ={A,C,G,T} [see Additional file 1]. The challenging instances for EMS turn out to be (8,1), (12,2), (16,3), (20,4) and so on. To compare with [13], we consider both types of instances, specifically, (8,1), (9,2), (11,3), (12,2), (13,4) and (16,3). Table 1 Expected number of spurious motifs in random instances for n=20,m=600. Here, ∞ represents value ≥1.0e+7 The sequential algorithm by Pathak et al. [13] solves the moderately hard instance (11,3) in a few hours and does not solve the next difficult instance (13,4) even after 3 days. A key time-consuming part of the algorithm is in the generation of the edit distance neighborhood of all substrings as there are many common neighbors. In this paper we present several improved algorithms for EMS that solve instance (11,3) in less than a couple of minutes and instance (13,4) in less than a couple of hours. On (16,3) our algorithm is more than 20 times faster than EMS1. Our algorithm uses an efficient technique (introduced in this paper) to generate the edit distance neighborhood of length l with distance atmost d of all substrings of an input string. Our parallel algorithm in the multi-core shared memory setting has more than 600 % scaling performance on 16 threads. Our approach uses following five ideas which can be applied to other motif search problems as well: Efficient neighborhood generation: We show that it is enough to consider the neighbors which are at a distance exactly d from all possible substrings of the input strings. This works because the neighbors at a lesser distance are also included in the neighborhood of some other substrings. Compact representation using wildcard characters: We represent all possible neighbors which are due to an insertion or a substitution at a position by a single neighbor using a wildcard character at the same position. This compact representation of the candidate motifs in the neighborhood requires less space. Avoiding duplication of candidate motifs: Our algorithm uses several rules to avoid duplication in candidate motifs and we prove that our technique generates neighborhood that is nearly duplication free. In other words, our neighborhood generation technique does not spend a lot of time generating neighbors that have already been generated. Trie based data structure for storing compact motifs: We use a trie based data structure to efficiently store the neighborhood. This not only simplifies the removal of duplicate neighbors but also helps in outputting the final motifs in sorted order using a depth first search traversal of the trie. Modified radix-sort for compact motifs: Our parallel algorithm stores the compact motifs in an array and uses a modified radix-sort algorithm to sort them. Use of arrays instead of tries simplifies updating the set of candidate motifs by multiple threads. In this section we introduce some notations and observations. An (l,d)-friend of a k-mer L is an l-mer at an exact distance of d from L. Let F l,d (L) denote the set of all (l,d)-friends of L. An (l,d)-neighbor of a k-mer L is an l-mer at a distance of atmost d from L. Let N l,d (L) denote the set of all (l,d)-neighbors of L. Then $$\begin{array}{{20}l} N_{l,d}(L) = \cup_{t = 0}^{d} F_{l,t}(L). \end{array} $$ For a string S of length m, an (l,d)-motif of S is an l-mer at a distance atmost d from some substring of S. Thus an (l,d)-motif of S is an (l,d)-neighbor of atleast one substring S j,k =S j S j+1…S j+k−1 where k∈[l−d,l+d]. Therefore, the set of (l,d)-motifs of S, denoted by M l,d (S), is given by $$\begin{array}{{20}l} M_{l,d}(S) = \cup_{k=l-d}^{l+d} \cup_{j=1}^{m-k+1} N_{l,d}(S_{j,k}). \end{array} $$ For a collection of strings $\mathcal {S} = \{S^{(1)}, S^{(2)}, \ldots, S^{(m)}\}$, a (common) (l,d)-motif is an l-mer at a distance atmost d from atleast one substring of each S (i). Thus the set of (common) (l,d)-motifs of $\mathcal {S}$, denoted by $M_{l,d}(\mathcal {S})$, is given by $$\begin{array}{{20}l} M_{l,d}(\mathcal{S}) = \cap_{i=1}^{n} M_{l,d}(S^{(i)}). \end{array} $$ One simple way of computing F l,d (L) is to grow the friendhood of L by one distance at a time for d times and to select only the friends having length l. Let G(L) denote the set of strings obtained by one edit operation on L and $G(\{L_{1}, L_{2}, \ldots, L_{r}\}) = \cup _{t=1}^{r} G(L_{t})$. If G 1(L)=G(L), and for t>1, G t(L)=G(G t−1(L)) then $$\begin{array}{{20}l} F_{l,d}(L) = \{x \in G^{d}(L) : \|x\| = l\}. \end{array} $$ Using Eqs. (1), (2), (3) and (4), Pathak et al. [13] gave an algorithm that stores all possible candidate motifs in an array of size \|Σ\|l. However the algorithm is inefficient in generating the neighborhood as the same candidate motif is generated by several combinations of the basic edit operations. Also, the O(\|Σ\|l) memory requirement makes the algorithm inapplicable for larger instances. In this paper we mitigate these two limitations. Efficient neighborhood generation We now give a more efficient algorithm to generate the (l,d)-neighborhood of all possible k-mers of a string. Instead of computing (l,t)-friendhood for all 0≤t≤d, we compute only the exact (l,d)-friendhood. Lemma 1. $M_{l,d}(S) = \cup _{k=l-d}^{l+d} \cup _{j=1}^{m-k+1} F_{l,d}(S_{j,k})$. Proof. Consider the k-mer L=S j,k . If k=l+d then we need d deletions to make L an l-mer. There cannot be any (l,t)-neighbor of L for t<d. Thus $$\begin{array}{{20}l} \cup_{t = 0}^{d} F_{l,t}(S_{j,l+d}) = F_{l,d}(S_{j,l+d}). \end{array} $$ Suppose k<l+d. Any (l,d−1)-neighbor B of L is also an (l,d)-neighbor of L ′=S j,k+1 because E D(B,L ′)≤E D(B,L)+E D(L,L ′)≤(d−1)+1=d. Thus $$\begin{array}{{20}l} \cup_{t=0}^{d} F_{l,t}(S_{j,k}) \subseteq F_{l,d}(S_{j,k}) \bigcup \cup_{t=0}^{d} F_{l,t}(S_{j,k+1}) \end{array} $$ which implies that $$\begin{array}{{20}l} \cup_{r=k}^{k{+}1}\cup_{t{=}0}^{d} F_{l,t}(S_{j,r}) = F_{l,d}(S_{j,k}) \bigcup \cup_{t=0}^{d} F_{l,t}(S_{j,k{+}1}). \end{array} $$ Applying (6) repeatedly for k=l−d,l−d+1,…,l+d−1, along with (5) in (1) and (2) gives the result of the lemma. We generate F l,d (S j,k ) in three phases: we apply δ deletions in the first phase, β substitutions in the second phase, and α insertions in the final phase, where d=δ+α+β and l=k−δ+α. Solving for α,β,δ gives max{0,q}≤δ≤(d+q)/2, α=δ−q and β=d−2δ+q where q=k−l. In each of the phases, the neighborhood is grown by one edit operation at a time. Compact motifs The candidate motifs in F l,d (S j,k ) are generated in a compact way. Instead of inserting each character in Σ separately at a required position in S j,k , we insert a new character ∗∉Σ at that position. Similarly, instead of substituting a character σ∈S j,k by each σ ′∈Σ∖{σ} separately, we substitute σ by ∗. The motifs common to all strings in $\mathcal {S}$ is determined by using the usual definition of union and the following definition of intersection on compact strings A,B∈(Σ∪{∗})l in (3): $$\begin{array}{@{}rcl@{}} \arraycolsep=1pt A {\cap} B = \left\{ \begin{array}{ll} \emptyset & \text{if}~ \exists j~\text{s.t.}~A_{j}, B_{j} \in \Sigma, A_{j} \ne B_{j}\\ \sigma_{1}\sigma_{2}\ldots \sigma_{l} & \text{else, where}~\sigma_{j} = \left\{ \begin{array}{ll} b_{j} & \text{if}~a_{j} {=} \\ a_{j} & \text{if}~b_{j} {=} *. \end{array} \right. \end{array} \right. \end{array} $$ Trie for storing compact motifs We store the compact motifs in a trie based data structure which we call a motif trie. This helps implement the intersection defined in (7). Each node in the motif trie has atmost \|Σ\| children. The edges from a node u to its children v are labeled with mutually exclusive subsets l a b e l(u,v)⊆Σ. An empty set of compact motifs is represented by a single root node. A non-empty trie has l+1 levels of nodes, the root being at level 0. The trie stores the l-mer σ 1 σ 2…σ l , all σ j ∈Σ, if there is a path from the root to a leaf where σ j appears in the label of the edge from level j−1 to level j. For each string $S=\mathcal {S}^{(i)}$ we keep a separate motif trie M (i). Each compact neighbor A∈F l,d (S j,k ) is inserted into the motif trie recursively as follows. We start with the root node where we insert A 1 A 2…A l . At a node u at level j where the prefix A 1 A 2…A j−1 is already inserted, we insert the suffix A j A j+1…A l as follows. If A j ∈Σ we insert A ′=A j+1 A j+2…A l to the children v of u such that A j ∈l a b e l(u,v). If l a b e l(u,v)≠{A j }, before inserting we make a copy of subtrie rooted at v. Let v ′ be the root of the new copy. We make v ′ a new child of u, set l a b e l(u,v ′)={A j }, remove A j from l a b e l(u,v), and insert A ′ to v ′. On the other hand if A j =∗ we insert A ′ to each children of u. Let T=Σ if A j =∗ and T={A j } otherwise. Let R=T∖∪ v l a b e l(u,v). If T≠∅ we create a new child v ′ of u, set l a b e l(u,v ′)=R and recursively insert A ′ to v ′. Figure 1 shows examples of inserting into the motif trie. Inserting into motif trie for Σ={A,C,G,T} and l=3. a After inserting ∗G T into empty trie. b After inserting another string A∗C We also maintain a motif trie $\mathcal {M}$ for the common compact motifs found so far, starting with $\mathcal {M} = M^{(1)}$. After processing string S (i) we intersect the root of M (i) with the root of $\mathcal {M}$. In general a node u 2∈M (i) at level j is intersected with a node $u_{1} \in \mathcal {M}$ at level j using the procedure shown in Algorithm 1. Figure 2 shows an example of the intersection of two motif tries. Intersection of motif tries. a Trie for A G∗∪C∗T. b Intersection of trie in Fig. 1 b and trie in Fig. 2 a The final set of common motifs is obtained by a depth-first traversal of $\mathcal {M}$ outputting the label of the path from the root whenever a leaf is traversed. An edge (u,v) is traversed separately for each σ∈l a b e l(u,v). Efficient compact neighborhood generation A significant part of the time taken by our algorithm is in inserting compact neighbors into the motif trie as it is executed for each neighbor in the friendhood. Our efficient neighborhood generation technique and the use of compact neighbors reduce duplication in neighborhood but do not guarantee completely duplication free neighborhood. In this section, we design few simple rules to reduce duplication further. Later we will see that these rules are quite close to the ideal as we will prove that the compact motif generated after skipping using the rules, are distinct if all the characters in the input string are distinct. To differentiate multiple copies of the same compact neighbor, we augment it with the information about how it is generated. This information is required only in the proof and is not used in the actual algorithm. Formally, each compact neighbor L of a k-mer S j,k is represented as an ordered tuple 〈S j,k ,T〉 where T denotes the sequence of edit operations applied to S j,k . Each edit operation in T is represented as a tuple 〈p,o〉 where p denotes the position (as in S) where the edit operation is applied and o∈{D,R,I} denotes the type of the operation – deletion, substitution and insertion, respectively. At each position there can be one deletion or one substitution but one or more insertions. The tuples in T are sorted lexicographically with the natural order for p and for o, D<R<I. The rules for skipping compact neighbors are given in Table 2. Rule 1 applies when S j,k is not the rightmost k-mer and the current edit operation deletes the leftmost base of S j,k , i.e., S j . Rule 2 applies when the current edit operation substitutes a base just after a base that was already deleted. Rule 3 skips the neighbor which is generated from a k-mer except the rightmost by deleting a base and substituting all bases before it. Rules 4–9 apply when the current operation is an insertion. Rule 4,6 apply when the insertion is just before a deletion and a substitution, respectively. Rule 5 applies when the insertion is just after a deletion. Rule 7,8 apply when the k-mer is not the leftmost. Rule 7 applies when the insertion is at the leftmost position and Rule 8 applies when all bases before the position of insertion are already substituted. Rule 9 applies when the k-mer is not the rightmost and the insertion is at the right end. The first in each pair of the figures in Fig. 3 illustrates the situation where the corresponding rule applies. Construction of L ′ under different rules in the proof of Lemma 2. Insertions are shown using arrows, deletions using − and substitutions using ∗. Rule 5 case (i) is similar to Rule 4 case (i) Table 2 Conditions for skipping motif L=〈M,S j,k ,T〉 Let $\bar {M}_{l,\,d}(S)$ denote the multi-set of tuples for the compact motifs of S that were not skipped by our algorithm using the rules in Table 2 and M l, d (S) be the set of compact motifs generated by (3). Let Γ(〈S j, k ,T〉) be the resulting string when the operations in T are applied to S j, k and Γ(Z)=∪ L∈Z Γ(L). $\Gamma (\bar {M}_{l,d}(S)) = M_{l,d}(S)$. By construction, $\Gamma (\bar {M}_{l,d}(S)) \subseteq M_{l,d}(S)$. We show $M_{l,d}(S) \subseteq \Gamma (\bar {M}_{l,d}(S))$ by giving a contradiction when $M_{l,d}(S) \setminus \Gamma (\bar {M}_{l,d}(S)) \ne \emptyset $. We define an order on the compact neighbors $\phantom {\dot {i}\!}L_{1} = \langle {S_{j_{1},k_{1}}, T_{1}}\rangle $ and $\phantom {\dot {i}\!}L_{2} = \langle {S_{j_{2},k_{2}}, T_{2}}\rangle $ as follows: L 1<L 2 if Γ(L 1)<Γ(L 2) and L 2<L 1 if Γ(L 2)<Γ(L 1). When Γ(L 1)=Γ(L 2) we have L 1<L 2 if and only if (k 1<k 2)∨((k 1=k 2)∧(p 1<p 2))∨((k 1=k 2)∧(p 1=p 2)∧(o 1<o 2)) where 〈p 1,o 1〉∈T 1,〈p 2,o 2〉∈T 2 are the leftmost edit operations where T 1,T 2 differ. Suppose $M \in M_{l,d}(S) \setminus \Gamma (\bar {M}_{l,d}(S))$. Let L=〈S j, k ,T〉 be the largest (in the order defined above) tuple skipped by our algorithm such that Γ(L)=M. For each r=1,…,9 we show a contradiction that if L is skipped by Rule r then there is another $\phantom {\dot {i}\!}L'=\langle {S_{j',\,k'},T'}\rangle $ with the same number of edit operations and Γ(L ′)=M but L<L ′. Figure 3 illustrates the choice of L ′ under different rules. Rule 1. Here j+k≤m and 〈j,D〉∈T. Consider T ′=(T∖{〈j,D〉})∪{j+k,D}, and j ′=j+1,k ′=k. Rule 2. Consider T ′=T∖{〈j+t,D〉,〈j+t+1,R〉}∪{〈j+t,R〉,〈j+t+1,D〉}, and j ′=j,k ′=k. Rule 3. T ′=T∖{〈j,R〉,〈j+t+1,D〉}∪{〈j+t+1,R〉,〈j+k,D〉}, j ′=j+1,k ′=k. Rule 4. For this and subsequent rules k<l+d as there is atleast one insertion and hence k ′ could possibly be equal to k+1. We consider two cases. Case (i) j+k≤m: T ′=T∖{〈j+t,D〉,〈j+t,I〉}∪{〈j+t,R〉,〈j+k,D〉}, j ′=j,k ′=k+1. Case (ii) j+k=m+1: Here deletion of S j is allowed by Rule 1. T ′=T∖{〈j+t,D〉,〈j+t,I〉}∪{〈j−1,D〉,〈j+t,R〉}, j ′=j−1,k ′=k+1. Rule 5. The same argument for Rule 4 applies considering 〈j+t+1,I〉 instead of 〈j+t,I〉. Rule 6. T ′=T∖{〈j+t,I〉}∪{〈j+t+1,I〉}, and j ′=j,k ′=k. Rule 7. T ′=T∖{〈j,I〉}∪{〈j−1,R〉}, j ′=j−1,k ′=k+1. Rule 8. T ′=T∖{〈j+t,I〉}∪{〈j−1,R〉}, j ′=j−1,k ′=k+1. Rule 9. T ′=T∖{〈j+k,I〉}∪{〈j+k,R〉}, j ′=j,k ′=k+1. Consider two compact motifs $\phantom {\dot {i}\!}M_{1} = \langle {S_{j_{1},k_{1}}, T_{1}}\rangle $ and $\phantom {\dot {i}\!}M_{2} = \langle {S_{j_{2},k_{2}}, T_{2}}\rangle $ in $\bar {M}_{l,d}(S)$. For q∈{1,2}, let $\left \langle {p_{q}^{(1)}, o_{q}^{(1)}}\right \rangle, \left \langle {p_{q}^{(2)}, o_{q}^{(2)}}\right \rangle, \ldots, \left \langle {p_{q}^{(d)}, o_{q}^{(d)}}\right \rangle $ be the sequence of edit operations in T q arranged in the order as the neighbors are generated by our algorithm, and the intermediate neighbors be $L_{q}^{(h)} = \left \langle S_{j_{q},k_{q}}, \left \{\left \langle {p_{q}^{(1)}, o_{q}^{(1)}}\right \rangle,\right.\right.\left.\left. \left \langle {p_{q}^{(2)}, o_{q}^{(2)}}\right \rangle, \ldots, \left \langle {p_{q}^{(h)}, o_{q}^{(h)}}\right \rangle \right \} \right \rangle $ for all h=1,2,…,d. We also denote the initial k-mer as a neighbor $L_{q}^{(0)} = \langle {S_{j_{q},k_{q}}, \emptyset }\rangle $. If S j s are all distinct and $\Gamma \left (L_{1}^{(h)}\right) = \Gamma \left (L_{2}^{(h)}\right)$ for 1≤h≤d then $\left \langle {p_{1}^{(h)}, o_{1}^{(h)}}\right \rangle = \left \langle {p_{2}^{(h)}, o_{2}^{(h)}}\right \rangle $ and $\Gamma \left (L_{1}^{(h-1)}\right) = \Gamma \left (L_{2}^{(h-1)}\right)$. To simplify the proof, we use p q ,o q ,L q to denote $p_{q}^{(h)}, o_{q}^{(h)}, L_{q}^{(h)}$, respectively, for all q∈{1,2}. Without loss of generality we assume p 1≤p 2. As p 1,p 2 are positions in S, it would be enough to prove 〈p 1,o 1〉=〈p 2,o 2〉 because that would imply $\Gamma \left (L_{1}^{(h-1)}\right) = \Gamma \left (L_{2}^{(h-1)}\right)$. If 〈p 1,o 1〉≠〈p 2,o 2〉 then either (a) o 1=o 2 and p 1<p 2 or (b) o 1≠o 2 and p 1≤p 2, giving us the following 9 possible cases. We complete the proof by giving a contradiction in each of these 9 cases: 1 D D p 1<p 2 4 R D p 1≤p 2 7 I D p 1≤p 2 2 D R p 1≤p 2 5 R R p 1<p 2 8 I R p 1≤p 2 3 D I p 1≤p 2 6 R I p 1≤p 2 9 I I p 1<p 2 Cases 2, 3, 4, 7 Our algorithm applies edit operations in phases: first deletions, followed by substitutions and finally insertions. In all these cases, one of Γ(L 1),Γ(L 2) does not have any ∗ because only deletions have been applied so far and the other has at least one ∗ because a substitution or an insertion has been applied. This implies Γ(L 1)≠Γ(L 2), a contradiction. L 2 has $S_{p_{2}}$ deleted. As Γ(L 1)=Γ(L 2), $S_{p_{2}}$ must have been deleted in some operation prior to reaching L 1. As the deletions are applied in order, left to right, we must have p 1=p 2 which is a contradiction. This case has been illustrated in Fig. 4 a. L 1 has no substitution at a position >p 1 and no insertion at all. The ∗ at p 2 in L 2 must be matched with the ∗ at p 1 in L 1 and as the characters in S are distinct, all of $S_{p_{1}+1},\ldots,S_{p_{2}}$ cannot appear in L 1 and hence must be deleted in L 1. Proof of uniqueness (Lemma 2). Subfigures a,b,c,d illustrates the cases 5,6,7,8,9 respectively Now for each t<p 1, right to left, and y=t+p 2−p 1, we have the following: S y is either deleted or substituted in L 1, which implies that S y must be substituted in L 2 as the deletion of S y in L 2 is prohibited by Rule 2, and finally to match this ∗ in L 2, S t must be substituted in L 1 as S t cannot be deleted in L 1, again by Rule 2. But this makes Rule 3 applicable to L 1 and L 1 must have been skipped. This is a contradiction. By Rule 9 the insertion in L 2 cannot be at the rightmost position and hence L 2 must have at least one character after the insertion. By Rules 4 and 6, $S_{p_{2}}$ must not be deleted or substituted in L 2 and hence it must not be deleted or substituted in L 1 either. Thus p 1<p 2. There cannot be any insertion or substitution at a position >p 1 in L 1. Thus the ∗ due to the insertion at p 2 in L 2 must be matched by the ∗ due to the substitution at p 1 in L 1 and all of $S_{p_{1}+1},\ldots,S_{p_{2}-1}$ must be deleted in L 1. By Rule 7, $S_{p_{2}}$ cannot be the leftmost in $S_{j_{2},k_{2}}$. So we consider $S_{p_{2}-1}$ in L 1,L 2. It is either deleted or substituted in L 1 and hence by Rule 5, it must be substituted in $S_{p_{2}}$ (there can be multiple insertions at p 2 in L 2 but that does not affect this argument). To match this ∗, $S_{p_{1}-1}$ must be substituted in L 1. Using a similar argument as in Case 5, S t must be substituted in L 1 for each t<p 1−1. But this again makes Rule 3 applicable to L 1 and L 1 must have been skipped, which is not possible. This case has been illustrated in Fig. 4 b. Due to Rules 4, 6 and 9, $S_{p_{1}}$ must not be deleted or substituted in L 1 and hence it must not be deleted or substituted in L 2 either. Thus p 1<p 2. The ∗ due to the insertion in L 1 must be matched by a substitution at p 3<p 1 such that all of $S_{p_{3}+1}, \dots, S_{p_{1}-1}$ are deleted in L 2. By Rule 7, p 1 cannot be the leftmost in L 1. For each t<p 1, right to left, and y=t+p 3−p 1, we have the following: S y is substituted in L 1 because as the deletion of S y in L 1 is prohibited by Rules 2 and 5, S y must be substituted in L 2 again by Rule 2, and to match this ∗, S t must be substituted in L 1. But this makes Rule 8 applicable to L 1 and L 1 must have been skipped which is not possible. This case has been illustrated in Fig. 4 c. This case has been illustrated in Fig. 4 d. Due to Rules 4, 6 and 9, $S_{p_{1}},S_{p_{2}}$ must not be deleted or substituted in L 1,L 2. The insertion at p 2 in L 2 must be matched by a substitution at a position p 3 in L 1 such that p 1<p 3<p 2 and all of $S_{p_{3}+1},\ldots,S_{p_{2}-1}$ must be deleted in L 1. Now for each position y, from right to left, where p 1<y<p 2, S y is either deleted or substituted in S 1, S y cannot be deleted in L 2 by Rules 2 and 5 and hence must be substituted in L 2, which again must be matched by a substitution at a position t in L 1 such that p 1<t<p 3. However this is impossible as the number of possible ys is larger than the number of possible ts. If all S j s are distinct and Γ(M 1)=Γ(M 2) then applying Lemma 3 repeatedly for h=d,d−1,…,0 gives us the fact that starting k-mers $S_{j_{1},k_{1}},S_{j_{2},k_{2}}$ as well as the corresponding edit operations in T 1,T 2 for M 1,M 2 must be the same. This is another way of stating the following theorem. Theorem 1. If S j s are all distinct then $\bar {M}_{l,d}(S)$ is duplication free. In general S j s are not distinct. However, as the input strings are random, the duplication due to repeated characters are limited. On instance (11,3) our algorithm generates each compact motif, on an average, 1.55 times using the rules compared to 3.63 times without the rules (see Fig. 5). Histogram of number of times a motif is repeated with and without using the skipping rules 1–9 Implementation To track the deleted characters, instead of actually deleting we substitute them by a new symbol − not in Σ ′. We populate the motif trie M (i) by calling g e n A l l(S (i)) given in Algorithm 2. Rules 1–8 are incorporated in G(L,j,δ,β,α), H(L,j,β,α) and I(L,j,α) which are shown in Algorithms 3, 4, and 5, respectively where s u b(L,j,σ) substitutes L j by σ and i n s(L,j,σ) inserts σ just before L j . Modified radix-sort for compact motifs A simpler data structure alternative to tries for storing compact motifs could be an array. However, it becomes difficult to compute the intersection in (3) as defined in (7) when the compact motifs are stored in arrays. One straight-forward solution is to first expand the ∗s in the compact motifs, then sort the expanded motifs and finally compute the intersection by scanning through the two sorted arrays. This, to a great extent, wipes out the advantage using the ∗s in the compact motifs. However, we salvage execution time by executing a modified radix-sort that simultaneously expands and sorts the array of compact motifs: Compact-Radix-Sort(A,l) where the first parameter A represents the array of compact motifs and the second parameter represents the number of digits of the elements in A which is equal to the number of base positions l in a motif. As in the standard radix-sort, our algorithm uses l phases, one for each base position in the motif. In the ith phase it sorts the motifs using bucket sort on the ith base of the motifs. However, in case of compact motifs, for each ∗ at a base position, the bucket counters for all σ∈Σ are incremented. While reordering the motifs as per the bucket counts, if there is a ∗ at ith base position of a motif, \|Σ\| copies of the motif are created and they are placed at appropriate locations in the array after finalizing the correct σ for the ∗. The details are given in Algorithm 6. In each phase a bucket counter B and a cumulative counter C are used. The temporary array T stores the partially expanded motifs from the current phase. Discussion We did an experiment to compare the time taken by the two approaches – (i) using the expanded motifs, i.e., without using the wildcard character, and (ii) using compact motifs and sorting them using Compact-Radix-Sort. For a single input string of instance (16,3), the first approach generated in 24.4 s 198,991,822 expanded motifs in which 53,965,581 are unique. The second approach generated in 13.7 s 11,474,938 compact motifs with the same number of unique expanded motifs. This shows the effectiveness of the second approach. We now give our parallel algorithm in the multi-core shared memory setting. To process each input sequence S (i) the algorithm uses p+1 threads. The main thread first prepares the workload for other p threads. A workload involves the generation of the neighborhood for a k-mer of S (i), where l−d≤k≤l+d. There are total $\sum _{k=l-d}^{l+d} (m-k+1) = (2d+1)(m-l+1)$ workloads. The number of neighbors generated in the workloads are not the same due to the skipping of some neighbors using rules 1–9. For load balancing, we randomly and evenly distribute workloads to threads. Each thread first generates all the compact motifs in its workloads and then sort them using Compact-Radix-Sort. If i>2 then it removes all neighbors not present in M (i−1) which is the set of common motifs of S (1),S (2),…,S (i−1). The master thread then merges the residue candidate motifs from all the p threads to compute M (i). The merging takes place in log2p phases in a binary tree fashion where the jth phase uses $2^{\log _{2}{p} - j}$ threads each merging two sorted arrays of motifs. We implemented our algorithms in C++ and evaluated on a Dell Precisions Workstation T7910 running RHEL 7.0 on two sockets each containing 8 Dual Intel Xeon Processors E5-2667 (8C HT, 20 MB Cache, 3.2 GHz) and 256 GB RAM. For our experiments we used only one of the two sockets. We generated random (l,d) instances according to Pevzner and Sze [2] and as described in the background section. For every (l,d) combination we report the average time taken by 4 runs. We compare the following four implementations: EMS1: A modified implementation of the algorithm in [13] which considered the neighborhood of only l-mers whereas the modified version considers the neighborhood of all k-mers where l−d≤k≤l+d. EMS2: A faster implementation of our sequential algorithm which uses tries for storing candidate motifs where each node of the trie stores an array of pointers to each children of the node. However, this makes the space required to store a tree node dependent on the size of the alphabet Σ. EMS2M: A slightly slower but memory efficient implementation of our sequential algorithm where each node of the trie keeps two pointers: one to the leftmost child and the other to the immediate right sibling. Access to the other children are simulated using the sibling pointers. EMS2P: Our parallel algorithm which uses arrays for storing motifs. We experimented with p=1,2,4,8,16 threads. We run the four algorithms on the challenging instances (8,1), (12,2), (16,3) and on the instances (9,2), (11,3), (13,4) which are challenging for PMS and have been used for experimentation in [13]. We report the runtime and the memory usage of the four algorithms in Table 3. Table 3 Comparison between EMS1 and three implementations of EMS2 Our efficient neighborhood generation enables our algorithm to solve instance (13,4) in less than two hours which EMS1 could not solve even in 3 days. The factor by which EMS2 takes more memory compared to EMS1 gradually decreases as instances become harder. As EMS2 stores 4 child pointers for A,C,G,T in each node of the motif trie whereas EMS2M simulates access to children using only 2 pointers, EMS2 is faster. Memory reduction in EMS2M is not exactly by a factor 2(=4/2) because we also keep a bit vector in each node to represent the subset of {A,C,G,T} a child corresponds to. The memory reduction would be significant for protein strings. Our parallel algorithm EMS2P using one thread is significantly faster than the sequential algorithms EMS2 and EMS2M but uses more memory. This space-time trade off is due to the fact that the arrays are faster to access but the tries use lesser memory. Moreover, the repeated motifs are uniquely stored in a single leaf node in the trie but stored separately in the array. The scaling performance using multiple threads are shown in Fig. 6 where we plot the ratio of time taken by p threads to the time taken by a single thread on the Y-axis. The time required for handling 16 threads turns out to be costlier than actually processing the motifs in the smallest instance (8,1). We observe speed up consistent across other bigger instances. For example, instance (16,3) takes about 224 s using 1 thread and 37 s using 16 threads. This gives more than 600 % scaling performance using 16 threads. Scaling performance of our parallel algorithm We presented several efficient sequential and parallel algorithms for the EMS problem. Our algorithms use some novel and elegant rules to explore the candidate motifs in such a way that only a small fraction of the candidate motifs are explored twice or more. In fact, we also proved that these rules are close to ideal in the sense that no candidate motif is explored twice if the characters in the input string are all distinct. This condition may not be practical and ideas from [14] can be used when the characters in the input string are repeated. Nevertheless, the rules help because the instances are randomly generated and the k-mers in the input string are not much frequent. The second reason for the efficiency of our sequential algorithms is the use of a trie based data structure to compactly store the motifs. Our parallel algorithm stores candidate motifs in an array and uses a modified radix-sort based method for filtering out invalid candidate motifs. Our algorithms pushed up the state-of-the-art of EMS solvers to a state where the challenging instance (16,3) is solved in slightly more than half a minute using 16 threads. 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Wang X, Miao Y. GAEM: A Hybrid Algorithm Incorporating GA with EM for Planted Edited Motif Finding Problem. Curr Bioinformatics. 2014; 9(5):463–9. Rajasekaran S, Balla S, Huang CH, Thapar V, Gryk M, Maciejewski M, Schiller M. High-performance Exact Algorithms for Motif Search. J Clin Monitoring Comput. 2005; 19(4–5):319–28. Pathak S, Rajasekaran S, Nicolae M. EMS1: An Elegant Algorithm for Edit Distance Based Motif Search. Int J Foundations Comput Sci. 2013; 24(04):473–86. Knuth DE. The Art of Computer Programming, Volume 4, Generating All Tuples and Permutations, Fascicle 2. New Jersey, USA: Addison Wesley; 2005. This work has been supported in part by the NIH grant R01-LM010101 and NSF grant 1447711. Publication of this article was funded by the NIH grant R01-LM010101 and NSF grant 1447711. This article has been published as part of BMC Genomics Vol 17 Suppl 4 2016: Selected articles from the IEEE International Conference on Bioinformatics and Biomedicine 2015: genomics. The full contents of the supplement are available online at https://github.com/soumitrakp/ems2.git. A C++ based implementation of our algorithm can be found at the following github public repository: https://github.com/soumitrakp/ems2.git. SP and SR conceived the study. SP implemented the algorithms and PX carried out the experiments. SP and SR analyzed the results and wrote the paper. All authors reviewed the manuscript. All authors read and approved the final manuscript. Department of Computer Science and Engineering, University of Connecticut, 371 Fairfield Road,, Storrs, 06269, CT, USA Soumitra Pal & Peng Xiao Sanguthevar Rajasekaran Soumitra Pal Peng Xiao Correspondence to Sanguthevar Rajasekaran. Additional file Expected number of spurious motifs. This file gives the expression for the expected number of spurious (l,d)-motifs in n random strings of length m from the alphabet Σ. (PDF 143 kb) Pal, S., Xiao, P. & Rajasekaran, S. Efficient sequential and parallel algorithms for finding edit distance based motifs. BMC Genomics 17, 465 (2016). https://doi.org/10.1186/s12864-016-2789-9 Edit distance Trie Radix sort	CommonCrawl
You're reading: Posts Tagged: maths on TV Where could you (or your rich pal) give everyone $1 million? By Christian Lawson-Perfect. Posted March 7, 2020 Recently someone on Twitter, and then two people on US cable news, said that Michael Bloomberg could have used the \$500 million he spent on his presidential campaign to give everyone in the USA \$1 million. This caused quite a fuss. In short, someone divided 500 by 327, saw that the answer was bigger than 1 and the units were "millions", and concluded that the money could instead have been distributed to give everyone \$1 million. That's an easy mistake to make for someone writing a tweet, but the kind of error that should have made someone think "does that make sense?" before planning a segment on TV news about it. It's raised a couple of interesting questions, though: If that money was shared between every American citizen, how much would each one get? If Michael Bloomberg wanted to give \$1 million to everyone in a smaller area, where could he choose? I realised that all the data I need is freely available on the internet, so I made a website to do the calculations for you: make-it-rain-bloomberg.glitch.me It asks you how much money you've got, then for every power of 10 dollars, it tells you where in the USA you could give every resident that much. To give you an idea of how far the net worths of people like Michael Bloomberg could go, it's got a list of shortcuts for billionaires. Appropriately, I got that data from Bloomberg's own website. Bloomberg himself was mysteriously missing from the list, so I got his net worth from Google and added it in myself. The most unexpected thing for me was seeing how much money these people would have left over after giving everyone in the USA \$100. They'd still be enormously, unimaginably rich! I'll describe a few of the fiddly details of the implementation now. At first the "how much money have you got?" input was a text field, but I realised it'd be much better to have a slider that you can swing from \$1 all the way up to \$1 trillion. It's a logarithmic scale, so powers of 10 are equally spaced. I got data on the populations of US cities and states from data.census.gov. Working out which amounts and places to show you wasn't completely straightforward. I thought it'd be easiest to fix the amounts given away to a power of 10 per person, and to find places where the population meant that the amount left over would be as small as possible. To do that, my code works through the list of places in ascending order of population, and stops at the last place whose population is big enough to give everyone at least the target amount. I enjoyed making this tool, and I hope it helps somebody get a better feel for what these big numbers mean. Spread your wealth at make-it-rain-bloomberg.glitch.me. Steckles on QI! By Christian Lawson-Perfect. Posted December 19, 2018 Our Katie was on BBC Two last night! As part of the QI Christmas special, Katie told that old chestnut about infinitely many mathematicians walking into a bar. Viewers in the UK can see the show on the iPlayer; Katie's segment starts about 12 minutes in. How to Win at Pointless By Paul Taylor. Posted July 11, 2013 For the benefit of overseas readers, or British readers in full-time employment, I should briefly explain the concept of daytime TV quiz phenomenon Pointless. The pinnacle of British public service broadcasting, it's shown at 5.15pm every weekday on BBC One and is hosted by Alexander Armstrong of comedy double-act Armstrong & Miller, and Richard Osman of comedy double-act Armstrong & Osman. We shall investigate how we can use maths to analyse the show, improve our chances of winning it, and ultimately perhaps improve the show itself. The aim of the game is in each round to give the most obscure correct answer to a given question. Each question ($Q$) has a large set of valid answers $A_Q$, questions perhaps asking contestants to name "Films starring Bruce Willis" or "Countries without an O in their name". All the questions have been asked to 100 members of the public prior to the quiz (call this set $P$), and they each have 100 seconds to name as many examples as they can (giving rise to a set $A_p\subseteq A_Q$ for each $p\in P$. The contestant gets a point for every one of the 100 people who named their answer $a$: \[ \mbox{score}(a) = \begin{cases} \| \{p\in P : a\in A_p \} \| & \mbox{if}\ a\in A_Q \\ 100 & \mbox{if}\ a\not\in A_Q. \end{cases} \] So an obvious answer like Die Hard or France will score a lot of points, and an obscure answer like Striking Distance or Central African Republic will score fewer points. Points are bad (hence the title) so it's better to dredge up an obscure answer than stick with something safe. However an incorrect answer like Avatar or Mexico scores the maximum 100 points. At the end of the round the contestant with the most points is eliminated. Dara O Briain: School of Hard Sums to return; maths students sought to take part By Peter Rowlett. Posted November 12, 2012 A tweet purporting to be1 from the press office of UKTV, the company that owns the channel Dave, has confirmed that the TV show Dara O Briain: School of Hard Sums is to return for a second series (we at least thought we knew this in July). It also says that production company Wild Rover are looking for maths students to take part. The tweet asks you to email maths@wild-rover.com to express an interest. You might remember that the first series, which aired in April-June, did very well compared with other programmes on the channel. Yes, I know, but it was retweeted by Thomas Woolley, who should know. [↩] Probabilitelly By Christian Lawson-Perfect. Posted October 8, 2012 On the 18th of October BBC Four is going to broadcast a programme called Tails You Win: The Science of Chance, presented by Prof David Spiegelhalter, as part of its Big Science series. Here's the BBC's description: Smart and witty, jam-packed with augmented-reality graphics and fascinating history, this film, presented by Professor David Spiegelhalter, tries to pin down what chance is and how it works in the real world. For once this really is 'risky' television1. The film follows in the footsteps of The Joy of Stats, which won the prestigious Grierson Award for Best Science/Natural History programme of 2011. Now the same blend of wit and wisdom, animation, graphics and gleeful nerdery is applied to the joys of chance and the mysteries of probability, the vital branch of mathematics that gives us a handle on what might happen in the future. Professor Spiegelhalter is ideally suited to that task, being Winton Professor of the Public Understanding of Risk at Cambridge University, as well as being a recent Winter Wipeout contestant on BBC TV. I'm going to guess this sentence is what clinched the commission – CP [↩] 2nd series of School of Hard Sums By Katie Steckles. Posted July 29, 2012 Fans of scandalous gossip (and TV channel Dave's recent foray into maths based light entertainment, Dara O Briain's School of Hard Sums) will be interested to note the following tweet from Marcus Du Sautoy: "@pip6390: Is there another series of school of math in the pipe line?" yes! Filming in the new year. — Marcus du Sautoy (@MarcusduSautoy) July 24, 2012 This presumably refers to the show mentioned above, which featured Marcus as a maths question/task-master, providing both fiendish puzzles and mathematical insight – but who knows? People say all kinds of things on Twitter. Would you be interested to see another series? Which puzzles would you include? Comments below. School of Hard Sums doubles the normal Dave audience By Peter Rowlett. Posted April 17, 2012 Last night saw the debut of Dave's 'School of Hard Sums', a slightly strange but enjoyable maths show from Dara O Briain and Marcus du Sautoy. Was the show a success? Today Dara tweeted: So, would viewers of Dave actually want to watch a show about maths? Turns out… yes. We got double the normal audience. Yay for maths! — Dara O Briain (@daraobriain) April 17, 2012 Of course, the show received a good deal of advertising – but it seems like good news nonetheless.	CommonCrawl
Results for 'Miklós Erdélyi-Szabó' Listing dateFirst authorImpactPub yearRelevanceDownloads Order 1 filter applied BibTeX / EndNote / RIS / etc Export this page: Choose a format.. Formatted textPlain textBibTeXZoteroEndNoteReference Manager Limit to items. pro authors only published only Configure languages here. Sign in to use this feature. categorization shortcuts hide abstracts open articles in new windows Open Category Editor Undecidability of the Real-Algebraic Structure of Scott's Model.Miklós Erdélyi-Szabó - 1998 - Mathematical Logic Quarterly 44 (3):344-348.details We show that true first-order arithmetic of the positive integers is interpretable over the real-algebraic structure of Scott's topological model for intuitionistic analysis. From this the undecidability of the structure follows. Areas of Mathematics in Philosophy of Mathematics Direct download (3 more) Bookmark 2 citations Decidability in the Constructive Theory of Reals as an Ordered ℚ‐Vectorspace.Miklós Erdélyi-Szabó - 1997 - Mathematical Logic Quarterly 43 (3):343-354.details We show that various fragments of the intuitionistic/constructive theory of the reals are decidable. Intuitionism and Constructivism in Philosophy of Mathematics Bookmark 1 citation Decidability of Scott's Model as an Ordered $\Mathbb{Q}$-Vectorspace.Miklós Erdélyi-Szabó - 1997 - Journal of Symbolic Logic 62 (3):917-924.details Let $L = \langle, +, h_q, 1\rangle_{q \in \mathbb{Q}}$ where $\mathbb{Q}$ is the set of rational numbers and $h_q$ is a one-place function symbol corresponding to multiplication by $q$. Then the $L$-theory of Scott's model for intuitionistic analysis is decidable. Model Theory in Logic and Philosophy of Logic Towards a Natural Language Semantics Without Functors and Operands.Miklós Erdélyi-Szabó, László Kálmán & Agi Kurucz - 2008 - Journal of Logic, Language and Information 17 (1):1-17.details The paper sets out to offer an alternative to the function/argument approach to the most essential aspects of natural language meanings. That is, we question the assumption that semantic completeness (of, e.g., propositions) or incompleteness (of, e.g., predicates) exactly replicate the corresponding grammatical concepts (of, e.g., sentences and verbs, respectively). We argue that even if one gives up this assumption, it is still possible to keep the compositionality of the semantic interpretation of simple predicate/argument structures. In our opinion, compositionality presupposes (...) that we are able to compare arbitrary meanings in term of information content. This is why our proposal relies on an 'intrinsically' type free algebraic semantic theory. The basic entities in our models are neither individuals, nor eventualities, nor their properties, but 'pieces of evidence' for believing in the 'truth' or 'existence' or 'identity' of any kind of phenomenon. Our formal language contains a single binary non-associative constructor used for creating structured complex terms representing arbitrary phenomena. We give a finite Hilbert-style axiomatisation and a decision algorithm for the entailment problem of the suggested system. (shrink) Semantic Theories in Philosophy of Language Undecidability of the Real-Algebraic Structure of Models of Intuitionistic Elementary Analysis.Miklós Erdélyi-Szabó - 2000 - Journal of Symbolic Logic 65 (3):1014-1030.details We show that true first-order arithmetic is interpretable over the real-algebraic structure of models of intuitionistic analysis built upon a certain class of complete Heyting algebras. From this the undecidability of the structures follows. We also show that Scott's model is equivalent to true second-order arithmetic. In the appendix we argue that undecidability on the language of ordered rings follows from intuitionistically plausible properties of the real numbers. Intuitionistic Logic in Logic and Philosophy of Logic The Principle of the Common Cause.Miklós Redei, Gabor Hofer-Szabo & Laszlo Szabo - 2013 - Cambridge, U.K: Cambridge University Press.details The common cause principle says that every correlation is either due to a direct causal effect linking the correlated entities or is brought about by a third factor, a so-called common cause. The principle is of central importance in the philosophy of science, especially in causal explanation, causal modeling and in the foundations of quantum physics. Written for philosophers of science, physicists and statisticians, this book contributes to the debate over the validity of the common cause principle, by proving results (...) that bring to the surface the nature of explanation by common causes. It provides a technical and mathematically rigorous examination of the notion of common cause, providing an analysis not only in terms of classical probability measure spaces, which is typical in the available literature, but in quantum probability theory as well. The authors provide numerous open problems to further the debate and encourage future research in this field. (shrink) Causal Modeling in Epistemology $103.00 from Amazon Amazon page Bookmark 15 citations Reichenbachian Common Cause Systems of Arbitrary Finite Size Exist.Gábor Hofer-Szabó & Miklós Rédei - 2006 - Foundations of Physics 36 (5):745-756.details A partition $\{C_i\}_{i\in I}$ of a Boolean algebra Ω in a probability measure space (Ω, p) is called a Reichenbachian common cause system for the correlation between a pair A,B of events in Ω if any two elements in the partition behave like a Reichenbachian common cause and its complement; the cardinality of the index set I is called the size of the common cause system. It is shown that given any non-strict correlation in (Ω, p), and given any finite (...) natural number n > 2, the probability space (Ω,p) can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size n for the correlation. (shrink) Philosophy of Physical Science, Misc in Philosophy of Physical Science Probabilistic Causation in Metaphysics Probabilistic Frameworks in Philosophy of Probability Probabilistic Principles in Philosophy of Probability Quantum Mechanics, Misc in Philosophy of Physical Science Space and Time in Philosophy of Physical Science Statistical Theories of Causation in Metaphysics Common‐Causes Are Not Common Common‐Causes.Gábor Hofer-Szabó, Miklos Redei & Laszlo E. Szabo - 2002 - Philosophy of Science 69 (4):623-636.details A condition is formulated in terms of the probabilities of two pairs of correlated events in a classical probability space which is necessary for the two correlations to have a single (Reichenbachian) common-cause and it is shown that there exists pairs of correlated events probabilities of which violate the necessary condition. It is concluded that different correlations do not in general have a common common-cause. It is also shown that this conclusion remains valid even if one weakens slightly Reichenbach's definition (...) of common-cause. The significance of the difference between common-causes and common common-causes is emphasized from the perspective of Reichenbach's Common Cause Principle. (shrink) Quantum Mechanics in Philosophy of Physical Science Reichenbachian Common Cause Systems.Gábor Hofer-Szabó & Miklos Redei - 2004 - International Journal of Theoretical Physics 43:1819-1826.details A partition $\{C_i\}_{i\in I}$ of a Boolean algebra $\cS$ in a probability measure space $(\cS,p)$ is called a Reichenbachian common cause system for the correlated pair $A,B$ of events in $\cS$ if any two elements in the partition behave like a Reichenbachian common cause and its complement, the cardinality of the index set $I$ is called the size of the common cause system. It is shown that given any correlation in $(\cS,p)$, and given any finite size $n>2$, the probability space (...) $(\cS,p)$ can be embedded into a larger probability space in such a manner that the larger space contains a Reichenbachian common cause system of size $n$ for the correlation. It also is shown that every totally ordered subset in the partially ordered set of all partitions of \cS$ contains only one Reichenbachian common cause system. Some open problems concerning Reichenbachian common cause systems are formulated. (shrink) Causal Reasoning, Misc in Epistemology Kreativitási Gyakorlatok, Fafej, Indigo: Erdély Miklós Művészetpedagógiai Tevékenysége, 1975-1986.Miklós Erdélyi, Sándor Hornyik & Annamária Szőke (eds.) - 2008 - Mta Művészettörténeti Kutatóintézet.details Aesthetic Cognition in Aesthetics Conditioning Using Conditional Expectations: The Borel–Kolmogorov Paradox.Zalán Gyenis, Gabor Hofer-Szabo & Miklós Rédei - 2017 - Synthese 194 (7):2595-2630.details The Borel–Kolmogorov Paradox is typically taken to highlight a tension between our intuition that certain conditional probabilities with respect to probability zero conditioning events are well defined and the mathematical definition of conditional probability by Bayes' formula, which loses its meaning when the conditioning event has probability zero. We argue in this paper that the theory of conditional expectations is the proper mathematical device to conditionalize and that this theory allows conditionalization with respect to probability zero events. The conditional probabilities (...) on probability zero events in the Borel–Kolmogorov Paradox also can be calculated using conditional expectations. The alleged clash arising from the fact that one obtains different values for the conditional probabilities on probability zero events depending on what conditional expectation one uses to calculate them is resolved by showing that the different conditional probabilities obtained using different conditional expectations cannot be interpreted as calculating in different parametrizations of the conditional probabilities of the same event with respect to the same conditioning conditions. We conclude that there is no clash between the correct intuition about what the conditional probabilities with respect to probability zero events are and the technically proper concept of conditionalization via conditional expectations—the Borel–Kolmogorov Paradox is just a pseudo-paradox. (shrink) Conditionalization in Philosophy of Probability Probabilistic Principles, Misc in Philosophy of Probability Updating Principles in Philosophy of Probability Direct download (10 more) Problems of Hungarian National Consciousness in the Second Half of the 20th Century.Miklos Szabo - 1988 - Social Research 55.details Eastern European Philosophy in European Philosophy Transition Into the Rule of Law: Deconstruction, Reconstruction, Construction.Miklos Szabo - 2002 - Rechtstheorie 33 (2-4):283-295.details Une fibule celtique à Délos.Miklós Szabó - 1971 - Bulletin de Correspondance Hellénique 95 (2):503-514.details Hungarian Language and Law: Developing a Grammar for Social Inclusion, a Vocabulary for Political Emancipation. Special Issue (IJSL)—Editorial Preface.Mate Paksy, Miklós Szabó & Edina Vinnai - 2020 - International Journal for the Semiotics of Law - Revue Internationale de Sémiotique Juridique 33 (3):707-727.details Having been invited by editor-in-chief, Professor Anne Wagner, to edit the present special issue, we decided to fulfil a longstanding wish to provide a panorama about the Hungarian Language and Law. Along with other 'law and …' movements, Law and Language has attracted a great deal of attention from subsequent generations of Hungarian academic lawyers, because the political transition served as a wonderful subject and context for scholarly papers and text books, for examining the putative or real influence of this (...) or that popular social scientist or for undertaking literature overviews. Unfortunately, there have been relatively few academic papers that have sought to draw general conclusions from empirically well-founded case studies. In order to fill that important gap, this special issue has taken the opportunity to select only those interdisciplinary papers whose goals include an analysis of Hungarian legal discourse written from a critical angle and using critical empirical methodology. At the very outset of the editing process—back in 2018—for the purposes of this special issue we defined as 'empirical' any sufficiently coherent fact-based research that reflects the language of legal discourse. And 'critical' means an engagement with the values of the Rule of Law. This double methodological and axiological feature is manifest throughout the selected papers classified as 'law and language'. (shrink) The Vienna Circle in Hungary by András Máté; Miklós Rédei; Friedrich Stadler. [REVIEW]Maté Szabó - forthcoming - Association for Symbolic Logic: The Bulletin of Symbolic Logic.details Review by: Maté Szabó The Bulletin of Symbolic Logic, Volume 19, Issue 1, Page 110-112, March 2013. Logical Empiricism in 20th Century Philosophy The Vienna Circle in Hungary, Edited by András Máté, Miklós Rédei and Friedrich Stadler, Springer, Wien–New York, 2011, 300 Pp. [REVIEW]Máté Szabó - 2013 - Bulletin of Symbolic Logic 19 (1):110-112.details Common Causes Love to Hide: Gábor Hofer-Szabó, Miklós Rédei and László E. Szabó: The Principle of the Common Cause. Cambridge: Cambridge University Press, 2013, Vii+202pp, $99.00 HB. [REVIEW]Chrysovalantis Stergiou - 2015 - Metascience 24 (2):247-251.details Anything other than paraphrasing the well-known Heraclitean aphorism would not be more appropriate to portray the crux of the contribution of the three philosophers of the Budapest School, Gábor Hofer-Szabó, Miklós Rédei and Lázló E. Szabó, in the ongoing discussion of the principle of the common cause . Indeed, 'common causes love to hide' and for that reason critics and aspirant falsifiers of PCC find correlations which, at a first level of analysis, might lack a common cause (...) explanation. But as the authors argue such correlations do not amount to disconfirming evidence for the principle, since PCC does not specify where to search for a common cause of a correlation; it just states that there is one. PCC is neither falsifiable, nor verifiable; it is a metaphysical doctrine that can only be assessed for its plausibility in the light of theories of empirical science. This idea fosters the investigation of the existence of common causes of correlations in two fundamental physical t .. (shrink) Jogosultságok-Elmélet És Gyakorlat: A Miskolci Egyetem És a Miskolci Akadémiai Bizottság Által 2008. December 5-Én És 6-Án Rendezett Konferencia Anyaga. [REVIEW]Ildikó Bartha, Krisztina Ficsor, Tamás Győrfi & Miklós Szabó (eds.) - 2009 - Bíbor.details Jogosultságok-Elmélet És Gyakorlat: A Miskolci Egyetem És a Miskolci Akadémiai Bizottság Által 2008.Ildikó Bartha, Krisztina Ficsor, Tamás Győrfi & Miklós Szabó (eds.) - 2009 - Bíbor.details Janos erdelyi: The individual and the ideal (Janos erdelyi: Das individuelle und Das ideale).Papp Zoltan & Erdelyi Janos - 2008 - Estetika: The Central European Journal of Aestetics; Until 2008: Estetika (Aesthetics) 45 (2).details From "Liberal Minimum" to the "Complete Catalog of Human Rights": On Central Concepts of Hungarian Postdissident Liberals. [REVIEW]Ferenc Laczó - 2013 - Contributions to the History of Concepts 8 (2):106-118.details This article analyzes how five leading Hungarian postdissident liberal thinkers conceptually constructed their view of liberalism in the early years of postcommunism. Studying Beszélő, the most signi cant liberal journal during the early years of representative democracy, it shows how they did so through references to political "threats" and the idea of a "liberal minimum" (János Kis), local liberal and democratic traditions and "progressive patriotism" (Miklós Szabó), the ongoing "liberal-conservative revolution" and the creation of a "new political community" (...) (Gáspár Miklós Tamás), antipolitics and "expertise" (György Konrád), and the "complete catalog of human rights" and the agenda of "modernization" (István Eörsi), respectively. Next to its conceptual analysis of heavily influential individual thinkers, the article discusses the ambition of postdissident Hungarian liberals to harmonize liberal and democratic tenets. Last but not least, it elaborates on the left-wing origins of many of their central concepts that, as suggested here, ultimately hindered liberalism's assumption of a central position in the new political system. (shrink) Autonomy in Political Theories in Social and Political Philosophy A New Look at the New Look: Perceptual Defense and Vigilance.Matthew H. Erdelyi - 1974 - Psychological Review 81 (1):1-25.details Modularity and Cognitive Penetrability in Philosophy of Mind Unconscious Processes, Misc in Philosophy of Cognitive Science Bookmark 123 citations Experimental Indeterminacies in the Dissociation Paradigm of Subliminal Perception.Matthew Hugh Erdelyi - 1986 - Behavioral and Brain Sciences 9 (1):30-31.details Unconscious Perception in Philosophy of Cognitive Science The Effect of Response Bias on Recall Performance, with Some Observations on Processing Bias.Matthew H. Erdelyi, Joyce Finks & Merryl B. Feigin-Pfau - 1989 - Journal of Experimental Psychology: General 118 (3):245-254.details Philosophy of Psychology in Philosophy of Cognitive Science The Unified Theory of Repression.Matthew Hugh Erdelyi - 2006 - Behavioral and Brain Sciences 29 (5):499-511.details Repression has become an empirical fact that is at once obvious and problematic. Fragmented clinical and laboratory traditions and disputed terminology have resulted in a Babel of misunderstandings in which false distinctions are imposed (e.g., between repression and suppression) and necessary distinctions not drawn (e.g., between the mechanism and the use to which it is put, defense being just one). "Repression" was introduced by Herbart to designate the (nondefensive) inhibition of ideas by other ideas in their struggle for consciousness. Freud (...) adapted repression to the defensive inhibition of "unbearable" mental contents. Substantial experimental literatures on attentional biases, thought avoidance, interference, and intentional forgetting exist, the oldest prototype being the work of Ebbinghaus, who showed that intentional avoidance of memories results in their progressive forgetting over time. It has now become clear, as clinicians had claimed, that the inaccessible materials are often available and emerge indirectly (e.g., procedurally, implicitly). It is also now established that the Ebbinghaus retention function can be partly reversed, with resulting increases of conscious memory over time (hypermnesia). Freud's clinical experience revealed early on that exclusion from consciousness was effected not just by simple repression (inhibition) but also by a variety of distorting techniques, some deployed to degrade latent contents (denial), all eventually subsumed under the rubric of defense mechanisms ("repression in the widest sense"). Freudian and Bartlettian distortions are essentially the same, even in name, except for motive (cognitive vs. emotional), and experimentally induced false memories and other "memory illusions" are laboratory analogs of self-induced distortions. Key Words: avoidance; Bartlett; defense; denial; distortion; Ebbinghaus; false-memories; Freud; inhibition; repression; suppression. (shrink) Autobiographical Memory in Philosophy of Mind Memory and Cognitive Science in Philosophy of Mind Philosophy of Psychology, Misc in Philosophy of Cognitive Science Sigmund Freud in 19th Century Philosophy Subliminal Perception and its Cognates: Theory, Indeterminacy, and Time.Matthew Hugh Erdelyi - 2004 - Consciousness and Cognition 13 (1):73-91.details Unconscious processes, by whatever name they may be known , are invariably operationalized by the dissociation paradigm, any situation involving the dissociation between two indicators , one of availability and the other, of accessibility , such that, ε>α. Subliminal perception has been traditionally defined by a special case of the dissociation paradigm in which availability exceeds accessibility when accessibility is null . Construct validity issues bedevil all dissociation paradigms since it is not clear what might constitute appropriate indicators that, moreover, (...) are pure and exhaustive. Semantic and theoretic drifts in the recent literature—e.g., the confusion of different versions of the dissociation paradigm, the equation of conscious–unconscious with direct–indirect tests, and the foisting of the criterion of qualitative differences—have tended to undermine emerging theoretic parsimony. On the other hand, a crucial factor has been left out of theory development: time. Both ε and α can rise and fall over time, often asynchronously, and so dissociations may wax and wane and, even, reverse over time. Some laboratory evidence suggests that accessibility measures , as they approach chance, may actually dip below chance . If so, d′=0 , could be an averaging artifact of positive and negative d′s. Conscious accessibility is not either–or but more or less, and variable over time. (shrink) Exploiting Injustice in Mutually Beneficial Market Exchange: The Case of Sweatshop Labor.András Miklós - 2019 - Journal of Business Ethics 156 (1):59-69.details Mutually beneficial exchanges in markets can be exploitative because one party takes advantage of an underlying injustice. For instance, employers of sweatshop workers are often accused of exploiting the desperate conditions of their employees, although the latter accept the terms of their employment voluntarily. A weakness of this account of exploitation is its tendency for over-inclusiveness. Certainly, given the prevalence of global and domestic socioeconomic inequalities, not all exchanges that take place against background injustices should be considered exploitative. This paper (...) offers a framework to identify exploitation in mutually beneficial exchange, focusing on the case of sweatshop labor. It argues that an employer can be viewed as taking unfair advantage of an underlying injustice if and only if the employer's surplus from the exchange in the unjust state of affairs exceeds the surplus it could maximally obtain in a just state of affairs. The paper illustrates the applicability of this framework using three different conceptions of justice and argues that it is superior to microlevel accounts of exploitation that regard background justice as irrelevant. The paper concludes by describing some normative implications that follow from judging an exchange exploitative. (shrink) Business Ethics in Applied Ethics The Compositionality Papers.Zoltán Gendler Szabó - 2004 - Mind 113 (450):340-344.details Compositionality in Philosophy of Language Quantum Probability Theory.Miklós Rédei & Stephen Jeffrey Summers - 2007 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 38 (2):390-417.details Probabilities in Quantum Mechanics in Philosophy of Physical Science Art, Politics, and Taking Sides : An Interview with Istvan Szabo.Marty Fairbairn & Istvan Szabo - 2002 - Film-Philosophy 6 (1).details Philosophy of Film in Aesthetics Alief and Belief.Tamar Szabó Gendler - 2008 - Journal of Philosophy 105 (10):634-663.details Forthcoming, Journal of Philosophy [pdf manuscript]. Explanation of Action in Philosophy of Action The Nature of Belief in Philosophy of Mind Local Primitive Causality and the Common Cause Principle in Quantum Field Theory.Miklos Redei & Stephen J. Summers - 2001 - Foundations of Physics 32 (3):335-355.details If $\mathcal{A}$ (V) is a net of local von Neumann algebras satisfying standard axioms of algebraic relativistic quantum field theory and V 1 and V 2 are spacelike separated spacetime regions, then the system ( $\mathcal{A}$ (V 1 ), $\mathcal{A}$ (V 2 ), φ) is said to satisfy the Weak Reichenbach's Common Cause Principle iff for every pair of projections A∈ $\mathcal{A}$ (V 1 ), B∈ $\mathcal{A}$ (V 2 ) correlated in the normal state φ there exists a projection C (...) belonging to a von Neumann algebra associated with a spacetime region V contained in the union of the backward light cones of V 1 and V 2 and disjoint from both V 1 and V 2 , a projection having the properties of a Reichenbachian common cause of the correlation between A and B. It is shown that if the net has the local primitive causality property then every local system ( $\mathcal{A}$ (V 1 ), $\mathcal{A}$ (V 2 ), φ) with a locally normal and locally faithful state φ and suitable bounded V 1 and V 2 satisfies the Weak Reichenbach's Common Cause Principle. (shrink) Causation, Misc in Metaphysics A Subject with No Object.Zoltan Gendler Szabo, John P. Burgess & Gideon Rosen - 1999 - Philosophical Review 108 (1):106.details This is the first systematic survey of modern nominalistic reconstructions of mathematics, and for this reason alone it should be read by everyone interested in the philosophy of mathematics and, more generally, in questions concerning abstract entities. In the bulk of the book, the authors sketch a common formal framework for nominalistic reconstructions, outline three major strategies such reconstructions can follow, and locate proposals in the literature with respect to these strategies. The discussion is presented with admirable precision and clarity, (...) and should be accessible even to readers with only minimal background in logic and mathematics. There will be many who will turn directly to these pages and use them as a brief manual on the state of the art of nominalism in mathematics. But the most intriguing parts of this elegant book—at least in my view—are the introduction and the conclusion, where the authors examine the significance of reconstructive nominalism. (shrink) British Philosophy in European Philosophy Psychodynamics and the Unconscious.Matthew H. Erdelyi - 1992 - American Psychologist 47:784-87.details Separate- Versus Common -Common-Cause-Type Derivations of the Bell Inequalities.Gábor Hofer-Szabó - 2008 - Synthese 163 (2):199 - 215.details Standard derivations of the Bell inequalities assume a common common cause system that is a common screener-off for all correlations and some additional assumptions concerning locality and no-conspiracy. In a recent paper (Grasshoff et al., 2005) Bell inequalities have been derived via separate common causes assuming perfect correlations between the events. In the paper it will be shown that the assumptions of this separate-common-cause-type derivation of the Bell inequalities in the case of perfect correlations can be reduced to the assumptions (...) of common-common-cause-system-type derivation. However, in the case of non-perfect correlations a non-reducible separate-common-cause-type derivation of some Bell-like inequalities can be given. The violation of these Bell-like inequalities proves Szabó's (2000) conjecture concerning the non-existence of a local, non-conspiratorial, separate-common-cause-model for a delta δ-neighborhood of perfect EPR correlations. (shrink) Bell's Theorem in Philosophy of Physical Science Repression, Reconstruction, and Defense: History and Integration of the Psychoanalytic and Experimental Frameworks.Matthew H. Erdelyi - 1990 - In Jerome L. Singer (ed.), Repression and Dissociation. University of Chicago Press. pp. 1--31.details Psychoanalysis and Consciousness in Philosophy of Cognitive Science Psychotherapy and Psychoanalysis in Philosophy of Cognitive Science $12.00 used $49.00 new $52.00 from Amazon (collection) Amazon page Adjectives in Context.Zoltán Gendler Szabó - 2001 - In Darragh Byrne & Max Kölbel (eds.), Arguing About Language. Routledge. pp. 119--146.details 0. Abstract In this paper, I argue that although the behavior of adjectives in context poses a serious challenge to the principle of compositionality of content, in the end such considerations do not defeat the principle. The first two sections are devoted to the precise statement of the challenge; the rest of the paper presents a semantic analysis of a large class of adjectives that provides a satisfactory answer to it. In section 1, I formulate the context thesis, according to (...) which the content of a complex expression depends on the context of its utterance only insofar as the contents of its constituents do. If the context thesis is false, the content of some complex expression is not compositionally determined. In section 2, using an example due to Charles Travis, I construct an objection to the context thesis based on the behavior of the adjective 'green'. In section 3 and 4, I look at some of the difficulties surrounding the semantics of 'good', which provide the motivation for the thesis that most adjectives are contextually incomplete one-place predicates. In section 5, I discuss how 'green' and other color adjectives can be treated within such a semantic theory. Since this theory is compatible with the context thesis, the objection against the compositionality of content looses its force. (shrink) Practical Reason in Philosophy of Action Predicates in Philosophy of Language Predicates and Context-Dependence in Philosophy of Language $31.35 used $64.95 from Amazon (collection) Amazon page Cognitive Masking: The Disruptive Effect of an Emotional Stimulus Upon the Perception of Contiguous Neutral Items.Matthew Hugh Erdelyi & Anat Gordon Appelbaum - 1973 - Bulletin of the Psychonomic Society 1 (1):59-61.details Aspects of Consciousness in Philosophy of Mind Emotions, Misc in Philosophy of Mind John von Neumann and the Foundations of Quantum Physics.Miklós Rédei, Michael Stöltzner, Walter Thirring, Ulrich Majer & Jeffrey Bub - 2001 - Springer Verlag.details ... of Quantum Physics Book Editors Miklós Rédei1 Michael Stöltzner2 Eötvös University, Budapest, Hungary Institute Vienna Circle, Vienna, University of Salzburg, Vienna, Austria ISSN 09296328 ISBN 9789048156511 ISBN 9789401720120 ... Quantum Mechanics, Miscellaneous in Philosophy of Physical Science Quantum Theories in Philosophy of Physical Science Why John von Neumann Did Not Like the Hilbert Space Formalism of Quantum Mechanics (and What He Liked Instead).Miklos Rédei - 1996 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 27 (4):493-510.details History of Quantum Mechanics in Philosophy of Physical Science Mathematical Structure of Quantum Mechanics in Philosophy of Physical Science Sincere‐Strategy Preference‐Based Approval Voting Fully Resists Constructive Control and Broadly Resists Destructive Control.Gábor Erdélyi, Markus Nowak & Jörg Rothe - 2009 - Mathematical Logic Quarterly 55 (4):425-443.details We study sincere-strategy preference-based approval voting , a system proposed by Brams and Sanver [1] and here adjusted so as to coerce admissibility of the votes , with respect to procedural control. In such control scenarios, an external agent seeks to change the outcome of an election via actions such as adding/deleting/partitioning either candidates or voters. SP-AV combines the voters' preference rankings with their approvals of candidates, where in elections with at least two candidates the voters' approval strategies are adjusted (...) – if needed – to approve of their most-preferred candidate and to disapprove of their least-preferred candidate. This rule coerces admissibility of the votes even in the presence of control actions, and hybridizes, in effect, approval with pluralitiy voting. We prove that this system is computationally resistant to 19 out of 22 types of constructive and destructive control. Thus, SP-AV has more resistances to control than is currently known for any other natural voting system with a polynomial-time winner problem. In particular, SP-AV is the second natural voting system with an easy winner-determination procedure that is known to have full resistance to constructive control, and unlike Copeland voting it in addition displays broad resistance to destructive control. (shrink) Social Choice Theory in Social and Political Philosophy Reichenbach's Common Cause Principle and Quantum Field Theory.Miklós Rédei - 1997 - Foundations of Physics 27 (10):1309-1321.details Reichenbach's principles of a probabilistic common cause of probabilistic correlations is formulated in terms of relativistic quantum field theory, and the problem is raised whether correlations in relativistic quantum field theory between events represented by projections in local observable algebrasA andA pertaining to spacelike separated spacetime regions V1 and V2 can be explained by finding a probabilistic common cause of the correlation in Reichenbach's sense. While this problem remains open, it is shown that if all superluminal correlations predicted by the (...) vacuum state between events inA andA have a genuinely probabilistic common cause, then the local algebrasA andA must be statistically independent in the sense of C*-independence. (shrink) Causation, Miscellaneous in Metaphysics Quantum Field Theory in Philosophy of Physical Science Semantics Versus Pragmatics.Zoltan Gendler Szabo (ed.) - 2004 - Oxford University Press UK.details Leading scholars in the philosophy of language and theoretical linguistics present brand-new papers on a major topic at the intersection of the two fields, the distinction between semantics and pragmatics. Anyone engaged with this issue in either discipline will find much to reward their attention here. Contributors: Kent Bach, Herman Cappelen, Michael Glanzberg, Jeffrey C. King, Ernie Lepore, Stephen Neale, F. Recanati, Nathan Salmon, Mandy Simons, Scott Soames, Robert J. Stainton, Jason Stanley, Zoltan Gendler Szabo. Semantics-Pragmatics Distinction in Philosophy of Language $30.57 used $75.63 new $158.93 from Amazon Amazon page [Comment] A Brief Note on the Ambiguity of 'Ought'. Reply to Moti Mizrahi's 'Ought, Can and Presupposition: An Experimental Study'.Miklos Kurthy & Holly Lawford-Smith - 2015 - Methode: Analytic Perspectives 4 (6):244-249.details Moti Mizrahi provides experimental evidence according to which subjects judge that a person ought to ? even when she cannot ?. He takes his results to constitute a falsification of the alleged intuitiveness of the 'Ought Implies Can' principle. We point out that in the light of the fact that (a) 'ought' is multiply ambiguous, that (b) only a restricted set of readings of 'ought' will be relevant to the principle, and that (c) he did not instruct his subjects appropriately (...) – or otherwise ensure that in their 'ought' judgements they applied the relevant concept(s) – Mizrahi's conclusions appear premature. We suggest two ways in which the experimental design could be adjusted or supplemented. First, Mizrahi could instruct (or prime) subjects to read the 'ought' question in a particular way. Second, he could complement his experiment by asking follow-up questions aimed at uncovering the implications for blame of subjects' judgements. Once these adjustments are applied, an experiment with a similar outcome would be more significant. (shrink) Experimental Philosophy: Folk Morality in Metaphilosophy Moral Concepts in Meta-Ethics On Cylindric Algebras Satisfying Merry-Go-Round Properties.Miklós Ferenczi - 2007 - Logic Journal of the IGPL 15 (2):183-197.details Three classes are introduced which are closely related to the class included in the title. It is proven that the class obtained from by replacing axiom C4 by the commutativity of single substitutions can be considered as the abstract class in the Resek–Thompson theorem, thus it is representable by set algebras. Then the class is defined and it is shown that the necessary and sufficient condition for neat embeddability of an algebra in CAα into is the validity of the merry-go-round (...) properties. Finally, the class is introduced which class is a counterpart of among the polyadic like algebras. (shrink) Sincere-Strategy Preference-Based Approval Voting Fully Resists Constructive Control and Broadly Resists Destructive Control.Gábor Erdélyi, Markus Nowak & Jörg Rothe - 2009 - Mathematical Logic Quarterly 55 (4):425-443.details We study sincere-strategy preference-based approval voting, a system proposed by Brams and Sanver [1] and here adjusted so as to coerce admissibility of the votes, with respect to procedural control. In such control scenarios, an external agent seeks to change the outcome of an election via actions such as adding/deleting/partitioning either candidates or voters. SP-AV combines the voters' preference rankings with their approvals of candidates, where in elections with at least two candidates the voters' approval strategies are adjusted – if (...) needed – to approve of their most-preferred candidate and to disapprove of their least-preferred candidate. This rule coerces admissibility of the votes even in the presence of control actions, and hybridizes, in effect, approval with pluralitiy voting. We prove that this system is computationally resistant to 19 out of 22 types of constructive and destructive control. Thus, SP-AV has more resistances to control than is currently known for any other natural voting system with a polynomial-time winner problem. In particular, SP-AV is the second natural voting system with an easy winner-determination procedure that is known to have full resistance to constructive control, and unlike Copeland voting it in addition displays broad resistance to destructive control. (shrink) Action Theory in Philosophy of Action How Local Are Local Operations in Local Quantum Field Theory?Miklós Rédei & Giovanni Valente - 2010 - Studies in History and Philosophy of Science Part B: Studies in History and Philosophy of Modern Physics 41 (4):346-353.details Separate- Versus Common-Common-Cause-Type Derivations of the Bell Inequalities.Gábor Hofer-Szabó - 2008 - Synthese 163 (2):199-215.details Standard derivations of the Bell inequalities assume a common-commoncause-system that is a common screener-off for all correlations and some additional assumptions concerning locality and no-conspiracy. In a recent paper Graßhoff et al., "The British Journal for the Philosophy of Science", 56, 663–680 ) Bell inequalities have been derived via separate common causes assuming perfect correlations between the events. In the paper it will be shown that the assumptions of this separate-common-cause-type derivation of the Bell inequalities in the case of perfect (...) correlations can be reduced to the assumptions of a common-common-cause-system-type derivation. However, in the case of non-perfect correlations a non-reducible separate-common-cause-type derivation of some Bell-like inequalities can be given. The violation of these Bell-like inequalities proves Szabo's ) conjecture concerning the non-existence of a local, non-conspiratorial, separate-common-cause-model for a δ-neighborhood of perfect EPR correlations. (shrink) Conceivability and Possibility.Tamar Szabo Gendler & John Hawthorne (eds.) - 2002 - Oxford University Press.details The capacity to represent things to ourselves as possible plays a crucial role both in everyday thinking and in philosophical reasoning; this volume offers much-needed philosophical illumination of conceivability, possibility, and the relations between them. Conceivability, Imagination, and Possibility in Metaphysics Epistemology of Intuition in Epistemology Kripke's Modal Argument Against Materialism in Philosophy of Mind Modal Epistemology, Misc in Metaphysics Modal Rationalism in Metaphysics Specific Expressions in Philosophy of Language Thought Experiments in Metaphilosophy Zombies and the Conceivability Argument in Philosophy of Mind $180.00 new Amazon page Using PhilPapers from home? Create an account to enable off-campus access through your institution's proxy server. Be alerted of all new items appearing on this page. Choose how you want to monitor it: Email RSS feed	CommonCrawl
Petroleum Science pp 1–20 \| Cite as Methods for simultaneously evaluating reserve and permeability of undersaturated coalbed methane reservoirs using production data during the dewatering stage Jun-Tai Shi Jia-Yi Wu Zheng Sun Zhi-Hua Xiao Cheng Liu Kamy Sepehrnoori In this work, a flowing material balance equation (FMBE) is established for undersaturated coalbed methane (CBM) reservoirs, which considers immobile free gas expansion effect at the dewatering stage. Based on the established FMBE, five straight-line methods are proposed to determine the control area, initial water reserve, initial free gas reserve, initial adsorbed gas reserve, original gas in place, as well as permeability at the same time. Subsequently, the proposed FMBE methods for undersaturated CBM reservoirs are validated against a reservoir simulation software with and without considering free gas expansion. Finally, the proposed methods are applied in a field case when considering free gas expansion effect. Validation cases show that the straight-line relationships for the proposed five FMBE methods are excellent, and good agreements are obtained among the actual reserves and permeabilities and those evaluated by the proposed five FMBE methods, indicating the proposed five FMBE methods are effective and rational for CBM reservoirs. Results show that a small amount of free gas will result in a great deviation in reserve evaluation; hence, the immobile free gas expansion effect should be considered when establishing the material balance equation of undersaturated CBM reservoirs at the dewatering stage. Coalbed methane OGIP Permeability evaluation Flowing material balance equation Gas expansion List of symbols Gas volume factor at current state (sm3/m3) Initial gas volume factor (sm3/m3) Water volume factor at current state (sm3/m3) Initial water volume factor (sm3/m3) y-intercept of the straight line for Method 1 [(m3/d)/MPa] y-intercept of the straight line for Method 2 [MPa/(m3/d)] y-intercept of the straight line for Method 3 [MPa/m3] Gas compressibility (MPa−1) $\bar{c}_{\text{g}}$ Average gas compressibility (MPa−1) Pore compressibility (MPa−1) Total compressibility (MPa−1) Water compressibility (MPa−1) Initial free gas reserve (m3) Cumulative gas production (m3) Residual gas reserve (m3) Reservoir thickness (m) Relative permeability (fraction) Permeability at current pressure (mD) Slope of the straight line for Method 1 (d−1) Slope of the straight line for Method 2 (MPa/m3) Slope of the straight line for Method 3 [MPa/(m3/d)] $\bar{p}$ Current average formation pressure (MPa) Initial reservoir pressure (MPa) pwf Bottom-hole pressure (MPa) ${\bar{p}_{wf}}$ Average bottom-hole pressure (MPa) Water production rate (m3/d) Control radius (m) Wellbore radius (m) Skin factor (dimensionless) Water saturation (fraction) Irreducible water saturation (fraction) Initial water saturation (fraction) Initial gas saturation (fraction) Residual gas saturation or the critical flowing gas saturation (fraction) Pore volume of the CBM reservoir (m3) Initial mobile water reserve (m3) Encroached water volume at the reservoir condition (m3) Cumulative water production (m3) Residual mobile water reserve (m3) Cumulative water production per producing pressure drop, which is the value of x axis for Method 1 (m3/MPa) Average producing time, which is the value of x axis for Method 2 (d) Reciprocal of the average producing time, which is the value of x axis for Method 3 (d−1) Ratio of yesterday's water production rate to today's water production rate, which is the value of x axis for Method 4 (dimensionless) Ratio of the average cumulative water production to the average water production rate, which is the value of x axis for Method 5 (d) Water productivity index, which is the value of y axis for Method 1 [(m3/d)/MPa] Reciprocal of water productivity index, which is the value of y axis for Method 2 [MPa/(m3/d)] Producing pressure drop per cumulative water production, which is the value of y axis for Method 3 (MPa/m3) Ratio of bottom-hole pressure change from yesterday to today to the today's water production rate, which is the value of y axis for Method 4 [MPa/(m3/d)] Ratio of the average producing pressure drop to the average water production rate, which is the value of y axis for Method 5 [MPa/(m3/d)] μw Dynamic viscosity of water (mPa s) ϕi Initial porosity of coal formation (fraction) Edited by Yan-Hua Sun Coalbed methane (CBM) is a green, clean, and environmentally friendly natural resource which can make up the energy shortage (Clarkson 2013; Liu and Harpalani 2013; Adeboye and Bustin 2013). The CBM reservoir, as one of the unconventional gas reservoirs, has unique flow mechanism and production schedule (Aminian et al. 2004; Clarkson and Salmachi 2017; Jenkins and Boyer 2008). CBM is produced through dewatering to make adsorbed gas desorb from the interface of coal matrix after the critical desorption pressure is achieved (Jenkins and Boyer 2008; Sun et al. 2017, 2018a). Before gas production, only water can flow in the cleat system, even though in some cases there is a small amount of free gas; but since its saturation is less than the critical flowing saturation, gas cannot flow but will expand in volume. Reserve evaluation is one of the important issues before and during the development of CBM reservoirs (Zhou and Guan 2016). The volumetric method is often applied to estimate the original gas in place (OGIP) of a CBM reservoir before its development (Saulsberry et al. 1996; Zahner 1997). Dynamic methods (King 1990, 1993; Clarkson et al. 2007; Ahmed et al. 2006; Salmachi and Karacan 2017) are usually used to evaluate and prove the previous calculated OGIP of a CBM reservoir by using production data during its development. Because the control area of the coal formation is not easy to determine, the OGIP evaluated by the volumetric method is a low probability value and often considered as a reference, while the dynamic methods which use the production performances of CBM wells are more credible (Guzman et al. 2014). However, most dynamic methods, such as the material balance equation (MBE) method, are limited in use because it is impossible to shut in all CBM wells to measure the average pressure (Morad and Clarkson 2008). Shi et al. (2018a) proposed a history matching method to generate the average pressure history with gas and water productions of the CBM wells, and then applied the proposed material balance equation for coalbed methane to estimate the OGIP on the basis of the generated average pressure history, the actual cumulative water and gas productions, as well as the CBM formation and fluid properties. Permeability of the coal formation is a very important parameter for the effective production of CBM reservoirs (Clarkson et al. 2011; Yan et al. 2015; Sun et al. 2018b, 2018c). Currently, there are some methods for determining the permeability of the coal formation, such as core laboratory test (Gash 1991; Wang et al. 2011; Adeboye and Bustin 2013; Li et al. 2014), well logging (Li et al. 2011; Fu et al. 2009; Karacan 2009), well testing (Al-Khalifa et al. 1989; Conway et al. 1995; Salmachi et al. 2019), and production performance analysis (Clarkson et al. 2007; Yarmohammadtooski et al. 2017; Zhu et al. 2018). Core laboratory test is time consuming, expensive, and limited in sampling: sometimes for the coal formation with a complex cleat system under high stress condition, the coal cores used in laboratory deviate from the actual situations from downhole to surface, resulting in a larger deviation of the measured permeability from the actual value (Yan et al. 2015). Well logging is a very convenient method for determining the permeability of the coal formation, but the evaluated permeability is proven to be much lower than the actual value based on many field case studies. The reason is that the measured permeability by well logging is actually the permeability of the coal seam in the vicinity of the wellbore, basically within a small region with a radius of 1 m, which has been damaged by well drilling and completion. Thus, the permeability evaluated by well logging cannot represent the whole CBM reservoir. Well testing method is a more concise method for evaluating the permeability of the coal formation (Conway et al. 1995; Fu et al. 2009): with some amount of water injected into the CBM wells and then these wells shut in for a while, the permeability of the coal formation can be determined by using the decreasing history of the bottom-hole pressure. Because the pressure propagated area is large after shut-in for a while, the permeability evaluated by this method is more credible. Otherwise, the well is shut in after a period of gas production without injecting water, and the bottom-hole pressure is measured and used to interpret the permeability of the coal formation (Salmachi et al. 2019). However, the well testing method needs to inject water into the well or to shut in the well for a period; it is time consuming and affects the production schedule; more importantly, it is impossible to shut in all wells to test the permeability; so other methods are needed to be proposed. Fortunately, production performance analysis method (Clarkson et al. 2007; Yarmohammadtooski et al. 2017; Zhu et al. 2018; Shi et al. 2018b, 2019a) can handle the aforementioned issues; it is not required to shut in the well and hence it does not affect the production schedule. The evaluated permeability is the average value within the control area of the CBM well, so it is more accurate and rational. Furthermore, only production performance data, such as the bottom-hole pressure history and water production history, are needed, which, however, are very easy to acquire. This method is simple, convenient, and should be broadly applied in CBM fields. The reserve evaluation methods can only be used to estimate the OGIP, while the permeability evaluation methods can only be used to determine the permeability of the coal formation. There are two types of methods for evaluating both reserve and permeability simultaneously, which are the flowing material balance equation (FMBE) method and history matching in numerical simulation. The history matching method is complicated and time consuming, resulting in that its usage is limited in reality, while the FMBE method is a very good method for determining both reserve and permeability simultaneously using only the production performance data and the properties of the CBM formation and fluids. FMBE for gas reservoirs suitable for boundary-dominated flow period was first proposed by Mattar and McNeil (1995). This method utilizes information obtained from production and bottom-hole flowing pressure to quantify the gas reserve, without having to shut-in the well. Hence, the FMBE has been widely used to determine the reservoir properties and reserves. Mattar et al. (2006), Ibrahim and Wattenbarger (2006), Clarkson (2008), Clarkson et al. (2007, 2008, 2012), Clarkson and Salmachi (2017), Gerami et al. (2007) and Sun et al. (2018d) modified the FMBE of CBM reservoirs considering the matrix shrinkage, stress sensitivity, gas desorption, gas–water two phase, and pressure–saturation relationship. Clarkson et al. (2007) and Clarkson (2008) proposed a new FMBE method considering complex CBM reservoir behavior, such as dynamic permeability and two-phase flow, which can be used to determine the water reserve, gas reserve and permeability of the coal formation by the way of straight-line fitting. However, this method is primarily limited to analyzing single-layer reservoirs. Clarkson (2008) extended their previous work; the new FMBE can be applied to CBM wells producing with multi-layers. Clarkson et al. (2012) developed the FMBE method to two-phase (gas and water) CBM reservoirs producing from vertically fractured and horizontal wells. In the next endeavor, Clarkson and Salmachi (2017) amended both gas and water phase version of the FMBE, accounting for absolute permeability (stress-dependent and desorption-dependent) and gas/water relative permeability change. It should be noted that the effects of absolute permeability and relative permeability were first time incorporated into rate-transient analysis in their research. However, the free gas expansion is not considered in their models, resulting in the prospect that the control area of the CBM well is often overestimated and even reaches an unrealistic value for some CBM wells. Thus, a more realistic FMBE method considering free gas expansion effect should be established. In all, the reserve and permeability evaluations of the coal formation are very important for the development and effective production of CBM reservoirs. As one of the unconventional gas reservoirs, the unique flow mechanism and production schedule of CBM reservoirs make the evaluation of reserve and permeability complicated. Many methods have been proposed in the literature to estimate the reserve and permeability separately. Evaluating these two important parameters simultaneously is challenging. The FMBE may be one effective approach to satisfy this acquisition. Few studies have considered the immobile free gas expansion effect on the reserve and permeability evaluations. However, the free gas expansion may make contribution to water production of CBM wells at the dewatering stage; it is necessary to consider this effect during reserve and permeability evaluations. In this work, the MBE of an undersaturated CBM reservoir at the dewatering stage is derived, in which the immobile free gas expansion is considered in the total compressibility expression. Then, coupling the water productivity equation of the CBM well and the MBE for undersaturated CBM reservoirs at the dewatering stage before gas production, the FMBE for an undersaturated CBM reservoir considering immobile free gas expansion effect is established. On the basis of the proposed FMBE, five straight-line methods are proposed to determine the control area, initial water reserve, initial free gas reserve, initial adsorbed gas reserve, OGIP, as well as permeability at the same time. Subsequently, the proposed FMBE methods for undersaturated CBM reservoirs are validated against the reservoir simulation software with and without considering free gas expansion. Finally, the proposed FMBE is applied in a field case considering the free gas expansion effect. 2 Model establishment In this section, the MBE for an undersaturated CBM reservoir at the early dewatering stage, the water productivity equation of a CBM well, and the FMBE for an undersaturated CBM reservoir at the early dewatering stage are established. The MBE, water productivity equation, and FMBE of an undersaturated CBM reservoir are developed on the basis of the following assumptions. Although there is a small amount of free gas, only water phase can flow in coal formation because the gas saturation is lower than the critical flowing gas saturation. The well bottom-hole pressure is higher than the critical desorption pressure, i.e., the adsorbed gas does not start to desorb. Single water phase flow lasts for a long time and the pressure has propagated to the boundary or the middle of multiple CBM wells, i.e., the pseudo-steady state has been achieved. Pore compressibility cp, water compressibility cw, initial water saturation Swi, reservoir thickness h, and initial porosity φi are assumed to be acquired through core tests or well logs before data fitting. 2.2 The MBE for an undersaturated CBM reservoir at the early dewatering stage For an undersaturated CBM reservoir with some small amount of free gas, in case that the initial reservoir pressure is much higher than the critical desorption pressure, and the actual gas saturation is lower than the residual gas saturation, i.e., critical flowing gas saturation, there will be a long period of dewatering stage before gas production. The material balance equation is applicable after the pseudo-steady state is achieved, i.e., the pressure should have propagated to the outer boundary. The material balance equation for a CBM reservoir after desorption is more complicated (Shi et al. 2018a), so in order to avoid the interferences of porosity change and water saturation change resulting from gas desorption on reserve and permeability evaluation, the material balance equation before gas desorption stage is analyzed in this study. During the establishment of the material balance equation, it is assumed that the pseudo-steady state should have been achieved and the bottom-hole pressure should be higher than the critical desorption pressure, i.e., gas desorption has not happened. According to the material balance principle, the residual fluid reserve is equal to the difference between the initial fluid reserve and the cumulative fluid production. $$\begin{aligned} G_{\text{r}} & = G - G_{\text{p}} \\ W_{\text{r}} & = W - W_{\text{p}} \\ \end{aligned}$$ The initial pore volume (which includes the pore volumes occupied by gas, mobile water, and immobile water at the initial reservoir conditions) is equal to the volumes occupied by residual gas, residual mobile water, and immobile water at the current reservoir conditions, plus the pore shrinkage volume owing to the pore compressibility and the encroached water volume. In addition, the pore volume occupied by the irreducible water at the current reservoir conditions is actually equal to the pore volume occupied by immobile water at the initial reservoir conditions plus the expansion volume of immobile water. Thus, the following equation can be derived $$GB_{\text{gi}} + WB_{\text{wi}} + V_{\text{pi}} S_{\text{wc}} = G_{\text{r}} B_{\text{g}} + W_{\text{r}} B_{\text{w}} + V_{\text{pi}} S_{\text{wc}} + \Delta V_{\text{p}} + \Delta V_{\text{wc}} + W_{\text{e}}$$ where ∆Vp and ∆Vwc can be derived using the definitions of pore compressibility and water compressibility, which can be expressed as $$\begin{aligned} \Delta V_{\text{p}} & = V_{\text{pi}} c_{\text{p}} \left( {p_{\text{i}} - \bar{p}} \right) \\ \Delta V_{\text{wc}} & = V_{\text{pi}} S_{\text{wc}} c_{\text{w}} \left( {p_{\text{i}} - \bar{p}} \right) \\ \end{aligned}$$ Substituting Eqs. (3) into (2) yields $$GB_{\text{gi}} + WB_{\text{wi}} = \left( {G - G_{\text{p}} } \right)B_{\text{g}} + \left( {W - W_{p} } \right)B_{\text{w}} + V_{\text{pi}} c_{\text{p}} \left( {p_{\text{i}} - \bar{p}} \right) + V_{\text{pi}} S_{\text{wc}} c_{\text{w}} \left( {p_{\text{i}} - \bar{p}} \right) + W_{\text{e}} .$$ Organizing Eq. (4) gives $$G_{\text{p}} B_{\text{g}} { + }W_{\text{p}} B_{\text{w}} - W_{\text{e}} = G\left( {B_{\text{g}} - B_{\text{gi}} } \right) + W\left( {B_{\text{w}} - B_{\text{wi}} } \right) + V_{\text{pi}} \left( {c_{\text{p}} { + }S_{\text{wc}} c_{\text{w}} } \right)\left( {p_{\text{i}} - \bar{p}} \right).$$ $$G{ = }\frac{{V_{\text{pi}} \left( {1 - S_{\text{wi}} } \right)}}{{B_{\text{gi}} }}$$ $$W = \frac{{V_{\text{pi}} \left( {S_{\text{wi}} - S_{\text{wc}} } \right)}}{{B_{\text{wi}} }}.$$ Substituting Eqs. (6) and (7) into Eq. (5) yields $$G_{\text{p}} B_{\text{g}} { + }W_{\text{p}} B_{\text{w}} - W_{\text{e}} = V_{\text{pi}} \left( {1 - S_{\text{wi}} } \right)\frac{{\left( {B_{\text{g}} - B_{\text{gi}} } \right)}}{{B_{\text{gi}} }} + V_{\text{pi}} \left( {S_{\text{wi}} - S_{\text{wc}} } \right)\frac{{\left( {B_{\text{w}} - B_{\text{wi}} } \right)}}{{B_{\text{wi}} }} + V_{\text{pi}} \left( {c_{\text{p}} { + }S_{\text{wc}} c_{\text{w}} } \right)\left( {p_{\text{i}} - \bar{p}} \right)$$ At the dewatering stage of undersaturated CBM reservoirs, before the gas production, Gp is zero; hence, Eq. (8) can be changed to $$W_{\text{p}} B_{\text{w}} - W_{\text{e}} = V_{\text{pi}} \left( {1 - S_{\text{wi}} } \right)\frac{{\left( {B_{\text{g}} - B_{\text{gi}} } \right)}}{{B_{\text{gi}} }} + V_{\text{pi}} \left( {S_{\text{wi}} - S_{\text{wc}} } \right)\frac{{\left( {B_{\text{w}} - B_{\text{wi}} } \right)}}{{B_{\text{wi}} }} + V_{\text{pi}} \left( {c_{\text{p}} { + }S_{\text{wc}} c_{\text{w}} } \right)\left( {p_{\text{i}} - \bar{p}} \right)$$ According to the definitions of water compressibility and gas compressibility, $$c_{\text{w}} = - \frac{{\Delta B_{\text{w}} }}{{B_{\text{wi}} \Delta p}}$$ $$c_{\text{g}} = - \frac{{\Delta \left[ {\left( {G - G_{\text{p}} } \right)B_{\text{g}} } \right]}}{{GB_{\text{gi}} \Delta p}}.$$ Because Gp is zero at the early dewatering stage, $$c_{\text{g}} = - \frac{{\Delta B_{\text{g}} }}{{B_{\text{gi}} \Delta p}}.$$ Thus, the following two equations can be obtained: $$\frac{{ {B_{\text{w}} - B_{\text{wi}} }}}{{B_{\text{wi}} }} = c_{\text{w}} \left( {p_{\text{i}} - \bar{p}} \right)$$ $$\frac{{ {B_{\text{g}} - B_{\text{gi}} }}}{{B_{\text{gi}} }} = \bar{c}_{\text{g}} \left( {p_{\text{i}} - \bar{p}} \right)$$ where $\bar{c}_{\text{g}}$ can be calculated using the Z factor plot versus pressure, which can be expressed as $\bar{c}_{\text{g}} = 1/\bar{p} - (1/Z)(\partial Z /\partial \bar{p})$, in which the average pressure at the time range for data fitting can be simply calculated by $\bar{p} = (p_{\text{i}} + \bar{p}_{\text{wf}} ) /2$. Substituting Eqs. (13) and (14) into Eq. (9) and organizing it gives $$W_{\text{p}} B_{\text{w}} - W_{\text{e}} = V_{\text{pi}} \left( {p_{\text{i}} - \bar{p}} \right)\left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]$$ For homogeneous undersaturated CBM reservoirs, if no free gas exists, before the bottom-hole pressure decreases below the critical desorption pressure, single water phase flow exists. The water is produced owing only to the pore and water expansion. If there is a small amount of free gas at the initial state in undersaturated CBM reservoirs and the initial gas saturation is less than the critical flowing gas saturation, this small amount of gas will expand with the water production at the early dewatering stage. In this case, the total compressibility will increase dramatically because of gas expansion, even though the initial gas saturation is very small. The total compressibility can be expressed as $$c_{\text{t}} = c_{\text{p}} + S_{\text{wi}} c_{\text{w}} + \left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} .$$ 2.3 The water productivity equation of a CBM well Based on the Darcy flow equation, the relationship between the water production and the pressure gradient can be expressed as $$q_{\text{w}} = \frac{{2\pi rhk{_\text{w}}}}{{\mu_{\text{w}} B_{\text{w}} }}\frac{{\text{d} p}}{{\text{d} r}}.$$ Integrating Eq. (17) from the wellbore to the reservoir and converting SI units to field units yield $$\frac{{0.543k_{_\text{w}}h}}{{\mu_{\text{w}} B_{\text{w}} q_{\text{w}} }}\int\limits_{{p_{\text{wf}} }}^{{\bar{p}}} {\text{d} p} = \int\limits_{{r_{\text{w}} }}^{{\bar{r}}} {\frac{1}{r}\text{d} r} .$$ Organizing Eq. (18) gives $$\frac{{0.543k_{\text{w}}h\left( {\bar{p} - p_{\text{wf}} } \right)}}{{\mu_{\text{w}} B_{\text{w}} q_{\text{w}} }} = \ln \frac{{\bar{r}}}{{r_{\text{w}} }}.$$ According to fluid flow principle in porous media and oil and gas reservoir engineering (Li 2008; Cheng 2011), one obtains $$\bar{r} = 0.472r_{\text{e}}$$ Considering the well completion pattern and skin factor, rw in Eq (19) is replaced by rwc. For a vertically fractured CBM well, $r_{\text{wc}} = ({{L_{\text{f}} } \mathord{\left/ {\vphantom {{L_{\text{f}} } 2}} \right. \kern-0pt} 2}) \cdot \text{e}^{ - s}$ (Shi et al. 2018b, c; Dejam et al. 2014, 2017, 2018a, b; Dejam 2019; Zhang et al. 2018); for a damaged or stimulated vertical well, $r_{\text{wc}} = r_{\text{w}} \cdot \text{e}^{ - s}$. If a well is damaged, the skin factor s will be a positive value, while if the well is stimulated, the skin factor s will be a negative value. Thus, Eq. (19) will be changed to $$\frac{{0.543k_{\text{w}}h\left( {\bar{p} - p_{\text{wf}} } \right)}}{{\mu_{\text{w}} B_{\text{w}} q_{\text{w}} }} = \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ 2.4 The FMBE for an undersaturated CBM reservoir at the early dewatering stage The FMBE of CBM reservoirs can be derived by coupling the MBE of CBM reservoirs with the productivity equation of a CBM well. The water productivity equation of a CBM well Eq. (21) can be rewritten into the following form: $$\left( {\bar{p} - p_{\text{i}} } \right) + \left( {p_{\text{i}} - p_{\text{wf}} } \right) = \frac{{\mu_{\text{w}} B_{\text{w}} q_{\text{w}} }}{{0.543k_{\text{w}}h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ Substituting Eqs. (15) into (22) yields $$\left( {p_{\text{i}} - p_{\text{wf}} } \right) - \frac{{W_{\text{p}} B_{\text{w}} - W_{\text{e}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} = \frac{{\mu_{\text{w}} B_{\text{w}} q_{\text{w}} }}{{0.543k_{\text{w}}h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ If encroached water is not considered, i.e., We is equal to 0, Eq. (23) can be written as: $$\left( {p_{\text{i}} - p_{\text{wf}} } \right) - \frac{{W_{\text{p}} B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} = \frac{{\mu_{\text{w}} B_{\text{w}} q_{\text{w}} }}{{0.543k_{\text{w}}h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ Equations (23) and (24) will be the FMBEs for an undersaturated CBM reservoir at the early dewatering stage considering the immobile free gas expansion effect. 3 Five methods for evaluating reserve and permeability of undersaturated CBM reservoirs In this section, five methods for evaluating reserve and permeability of undersaturated CBM reservoirs, considering free gas expansion, are developed on the basis of the proposed FMBE for an undersaturated CBM reservoir at the early dewatering stage. 3.1 Method 1 Organizing Eq. (24) yields $$\frac{{0.543k_{\text{w}}h}}{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}\left( {p_{\text{i}} - p_{\text{wf}} } \right) - \frac{{0.543k_{\text{w}}h}}{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}\frac{{W_{\text{p}} B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} = q_{\text{w}} .$$ Finally, the following equation is derived: $$\frac{{q_{\text{w}} }}{{p_{\text{i}} - p_{\text{wf}} }} = \frac{{0.543k_{\text{w}}h}}{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}} - \frac{{0.543k_{\text{w}}h}}{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}} \cdot \frac{{B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} \cdot \frac{{W_{\text{p}} }}{{p_{\text{i}} - p_{\text{wf}} }}.$$ This equation can be rewritten as $$Y_{1} = b_{1} - m_{1} X_{1}$$ $$Y_{1} = \frac{{q_{\text{w}} }}{{p_{\text{i}} - p_{\text{wf}} }}$$ $$X_{1} = \frac{{W_{\text{p}} }}{{p_{\text{i}} - p_{\text{wf}} }}$$ $$b_{1} = \frac{{0.543k_{\text{w}}h}}{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}$$ $$m_{1} = \frac{{b_{1} B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}}.$$ In the plot of Y1 versus X1, a straight line will be obtained and the slope and the y-intercept of the straight line will be determined. Using pore compressibility, water compressibility, initial water saturation, the average gas compressibility, and the slope and y-intercept of the straight line, the control volume of this CBM reservoir can be determined as $$V_{\text{pi}} = \frac{{b_{1} B_{\text{w}} }}{{m_{1} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}}.$$ Thus, the control radius of this CBM well will be determined through substituting the values of formation thickness, the initial porosity, and the control volume evaluated by Eq. (32) into the following equation: $$r_{\text{e}} = \sqrt {\frac{{V_{\text{pi}} }}{{\pi h\phi_{\text{i}} }}} .$$ Using reservoir thickness, the water formation volume factor, the water viscosity, the y-intercept of the straight line and the control radius evaluated by Eq. (33), the cleat permeability of the coal formation can be evaluated to be $$k_{\text{w}} = \frac{{b_{1} \mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}{0.543h}.$$ Equation (24) can be organized to be the following form: $$\frac{{p_{\text{i}} - p_{\text{wf}} }}{{q_{\text{w}} }} = \frac{{\mu_{\text{w}} B_{\text{w}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }} + \frac{{B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}}\frac{{W_{\text{p}} }}{{q_{\text{w}} }}.$$ $$Y_{2} = b_{2} + m_{2} X_{2}$$ $$Y_{2} = \frac{{p_{\text{i}} - p_{\text{wf}} }}{{q_{\text{w}} }}$$ $$X_{2} = \frac{{W_{\text{p}} }}{{q_{\text{w}} }}$$ $$b_{2} = \frac{{\mu_{\text{w}} B_{\text{w}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}$$ $$m_{2} = \frac{{B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}}.$$ In the plot of Y2 versus X2, a straight line will be obtained and the slope and the y-intercept of the straight line will be determined. The control volume and control radius of the CBM reservoir can be determined by using Eqs. (40) and (33). And the cleat permeability of the coal formation can be evaluated by substituting the value of the control radius into Eq. (39). Equation (24) can be transformed as the following equation: $$\frac{{p_{\text{i}} - p_{\text{wf}} }}{{W_{\text{p}} }} = \frac{{B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} + \frac{{\mu_{\text{w}} B_{\text{w}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}\frac{{q_{\text{w}} }}{{W_{\text{p}} }}.$$ $$Y_{3} = \frac{{p_{\text{i}} - p_{\text{wf}} }}{{W_{\text{p}} }}$$ $$X_{3} = \frac{{q_{\text{w}} }}{{W_{\text{p}} }}$$ $$b_{3} = \frac{{B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}}$$ $$m_{3} = \frac{{\mu_{\text{w}} B_{\text{w}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ Similarly, in the plot of Y3 versus X3, a straight line will be obtained and the slope and y-intercept of the straight line will be determined. Similar to the above methods, the control volume, control radius, and the cleat permeability of the CBM reservoir can be determined by using Eqs. (45), (33), and (46). Rearranging Eq. (23), the bottom-hole pressure can be expressed as $$p_{\text{wf}} = p_{\text{i}} - \frac{{W_{\text{p}} B_{\text{w}} - W_{\text{e}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} - \frac{{\mu_{\text{w}} B_{\text{w}} q_{\text{w}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ The bottom-hole pressure at the last time step (for instance, yesterday) can be expressed as $$p_{{{\text{wf,}}\left( {j - 1} \right)}} = p_{\text{i}} - \frac{{W_{{{\text{p,}}\left( {j - 1} \right)}} B_{\text{w}} - W_{\text{e}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} - \frac{{\mu_{\text{w}} B_{\text{w}} q_{{{\text{w,}}\left( {j - 1} \right)}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ The bottom-hole pressure at the current state (for instance, today) can be expressed as $$p_{{{\text{wf,}}\left( j \right)}} = p_{\text{i}} - \frac{{W_{{{\text{p,}}\left( j \right)}} B_{\text{w}} - W_{\text{e}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} - \frac{{\mu_{\text{w}} B_{\text{w}} q_{{{\text{w,}}\left( j \right)}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ Subtracting Eqs. (49) from (48) yields $$p_{{{\text{wf,}}\left( {j - 1} \right)}} - p_{{{\text{wf,}}\left( j \right)}} = \frac{{\left( {W_{{{\text{p,}}\left( j \right)}} - W_{{{\text{p,}}\left( {j - 1} \right)}} } \right)B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} + \frac{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}{{0.543k_{\text{w}} h}}\left( {q_{{{\text{w,}}\left( j \right)}} - q_{{{\text{w,}}\left( {j - 1} \right)}} } \right).$$ Because the product of water production rate at the current state and the time step δt plus the cumulative water production at the last time step is equal to the cumulative water production at the current state, the following equation can be derived: $$W_{{{\text{p,}}\left( j \right)}} - W_{{{\text{p,}}\left( {j - 1} \right)}} = q_{{{\text{w,}}\left( j \right)}} \cdot \delta t$$ where δt is the time step, which is often set as 1 day because the dynamic performance data of CBM wells are daily data usually. So, Eq. (50) can be expressed as $$p_{{{\text{wf,}}\left( {j - 1} \right)}} - p_{{{\text{wf,}}\left( j \right)}} = \left\{ {\frac{{B_{\text{w}} \delta t}}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} + \frac{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}{{0.543k_{\text{w}} h}}} \right\}q_{{{\text{w,}}\left( j \right)}} - \frac{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}{{0.543k_{\text{w}} h}}q_{{{\text{w,}}\left( {j - 1} \right)}} .$$ $$\frac{{p_{{{\text{wf,}}\left( {j - 1} \right)}} - p_{{{\text{wf,}}\left( j \right)}} }}{{q_{{{\text{w,}}\left( j \right)}} }} = \left\{ {\frac{{B_{\text{w}} \delta t}}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} + \frac{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}{{0.543k_{\text{w}} h}}} \right\} - \frac{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}{{0.543k_{\text{w}} h}}\frac{{q_{{{\text{w,}}\left( {j - 1} \right)}} }}{{q_{{{\text{w,}}\left( j \right)}} }}.$$ $$Y_{4} = \frac{{p_{{{\text{wf,}}\left( {j - 1} \right)}} - p_{{{\text{wf,}}\left( j \right)}} }}{{q_{{{\text{w,}}\left( j \right)}} }}$$ $$X_{4} = \frac{{q_{{{\text{w,}}\left( {j - 1} \right)}} }}{{q_{{{\text{w,}}\left( j \right)}} }}$$ $$m_{4} = \frac{{\mu_{\text{w}} B_{\text{w}} \ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}}}{{0.543k_{\text{w}} h}}$$ $$b_{4} = \frac{{B_{\text{w}} \delta t}}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} + m_{4} .$$ Similarly, in the plot of Y4 versus X4, a straight line will be obtained. The slope and y-intercept of the straight line will be determined by fitting this straight line with linear relationship. Then the control volume, control radius, and the cleat permeability of the CBM reservoir can be determined by substituting the fitted slope and y-intercept of the straight line into Eqs. (58), (33), and (57), respectively. Equation (24) can be changed to $$p_{\text{i}} - p_{\text{wf}} = \frac{{W_{\text{p}} B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}} + \frac{{\mu_{\text{w}} B_{\text{w}} q_{\text{w}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ Then integrating Eq. (59), we can get $$\int\limits_{0}^{t} {\left( {p_{\text{i}} - p_{\text{wf}} } \right)\text{d} t} = \frac{{B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}}\int\limits_{0}^{t} {W_{\text{p}} \text{d} t} + \frac{{\mu_{\text{w}} B_{\text{w}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}\int\limits_{0}^{t} {q_{\text{w}} \text{d} t} .$$ When the equations on both sides of the equal sign are simultaneously divided by the cumulative water production (Wp), the following expression can be obtained: $$\frac{{\int\limits_{0}^{t} {\left( {p_{\text{i}} - p_{\text{wf}} } \right)\text{d} t} }}{{W_{\text{p}} }} = \frac{{B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}}\frac{{\int\limits_{0}^{t} {W_{\text{p}} \text{d} t} }}{{W_{\text{p}} }} + \frac{{\mu_{\text{w}} B_{\text{w}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ Equation (60) can be seen as a linear equation: $$Y_{5} = m_{5} X_{5} + b_{5}$$ $$Y_{5} = \frac{{\int\limits_{0}^{t} {\left( {p_{\text{i}} - p_{\text{wf}} } \right)\text{d} t} }}{{W_{\text{p}} }}$$ $$X_{5} = \frac{{\int\limits_{0}^{t} {W_{\text{p}} \text{d} t} }}{{W_{\text{p}} }}$$ $$m_{5} = \frac{{B_{\text{w}} }}{{V_{\text{pi}} \left[ {c_{\text{p}} + S_{\text{wi}} c_{\text{w}} { + }\left( {1 - S_{\text{wi}} } \right)\bar{c}_{\text{g}} } \right]}}$$ $$b_{5} = \frac{{\mu_{\text{w}} B_{\text{w}} }}{{0.543k_{\text{w}} h}}\ln \frac{{0.472r_{\text{e}} }}{{r_{\text{wc}} }}.$$ It can be seen from the above derivation that we only need to obtain the thickness of the reservoir around the CBM well, the water formation volume factor, the water viscosity, the bottom-hole pressure during the dewatering period and the water production data, then the control pore volume of this CBM reservoir and the initial reservoir permeability can be easily extrapolated. The detailed data processing steps are as follows: Substituting the cumulative water production data at different production times into Eq. (64), a set of data that changes over time can be obtained, which is recorded as X5. Substituting the initial reservoir pressure, bottom-hole pressure, and the cumulative water production into Eq. (63), we can obtain another set of data Y5 that varies with production time. Depicting X5 and Y5 in a rectangular coordinate system and fitting the data with a linear trend line, a linear equation with the same expression as Eq. (62) can be obtained. The slope and y-intercept of the fitted trend line in the coordinate system are m5 and b5 in Eq. (62), respectively. The control pore volume of this CBM reservoir can be calculated by substituting pore compressibility, water compressibility, initial water saturation, the average gas compressibility, and the slope of straight line m5 into Eq. (65). Thus, the control radius of this CBM well will be determined by substituting the formation thickness, the initial porosity, and the calculated control volume into Eq. (33). The initial permeability around a CBM well can be calculated by substituting the reservoir thickness, the water formation volume factor, the water viscosity, the control radius of this CBM well, and the y-intercept of straight line b5 into Eq. (66). After the control volume and the permeability of this CBM reservoir are evaluated using the above five methods, the initial free gas reserve and the initial water reserve can be determined using Eqs. (6) and (7), respectively. Substituting the evaluated control volume, initial porosity, Langmuir volume, Langmuir pressure, and critical desorption pressure into Eq. (67), the initial adsorbed gas reserve can be determined. $$G_{\text{a}} { = }\frac{{V_{\text{pi}} }}{{\phi_{\text{i}} }} \cdot \frac{{V_{\text{L}} p_{\text{d}} }}{{p_{\text{d}} + p_{\text{L}} }}.$$ 4 Validation A CBM dynamic analysis software developed by Shi et al. (2018a, 2019b) is used to verify the proposed FMBE methods. The CBM dynamic analysis software has been validated against commercial reservoir simulators, such as CMG and Eclipse, and shown to be effective and rational based on some field applications in the Hancheng CBM reservoir, Baode CBM reservoir, Muai CBM reservoir, Qimei CBM reservoir, Liulin CBM reservoir, etc. Thus, it is reasonable to apply this software to verify the proposed FMBE methods. In this work, two case studies are conducted based on the formation and fluid properties as shown in Table 1. The rest parameters for these two cases are the same except of the initial water saturation, critical flowing gas saturation, and relative permeability curves. One is for an undersaturated CBM reservoir without any free gas, i.e., the initial water saturation is 1; the other is for an undersaturated CBM reservoir with 0.05 of free gas in gas saturation. The dynamic analysis software is applied to generate the water and gas production histories by inputting the given bottom-hole pressure schedule and formation and fluid parameters. Then the output water production rate and the input bottom-hole pressure are used to test the effectiveness of the proposed five FMBE methods. If the straight-line relationships between Y and X are good and the evaluated results including the control area, water reserve, free gas reserve, adsorbed gas reserve, OGIP, and permeability of the coal formation are coincident with the actual values used in the dynamic analysis software, the proposed FMBE methods will be proven to be effective, rational, and applicable for evaluating both reserve and permeability of undersaturated CBM reservoirs. The formation and fluid properties for Case I and Case II Case I Case II Initial water saturation Swi, fraction Critical flowing gas saturation Sgc, fraction Control radius re, m Wellbore radius rw, m Coal formation thickness h, m Porosity of coal formation ϕi, fraction Water viscosity μw, mPa s Water volume factor Bw, sm3/m3 Pore compressibility cp, MPa−1 Water compressibility cw, MPa−1 Initial reservoir pressure pi, MPa Critical desorption pressure pd, MPa Langmuir volume VL, m3/m3 Langmuir pressure pL, MPa Permeability of coal formation k, mD Coal formation temperature T, °C Gas specific gravity, dimensionless Initial gas deviation factor Zi, dimensionless The relative permeability curves used for Case I and Case II are shown in Fig. 1. The CBM wells for these two cases are produced by controlling the bottom-hole pressure as shown black triangles in Figs. 2 and 3. On the basis of the formation and fluid parameters in Table 1 and the given bottom-hole pressure schedules, water and gas production rates for Case I and Case II are generated from the dynamic analysis software, which are shown in Figs. 2 and 3, respectively. Relative permeability curves of water and gas for Case I (a) and Case II (b). The critical flowing gas saturation is 0.03 and 0.15 for Case I and Case II, respectively Water and gas production rates generated from the dynamic analysis software produced at a given bottom-hole pressure schedule for Case I Water and gas production rates generated from the dynamic analysis software produced at a given bottom-hole pressure schedule for Case II Using the water production rates before the gas desorption stage generated from the software, which are shown as blue circles before 500 days of production in Fig. 2b for Case I, blue circles before 400 days of production in Fig. 3b for Case II, and the given bottom-hole pressure schedules in Fig. 2b for Case I and Fig. 3b for Case II, the proposed five FMBE methods are applied to form the straight lines of Y versus X for these two cases. Then, the control radius of these two CBM wells, water reserve, OGIP, and permeability of the coal formation are evaluated from the slopes and y-intercepts of these straight lines on the basis of some given formation and fluid parameters except the control radius and the permeability for these two cases. Figures 4 and 5 present the fitting plots by these five FMBE methods for Case I and Case II. Tables 2 and 3 show the fitting results from these five FMBE methods and the actual data for Case I and Case II, respectively. From Figs. 4 and 5, it can be clearly seen that the straight-line relationships for the proposed five FMBE methods are very excellent for these two cases. From the comparisons of results between the evaluated values and actual values, as shown in Table 2 for Case I and Table 3 for Case II, the evaluated reserves and permeability are nearly equal to the actual values for Case I, and within 1% in relative errors of reserve evaluations and 2% in relative errors of permeability evaluations for Case II, indicating that the proposed five FMBE methods are effective and rational even for CBM reservoirs with small amount of free gas. The fitting plots by these five FMBE methods for Case I. aX1 is calculated by Eq. (29), and Y1 is calculated by Eq. (28); bX2 is calculated by Eq. (38), and Y2 is calculated by Eq. (37); cX3 is calculated by Eq. (44), and Y3 is calculated by Eq. (43); dX4 is calculated by Eq. (56), and Y4 is calculated by Eq. (55); eX5 is calculated by Eq. (64), and Y5 is calculated by Eq. (63) The fitting plots by these five FMBE methods for Case II. aX1 is calculated by Eq. (29), and Y1 is calculated by Eq. (28); bX2 is calculated by Eq. (38), and Y2 is calculated by Eq. (37); cX3 is calculated by Eq. (44), and Y3 is calculated by Eq. (43); dX4 is calculated by Eq. (56), and Y4 is calculated by Eq. (55); eX5 is calculated by Eq. (64), and Y5 is calculated by Eq. (63) The fitting results from the proposed five FMBE methods and the actual data for Case I Actual values Slope of the straight line m 9.323 × 10−3 y-intercept of the straight line b Control pore volume Vpi, m3 Water reserve, m3 Adsorbed gas reserve Ga, 104 m3 Free gas reserve Gf, 104 m3 OGIP, 104 m3 The fitting results from the proposed five FMBE methods and the actual data for Case II Relative error of OGIP, % − 0.003 Relative error of water reserve, % Relative error of permeability, % For Case II, because there is a small amount of free gas, during the dewatering stage, the gas expansion effect cannot be ignored. Since by using the water production data and bottom-hole pressure from 40 and 262 days, the best fitting results for the straight-line relationship between Y and X are obtained, the bottom-hole pressure history between 40 and 262 days is used to calculate the average gas compressibility. For this case, the average value of the bottom-hole pressure from 40 to 262 days is 4.4641 MPa, the average reservoir pressure is calculated to be 4.8620 MPa, Z factor is 0.9293 at this average reservoir pressure, ${{\partial Z} \mathord{\left/ {\vphantom {{\partial Z} {\partial \bar{p}}}} \right. \kern-0pt} {\partial \bar{p}}}$ is − 0.01271 from the plot of Z factor versus pressure as shown in Fig. 6, and thus, the average gas compressibility is calculated to be 0.2194 MPa−1. The plot of Z factor of gas versus pressure for Case II and the field case. The gas specific gravity is 0.552, and the coal formation temperature is 32 °C If the initial water saturation is mistaken as 1 for Case II, using the bottom-hole pressure and water production data in Fig. 3b, the straight-line relationship in the plots of Y versus X is still good when using the proposed five FMBE methods, but the evaluated results including the control radius, water reserve, OGIP, and permeability largely deviate from the actual values, as shown in Table 4. The evaluated control radius is larger than the actual control radius of this CBM well up to 40% of the actual value, the evaluated water reserves are more than two times the actual values, and the evaluated initial adsorbed gas reserve and OGIP are larger than the corresponding actual values up to 96% and 94%, respectively. In addition, the permeability is also overestimated. Therefore, the effect of gas expansion on the reserve and permeability evaluations using FMBE methods is very sensitive and important; so it cannot be ignored. Even though the amount of free gas is small, its expansion effect on water production rate is dramatic. A comparison between the actual data and those evaluated by the proposed five FMBE methods when ignoring free gas expansion for Case II Relative error of re, % Relative error of Ga, % 5 Field application After validation of the proposed five FMBE methods, it is necessary to test their effectiveness in field application. One well in the Muai CBM reservoir is taken as an example; the formation and fluid properties are listed in Table 5. The gas and water relative permeability curves are shown in Fig. 1b. The actual bottom-hole pressure history and the corresponding water and gas production rate histories are shown in Fig. 7. The formation and fluid properties for one well in the Muai CBM reservoir Equivalent wellbore radius rwc, m Water viscosity μw, mPa·s Water volume factor, sm3/m3 The actual bottom-hole pressure history and the corresponding water and gas production rate histories of the well in the Muai CBM reservoir From Fig. 7, it can be clearly seen that before 300 days, the bottom-hole pressure is higher than the critical desorption pressure and there is no gas production. Thus, the bottom-hole pressure and water production rate data before 300 days are selected, and the proposed five FMBE methods are applied to generate the straight lines of Y versus X. Finally, the bottom-hole pressure and water production rate data from 30 days to 148 days are selected to make sure that pseudo-steady state has been achieved and avoided the influence of fracturing fluid flowback. Figure 8 presents the fitting plots by these five FMBE methods for this field case. From Fig. 8, it can be seen that the straight-line relationship of methods 1, 2, 3, and 5 is very good, while the straight-line relationship of method 4 is not good; the reason is that the water production rate nearly remains constant during dewatering, as shown in Fig. 7, resulting in X values close to 1. The fitting plots by these five FMBE methods for the field case. aX1 is calculated by Eq. (29), and Y1 is calculated by Eq. (28); bX2 is calculated by Eq. (38), and Y2 is calculated by Eq. (37); cX3 is calculated by Eq. (44), and Y3 is calculated by Eq. (43); dX4 is calculated by Eq. (56), and Y4 is calculated by Eq. (55); eX5 is calculated by Eq. (64), and Y5 is calculated by Eq. (63) The average gas compressibility is calculated using the average reservoir pressure and Z factor plot versus pressure, where the average reservoir pressure is calculated using the initial reservoir pressure and the average value of bottom-hole pressure from 30 to 148 days. For this field case, the average value of the bottom-hole pressure from 30 to 148 days is 5.4175 MPa, the average reservoir pressure is calculated to be 5.9588 MPa, Z factor is 0.9159 at this average reservoir pressure, ${{\partial Z} \mathord{\left/ {\vphantom {{\partial Z} {\partial \bar{p}}}} \right. \kern-0pt} {\partial \bar{p}}}$ is − 0.0119 from the plot of Z factor versus pressure which is shown in Fig. 6; thus, the average gas compressibility is calculated to be 0.1807 MPa−1. Then, on the basis of the formation and fluid parameters in Table 5 and calculated average gas compressibility, using the slope and y-intercept of these straight lines, the control radius of this CBM well, water reserve, initial adsorbed gas reserve, initial free gas reserve, OGIP, and the permeability of the coal formation are evaluated, which are shown in Table 6. The fitting results from methods 1, 2, 3, and 5 are very close to each other, while the fitting results from method 4 is not good; so the evaluated results by method 4 is not used, but those evaluated by methods 1, 2, 3, and 5 are used as the final results. Thus, the control radius of this CBM well is about 120 m, the OGIP controlled by this CBM well is estimated to be about 540 × 104 m3, which is in accordance with OGIP evaluated by Shi's MBE method (Shi et al. 2018a). The permeability of the coal formation is evaluated to be about 0.22 mD, which agrees with the evaluated permeability for Muai research area by Shi's method using dewatering data (Shi et al. 2018b, 2019a). The fitting results from the proposed five FMBE methods for the field case Free gas may exist in undersaturated CBM reservoirs Based on the current classification of CBM reservoirs, CBM reservoirs are classified as saturated and undersaturated according to the difference between the measured and theoretical gas contents (Zhao et al. 2014). Although the measured total gas amount is less than the theoretical adsorption gas content estimated by the Langmuir equation at the initial reservoir pressure, few evidences indicate that all the measured gas amounts are in adsorbed state. In reality, the existence of free gas in undersaturated CBM reservoirs has already been proven through field applications (Sun et al. 2017, 2018b; Shi et al. 2018a, 2019b), such as the Muai CBM reservoir in the Junlian production area in the southern Sichuan Basin, the initial water saturation is fitted to be less than 1 during the history matching process, demonstrating there is a small amount of free gas in this undersaturated CBM reservoir. Furthermore, some researchers have concluded that there exist tight sandstone gas layers with free gas from nearby coal seams although these coal seams are measured and classified as undersaturated CBM reservoirs (Li et al. 2018), indicating that there must exist free gas in these undersaturated CBM reservoirs in the past and there may still exist some free gas at the current state. The possible forming mechanism of such CBM reservoirs can be described as follows. When a saturated CBM reservoir (which contains excessive methane) subsides to a deeper formation because of tectonic movement, the pressure increases rapidly, but the methane generation is very gradual, resulting in that the actual adsorption gas amount is less than the expected adsorption gas amount after subsidence. In this case, the actual adsorption gas amount in this CBM reservoir is equal to the expected adsorption gas amount at the formation pressure before subsidence, and the free gas in this saturated CBM reservoir before subsidence cannot re-adsorb to the coal surface to become adsorption gas again because of water existence in coal formation; this CBM reservoir will be called undersaturated CBM reservoir with some free gas. The application condition and effectiveness of the proposed five FMBE methods As mentioned above in the field case study, the FMBE method 4 is not applicable when the water production rate approximately remains constant, but it is effective for the case that the daily water production is continuously changing. Different from the method 4, the other four FMBE methods are constantly suitable no matter whether the water production rate is stable or not. The FMBE method 1 is more applicable for the case with relatively high water production rate. On the contrary, method 2 is more accurate for CBM wells with low water production rate. As for method 3, since it focuses more on the early dewatering stage, it has more accuracy than other methods for the case with large variation of water production at the late dewatering stage. The FMBE method 5 is the most stable method with almost the highest R2 in fitting plot. It is worth noting that from derivation processes of these five methods, only in method 4 the water influx We is not assumed to be 0, demonstrating that method 4 is still applicable for undersaturated CBM reservoirs with water influx. In other words, method 4 enjoys higher priority compared to the other four methods for the case without information about water influx. In field application, these five FMBE methods can be used together to evaluate the control area of the CBM well, the water reserve, the initial water reserve, the initial adsorbed gas reserve, the initial free gas reserve, OGIP, and the permeability of the coal formation. The most rational values can be determined from the final results via comparing and analyzing these fitting results evaluated by these five methods. 7 Summary and conclusions On the basis of water productivity equation of a CBM well and the MBE for undersaturated CBM reservoirs at the dewatering stage, the FMBE is established for undersaturated CBM reservoirs, which considers immobile free gas expansion effect; then five straight-line methods are proposed to determine the control area, initial water reserve, initial free gas reserve, initial adsorbed gas reserve, OGIP, and permeability at the same time. Two validation cases with and without considering free gas expansion prove the effectiveness of the proposed five FMBE methods. Only the bottom-hole pressure and water production rate data during the time range after the pseudo-steady state and before gas desorption are needed for evaluating the water and gas reserves controlled by the CBM well and the permeability of coal formation simultaneously using the proposed five FMBE methods. These five methods should be broadly applied in field cases. The immobile free gas expansion should be considered in the total compressibility expression when establishing the MBE of undersaturated CBM reservoirs at the dewatering stage. A small amount of free gas will result in a large increase in the total compressibility. If the free gas expansion effect is ignored, the control area of the CBM well, water reserve and OGIP will be greatly overestimated. The research was supported by the National Science and Technology Major Projects of China (No. 2016ZX05042 and No. 2017ZX05039) and the National Natural Science Foundation Projects of China (No. 51504269 and No. 51490654). 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To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. 1.State Key Laboratory of Petroleum Resources and ProspectingChina University of Petroleum BeijingBeijingChina 2.MOE Key Laboratory of Petroleum EngineeringChina University of Petroleum BeijingBeijingChina 3.PetroChina Coalbed Methane Company LimitedBeijingChina 4.PetroChina Zhejiang Oil Field Company LimitedHangzhouChina 5.The University of TexasAustinUSA Shi, JT., Wu, JY., Sun, Z. et al. Pet. Sci. (2020). https://doi.org/10.1007/s12182-019-00410-3 Publisher Name China University of Petroleum (Beijing)	CommonCrawl
← The Born rule is obvious How to manipulate numbers and get any result you want → The many-worlds interpretation of objective probability Posted on 11th April 2019 by Mateus Araújo Philosophers really like problems. The more disturbing and confusing the better. If there's one criticism you cannot levy at them is that they are not willing to tackle the difficult issues. I have argued with philosophers endlessly about Bell's theorem, the Trolley problem, Newcomb's paradox, Searle's Chinese room, the sleeping beauty problem, etc. Which made me very surprised when I asked a couple of philosophers about objective probability, and found them strangely coy about it. The argument went along the lines of "objective probability is frequentism, frequentism is nonsense, subjective probability makes perfect sense, there's only subjective probability". Which is really bizarre argument. Yes, frequentism is nonsense, and yes, subjective probability makes perfect sense. But that's all that is true about it. No, objective probability is not the same thing as frequentism, and no, subjective probability is not the only probability that exists. Come on, that's denying the premise! The question is interesting precisely because we strongly believe that objective probability exists; either because of quantum mechanics, or more directly from the observation of radioactive decay. Does anybody seriously believe that whether some atom decays or not depends on the opinion of an agent? There even existed natural nuclear reactors, where chain reactions occurred much before any agent existed to wonder about them. In any case, it seems that philosophers won't do anything about it. What can we say about objective probability, though? It is easy to come up with some desiderata: it should to be objective, to start with. The probability of some radioactive atom decaying should just be a property of the atom, not a property of some agent betting about it. Agents and bets are still important, though, as it should make sense to bet according to the objective probabilities. In other words, Lewis' Principal Principle should hold: rational agents should set their subjective probabilities to be equal to the objective probabilities, if the latter are known1This is arguably a property that subjective, not objective probabilities should obey. But I think it is fair to include it in the list of desiderata, as a notion of objective probability that didn't allow for such a connection would be rather undesirable.. Last but not least, objective probabilities should be connected to relative frequencies via the law of large numbers, that is, we need that \[ \text{Pr}(\|f_N-p\|\ge\varepsilon) \le 2e^{-2N\varepsilon^2}, \] or, in words, the (multi-trial) probability that the frequency deviates more than $\varepsilon$ from the (single-trial) probability after $N$ trials goes down exponentially with $\varepsilon$ and $N$ 2I'm using on purpose the more complicated version of the law of large numbers to prevent people from confusing it with the nonsensical statement $p=\lim_{N\to\infty} f_N$.. I think it is also easy to come up with a definition of objective probability that fulfills these desiderata, if we model objectively random processes as deterministic branching processes. Let's say we are interested the decay of an atom. Instead of saying that it either decays or not, we say that the world branches in several new worlds, in some of which the atom decays, and some of which it does not. Moreover, we say that we can somehow count the worlds, that is, that we can attribute a measure $\mu(E)$ to the set of worlds where event $E$ happens and a measure $\mu(\neg E)$ to the set of worlds where event $\neg E$ happens. Then we say that the objective probability of $E$ is \[p(E) = \frac{\mu(E)}{\mu(E)+\mu(\neg E)}.\] Now, before you shut off saying that this is nonsense, because the Many-Worlds interpretation is false, so we shouldn't consider branching, let me introduce a toy theory where this deterministic branching is literally true by fiat. In this way we can separate the question of whether the Many-Worlds interpretation is true from the question of whether deterministic branching explains objective probability. This toy theory was introduced by Adrian Kent to argue that probability makes no sense in the Many-Worlds interpretation. Well, I think it is a great illustration of how probability actually makes perfect sense. It goes like this: the universe is a deterministic computer simulation3Ran by some advanced beings that not only have cracked the strong AI problem, but also have a truly astounding amount of computational power. Whatever, it's not mean to be realistic. where some agents live. In this universe there is a wall with two lamps, and below each a display that shows a non-negative integer. This wall also has a "play" button, that when pressed makes either of the lamps light up. The agents there can't really predict which lamp will light up, but they have learned two things about how the wall works. The first is that if the number below a lamp is zero, that lamp never lights up. The second is that if the numbers are set to $n_L$ and $n_R$, respectively, and they press "play" multiple times, the fraction of times where the left lamp lights up is often close to $n_L/(n_L+n_R)$. What is going on, of course, is that when "play" is pressed the whole computer simulation is deleted and $n_L+n_R$ new ones are initiated, $n_L$ with the left lamp lit, and $n_R$ with the right lamp lit. My proposal is to define the objective probability of some event as the proportion of simulations where this event happens, as this quantity fulfills all our desiderata for objective probability. This clearly fulfills the "objectivity" desideratum, as a proportion of simulations is a property of the world, not some agent's opinion. It also respects the "law of large numbers" desideratum. To see that, fist notice that for a single trial the proportion of simulations where the left lamp lights up is \[p(L) = \frac{n_L}{n_L+n_R}.\] Now the number of simulations where the left lamp lights up $k$ times out of $N$ trials is \[ {N \choose k}n_L^kn_R^{N-k},\] so if we divide by total number of simulations $(n_L+n_R)^N$, we see that the proportion of simulations where the left lamp lit $k$ times out of $N$ is given by \[\text{Pr}(N,k) = {N \choose k}p(L)^k(1-p(L))^{N-k}.\]Since this is formally identical to the binomial distribution, it allows us to prove a theorem formally identical to the law of large numbers: \[ \text{Pr}(\|k/N-p(L)\|\ge\varepsilon) \le 2e^{-2N\varepsilon^2}, \]which says that the (multi-trial) proportion of simulations where the frequency deviates more than $\varepsilon$ from the (single-trial) proportion of simulations after $N$ trials goes down exponentially with $\varepsilon$ and $N$. Last but not least, to see that if fulfills the "Principal Principle" desideratum, we need to use the decision-theoretic definition of subjective probability: the subjective probability $s(L)$ of an event $L$ is the highest price a rational agent should pay to play a game where they receive $1$€ if event $L$ happens and nothing otherwise. In the $n_L$ simulations where the left lamp lit the agent ends up with $(1-s(L))$ euros, and in the $n_R$ simulations where the right lamp lit the agent ends up with $-s(L)$ euros. If the agent cares equally about all its future selves, they should accept to pay $s(L)$ as long as \[(1-s(L))n_L-s(L)n_R \ge 0,\]which translates to \[s(L) \le \frac{n_L}{n_L+n_R},\] so indeed the agent should bet according to the objective probability if they know $n_L$ and $n_R$4I know, decision theory is much more subtle than this; I'm just doing the quick and dirty version of the argument here, it is done properly in the paper.. And this is it. Since it fulfills all our desiderata, I claim that deterministic branching does explain objective probability. Furthermore, it is the only coherent explanation I know of. It is hard to argue that nobody will ever come up with a single-world notion of objective probability that makes sense, but at least in one point such a notion will always be unsatisfactory: why would something be in principle impossible to predict? Current answers are limited to saying that quantum mechanics say so, or that if we could predict the result of a measurement we would run into trouble with Bell's theorem. But that's not really an explanation, it's just saying that there is no alternative. Deterministic branching theories do offer an explanation, though: you cannot predict which outcome will happen because all will. Now the interesting question is whether this argument applies to the actual Many-Worlds interpretation, and we can get a coherent definition of objective probability there. The short answer is that it's complicated. The long answer is the paper I wrote about it =) 8 Responses to The many-worlds interpretation of objective probability Jacques Pienaar says: Nice post, but I can't let you get away with straw-manning the subjective Bayesians. A subjective Bayesian does not "believe that whether some atom decays or not depends on the opinion of an agent". It's the other way around: a subjective Bayesian's opinions about the atom (i.e. about their future interactions with the atom or ones like it) depends on whether the atom decays. When you put it in the correct order, it sounds fairly reasonable. A subjective Bayesian might also agree that nuclear reactions happened before agents were around. They would merely disagree that there were any probabilities around at that time. Any probabilities assigned to those events would just represent an agent's beliefs right now about what happened back then. A question: when you reject the idea of things being in principle unpredictable, do you really mean non-deterministic? Because there are reasons why things might be in-principle unpredictable even in a deterministic universe, eg, physical constraints on the computing power of the would-be predictor. Mateus Araújo says: Thanks for your comment. I don't think I'm straw-manning the subjective Bayesians; I wrote "Does anybody seriously believe that whether some atom decays or not depends on the opinion of an agent?", a rhetorical question implying that I don't think anybody does. But you are saying that there were no probabilities around at that time. What was around then? The atoms were decaying or not, but not probabilistically? How then? And I don't reject the idea of things being in principle unpredictable, on the contrary: I'm saying that they are in principle unpredictable, and I want to know why. I'm struggling to make more concrete your idea of in principle unpredictability because of computational limitations. You are suggesting that there would be an algorithm to predict whether a certain atom would decay in the next hour, but it would be in principle impossible to run this algorithm? Why? Couldn't I just wait longer, and add more memory to the computer? It is immaterial whether the algorithm would only finish after the hour had passed; since it is deterministic, the answer couldn't be influenced by whether the atom in fact decayed. Maybe an analogy would help. Imagine you said "the ocean smells nice" and someone asked you "did it smell nice before anyone was around to smell it?". The answer depends on whether you think "smelling nice" is a property of the ocean in itself, or is relative to someone or something with the ability to smell and to categorize smells as nice or stinky. If it is relative, then it is hard to see how one could talk about the smell of things prior to the existence of smelling organisms or people. You could do it via a counterfactual, i.e. if someone had been there, the ocean would have smelled nice to them — but you have to posit someone who is doing the smelling. The subjective Bayesian views claims like "X is more likely" as on the same footing as "X smells nice". The statement is objective insofar as it is widely agreed upon and independent of our wishes. Notice that you can't make poo smell good by any effort of the will; nor can you make yourself think it unlikely to rain when you see ominous grey clouds filling the sky. Probability is a relative property of how the world appears to beings that have a "nose for uncertainty". About the physical limits of predictors, keep in mind that you don't necessarily have all the time you need — eventually the universe will either thermalize, freeze or collapse. Another more speculative limitation would arise if some laws of physics are uncomputable, i.e. if being able to predict the state following any initial condition would require a computer that could solve the halting problem. In either case, these limits on prediction don't exclude determinism per se, so the concepts are distinct. The smell example is a quite useful one; I grant you that it is subjective, but it is based on something that was there before the agent came to feel it, namely whatever odor molecules that were in the air. Subjective probabilities are subjective (duh), but what I'm interested in is what was there before an agent with a "nose for uncertainty" came along to assign them. To put it another way: in those natural nuclear reactors one can ascertain that chain reactions occurred when the concentration of uranium got pretty close to the critical mass. Afterwards, the fraction of radioactive isotopes that did decay is pretty close to what their half-life predicts. Why did this happen? How did this happen? We both agree that it doesn't make sense to say that the critical mass is such and half-life is such because the subjective probability is such. But then what determines the critical mass or half-life? What do their numbers even mean? As for the limited predictor, I'm still very skeptical that you can make a remotely plausible theory out of it. If you couldn't predict whether an atom would decay because the computation would take longer than the lifetime of the universe, then somehow the decay law would need to depend on the lifetime of the universe. And you would have a bunch of atoms decaying, each of which somehow encoding such a difficult problem, and the problems would need to be so distributed that the results turn out to approximate very well the half-life of that element? Its computability version doesn't really help either. Keep in mind that it is still a matter of fact whether a giving program will halt or not; the problem being uncomputable merely means that no algorithm can decide that. But it can still be decided. The prototypical example, the program that lists all proofs in ZF and halts if it finds a proof of its consistency, will obviously never halt. "…it is based on something that was there before the agent came to feel it…" If you keep insisting that things have properties before they are measured, you're going to run into trouble when you get to EPR and Bell! A QBist might be willing to say that something existed before experience, but all substantive claims must be understood as shorthand for anticipations about future experiences conditioned on past ones. Saying there were molecules around with a certain shape before humans is, to a QBist, just a short-hand for the expectation that, eg, if you dig up samples from mines or ice cores, then you will find such molecules right there next to the dinosaur bones (or something like that). When you say "the moon is there when I don't look at it", you're really saying that you expect to see it there whenever you do look. To ask "what is there when nobody is looking" is as much a non-sequitur to the QBist as asking "which outcome really happens" to a many-worlds-er. Measuring and happening are inextricable from each other. So the "half-life of a Uranium atom" is a statement about my expectation that a given atom will decay in a given time interval, or, than an atom taken at random from a sample will be found to have already decayed. You ask: how do I explain this? For a QBist, explaining the half-life of Uranium means explaining why you have come to believe that Uranium atoms will decay as a certain function of time (characterized by that half-life). The explanation means giving an account of how you have updated your beliefs in light of new evidence, starting from some prior, and how your belief is consistent with other beliefs that you hold. The whole mode of `explanation' for a Bayesian focuses on the inter-relations and coherence between expectations conditioned on actual measurement events. Models of the world often play a role in this, as short-hand that captures a whole bundle of expectations about hypothetical measurements, but these models are never mistaken as descriptions of "the world in itself". You might say that doesn't account for why the atom's decay is spontaneous and random. But for a QBist, spontaneity and "intrinsic uncertainty" of the world is an axiom, not something to be explained. Indeed, to a QBist, "the world" refers to that part of experience that doesn't conform to our wishes and that defies our expectations. If the world were not spontaneous, we wouldn't call it "the world"! A QBist takes for granted that the outcomes of our interactions with the world are intrinsically random, and this applies as well to observations of Uranium atoms. What is of interest is the non-trivial inferences we can make about them, using models based on accumulated experience of interactions with such atoms. About the limits of prediction, I think we're talking past each other. My original question was motivated by what you said was an unsatisfactory feature of single-world objective probability interpretations, namely, that they don't explain why something would be "in principle impossible to predict". I just wanted to know if you really meant "in principle non-deterministic". I'm not defending any thesis about the plausibility of physical predictors. I'm just pointing out that "determinism" and "unpredictability" are distinct concepts. The extent to which they coincide is only the extent to which you believe a "perfect predictor" is physically realizable within a deterministic universe. Maybe you think it is realizable, which is fine, but you could save yourself a lot of arguments with people who don't think so, just by talking about whether the world is "deterministic", if indeed that's what you really meant. "If you keep insisting that things have properties before they are measured, you're going to run into trouble when you get to EPR and Bell!" No, I won't. This is a common misconception. Nothing about EPR and Bell disproves the idea of an objective reality. You can't have determinism or local causality, in the most common interpretations, but that's it. I'm afraid you might find this a bit rude, but I don't see any explanation in the three paragraphs you wrote stating the QBist position. Yes, I know that the QBists have this deeply agent-centric view of the world. I'm not interested in that. I'm interested in what is actually happening, independently of any agent's expectations. If QBism can't provide such an objective explanation of what is going on in atomic decay, then I'm just not interested. About the limits of prediction, no, I really meant "in principle unpredictable", not "in principle non-deterministic". If you could actually pull off a deterministic theory that has in principle unpredictable outcomes in a single world, I would be satisfied. If you could pull off an explanation of in principle non-determinism in a single world, I would also be satisfied. 2nd May 2019 at 05:20 I don't think it's rude of you to dismiss my account of "explanation" — I expected you would. Besides, philosophers disagree about what it means, so we might as well join in the fun :). I did think it was rude to accuse me of making a "common misconception" about Bell's theorem. I think you slipped up in equating my phrase "things have properties before they are measured" with the weaker notion of "objective reality", by which I guess you mean any model that purports to represent the world as independent and external to us. I was not by any means claiming that Bell/EPR causes trouble for such a notion (much less that it "disproves" anything! Quit putting words in my mouth). What I meant was: if you assume there is some local property or `propensity' of a system prior to its measurement that serves to determine the probabilities of the measurement outcomes, you will encounter "trouble", by which I mean non-locality. Possibly with all your talk about `what is actually there before the agent comes along' you instead meant something like the wavefunction of the universe, as in many-worlds. My critique of that interpretation is that it hardly does a good job of telling you `what is actually happening'. As far as I understand it, unitary evolution of the universal wavefunction doesn't describe anything actually happening, except maybe in our minds. What does actually happen is that we hear a detector go `click'. But maybe I am just talking past you again, because as with `explanation', you won't agree with me about what it means for something "to actually happen"… Ah, ok, so you simply meant non-locality. I find it much less troubling than things not having properties before they are measured. And as you know, in Many-Worlds violation of a Bell inequality does not imply in non-locality. Also, I'm not equating "what is actually there before the agent comes along" with a universal wavefunction, even though the latter does a good job of providing an agent-free description. Agent-free descriptions were the norm in science for centuries before quantum mechanics came along, so we definitely know what this concept means independently of quantum mechanics. Note also that the subject of this blog post is how a decidedly no-quantum theory, Kent's universe, can account for objective probability.	CommonCrawl
GATE 2015 ME – SET 2 – Complete Solutions Q1. At least one eigenvalue of a singular matrix is (A) positive (B) zero (C) negative (D) imaginary Solution: (B) Q2. At x = 0, the function f(x) = \|x\| has (A) a minimum (B) a maximum (C) a point of inflexion (D) neither a maximum nor minimum Solution: (A) Q3. Curl of vector V(x, y, z) = 2x2i + 3z2 j – y3 k at x = y = z = 1 is (A) −3i (B) 3i (C) 3i – 4j (D) 3i – 6k Q4. The Laplace transform of ei5t where I = √−1, is (A) (B) (C) (D) Q5. Three vendors were asked to supply a very high precision component. The respective probabilities of their meeting the strict design specifications are 0.8, 0.7 and 0.5. Each vendor supplied one component. The probability that out of total three components supplied by the vendors, at least one will meet the design specification is _________ Solution: Key = 0.96 to 0.98 Q6. A small ball of mass 1 kg moving with a velocity of 12 m/s undergoes a direct central impact with a stationary ball of mass 2 kg. The impact is perfectly elastic. The speed (in m/s) of 2 kg mass ball after the impact will be__________ Solution: Key = 7.8 to 8.2 Q7. A rod is subjected to a uni-axial load within linear elastic limit. When the change in the stress is 200 MPa, the change in the strain is 0.001. If the Poisson's ratio of the rod is 0.3, the modulus of rigidity (in GPa) is _______ Solution: Key = 76 to 78 Q8. A gas is stored in a cylindrical tank of inner radius 7 m and wall thickness 50 mm. The gage pressure of the gas is 2MPa. The maximum shear stress (in MPa) in the wall is (A) 35 (B) 70 (C) 140 (D) 280 Solution: (C) Q9. The number of degrees of freedom of the planetary gear train shown in the figure is Q10. In a spring-mass system, the mass is m and the spring constant is k. The critical damping coefficient of the system is 0.1kg/s. In another spring-mass system, the mass is 2m and the spring constant is 8k. The critical damping coefficient (in kg/s) of this system is ____________ Q11. The uniaxial yield stress of a material is 300 MPa. According to von Mises criterion, the shear yield stress (in MPa) of the material is ________ Solution: Key = 171 to 175 Q12. If the fluid velocity for a potential flow is given by V(x, y) = u(x, y)i + v(x, y)j with usual notations, then slope of the potential line at (x, y) is (A) $$\frac{v}{u}$$ (B) $$-\frac{u}{v}$$ (C) $$\frac{v^{2}}{u^{2}}$$ (D) $$\frac{u}{v}$$ Q13. Which of the following statements regarding a Rankine cycle with reheating are TRUE? (i) increase in average temperature of heat addition (ii) reduction in thermal efficiency (iii) drier steam at the turbine exit (A) only (i) and (ii) are correct (B) only (ii) and (iii) are correct (C) only (i) and (iii) are correct (D) (i), (ii) and (iii) are correct Q14. Within a boundary layer for a steady incompressible flow, the Bernoulli equation (A) holds because the flow is steady (B) holds because the flow is incompressible (C) holds because the flow is transitional (D) does not hold because the flow is frictional Solution: (D) Q15. If a foam insulation is added to a 4 cm outer diameter pipe as shown in the figure, the critical radius of insulation (in cm) is _______ Q16. In the laminar flow of air (Pr = .7) over a heated plate I, if δ and δT denote, respectively, the hydrodynamic and thermal boundary layer thicknesses, then Q17. The COP of a Carnot heat pump operating between 6℃ and 37℃ is _________ Solution: Key = 9.8 to 10.2 Q18. The Van der Waals equation of state is $$\left ( p+\frac{a}{v^{2}} \right )\left ( v-b \right )=RT$$ , where p is pressure, v is specific volume, T is temperature and R is characteristic gas constant. The SI unit of a is Q19. A rope-brake dynamometer attached to the crank shaft of an I.C. engine measures a brake power of 10 kW when the speed of rotation of the shaft is 400 rad/s. The shaft torque (in N-m) sensed by the dynamometer is ________ Q20. The atomic packing factor for a material with body centered cubic structure is ________ Q21. The primary mechanism of material removal in electrochemical machining (ECM) is (A) chemical corrosion (B) etching (C) ionic dissolution (D) spark erosion Q22. Which one of the following statements is TRUE? (A) The 'GO' gage controls the upper limit of a hole (B) The 'NO' gage controls the lower limit of a shaft (C) The 'GO' gage controls the lower limit of a hole (D) The 'NO GO' gage controls the lower limit of a hole Q23. During the development of a product, an entirely new process plan is made based on design logic, examination of geometry and tolerance information. This type of process planning is known as (A) retrieval (B) generative (C) variant (D) group technology based Q24. Annual demand of a product is 50000 units and the ordering cost is Rs. 7000 per order. Considering the basic economic order quantity model, the economic order quantity is 10000 units. When the annual inventory cost is minimized, th3e annual inventory holding cost (in Rs.) is ______ Solution: Key = 34000 to 36000 Q25. Sales data of a product is given in the following table: Regarding forecast for the month of June, which one of the following statements is TRUE ? (A) Moving average will forecast a higher value compared to regression. (B) Higher the value of order N, the greater will be the forecast value by moving average. (C) Exponential smoothing will forecast a higher value compared to regression. (D) Regression will forecast a higher value compared to moving average. Q26. The change of a student passing an exam is 20%. The chance of a student passing the exam and getting above 90% marks in it is 5%. GIVEN that a student passes the examination, the probability that the student gets above 90% marks is (A) 1/18 (B) 1/4 (C) 2/9 (D) 5/18 Q27. The surface integral $$\iint_{S}\frac{1}{\pi }(9xi-3yj)\cdot n dS$$ over the sphere given by x2 + y2 +z2 = 9 is ___________ Q28. Consider the following differential equation: initial condition: y = 2 at t = 0. The value of y at t = 3 is (A) $$-5e^{-10}$$ (B) $$2e^{-10}$$ (C) $$2e^{-15}$$ (D) $$-15e^{2}$$ Q29. The value of function f(x) at 5 discrete points are given below Using Trapezoidal rule with step size of 0.1, the value of is ________ Solution: Key = 21.8 to 22.2 Q30. The initial velocity of an object is 40 m/s. The acceleration a of the object is given by the following expression: a = −0.1v, where v is the instantaneous velocity of the object. The velocity of the object after 3 seconds will be _______ Q31. A cantilever beam OP is connected to another beam PQ with a pin joint as shown in the figure. A load of 10 kN is applied at the mid-point of PQ. The magnitude of bending moment (in kN-m) at fixed end O is (A) 2.5 (B) 5 (C) 10 (D) 25 Q32. For the truss shown in the figure, the magnitude of the force (in kN) in the member SR is (A) 10 (B) 14.14 (C) 20 (D) 28.28 Q33. A cantilever beam with square cross-section of mm side is subjected to a load of 2 kN normal to the top surface as shown in the figure. The Young's modulus of elasticity of the material of the beam is 210 GPa. The magnitude of slope (in radian) at Q(20 mm from the fixed end) is _____ Q34. In a plane stress condition, the components of stress at a point are σx = 20 MPa, σy = 80 MPa and τxy = 40 MPa. The maximum shear stress (in MPa) at the point is (A) 20 (B) 25 (C) 50 (D) 100 Q35. In a certain slider-crank mechanism, length of crank and connecting rod are equal. If the crank rotates with a uniform angular speed of 14 rad/s and the crank length is 300 mm, the maximum acceleration of the slider (in m/s2) is _______ Q36. A single-degree-freedom spring-mass system is subjected to a sinusoidal force of 10 N amplitude and frequency ω along the axis of the spring. The stiffness of the spring is 150 N/m, damping factor is 0.2 and the undamped natural frequency is 10ω. At steady state, the amplitude of vibration (in m) is approximately (A) 0.05 (B) 0.07 (C) 0.70 (D) 0.90 Q37. A hollow shaft of 1 m length is designed to transmit a power of 30 kW at 700 rpm. The maximum permissible angle of twist in the shaft is 1°. The inner diameter of the shaft is 0.7 times the outer diameter. The modulus of rigidity s 80 GPa. The outside diameter (in mm) of the shaft is _______ Q38. A hollow shaft (do = 2di where do and di are the outer and inner diameters respectively) needs to transmit 20 kW power at 3000 RPM. If the maximum permissible shear stress is 30 MPa, do is (A) 11.29 mm (B) 22.58 mm (C) 33.87 mm (D) 45.16 mm Q39. The total emissive power of a surface is 500 W/m2 at a temperature T1 and 1200 W/m2 at a temperature T2, where the temperatures are in Kelvin. Assuming the emissivity of the surface to be constant, the ratio of the temperatures is (A) 0.308 (B) 0.416 (C) 0.416 (D) 0.874 Q40. The head loss for a laminar incompressible flow through a horizontal circular pipe is h1. Pipe length and fluid remaining the same, if the average flow velocity doubles and the pipe diameter reduces to half its previous value, the head loss is h2. The ratio h2/h1 is (A) 1 (B) 4 (C) 8 (D) 16 Q41. For a fully developed laminar flow of water (dynamic viscosity 0.001 Pa-s) through a pipe of radius 5 cm, the axial pressure gradient is −10 Pa/m. The magnitude of axial velocity (in m/s) at a radial location is 0.2 cm is ______ Q42. A balanced counter flow heat exchanger has a surface area of 20 m2 and overall heat transfer coefficient of 20 W/m2-K. Air (Cp = 1000 J/kg-K) entering at 0.4 kg/s and 280 K is to be preheated by the air leaving the system at 0.4 kg/s and 300 K. The outlet temperature (in K) of the preheated air is (A) 290 (B) 300 (C) 320 (D) 350 Q43. A cylindrical uranium fuel rod of radius 5 mm in a nuclear reactor is generating heat at the rate of 4 × 107 W/m3. The rod is cooled by a liquid(convective heat transfer coefficient 1000 W/m2-K) at 25℃. At steady state, the surface temperature (in K) of the rods is Q44. Work is done on an adiabatic system due to which its velocity changes from 10 m/s to 20 m/s elevation increases by 20 m and temperature increases by 1K. he mass of the system is 10 kg, Cv = 100 J/(kg.K) and gravitational acceleration is 10 m/s2. If there is no change in any other component of the energy of the system, the magnitude of total work done (in kJ) on the system is ______ Solution: Key = 4.5 Q45. One kg of air (R = 287 J/kg-K) undergoes an irreversible process between equilibrium state 1 (20℃, 0.9 m3) and equilibrium state 2(20℃, 0.6 m3). The change in entropy s2– s1 (in J/kg-K) is ________ Solution: Key = -117 to -115 Q46. For the same values of peak pressure, peak temperature and heat rejection, the correct order of efficiencies for Otto, Dual and Diesel cycles is (A) (B) (C) (D) Q47. In a Rankine cycle, the enthalpies at turbine entry and outlet are 3159 kJ/kg and 2187 kJ/kg, respectively. If the specific pump work is 2 kJ/kg, the specific steam consumption (in kg/kW-h) of the cycle base on net output is ________ Q48. A cube and a sphere made of cast iron (each of volume 1000 cm3) were cast under identical conditions. The time taken for solidifying the cube was 4s. The solidification time (in s) for the sphere is _______ Q49. In a two-stage wire drawing operation, the fractional reduction (ratio of change in cross-sectional) area to initial cross-sectional area) in the first stage is 0.4. The fractional reduction in the second stage is 0.3. The overall fractional reduction is Q50. The flow stress (in MPa) of a material is given by σ = 500ε0.1, where ε is true strain. The young's modulus of elasticity of the material is 200 GPa. A block of thickness 100 mm made of this material is compressed to 95 mm thickness and then the load is removed. The final dimension of the block (in mm) is _______ Solution: Key = 95.14 to 95.20 Q51. During a TIG welding process, the arc current and arc voltage were 50 A and 60 V, respectively, when the welding speed was 150 mm/min. In another process, the TIG welding is carried out at a welding speed of 120 mm/min at the same arc voltage and heat input to the material so that weld quality remains the same. The welding current (in A) for this process is (A) 40.00 (B) 44.72 (C) 55.90 (D) 62.25 Q52. A single point cutting tool with 0° rake angle is used in an orthogonal machining process. At a cutting speed of 180 m/min, the thrust force is 490 N. If the coefficient of friction between the tool and the chip is 0.7, then the power consumption (in kW) for the machining operation is ______ Q53. A resistance-capacitance relaxation circuit is used in an electrical discharge machining process. The discharge voltage is 100 V. At a spark cycle time of 25 μs, the average power input required is 1 kW. The capacitance (in μF) in the circuit is (A) 2.5 (B) 5.0 (C) 7.5 (D) 10.0 Q54. A project consists of 7 activities. The network along with the time durations (in days) for various activities is shown in the figure. The minimum time (in days) for completion of the project is _______ Q55. A manufacturer has the following data regarding a product: Fixed cost per month = Rs .50000 Variable cost per unit = Rs. 200 Selling price per unit = Rs. 300 Production capacity = 1500 units per month If the production is carried out at 80% of the rated capacity, then the monthly profit (in Rs.) is __________ ← GATE 2015 ME – SET 1 – Complete Solutions GATE 2015 ME – SET 3 – Complete Solutions →	CommonCrawl
The Proofs We Know and Love Michael Asper A simple proofs essay using basic theorems while trying to get a grasp on LaTeX \documentclass[a4paper, 12pt]{article} \usepackage{geometry} \geometry{margin=1in} \usepackage[english]{babel} \usepackage[utf8]{inputenc} \usepackage{amsmath} \usepackage{commath} \usepackage{amsthm} \usepackage{amssymb} \usepackage{setspace} \doublespacing \title{the proofs we know and love} \paragraph{Introduction} In this paper, the author will be introducing two proofs: the difference of two squares and absolute value of two numbers equal to each other is less than $\varepsilon $. We will go through both proofs and find that the difference of two squares introduces factoring and distributing to a more useful degree. It will also allow us to find solutions to quadratic equations when we first meet them. The difference of two squares problem is shown: \paragraph{Theorem K:} For every $x,a,$ we have that: \[(x-a)(x+a) = {x}^{2} - {a}^{2} \] We will also go through the absolute value proof, which will introduce us to a basic definition of limits in the future, as $\varepsilon $ has many applications in proofs. The absolute value problem is: \paragraph{Theorem 1.4:} Two real numbers $a$ and $b$ are equal if and only if for every real number $\varepsilon > 0 $ it follows that $\left\| a-b \right\| < \varepsilon $. \newline Both of these theorems have uses in proving more complicated proofs later on in mathematics. We will start proving the first problem: difference of two squares. \begin{proof} Theorem K: Let $z=(x-a)$, \begin{equation} (x-a)(x+a) = (x-a)(x+a) \end{equation} Then we substitute in $z$ for $(x-a)$, z(x+a) = (x-a)(x+a) Using the distributive axiom, we distribute the $z$, resulting in zx + za = (x-a)(x+a) We then substitute in back the $(x-a)$ for $z$, (x-a)x + (x-a)a = (x-a)(x+a) The purpose for the $z$-substituion was to show that we could distribute something like $(x-a)$, a multi-variable part in the equation. Furthermore, we will continue by distributing the $x$ and $a$, respectively. xx-ax + ax - aa = (x-a)(x+a) We then apply the additive inverse property, xx-0-aa = (x-a)(x+a) xx-aa = (x-a)(x+a) The definition of a square is $\forall n \exists \mathbb{R} $ such that $nn \implies {n}^{2}$, x^2 - a^2 = (x-a)(x+a) \end{proof} \paragraph{} After this, we have proven the fact that ${x}^{2} - {a}^{2} = (x-a)(x+a) $, which gives us a glimpse of future quadratic equations. We will now prove the other theorem involving absolute values. Theorem 1.4: Let $a=b$ and $\varepsilon > 0$, a=b We then apply the additive inverse of $b$ to both sides using the equality axiom. a+(-b) = b + (-b) This simplifies to, a - b = 0 The definition of absolute value follows: \abs{x} = \begin{cases} \hfill x \hfill & \text{ if $x \geq$ 0} \\ \hfill -x \hfill & \text{ if $x < 0 $} \\ \end{cases} Using the definition of absolute value, we can say since $a-b = 0$ that, \|a-b\| = 0 And since we were given that $ \varepsilon > 0$. According to the axiom where if $x > y$ and $y > z$ then $x > z$, \|a-b\| < \varepsilon Since the proof is an if and only if, we must prove the problem in the reverse direction. This would mean if $\varepsilon > 0$ and $\|a-b\|<\varepsilon$ then $a=b$ for every real number. We will start with the knowledge that an absolute value of anything must be greater or equal to zero. % * <asper@utexas.edu> 2015-10-05T22:19:28.193Z: \|a-b\| \geq 0 This branches into two cases. \newline Suppose $\|a-b\| = 0$, then we can use the definition of absolute value to show this, a-b = 0 Using additive inverse and equality axioms, Suppose $\|a-b\| > 0$, this means there exists a number in between the absolute value and zero. Let's call this $\varepsilon$ as $\varepsilon$ can be any number above zero. This would give us, \|a-b\| \geq \varepsilon which contradicts the given that $\|a-b\| < \varepsilon$. This means that this case could not be true with the given, therefore the only viable case would be that $\|a-b\| = 0$. \paragraph{Conclusion:} Throughout the paper, we have proven two fundamental theorems for mathematics including the difference of two squares, which states that $(x-a)(x+a) = {x}^{2} - {a}^{2} $. The other theorem we proved shows that if two variables are equal to each other, the absolute value of their difference must be zero and that if $\varepsilon$ is greater than zero, then the absolute value of the difference must be less than $\varepsilon$. Some of the applications of the difference of squares includes factorization of polynomials, mental math, rationalizing denominators, and sum of two squares in the complex plane. The method of using difference of two squares to help find solutions for the sum of two squares goes as follows: Given ${x}^{2} + 13$, we can factor out a negative one from the $13$, x^2 - (-1)(13) Then we can substitute in $i^2$ in for 1, x^2 - 13i^2 To rearrange it in the form of difference of two squares, we square root the left-variable and move the exponent outside the parenthesis as shown, x^2 - (\sqrt[]{13} i)^2 Therefore the factors are, (x-\sqrt[]{13}i)(x+\sqrt[]{13}i) The other proof, absolute value epsilon proof, is used to setup a basic definition of a limit later in mathematics. The definition itself is called the epsilon-delta definition of a limit as it is built upon the original proof show in the paper. The epsilon-delta limit was not available to Netwon or Leibniz during their time, but in the 19th century mathematicians started using the definition to help further their arguments in calculus when trying to solve limits. \cite{bruce1} \begin{thebibliography}{9} \bibitem{bruce1} Pourciau, B. (2001). Newton and the Notion of Limit. \emph{Historia Mathematica}, 28(1). \end{thebibliography}	CommonCrawl
Advances in Continuous and Discrete Models Theory and Modern Applications Existence of solutions for a class of nonlinear fractional difference equations of the Riemann–Liouville type Pshtiwan Othman Mohammed ORCID: orcid.org/0000-0001-6837-80751, Hari Mohan Srivastava2,3,4,5, Juan L. G. Guirao6 & Y. S. Hamed7 Advances in Continuous and Discrete Models volume 2022, Article number: 32 (2022) Cite this article Nonlinear fractional difference equations are studied deeply and extensively by many scientists by using fixed-point theorems on different types of function spaces. In this study, we combine fixed-point theory with a set of falling fractional functions in a Banach space to prove the existence and uniqueness of solutions of a class of fractional difference equations. The most important part of this article is devoted to correcting a significant mistake made in the literature in using the power rule by providing further conditions for its validity. Also, we provide specific conditions under which difference equations have attractive solutions and the solutions are also asymptotically stable. Furthermore, we construct some fractional difference examples in order to illustrate the validity of the observed results. The idea of discrete fractional calculus is to replace the natural numbers in the order of the difference by fractional orders. However, since the emergence of the theory of discrete fractional calculus, different types of discrete fractional operators have been developed to deal with various situations in the applied and natural sciences due to their great importance as an advanced mathematical tool for the interpretation and modeling of many biological and physical phenomena, such as various biological studies, electrical circuits, mechanical fluids, relaxation processes, and damping-law models (see [1–6]). There are several possible ways to define discrete fractional operators (differences and sums), leading to a diverse and rich field of study (see [7–11]). Here, we shall focus principally on the most commonly used and classical definition, which is known as the Riemann–Liouville (RL) fractional calculus (see, for details, [12, 13]; see also the recent survey-cum-expository review articles [14, 15]). Fractional difference equations (FDEs) have become a hot research topic in the mathematical and physical sciences. It has been found that the role of FDEs is very important in treating and modeling nonlinear problems with applications in mathematical analysis and various branches of science, including diffusion, plasmas, dynamic systems, nonlinear optics, and many other areas (see [16–21]). In the last two decades, significant numbers of articles have appeared on this topic, and some of the papers deal with the existence and uniqueness of solutions for difference equation problems (see [22–26]). However, a significant mistake has been made by most of the researchers in using the fractional power rule (see Lemma 2.2). In some recent articles of Lu et al. [27] and Mohammed [28], some nonlinear RL fractional difference equations were established from the uncertain point of view, and the existence and uniqueness theorems were studied using the scheme of uncertainty theory. In general, the difference equations considered were of the following form: $$ \begin{aligned} & \bigl({}^{\mathrm{RL}}_{\nu -1}{ \Delta }^{\nu }y \bigr) (\mathrm{z})= \psi \bigl(\mathrm{z}+\nu ,y( \mathrm{z}+\nu ) \bigr)\quad \bigl(\forall \mathrm{z}\in \mathrm{N}_{0}, \nu \in (0,1) \bigr), \\ & \bigl({}^{\mathrm{RL}}_{\nu -1}{\Delta }^{\nu -1}y \bigr) ( \mathrm{z}) \big\|_{\mathrm{z}=0}=y_{0}, \end{aligned} $$ where ${}^{\mathrm{RL}}_{a}{\Delta }^{\nu }$ is the discrete RL fractional difference operator and ψ is supposed to be a real-valued function: $f:[0,\infty )\times \mathbb{R}\to \mathbb{R}$. Next, in [29] and [30], the problem of the power rule was solved by considering a new difference equation as follows: $$ \begin{aligned} & \bigl({}^{\mathrm{RL}}_{\nu -1}{ \Delta }^{\nu }y \bigr) (\mathrm{z})= \psi \bigl(\mathrm{z}+\nu -1,y( \mathrm{z}+\nu -1) \bigr)\quad \bigl( \forall \mathrm{z}\in \mathrm{N}_{0}, \nu \in (0,1) \bigr), \\ & \bigl({}^{\mathrm{RL}}_{\nu -1}{\Delta }^{\nu -1}y \bigr) ( \mathrm{z}) \big\|_{\mathrm{z}=0}=y_{0}. \end{aligned} $$ In the meantime, the existence and uniqueness of the Liouville–Caputo version of the difference equation (1.2) was obtained by Srivastava et al. [31] in the correct way as above. Moreover, in [32–34] some nonlinear RL and Liouville–Caputo fractional difference equations such as (1.1) and (1.2) were established from the mathematical point of view. Also, the existence and uniqueness theorems were proved there using the scheme of fixed-point theory. Unfortunately, the same mistake as above was made in those articles. The aim of this work is to present the existence and uniqueness of the solution of the nonlinear fractional difference equation (1.2) using fixed-point theorems in the correct way and correcting the above mistakes. The remainder of the study is structured as follows: In Sect. 2, we give related notations and make some preparations. In Sect. 3, we derive and prove the main theorems of the article: first determining a suitable power-rule condition corresponding to the difference equation (1.2), then proving existence and uniqueness, and finally rewriting the difference equation in such a way that the problem will be more useful in applications. In Sect. 4 we will illustrate our results with several examples of different types, providing specific nonlinear difference equations and conditions under which they have attractive solutions and the solutions are asymptotically stable. In Sect. 5, we conclude the article with some ideas and remarks for future directions of work in this area. Denote $\rho (\mathrm{z}):=\mathrm{z}-1$, $\sigma (\mathrm{z}):=\mathrm{z}+1$ and $\mathrm{N}_{a}:=\{a,a+1,a+2,\ldots \}$. Let ψ be defined on $\mathrm{N}_{a}$. Then, the forward and backward difference operators are given by $\Delta \psi (\mathrm{z})=\psi (\sigma (\mathrm{z}))-\psi (\mathrm{z})$ and $\nabla \psi (\mathrm{z})=\psi (\mathrm{z})-\psi (\rho (\mathrm{z}))$ for each $\mathrm{z}\in \mathrm{N}_{a}$, respectively. There are plenty of possible ways to define discrete fractional differences and sums, leading to a diverse and rich field of study [8–10]. Primarily, we shall focus on the discrete RL fractional operators, which is the most commonly used definition. Here, discrete fractional sums of order $\nu >0$ are defined by $$ \bigl({}_{a}{\Delta }^{-\nu }\psi \bigr) ( \mathrm{z}) = \frac{1}{\Gamma (\nu )}\sum_{\kappa =a}^{\mathrm{z}-\nu } \bigl( \mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)}\psi (\kappa ) \quad ( \forall \mathrm{z}\in \mathrm{N}_{a+\nu } ), $$ where ψ is defined on $\mathrm{N}_{a}$ and $\mathrm{z}^{(\nu )}$ is the falling factorial function, defined by $$ \mathrm{z}^{(\nu )}= \frac{\Gamma (\mathrm{z}+1 )}{\Gamma (\mathrm{z}+1-\nu )}\quad (\forall \mathrm{z} \text{ and } \nu \in {{ \mathbb{R}}} ). $$ The discrete RL fractional difference is, as an extension of the discrete fractional sum, defined by $$\begin{aligned} \bigl({}^{\mathrm{RL}}_{a}{\Delta }^{\nu }\psi \bigr) (\mathrm{z})&= \bigl(\Delta {}_{a}{ \Delta }^{-(1-\nu )}\psi \bigr) ( \mathrm{z}) \\ &=\frac{1}{\Gamma (1-\nu )}\Delta \Biggl(\sum_{\kappa =a}^{ \mathrm{z}+\nu -1} \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(-\nu )} \psi (\kappa ) \Biggr) \quad (\forall \mathrm{z}\in \mathrm{N}_{a+1- \nu } ) \end{aligned}$$ for $0\leqq \nu <1$. Lemma 2.1 If $\nu >0$, $\mathrm{z}^{(-\nu )}$ is nonincreasing on $\mathrm{N}_{0}$. From the forward difference operator and (2.2), we have $$\begin{aligned} \Delta \bigl(\mathrm{z}^{(-\nu )} \bigr)&=(\mathrm{z}+1)^{(-\nu )}- \mathrm{z}^{(-\nu )} = \biggl( \frac{\Gamma (\mathrm{z}+2 )}{\Gamma (\mathrm{z}+2+\nu )} - \frac{\Gamma (\mathrm{z}+1 )}{\Gamma (\mathrm{z}+1+\nu )} \biggr) \\ &= \frac{\Gamma (\mathrm{z}+1 )}{\Gamma (\mathrm{z}+1+\nu )} \biggl(\frac{\mathrm{z}+1}{\mathrm{z}+1+\nu }-1 \biggr) \\ &=-\nu \frac{\Gamma (\mathrm{z}+1 )}{\Gamma (\mathrm{z}+2+\nu )} =-\nu \mathrm{z}^{(-\nu -1)}. \end{aligned}$$ Since $\nu >0$ and $\mathrm{z}^{(-\nu -1)}= \frac{\Gamma (\mathrm{z}+1 )}{\Gamma (\mathrm{z}+2+\nu )} \geq 0$, it follows that $$ \Delta \bigl(\mathrm{z}^{(-\nu )} \bigr)=(\mathrm{z}+1)^{(-\nu )}- \mathrm{z}^{(-\nu )} =-\nu \mathrm{z}^{(-\nu -1)}\leqq 0, $$ which leads to $(\mathrm{z}+1)^{(-\nu )}\leqq \mathrm{z}^{(-\nu )}$. Thus, the proof is complete. □ (see [9]) If $\nu >0$ and $\mu >-1$, then $$ {}_{a+\mu }{\Delta }^{-\nu }( \mathrm{z}-a)^{(\mu )} = \frac{\Gamma (\mu +1)}{\Gamma (\mu +1+\nu )}(\mathrm{z}-a)^{(\nu + \mu )} $$ for $\mathrm{z}\in \mathrm{N}_{a+\mu +\nu }$. (see [6, 32, 34]) The falling factorial function satisfies the following conditions: $\mathrm{z}^{(\mu )}\cdot \mathrm{z}^{(-\nu )}\leqq \mathrm{z}^{(\mu - \nu )}$ for $\nu ,\mu \geq 0$ and $\mathrm{z}>\mu -1$. $\mathrm{z}^{(\nu +\mu )}=(\mathrm{z}-\mu )^{(\nu )}\mathrm{z}^{(\mu )}$. $(\mathrm{z}+\nu )^{(-\mu )}<\mathrm{z}^{(-\mu )}$ for each positive value of ν, μ and z. $[\mathrm{z}^{(-\gamma )} ]^{\beta }\leqq \mathrm{z}^{(- \beta \gamma )}$ for $\gamma <0$ and $\beta \in (0,1)$. Each of the above items can be found in [6, 34] and [32], respectively. Definition 2.1 (see [35]) A set ϒ of finite or infinite sequences in $\ell _{n}^{\infty }$ is uniformly Cauchy, if, for every $\epsilon >0$, there exists an integer m such that $\|y(i)-y(j) \|<\epsilon $ for $i, j>m$ and $y= \{y(n) \}$ in ϒ. The following theorem is known as a discrete Arzela–Ascoli theorem. Theorem 2.1 A bounded uniformly Cauchy subset ϒ of $\ell _{n}^{\infty }$ is relatively compact. The following theorem is known as the discrete Krasnoselskii fixed-point theorem. Let $\mathtt{S}\neq \emptyset $ be a bounded, closed and convex subset of the Banach space ϒ of $\ell _{n}^{\infty }$. Let $\mathtt{A}:\Upsilon \to \Upsilon $ and $\mathtt{B}:\mathtt{S}\to \Upsilon $ be two operators with the following constraints: A is a contraction mapping with constant $\mathtt{L}<1$; B is continuous and BS resides in a compact subset of ϒ; $y=\mathtt{A}y+\mathtt{B}z$, $z\in \mathtt{S}$ implies that $y\in \mathtt{S}$. Then, we can say that the operator equation $\mathtt{A}y+\mathtt{B}z=y$ has a solution in S. Let us now consider the difference equation (1.2) in a more explicit fractional Taylor difference equation form. Suppose that ψ is a given real-valued function. The difference equation (1.2) has one solution if and only if y is a solution of the following fractional Taylor difference equation: $$ y(\mathrm{z}) =\frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )}y_{0}+ \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl( \mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)}\psi \bigl(\kappa +\nu -1,y( \kappa +\nu -1) \bigr) $$ for $\mathrm{z}\in \mathrm{N}_{\nu }$. To proceed, we should define a functional operator P as follows: $$ (\mathtt{P}y ) (\mathrm{z}):=\frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )}y_{0}+ \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl( \mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)}\psi \bigl(\kappa +\nu -1,y( \kappa +\nu -1) \bigr)\quad (\forall \mathrm{z}\in \mathrm{N}_{ \nu } ). $$ Furthermore, we will try to show that the operator P has a unique fixed point in a possible function space. Let us separate P into two distinct operators as follows: $$\begin{aligned} (\mathtt{A}y ) (\mathrm{z})&:=\frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )}y_{0}, \end{aligned}$$ $$\begin{aligned} (\mathtt{B}y ) (\mathrm{z})&:=\frac{1}{\Gamma (\nu )} \sum _{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)}\psi \bigl(\kappa +\nu -1,y(\kappa +\nu -1) \bigr)\quad (\forall \mathrm{z}\in \mathrm{N}_{\nu } ). \end{aligned}$$ It is evident that $\mathtt{P}y=\mathtt{A}y+\mathtt{B}y$ and the operator A is a contraction mapping with the constant 0, which verifies condition (i) of Theorem 2.2. Moreover, it is clear from (2.5) and (2.6) that y is a fixed point of P iff y is a solution of (1.2). Establishment of the existence and uniqueness results Here, we consider the space $\Upsilon :=\ell _{\nu +1}^{\infty }$ of functions x that consist of the set of all real sequences $\{x(\mathrm{z}) \}_{\mathrm{z}=\nu +1}^{\infty }$. Note that ϒ is a Banach space under the norm $\Vert x \Vert :=\sup_{\mathrm{z}\in \mathrm{N}_{ \nu +1}} \|x(\mathrm{z}) \|$. Also, we define $$\begin{aligned} \mathtt{S}:=\bigl\{ x\in \Upsilon ; \bigl\vert x( \mathrm{z}) \bigr\vert \leqq ( \mathrm{z}-1)^{(-\gamma )}\ \forall \mathrm{z} \in \mathrm{N}_{ \nu +1}, \gamma >0 \bigr\} . \end{aligned}$$ It is clear that the set S is a nonempty bounded and closed subset of ϒ. Let the following condition on the function ψ hold true: (C1) Suppose that there exist positive constants C and β, with $\nu +\beta =1$ and $\beta >\nu $, such that $$ \bigl\vert \psi (\mathrm{z},y) \bigr\vert \leqq \mathtt{C} \mathrm{z}^{(-\beta )}\quad (\forall \mathrm{z}\in \mathrm{N}_{\nu +1} ). $$ Then, the operator B is continuous and $\mathtt{B}\mathtt{S}_{1}$ is a relatively compact subset of $\mathtt{S}_{1}$ for $\mathrm{z}\in \mathrm{N}_{\nu +n}$, where $$ \mathtt{S}_{1}:=\bigl\{ x\in \Upsilon ; \bigl\vert x( \mathrm{z}) \bigr\vert \leqq (\mathrm{z}-1)^{(-\gamma )}\ \forall \mathrm{z} \in \mathrm{N}_{\nu +n}, \gamma >0 \bigr\} , $$ $\gamma =\frac{\beta -\nu }{2}$ and n satisfies the following condition: $$ \frac{(\nu +n+\gamma -1)^{(-0.5)}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )} (\nu +n+\gamma -1)^{(- \gamma )}\leqq 1. $$ From the definition (2.8) of the operator B, Lemma 2.2 and assumption (C1), we have, for $\mathrm{z}\in \mathrm{N}_{\nu +n}$, $$\begin{aligned} \bigl\vert (\mathtt{B}y) (\mathrm{z}) \bigr\vert &{{\leqq }} \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl( \mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} \bigl\vert \psi \bigl( \kappa + \nu -1,y(\kappa +\nu -1) \bigr) \bigr\vert \\ &\leqq \frac{\mathtt{C}}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}- \nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)}(\kappa +\nu -1)^{(- \beta )} \\ &=\mathtt{C} \bigl({}_{0}{\Delta }^{-\nu }(\kappa +\nu -1)^{(- \beta )} \bigr) (\mathrm{z}) \\ &=\mathtt{C}\frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}( \mathrm{z}+\nu -1)^{(\nu -\beta )} \quad \text{provided that } \nu + \beta =1. \end{aligned}$$ Considering ν, $\beta -\nu $ and $\mathrm{z}-1$ are all positive for $\mathrm{z}\in \mathrm{N}_{\nu +n}$, $n=1,2,\ldots $ , by Lemmas 2.1 and 2.2, and assumption (3.3), we have $$\begin{aligned} \bigl\vert (\mathtt{B}y) (\mathrm{z}) \bigr\vert &< \mathtt{C} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}(\mathrm{z}-1)^{(\nu - \beta )} \\ &=\mathtt{C}\frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}( \mathrm{z}+\gamma -1)^{(-\gamma )}( \mathrm{z}-1)^{(-\gamma )} \\ &\leqq \mathtt{C}\frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}( \nu +\gamma +n-1)^{(-\gamma )}( \mathrm{z}-1)^{(-\gamma )} \\ &\leqq (\mathrm{z}-1)^{(-\gamma )}. \end{aligned}$$ This means that $y\in \mathtt{S}_{1}$ and thus $\mathtt{B}\mathtt{S}_{1}\subseteq \mathtt{S}_{1}$. For the continuity of B on $\mathtt{S}_{1}$, we let $\epsilon >0$ be given. Then, by using Lemmas 2.1 and 2.2, there exists $m\geq n$ in $\mathbb{N}_{1}$ such that $$ \mathtt{C} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )} ( \mathrm{z}-1)^{(\nu -\beta )}< \frac{\epsilon }{2} \quad \text{for } \mathrm{z}\in \mathrm{N}_{\nu +m}. $$ Let $\{y_{j} \}_{j=\nu +n}^{\infty }$ be a sequence defined on $\mathtt{S}_{1}$ that converges to y. For $\mathrm{z}\in \mathrm{N}_{\nu +m}$, it follows from assumption (C1) and (3.5) that $$\begin{aligned} & \bigl\vert (\mathtt{B}y_{j}) (\mathrm{z})-(\mathtt{B}y) ( \mathrm{z}) \bigr\vert \\ &\quad \leqq \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} \bigl[ \bigl\vert \psi \bigl(\kappa +\nu -1,y_{j}(\kappa +\nu -1) \bigr) \bigr\vert \\ &\qquad {}+ \bigl\vert \psi \bigl(\kappa +\nu -1,y(\kappa +\nu -1) \bigr) \bigr\vert \bigr] \\ &\quad \leqq \frac{2\mathtt{C}}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}- \nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)}(\kappa +\nu -1)^{(- \beta )} \\ &\quad =2\mathtt{C} \bigl({}_{0}{\Delta }^{-\nu }(\kappa +\nu -1)^{(- \beta )} \bigr) (\mathrm{z}) \\ &\quad =2\mathtt{C}\frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}( \mathrm{z}+\nu -1)^{(\nu -\beta )} \\ &\quad < 2\mathtt{C}\frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}( \mathrm{z}-1)^{(\nu -\beta )} \\ &\quad < \epsilon . \end{aligned}$$ For the rest of the interval $\mathrm{z}\in \{\nu +n,\nu +n+1,\ldots ,\nu +m-1 \}$, we use the continuity of ψ and Lemma 2.1 to obtain $$\begin{aligned} & \bigl\vert (\mathtt{B}y_{j}) (\mathrm{z})-(\mathtt{B}y) ( \mathrm{z}) \bigr\vert \\ &\quad \leqq \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} \bigl\vert \psi \bigl( \kappa +\nu -1,y_{j}(\kappa +\nu -1) \bigr)-\psi \bigl(\kappa +\nu -1,y( \kappa +\nu -1) \bigr) \bigr\vert \\ &\quad \leqq \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} \\ &\qquad {}\times \max_{{{\kappa \in }} \{\nu +n,\nu +n+1, \ldots ,\nu +m-1 \}} \bigl\vert \psi \bigl(\kappa +\nu -1,y_{j}(\kappa + \nu -1) \bigr)-\psi \bigl(\kappa +\nu -1,y(\kappa +\nu -1) \bigr) \bigr\vert \\ &\quad = \bigl({}_{0}{\Delta }^{-\nu }r^{(0)} \bigr) ( \mathrm{z}) \\ &\qquad {}\times \max_{{{\kappa \in }} \{\nu +n,\nu +n+1, \ldots ,\nu +m-1 \}} \bigl\vert \psi \bigl(\kappa +\nu -1,y_{j}(\kappa + \nu -1) \bigr)-\psi \bigl(\kappa +\nu -1,y(\kappa +\nu -1) \bigr) \bigr\vert \\ &\quad =\frac{\mathrm{z}^{(\nu )}}{\Gamma (\nu +1)} \\ &\qquad {}\times \max_{{{\kappa \in }} \{\nu +n,\nu +n+1, \ldots ,\nu +m-1 \}} \bigl\vert \psi \bigl(\kappa +\nu -1,y_{j}(\kappa + \nu -1) \bigr)-\psi \bigl(\kappa +\nu -1,y(\kappa +\nu -1) \bigr) \bigr\vert \\ &\quad \leqq \frac{(\nu +m-1)^{(\nu )}}{\Gamma (\nu +1)} \\ &\qquad {}\times \max_{{{\kappa \in }} \{\nu +n,\nu +n+1, \ldots ,\nu +m-1 \}} \bigl\vert \psi \bigl(\kappa +\nu -1,y_{j}(\kappa + \nu -1) \bigr)-\psi \bigl(\kappa +\nu -1,y(\kappa +\nu -1) \bigr) \bigr\vert \\ &\quad =\frac{\Gamma (\nu +m)}{\Gamma (\nu +1){{\Gamma (m)}}} \\ &\qquad {}\times \max_{{{\kappa \in }} \{\nu +n,\nu +n+1, \ldots ,\nu +m-1 \}} \bigl\vert \psi \bigl(\kappa +\nu -1,y_{j}(\kappa + \nu -1) \bigr)-\psi \bigl(\kappa +\nu -1,y(\kappa +\nu -1) \bigr) \bigr\vert , \end{aligned}$$ which approaches zero when $j\to \infty $. Therefore, we have proved for each $\mathrm{z}\in \mathrm{N}_{\nu +n}$, $$ \bigl\vert (\mathtt{B}y_{n}) (\mathrm{z})-( \mathtt{B}y) (\mathrm{z}) \bigr\vert \to 0\quad \text{as } n\to \infty , $$ and thus the operator B is continuous. In the following, we prove that the operator B is also relatively compact in $\mathtt{S}_{1}$. Let $\mathrm{z}_{1}, \mathrm{z}_{2}\in \mathrm{N}_{\nu +n}$ with $\mathrm{z}_{2}>\mathrm{z}_{1}$, yielding $$\begin{aligned} & \bigl\vert (\mathtt{B}y) (\mathrm{z}_{1})-(\mathtt{B}y) ( \mathrm{z}_{2}) \bigr\vert \\ &\quad \leqq \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}_{1}-\nu } \bigl(\mathrm{z}_{1}-\sigma (\kappa ) \bigr)^{(\nu -1)} \bigl\vert \psi \bigl(\kappa +\nu -1,y(\kappa +\nu -1) \bigr) \bigr\vert \\ &\qquad {}+\frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}_{2}-\nu } \bigl( \mathrm{z}_{2}-\sigma (\kappa ) \bigr)^{(\nu -1)} \bigl\vert \psi \bigl( \kappa +\nu -1,y(\kappa +\nu -1) \bigr) \bigr\vert \\ &\quad =\mathtt{C}_{1} \bigl({}_{0}{\Delta }^{-\nu }(\kappa +\nu -1)^{(- \beta )} \bigr) (\mathrm{z}_{1}) +\mathtt{C}_{2} \bigl( {}_{0}{\Delta }^{-\nu }( \kappa +\nu -1)^{(-\beta )} \bigr) ( \mathrm{z}_{2}) \\ &\quad =\mathtt{C}_{1}\frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}( \mathrm{z}_{1}+ \nu -1)^{(\nu -\beta )} +\mathtt{C}_{2} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}( \mathrm{z}_{2}+\nu -1)^{( \nu -\beta )} \\ &\quad < \underbrace{\frac{\epsilon }{2}+\frac{\epsilon }{2}}_{ \text{according to (3.5)}}= \epsilon . \end{aligned}$$ Therefore, $\{\mathtt{B}y: y\in \mathtt{S}_{1} \}$ is a bounded and uniformly Cauchy subset by Definition 2.1. Moreover, $\mathtt{B}\mathtt{S}_{1}$ is relatively compact in view of Theorem 2.1. Thus, the conclusion follows. □ Assume that a function ψ of two variables satisfies the assumption (C1) stated in Theorem 3.1. Then, there exists at least one solution $y(\mathrm{z})$ of the difference equation (1.2) for $\mathrm{z}\in \mathrm{N}_{\nu +1}$ in $\mathtt{S}_{1}$. It is enough to show that $y(\mathrm{z})$ is a fixed point of P in $\mathtt{S}_{1}$. Let $z\in \mathtt{S}_{1}$ be fixed. If $y:=\mathtt{A}y+\mathtt{B}z$, then we shall show that y is in $\mathtt{S}_{1}$. By means of (C1), Lemmas 2.1, 2.2 and 2.3(iii) one has for $\mathrm{z}\in \mathrm{N}_{\nu +n}$: $$\begin{aligned} \bigl\vert y(\mathrm{z}) \bigr\vert &\leqq \bigl\vert (\mathtt{A}y) ( \mathrm{z}) \bigr\vert + \bigl\vert (\mathtt{B}z) (\mathrm{z}) \bigr\vert \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl( \mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} \bigl\vert \psi \bigl( \kappa + \nu -1,z(\kappa +\nu -1) \bigr) \bigr\vert \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert +\mathtt{C} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}(\mathrm{z}+\nu -1)^{( \nu -\beta )} \\ &< \frac{(\mathrm{z}-1)^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert +\mathtt{C} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}(\mathrm{z}-1)^{(\nu - \beta )}. \end{aligned}$$ By considering the condition (3.3), and Lemmas 2.1 and 2.3(ii), it follows that $$\begin{aligned} \bigl\vert y(\mathrm{z}) \bigr\vert &\leqq \biggl[ \frac{(\mathrm{z}+\gamma -1)^{(-0.5)}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}\frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}(\mathrm{z}+ \gamma -1)^{(-\gamma )} \biggr](\mathrm{z}-1)^{(-\gamma )} \\ &\leqq \biggl[\frac{(\nu +n+\gamma -1)^{(-0.5)}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}(\nu +n+ \gamma -1)^{(-\gamma )} \biggr]( \mathrm{z}-1)^{(-\gamma )} \\ &\leqq (\mathrm{z}-1)^{(-\gamma )}, \end{aligned}$$ which means that $y(\mathrm{z})\in \mathtt{S}_{1}$ for $\mathrm{z}\in \mathrm{N}_{\nu +n}$. By Theorem 3.1 and 2.2, therefore, P has a fixed point in $\mathtt{S}_{1}$, which means that there exists at least one solution of the difference equation (1.2) on $\mathrm{z}\in \mathrm{N}_{\nu +n}$. The proof is now completed. □ Assume that a function ψ of two variables ψ satisfies the assumption (C1) stated in Theorem 3.1. Then, the solutions $y(\mathrm{z})$ of the difference equation (1.2) are attractive in $\mathtt{S}_{1}$. By means of Theorem 3.2, the solutions of the difference equation (1.2) exist in $\mathtt{S}_{1}$. Moreover, each of the functions $y(\mathrm{z})$ tend to 0 as ${{\mathrm{z}\to \infty }}$. Therefore, the solutions of the difference equation (1.2) tend to 0 as ${{\mathrm{z}\to \infty }}$. The proof is complete. □ There exist positive constants K and β, with $\nu +\beta =1$ and $\beta >\nu $, such that $$ {{ \bigl\vert \psi \bigl(\mathrm{z},y_{1}( \mathrm{z}) \bigr)- \psi \bigl(\mathrm{z},y_{2}(\mathrm{z}) \bigr) \bigr\vert \leqq \mathtt{K} \mathrm{z}^{(-\beta )} \Vert y-z \Vert \quad ( \forall \mathrm{z}\in \mathrm{N}_{\nu +1} ).}} $$ Then, the solutions of the difference equation (1.2) are stable if $$ \ell :=\mathtt{K} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )} \frac{\Gamma (1+\nu )}{\Gamma (1+\beta )}< 1. $$ Let ω, ϖ be two solutions of the difference equation (1.2) and let $\epsilon >0$. From the assumption (C2) and Lemmas 2.1, 2.2 and 2.3, one has the following for $\mathrm{z}\in \mathrm{N}_{\nu +1}$: $$\begin{aligned} \bigl\vert \omega (\mathrm{z})-\varpi (\mathrm{z}) \bigr\vert &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert \omega _{0}-\varpi _{0} \vert \\ &\quad {}+\frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl( \mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} \bigl\vert \psi \bigl( \kappa + \nu -1,\omega (\kappa +\nu -1) \bigr) \\ &\quad {}-\psi \bigl(\kappa +\nu -1, \varpi ( \kappa +\nu -1) \bigr) \bigr\vert \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert \omega _{0}- \varpi _{0} \vert + \frac{ \Vert \omega -\varpi \Vert }{\Gamma (\nu )}\mathtt{K}\sum _{ \kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{( \nu -1)}(\kappa +\nu -1)^{(-\beta )} \\ &=\frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert \omega _{0}- \varpi _{0} \vert +\mathtt{K} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}(\mathrm{z}+\nu -1)^{( \nu -\beta )} \Vert \omega -\varpi \Vert \\ &\leqq \frac{(\nu +1)^{(\nu -1)}}{\Gamma (\nu )} \vert \omega _{0}- \varpi _{0} \vert +\mathtt{K} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )} \nu ^{(\nu -\beta )} \Vert \omega -\varpi \Vert \\ &=\frac{\nu (\nu +1)}{2} \vert \omega _{0}-\varpi _{0} \vert + \mathtt{K}\frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )} \frac{\Gamma (1+\nu )}{\Gamma (1+\beta )} \Vert \omega -\varpi \Vert . \end{aligned}$$ By using (3.8), it follows that $$ \Vert \omega -\varpi \Vert \leqq \frac{\nu (\nu +1)}{2(1-\ell )} \vert \omega _{0}-\varpi _{0} \vert . $$ Now, chose $\delta =\frac{2(1-\ell )\epsilon }{\nu (\nu +1)}$. Therefore, $$\begin{aligned} \Vert \omega -\varpi \Vert &< \frac{\nu (\nu +1)}{2(1-\ell )}\cdot \delta \quad \text{whenever } \vert \omega _{0}-\varpi _{0} \vert < \delta \\ &=\epsilon . \end{aligned}$$ Thus, it is proven that the solutions of the difference equation (1.2) are stable. □ Corollary 3.1 Assume that a function ψ of two variables satisfies the assumptions (C1) and (C2) stated in Theorems 3.1and 3.4, respectively. Then, the solutions of the difference equation (1.2) are asymptotically stable. Corollary 3.1 follows from Theorems 3.3 and 3.4. □ Remark 3.1 It is important to state explicitly that the power rule (2.4) is used mistakenly in [27, 28, 32–34] as follows: $$ \bigl({}_{0}{\Delta }^{-\nu }(\kappa +\nu )^{(-\beta )} \bigr) ( \mathrm{z}) =\frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}( \mathrm{z}+\nu )^{(\nu -\beta )}. $$ In fact, according to Lemma 2.2, it is valid only when $\nu =-\beta $, which contradicts the positivity of ν and β. That is why we have chosen to study such a difference equation of the type (1.2). In this case, we have obtained $$ \bigl({}_{0}{\Delta }^{-\nu }(\kappa +\nu -1)^{(-\beta )} \bigr) (\mathrm{z}) = \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )}(\mathrm{z}+\nu -1)^{( \nu -\beta )}, $$ for which we need $\nu +\beta =1$ according to Lemma 2.2, as we have established in Theorems 3.1 to 3.4. We now prove a new attractiveness of the solutions of the difference equation (1.2) with a new condition in the following theorem. There exist positive constants $\mathtt{C}_{2}$, β and γ, with $\nu +\beta +\gamma =1$ and $\beta >\nu $, such that $$ {{ \bigl\vert \psi \bigl(\mathrm{z},y(\mathrm{z})\bigr) \bigr\vert \leqq \mathtt{C}_{2} (\mathrm{z}+\gamma )^{(-\beta )} \bigl\vert y(\mathrm{z}+1) \bigr\vert \quad (\forall \mathrm{z}\in \mathrm{N}_{\nu +1} ).}} $$ Then, the solutions of the difference equation (1.2) are attractive. To prove this theorem, we will verify the conditions of Theorem 2.2. The first condition is clear because A is a contraction as we discussed before. Also, the second condition is very similar to the one we proved in Theorem 3.1, so we omit it. Here, we prove the last condition so that $y(\mathrm{z})$ will be a fixed point of P in $\mathtt{S}_{2}$, where where $n\in \mathbb{N}_{1}$ satisfies the condition that $$ \frac{(\nu +n+\gamma -1)^{(-\beta )}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}_{2} \frac{\Gamma (1-\beta -\gamma )}{\Gamma (1+\nu -\beta -\gamma )}(\nu +n+ \gamma -1)^{(\nu -\beta )}\leqq 1. $$ Let $w\in \mathtt{S}_{2}$ be fixed. Now, if $y:=\mathtt{A}y+\mathtt{B}w$, then we shall show that y is in $\mathtt{S}_{2}$. By using assumption (C3), Lemmas 2.1, 2.2 and 2.3, we have for $\mathrm{z}\in \mathrm{N}_{\nu +n}$: $$\begin{aligned} \bigl\vert y(\mathrm{z}) \bigr\vert &\leqq \bigl\vert (\mathtt{A}y) ( \mathrm{z}) \bigr\vert + \bigl\vert (\mathtt{B}w) (\mathrm{z}) \bigr\vert \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl( \mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} \bigl\vert \psi \bigl( \kappa + \nu -1,w(\kappa +\nu -1) \bigr) \bigr\vert \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{\mathtt{C}_{2}}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} (\kappa +\nu + \gamma -1)^{(-\beta )}{{ \bigl\vert w(\kappa +\nu ) \bigr\vert }} \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{\mathtt{C}_{2}}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} (\kappa +\nu + \gamma -1)^{(-\beta )}(\kappa +\nu -1)^{(-\gamma )} \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{\mathtt{C}_{2}}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} (\kappa +\nu -1)^{(- \beta -\gamma )} \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}_{2} \frac{\Gamma (1-\beta -\gamma )}{\Gamma (1+\nu -\beta -\gamma )}( \mathrm{z}+\nu -1)^{(\nu -\beta -\gamma )}\quad \text{such that } \nu +\beta +\gamma =1 \\ &< \frac{(\mathrm{z}-1)^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}_{2} \frac{\Gamma (1-\beta -\gamma )}{\Gamma (1+\nu -\beta -\gamma )}( \mathrm{z}-1)^{(\nu -\beta -\gamma )}. \end{aligned}$$ By considering condition (3.10), and Lemmas 2.1 and 2.3(ii), it follows that $$\begin{aligned} \bigl\vert y(\mathrm{z}) \bigr\vert &\leqq \biggl[ \frac{(\mathrm{z}+\gamma -1)^{(-\beta )}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}_{2} \frac{\Gamma (1-\beta -\gamma )}{\Gamma (1+\nu -\beta -\gamma )}( \mathrm{z}+\gamma -1)^{(\nu -\beta )} \biggr]( \mathrm{z}-1)^{(- \gamma )} \\ &\leqq \biggl[\frac{(\nu +n+\gamma -1)^{(-\beta )}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}_{2} \frac{\Gamma (1-\beta -\gamma )}{\Gamma (1+\nu -\beta -\gamma )}(\nu +n+ \gamma -1)^{(\nu -\beta )} \biggr](\mathrm{z}-1)^{(-\gamma )} \\ &\leqq (\mathrm{z}-1)^{(-\gamma )}. \end{aligned}$$ This completes the required result. Therefore, by Theorem 3.1 and 2.2, P has a fixed point in $\mathtt{S}_{2}$, which means that there exists at least one solution of the difference equation (1.2) on $\mathrm{z}\in \mathrm{N}_{\nu +n}$. Moreover, by means of Theorem 3.2, each of the functions $y(\mathrm{z})$ in $\mathtt{S}_{2}$ tend to zero as $\mathrm{z}\to \infty $. Therefore, the solutions of the difference equation (1.2) tend to zero as $\mathrm{z}\to \infty $. This completes the proof. □ Assume that a function ψ of two variables satisfies the assumptions (C2) and (C3) stated in Theorems 3.4and 3.5, respectively. Then, the solutions of the difference equation (1.2) are asymptotically stable such that (3.8) holds true. This follows from Theorems 3.4 and 3.5. □ Let the following condition on ψ hold true: There exist $\eta \in (0,1)$ and the positive constants $\mathtt{C}_{3}$ and β such that $$ {{ \bigl\vert \psi \bigl(\mathrm{z},y(\mathrm{z})\bigr) \bigr\vert \leqq \mathtt{C}_{3} (\mathrm{z}+1)^{(-\beta )} \bigl\vert y(\mathrm{z}+1) \bigr\vert ^{\eta } \quad (\forall \mathrm{z}\in \mathrm{N}_{\nu +1} ).}} $$ We proceed with the same method as that used in Theorem 3.5. We only prove the last condition in 2.2 so that $y(\mathrm{z})$ will be a fixed point of P in $\mathtt{S}_{3}$, where where $\nu +\beta +\gamma \eta =1$, $\beta >\nu $, $\nu +\gamma \in (0,1)$, $\gamma =\frac{\beta -\nu }{2}$ and $n\in \mathbb{N}_{1}$ satisfies the condition that $$ \frac{(\nu +n+\gamma -1)^{(\nu +\gamma -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}_{3} \frac{\Gamma (1-\beta -\gamma \eta )}{\Gamma (1+\nu -\beta -\gamma \eta )}( \nu +n+\gamma -1)^{(-\gamma )}\leqq 1. $$ Let $w\in \mathtt{S}_{3}$ be fixed. Now, if $y:=\mathtt{A}y+\mathtt{B}w$, then we shall show that y is in $\mathtt{S}_{3}$. By using assumption (C4), $\nu <\beta +\gamma \eta <1$, Lemmas 2.1, 2.2 and 2.3(ii)–(iv), we have for $\mathrm{z}\in \mathrm{N}_{\nu +n}$: $$\begin{aligned} \bigl\vert y(\mathrm{z}) \bigr\vert &\leqq \bigl\vert (\mathtt{A}y) ( \mathrm{z}) \bigr\vert + \bigl\vert (\mathtt{B}w) (\mathrm{z}) \bigr\vert \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{1}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl( \mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} \bigl\vert \psi \bigl( \kappa + \nu -1,w(\kappa +\nu -1) \bigr) \bigr\vert \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{\mathtt{C}_{3}}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} (\kappa +\nu )^{(- \beta )}{{ \bigl\vert w(\kappa +\nu ) \bigr\vert ^{\eta }}} \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{\mathtt{C}_{3}}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} (\kappa +\nu + \gamma \eta -1)^{(-\beta )} \bigl[(\kappa +\nu -1)^{(-\gamma )} \bigr]^{\eta } \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{\mathtt{C}_{3}}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} (\kappa +\nu + \gamma \eta -1)^{(-\beta )}(\kappa +\nu -1)^{(-\gamma \eta )} \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \frac{\mathtt{C}_{3}}{\Gamma (\nu )}\sum_{\kappa =0}^{\mathrm{z}-\nu } \bigl(\mathrm{z}-\sigma (\kappa ) \bigr)^{(\nu -1)} (\kappa +\nu -1)^{(- \beta -\gamma \eta )} \\ &\leqq \frac{\mathrm{z}^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}_{3} \frac{\Gamma (1-\beta -\gamma \eta )}{\Gamma (1+\nu -\beta -\gamma \eta )} ( \mathrm{z}+\nu -1)^{(\nu -\beta -\gamma \eta )} \quad \text{such that } \nu +\beta +\gamma \eta =1 \\ &\leqq \frac{(\mathrm{z}-1)^{(\nu -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}_{3} \frac{\Gamma (1-\beta -\gamma \eta )}{\Gamma (1+\nu -\beta -\gamma \eta )} ( \mathrm{z}-1)^{(\nu -\beta )}. \end{aligned}$$ Considering condition (3.12), $\nu +\gamma \in (0,1)$, $\beta -\nu =2\gamma $, and Lemmas 2.1 and 2.3(ii), it follows that $$\begin{aligned} \bigl\vert y(\mathrm{z}) \bigr\vert &\leqq \biggl[ \frac{(\mathrm{z}+\gamma -1)^{(\nu +\gamma -1)}}{\Gamma (\nu )} \vert y_{0} \vert +\mathtt{C}_{3} \frac{\Gamma (1-\beta -\gamma \eta )}{\Gamma (1+\nu -\beta -\gamma \eta )}( \mathrm{z}+\gamma -1)^{(-\gamma )} \biggr]( \mathrm{z}-1)^{(-\gamma )} \\ &\leqq \biggl[ \frac{(\nu +n+\gamma -1)^{(\nu +\gamma -1)}}{\Gamma (\nu )} \vert y_{0} \vert + \mathtt{C}_{3} \frac{\Gamma (1-\beta -\gamma \eta )}{\Gamma (1+\nu -\beta -\gamma \eta )}( \nu +n+\gamma -1)^{(-\gamma )} \biggr] \\ &\quad {}\times (\mathrm{z}-1)^{(-\gamma )} \\ &\leqq (\mathrm{z}-1)^{(-\gamma )}. \end{aligned}$$ This proves the required condition (iii) in Theorem 2.2 and thus the proof is completed. □ The same mistakes of the power rule, as we discussed in Remark 3.1, are made in Theorems 3.6 and 3.8 in [32]. In those theorems, the used power rule would have been true when $\nu +\beta _{3}+\gamma _{2}=0$ and $\nu +\beta _{3}+\gamma _{2}\eta =0$, respectively. However, these contradict the positivity of ν, β, γ and η. The chosen parameters here are such that $\nu +\beta +\gamma =1$ in Theorem 3.5 and $\nu +\beta +\gamma \eta =1$ in Theorem 3.6 have appropriately corrected the above mistakes. In this section, we present three nonlinear difference examples that illustrate the results established in general above. In each case, Conditions (C1) to (C4) are verified to be true. Example 4.1 Consider the nonlinear difference equation $$\begin{aligned} \begin{aligned} & \bigl({}^{\mathrm{RL}}_{-0.75}{ \Delta }^{0.25}y \bigr) (\mathrm{z}) =0.2 (\mathrm{z}-0.75 )^{(-0.75)}\sin \bigl(y(\mathrm{z}-0.75) \bigr) \quad (\forall \mathrm{z}\in \mathrm{N}_{0} ), \\ & \bigl({}_{-0.75}{\Delta }^{-0.75}y \bigr) ( \mathrm{z})\big\|_{ \mathrm{z}=0}=y_{0}. \end{aligned} \end{aligned}$$ Here, $\nu +\beta =0.25+0.75=1$ and $\psi (\mathrm{z},y(\mathrm{z}) )=0.2 \mathrm{z}^{(-0.75)} \sin (y(\mathrm{z}))$. Thus, for $\mathrm{z}\in \mathrm{N}_{1.5}$, we have $$ \bigl\vert \psi \bigl(\mathrm{z},y(\mathrm{z}) \bigr) \bigr\vert = \bigl\vert 0.2 \mathrm{z}^{(-0.75)}\sin \bigl(y(\mathrm{z})\bigr) \bigr\vert \leqq 0.2 \mathrm{z}^{(-0.75)}, $$ so (C1) is satisfied. Also, we have $$ \bigl\vert \psi \bigl(\mathrm{z},y(\mathrm{z}) \bigr)-\psi \bigl(\mathrm{z},z( \mathrm{z}) \bigr) \bigr\vert \leqq 0.2 \mathrm{z}^{(-0.75)} \Vert y-z \Vert , $$ so (C2) is satisfied as well. Moreover, in view of Theorem 3.4 with $\mathtt{K}=0.2$, $\nu =0.25$ and $\beta =0.75$, we find that $$ \ell =\mathtt{K} \frac{\Gamma (1-\beta )}{\Gamma (1+\nu -\beta )} \frac{\Gamma (1+\nu )}{\Gamma (1+\beta )} =0.2 \frac{\Gamma (0.25)}{\Gamma (0.5)}\frac{\Gamma (1.25)}{\Gamma (1.75)}=0.4035< 1, $$ which verifies (3.8). Therefore, the solutions of the difference equation (4.1) are asymptotically stable according to Corollary 3.1. $$ \begin{aligned} & \bigl({}^{\mathrm{RL}}_{-0.8}{ \Delta }^{0.2}y \bigr) (\mathrm{z}) =0.4 (\mathrm{z}+0.2 )^{(-0.5)}y(\mathrm{z}-0.8)\quad (\forall \mathrm{z}\in \mathrm{N}_{0} ), \\ & \bigl({}_{-0.8}{\Delta }^{-0.8}y \bigr) ( \mathrm{z})\big\|_{ \mathrm{z}=0}=y_{0}. \end{aligned} $$ From the difference equation, we see that $\nu +\beta +\gamma =0.2+0.5+0.3=1$ and $\psi (\mathrm{z},y(\mathrm{z}) )=0.4 (\mathrm{z}+1)^{(-0.5)}y( \mathrm{z})$. Since $\mathrm{z}^{(-0.5)}$ is nonincreasing. Then, for $\mathrm{z}\in \mathrm{N}_{1.5}$, we have $$ \bigl\vert \psi \bigl(\mathrm{z},y(\mathrm{z}) \bigr) \bigr\vert = \bigl\vert 0.4 ( \mathrm{z}+1)^{(-0.5)}y(\mathrm{z}) \bigr\vert \leqq 0.4 ( \mathrm{z}+0.3)^{(-0.5)} \bigl\vert y(\mathrm{z}) \bigr\vert , $$ and so (C3) is satisfied. Also, we see that $$ \bigl\vert \psi \bigl(\mathrm{z},y(\mathrm{z}) \bigr)-\psi \bigl(\mathrm{z},z( \mathrm{z}) \bigr) \bigr\vert \leqq 0.4 (\mathrm{z}+1)^{(-0.5)} \Vert y-z \Vert \leqq 0.4 \mathrm{z}^{(-0.5)} \Vert y-z \Vert , $$ so (C2) is satisfied. Moreover, in view of Theorem 3.4 with $\mathtt{K}=0.2$, $\nu =0.25$ and $\beta =0.75$, we find that $$ \ell =0.4\frac{\Gamma (0.5)}{\Gamma (0.7)} \frac{\Gamma (1.2)}{\Gamma (1.5)}=0.5659< 1, $$ which verifies the condition (3.8). Therefore, the solutions of the difference equation (4.2) are asymptotically stable according to Corollary 3.2. Finally, we consider the following nonlinear difference equation $$\begin{aligned} \begin{aligned} & \bigl({}^{\mathrm{RL}}_{-0.61}{ \Delta }^{0.39}y \bigr) (\mathrm{z}) =0.4 (\mathrm{z}+0.39 )^{(-0.59)}y^{\frac{1}{5}}(\mathrm{z}-0.61)\quad (\forall \mathrm{z}\in \mathrm{N}_{0} ), \\ & \bigl({}_{-0.61}{\Delta }^{-0.61}y \bigr) ( \mathrm{z})\big\|_{ \mathrm{z}=0}=y_{0}. \end{aligned} \end{aligned}$$ From the given difference equation, we have $\nu =0.39$, $\beta =0.59$, $\gamma =\frac{0.59-0.39}{2}=0.1$, $\eta =0.2$ and $\psi (\mathrm{z},y(\mathrm{z}) )=0.4 (\mathrm{z}+1)^{(-0.59)}y^{ \frac{1}{5}}(\mathrm{z}+1)$ for $\mathrm{z}\in \mathrm{N}_{1.5}$. Since $\mathrm{z}^{(-0.5)}$ is nonincreasing, for $\mathrm{z}\in \mathrm{N}_{1.5}$, we have $$ \bigl\vert \psi \bigl(\mathrm{z},y(\mathrm{z}) \bigr) \bigr\vert = \bigl\vert 0.4 ( \mathrm{z}+1)^{(-0.59)}y^{\frac{1}{5}}(\mathrm{z}+1) \bigr\vert \leqq 0.4 (\mathrm{z}+1)^{(-0.59)} \bigl\vert y(\mathrm{z}+1) \bigr\vert ^{\frac{1}{5}}, $$ so (C4) is satisfied. Therefore, the solutions of the difference equation (4.3) are attractive according to Theorem 3.6. Conclusions and directions for further work In this work, we dealt with a class of nonlinear fractional difference equations in the sense of Riemann–Liouville. The power-rule mistakes made by some authors in [2, 3] are corrected by providing some further conditions. 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Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq Pshtiwan Othman Mohammed Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia, V8W 3R4, Canada Hari Mohan Srivastava Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007, Baku, Azerbaijan Section of Mathematics, International Telematic University Uninettuno, I-00186, Rome, Italy Department of Applied Mathematics and Statistics, Technical University of Cartagena, Hospital de Marina, ES-30203, Cartagena, Spain Juan L. G. Guirao Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif, 21944, Saudi Arabia Y. S. Hamed Conceptualization, POM, HMS and JLGG; methodology, POM, HMS; software, YSH, HMS, JLGG, KMA; validation, POM, HMS, JLGG; formal analysis, KMA; investigation, YSH, POM, HMS, KMA; resources, JLGG and YSH; writing, original draft preparation, YSH, POM, HMS, JLGG, KMA; writing, reviewing and editing, HMS, JLGG; funding acquisition, JLGG. All authors read and approved the final manuscript. Correspondence to Pshtiwan Othman Mohammed or Juan L. G. Guirao. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Mohammed, P.O., Srivastava, H.M., Guirao, J.L.G. et al. Existence of solutions for a class of nonlinear fractional difference equations of the Riemann–Liouville type. Adv Cont Discr Mod 2022, 32 (2022). https://doi.org/10.1186/s13662-022-03705-9 Discrete fractional calculus Riemann–Liouville fractional calculus Existence and uniquenes Fixed-point theorems Fractional difference equations Falling fractional functions	CommonCrawl
Effects of bloom-forming cyanobacterial extracellular polymeric substances on the adsorption of cadmium onto kaolinite: behaviors and possible mechanisms Xiaolin Kuang1, Jihai Shao1, Anwei Chen1, Si Luo1, Liang Peng1, Genyi Wu1 & Ji-Dong Gu2,3 Cyanobacterial blooms result in high level of cyanobacterial extracellular polymeric substances (EPS) in water. The effects of bloom-forming cyanobacterial EPS on the distribution of Cd(II) in the interface between sediment and water is unknown. Clay is a main component in sediment. The effects of EPS, originated from a typical bloom-forming cyanobacterium Microcystis aeruginosa, on the adsorption and desorption characteristics of Cd(II) by kaolinite were investigated in this study. Results of XRD analysis indicated that cyanobacterial EPS bound on the surface of kaolinite. The composite of kaolinite + EPS showed higher adsorption capacity toward Cd(II) than pure kaolinite, and hydroxyl groups were involved in the adsorption processes. The data for the adsorption of Cd(II) by kaolinite are well fitted by both Langmuir model and Freundlich model, whereas only Freundlich model well describes the adsorption data of Cd(II) by the composite of kaolinite + EPS. The adsorption of Cd(II) onto kaolinite was an exothermic process, but it became an endothermic process after EPS incorporation. Results of desorption showed that EPS incorporation increased the adsorption of kaolinite toward Cd(II) through physical adsorption, ion exchange and complexation. Heavy metal ions are toxic, non-biodegradable and can accumulate through food chain. Heavy metal pollution has caused serious ecological problems and posed a great health risk to human. Cadmium is a most hazardous heavy metal due to its high toxicity and carcinogenic effects (Son et al. 2012). In recent decades, industrial effluent and agricultural run-off caused widespread cadmium contamination in aquatic environments (Öztürk et al. 2009; Florian et al. 2011). Another world wide water problem is the eutrophication and harmful algal blooms. Microcystis is a typical bloom-forming cyanobacterium. It frequently dominates in eutrophic fresh waters. Take China as an example, two large lakes, Lake Taihu and Lake Dianchi, were all received severe Microcystis based water blooms (Ye et al. 2009; Wu et al. 2014). Microcystis could maintain very high cell density in water during bloom formation stage. Ye et al. (2009) reported that the total cyanobacterial density (mainly as Microcystis) reached as high as 2.93 × 1011 cells/mL in Lake Taihu, China. Microcystis can excrete EPS into water. High cell density of Microcystis frequently results in high concentration of EPS in water column. Xu et al. (2013) reported that the EPS in cultures of Microcystis aeruginosa researched 130 μg per 107 cells. The main component of EPS in Microcystis culture is polysaccharides, and then followed by proteins (Xu et al. 2013). EPS enrich hydroxyl groups, carboxylic groups, acetylated amino, and also contain some noncarbohydrate constituents, e.g. phosphate and sulfate (De Philippis et al. 2011). These chemical groups in EPS can effectively bind with heavy metal ions through ions exchange or complexation (Gong et al. 2005; Fang et al. 2011). Clay is a main component in sediment (Hou et al. 2013). Previous studies indicated that bacterial EPS could be absorbed by clays and sediments through hydrogen bonding and some other chemical bondings (Pierre et al. 2014; Cao et al. 2011; Fang et al. 2012). EPS addition changed the adsorption characteristics of heavy metal ions by clays, which in turn changed the concentration of heavy metal ions in water (Fang et al. 2010). The major part of heavy metal ions in aquatic environment is deposited in sediment through precipitation, sorption and complexation. The deposition of heavy metal ions from water column to sediment would decrease their concentration in water, and then decrease their bio-toxicity, and vice versa. Thus, studying on the transfer of heavy metal ions between water–sediment systems is crucial in evaluation of the ecological effect and the health risk of heavy metal contamination in aquatic environment. The structures of EPS originated from different bacteria are different (Pereira et al. 2009). Though the effects of some bacterial EPS, e.g. originated from Pseudomonas putida, Bacillus subtilis, on the adsorption characteristics of heavy metal ions onto clays were studied (Fang et al. 2010; Mikutta et al. 2012), the effects of the EPS, originated from bloom-forming cyanobacteria, on the adsorption characteristics of heavy metal ions by clays remain unknown. In order to elucidate the transfer characteristics of Cd(II) in eutrophic water received cyanobacterial blooms, the effects of EPS originated from Microcystis on the adsorption and desorption characteristics of Cd(II) by kaolinite and their possible mechanisms were investigated in this study. Cyanobacterial strain, culture conditions, EPS extraction, and reagents Bloom-forming cyanobacterial strain M. aeruginosa NIES-843 was originated from the National Institute of Environmental Science, Japan, and was kindly provided by Professor Renhui Li (Chinese Academy of Sciences). M. aeruginosa NIES-843 was grown axenically in CT medium (Ichimura 1979) at 25 ± 1 °C under a photoperiod cycle of 12:12 light/dark. The light intensity was set as 30 μmol photons/(s m2). The cell free cultures of M. aeruginosa NIES-843 were collected at stationary phase by centrifuge at 10,000×g for 10 min. The EPS in the cultures was purified in deionised water (18 MΩ cm) using dialysis bags (1000-Da cutoff). The purified EPS solutions were dried using vacuum freezer, and then stored at −20 °C. CdCl2·2.5H2O and other reagents used in this study were purchased from Sinopharm Group Chemical Reagent Ltd. (Shanghai, China), and were of analytical grade. Preparation of kaolinite Kaolinite was purchased from Shanghai 54 Chemical Reagent Ltd (Shanghai, China), and it was further purified by washing with ethanol for 3 times, and then followed by washing with deionised water (18 MΩ cm) for 3 times. The fractions of kaolinite, less than 2 μm, were prepared according to the method described by Cai et al. (2006). Adsorption experiments and adsorption isotherm Adsorption experiments were carried out in 10 mL centrifuge tube containing appropriate volume of deionised water (18 MΩ cm), 30 mg of kaolinite or the composite of kaolinite (30 mg) and EPS. The suspensions of kaolinite and the composite of kaolinite + EPS were incubated on a shaker for 30 min with a speed of 120 rpm, and then appropriate mount of Cd(II) and supporting electrolyte (KNO3, final concentration 0.01 M) were added into centrifuge tube, and the total volume was brought to 6 mL using deionised water. The centrifuge tubes were agitated on a shaker at a speed of 120 rpm for 4 h (reached equilibrium). The pH value was set as 7 except pH experiments, and the temperature was set as 25 °C except temperature experiments. In order to study the effect of EPS concentration on the adsorption of Cd(II) by kaolinite, the final EPS concentration was set as 0.1, 0.3, 0.6, 1, 2, and 3 g/L, and the initial Cd(II) concentration was set as 5 mg/L. In pH experiments, the pH value was set as 5, 6, 7, and 8, respectively, and the initial Cd(II) concentration was also set as 5 mg/L. For determination of the effect of initial Cd(II) concentration on its adsorption by kaolinite and the composite of kaolinite + EPS, the initial Cd(II) concentration was set from 5 to 500 mg/L, and the final EPS concentration in the treatment of kaolinite + EPS was set as 0.6 g/L. In temperature experiments, the temperature was set as 20, 25, 30, 35, and 40 °C, respectively. After equilibrium, the suspensions were centrifuged at 12,000×g for 10 min, and the Cd (II) in the supernatant was determined using atomic absorption spectrometer (Varian Techtron Pty. Ltd., Victoria, Australia). The amount of adsorbed Cd(II) was calculated from the differences between the initial Cd(II) concentration and the residual concentration after sorption. In order to study the adsorption isotherm of Cd(II) by kaolinite and the composite of kaolinite + EPS, adsorption data were fitted using Langmuir model and Freundlich model in linear form (Eqs. 1 and 2), respectively. $$\frac{1}{{q_{e} }} = \frac{1}{{q_{\text{max} } K_{L} C_{e} }} + \frac{1}{{q_{\text{max} } }}$$ $$\ln q_{e} = \ln K_{f} + \frac{1}{n}\ln C_{e}$$ where q e is the amount of adsorbate absorbed by adsorbent, C e , the equilibrium concentration, q max, the maximum adsorption capacity upon monolayer saturation adsorbent, K L , the constant related to the adsorption energy, and the K F and n are Freundlich parameters involved in the relative adsorption capacity and the affinity between adsorbent and adsorbate, respectively. X-ray diffraction and Fourier transform infrared spectroscopy analysis The crystal structures of kaolinite and the composite of kaolinite + EPS were recorded using a XRD-6000 instrument (Shimadzu Seisakusho Ltd., Japan) employing graphite monochromatized Cu Kα radiation, with scanning rate of 4°/min and ranging from 5° to 75°. Fourier transform infrared (FT-IR) spectra of kaolinite and the composite of kaolinite + EPS were obtained on a spectrometer (PerkinElmer Spectrum 65, Perkin-Elmer Co., Norwalk, CT, USA). Desorption of Cd(II) Desorption of Cd(II) from the kaolinite and the composite of kaolinite + EPS was performed using deionised water or NH4NO3 or EDTA as desorbent according to the methods previously described by Fang et al. (2011). Statistical analysis was done by one-way ANOVA using SPSS (version 13.0, SPSS Inc., Chicago, IL, USA). Difference was considered to be significant at P < 0.05 (LSD). Effects of EPS on the adsorption of Cd(II) by kaolinite As indicated in Fig. 1, the EPS had a positive effect on the adsorption of kaolinite toward Cd(II). With the increase of EPS addition, the adsorbed Cd(II) increased. Compared with the control, the amount of adsorbed Cd(II) increased 6.95, 19.68, 36.85, and 44.60 % at the EPS addition level of 0.1, 0.3, 0.6, and 1 g/L, respectively. The positive effects of EPS on the adsorption of Cd(II) by kaolinite reached plateau phase at the addition level of 1 g/L. Effects of cyanobacterial EPS on the adsorption of Cd(II) by kaolinite. Data are presented as average value ± standard deviation (n = 3) Characteristics of Fourier transform infrared spectroscopy The Vibrational spectra of EPS, kaolinite and the composite of kaolinite + EPS before and after Cd(II) adsorption, are shown in Fig. 2. The main absorption bands of EPS were corresponding to phosphorylated compounds (1044 cm−1), ring vibrations of polysaccharides (1164 cm−1), COO− groups (1410 and 1618 cm−1), C=O of amides (1660 cm−1), C=O of RCOOR (1742 cm−1), C-H (2936 cm−1), and O–H (3350-3470 cm−1), respectively. Typical frequency band corresponding to Si–O (1115, 1031, 1007 cm−1), Al-O (430 and 643 cm−1), and O–H (3486, 3620 and 3699 cm−1) presented in kaolinite and the composite of kaolinite + EPS. No matter Cd(II) adsorption or not, the spectral features of the composite of kaolinite + EPS were exhibited a same pattern. FT-IR spectra of kaolinite, EPS, and the composite of kaolinite + EPS before and after Cd(II) adsorption. Kao: Kaolinite; Kao + EPS: the composite of kaolinite + EPS before Cd(II) adsorption; Kao + EPS + Cd: the composite of kaolinite + EPS after Cd(II) adsorption Characteristics of X-ray diffraction Figure 3 shows the characteristics of X-ray diffraction of different treatments. The XRD pattern of kaolinite was similar with that of the composite of kaolinite + EPS. Typical diffraction peaks indexed as PDF#29-1488 and PDF#16-0409 for kaolinite presented in all treatments. EPS addition and Cd(II) adsorption did not change the diffraction patterns of kaolinite. XRD patterns of kaolinite and the composite of kaolinite + EPS before and after Cd(II) adsorption Effect of pH on the adsorption characteristics The adsorptions of Cd(II) by kaolinite and the composite of kaolinite + EPS were all significantly influenced by the pH value in the adsorption system (Fig. 4). With the increase of pH from 5 to 8, the adsorptions of Cd(II) by all treatments continue to increase. EPS and pH value has a synergistic effect on the adsorption of Cd(II) onto kaolinite. Compared with the amount of adsorbed Cd(II) at pH 5, the adsorbed Cd(II) by kaolinite increased 20.6 % at pH 8, whereas it increased 47.5 % under the condition of EPS addition at the level of 1 g/L under this pH value. Effects of pH on the adsorption of Cd(II) by kaolinite and the composite of kaolinite + EPS. Data are presented as average value ± standard deviation Different initial Cd(II) concentration and adsorption isotherm The adsorption of Cd(II) by kaolinite and the composite of kaolinite + EPS all increased with the increase of initial Cd(II) concentration (Fig. 5). The adsorption of Cd(II) by the composite of kaolinite + EPS was higher than that by kaolinite under the condition of a same initial Cd(II) concentration. In order to study the adsorption isotherm of Cd(II) by kaolinite and the composite of kaolinite + EPS, the adsorption data were fitted by Langmuir model and Freundlich model. As showed in Fig. 6 and Table 1, Both Langmuir model and Freundlich model were all well fitted by the adsorption data of kaolinite toward Cd(II) with a R square of 0.976 and 0.992, respectively. As the adsorption of Cd(II) by the composite of kaolinite + EPS, the R square is 0.958 for Langmuir model and 0.972 for Freundlich model. Effects of initial Cd(II) concentration on its adsorption onto kaolinite and the composite of kaolinite + EPS. Data are presented as average value ± standard deviation Langmuir (a) and Freundlich (b) isotherm plots for Cd(II) adsorption by kaolinite and the composite of kaolinite + EPS Table 1 Parameters of Langmuir model and Freundlich model for the adsorption of Cd(II) onto kaolinite and the composite of kaolinite + EPS Effect of temperature on adsorption characteristics The effects of temperature on the adsorption of Cd(II) by kaolinite and the composite of kaolinite + EPS are shown in Fig. 7. The adsorption of Cd(II) by kaolinite was not obviously influenced by the temperature at a range from 20 to 35 °C. However, the amount of adsorbed Cd(II) at 40 °C decrease 5–6 % when compared with those at 20–35 °C. As for the composite of kaolinite + EPS, the adsorption toward Cd(II) was not obviously influenced at a range from 20 to 30 °C, whereas it increased 7.4 % at 35 °C and 8.7 % at 40 °C when compared with that at 20 °C. Effects of temperature on the adsorption of Cd(II) by kaolinite and the composite of kaolinite + EPS. Data are presented as average value ± standard deviation Desorption characteristics Figure 8 shows the percentage of Cd(II) desorbed from kaolinite and the composite of kaolinite + EPS with different desorbents. Deionised water desorbed 9.31 and 14.72 % of Cd(II) from kaolinite and the composite of kaolinite + EPS, respectively. The desorption ratio for NH4NO3 treatment was 16.03 % for kaolinite and 26.31 % for the composite of kaolinite + EPS. The desorption ratio of Cd(II) by EDTA was 18.32 % for kaolinite and 30.60 % for the composite of kaolinite + EPS. Desorption ratio of Cd(II) from kaolinite and the composite of kaolinite + EPS using different desorbents. Data are presented as average value ± standard deviation The results in this study showed that the EPS originated from M. aeruginosa increased the adsorption capacity of kaolinite toward Cd (II), and this positive effect increased along with the increase of EPS concentration in solution. Similar results were reported by Fang et al. (2010), who found that the composite of montmorillonite and EPS (from Pseudomonas putida) showed higher adsorption capacity toward Cu(II) than pure montmorillonite. Some previous studies showed that bacterial EPS could be absorbed by kaolinite, montmorillonite through hydrogen bonding (Cao et al. 2011; Mikutta et al. 2012). Bacterial EPS enrich hydroxyl groups, carboxyl groups, acetylated amino, and some other negative charged groups (De Philippis et al. 2011). These groups can effectively binding with heavy metal ions. Based on the results of FT-IR determination, a schematic diagram for the mechanism of positive effects of cyanobacterial EPS on the adsorption of Cd(II) by kaolinite were proposed and showed in Fig. 9. The groups like PO4 3−, -COO−, -CONH2, RCOOR, and –OH on the EPS may response for the positive effects of EPS on the adsorption of Cd(II) by kaolinite. Schematic diagram for the adsorption of Cd(II) by kaolinite (a) and the composite of kaolinite + EPS (b) The interlayer spacing of kaolinite is 0.716 nm. Only small high polar molecules can enter into the interlayer of kaolinite (Tang et al. 2015). The EPS are large bio-molecules. The size of EPS is far larger than the interlayer spacing of kaolinite. Results of XRD determination showed that cyanobacterial EPS addition and Cd(II) adsorption did not affect the diffraction patterns of kaolinite, indicating that the EPS and Cd(II) all bound on the surface of kaolinite and not intercalated into the interlayers. The main absorption bands corresponding to C–O, C=O, and O–H are presented in EPS in this study. They are in consistent with previous studies that polysaccharides are the main constituents of bacterial EPS (Xu et al. 2013). Compared with the vibrational spectra of kaolinite + EPS before Cd(II) adsorption, no new absorption band was found after Cd(II) adsorption for this treatment. However, we also noted that the vibration intensity of the band corresponding to –OH was strong in the treatment of kaolinite + EPS before Cd(II), but it became weak after Cd(II) adsorption. Thus, we deduced that hydroxyl groups were involved in the adsorption of Cd(II) by the composite of kaolinite + EPS. Langmuir model is known as monolayer sorption, while the Freundlich model is suitable to multilayer sorption (He and Chen 2014). Our results indicated that both Langmuir model and Freundlich model were all well fitted by the data originated from the adsorption of Cd(II) by kaolinite, and the deduced q max from Langmuir model was in consistent with experimental data. However, the adsorption isotherm of Cd(II) by the composite of kaolinite + EPS was only suitable to Freundlich model but not Langmuir model since the deduced q max from Langmuir model was far lower than experimental data. Thus, we deduce that the addition of cyanobacterial EPS increased the heterogeneity on the surface of kaolinite. The parameter n from Freundlich model reflects the affinity between adsorbent and adsorbate. The value of n for the composite of kaolinite + EPS is higher than that of pure kaolinite, suggesting that the composite of kaolinite + EPS has higher affinity toward Cd(II) than pure kaolinite. As for the thermodynamics of the adsorption of Cd(II) by kaolinite, previous studies gave complex and contradictory conclusions. For example, Sari and Tuzen (2014) reported that the adsorption of Cd(II) onto kaolinite was an exothermic reaction while it was described as an endothermic reaction by Angove et al. (1998). Results in this study supported the conclusion that it was an exothermic reaction since the increase of temperature decreased the adsorption of Cd(II) by kaolinite. As for the composite of kaolinite + EPS, the adsorption of Cd(II) by this composite increased along with the increase of temperature, and it exhibited as an endothermic process. The adsorptions of EPS toward Pb(II) and Zn(II) were reported as endothermic processes (Wang et al. 2013). Thus, we deduced that the adsorption of EPS on the surface of kaolinite response for the shift from exothermic process (kaolinite) to endothermic process (composite of kaolinite + EPS). The fractions of Cd(II) desorbed by deionised water corresponding to physical adsorption ones (Fang et al. 2011). Ammonium nitrate could release the part of Cd(II) adsorbed by physical adsorption and ion exchange (Brady and Tobin 1995). EDTA could release the part of Cd(II) adsorbed through physical adsorption, ion exchange, and the complexation with carboxylic groups, acetylated amino and phosphate (Volesky and Holan 1995; Li et al. 2010). Compared with the treatment of pure kaolinite, the ratio of desorbed Cd(II) by H2O, NH4NO3, and EDTA all increased in the treatment of kaolinite + EPS, suggesting that EPS addition increased the adsorption of Cd(II) by kaolinite through physical adsorption, ion exchange, and complexation. Cyanobacterial EPS bound on the surface of kaolinite. The composite of kaolinite + EPS showed higher adsorption capacity toward Cd(II) than pure kaolinite, and hydroxyl groups were involved in the adsorption process. The addition of cyanobacterial EPS increased the heterogeneity on the surface of kaolinite, and change the thermodynamics from exothermic process to endothermic one. Angove MJ, Johnson BB, Wells JD (1998) The influence of temperature on the adsorption of cadmium(II) and cobalt(II) on kaolinite. J Colloid Interface Sci 204(1):93–103 Brady JM, Tobin JM (1995) Binding of hard and soft metal ions to Rhizopus arrhizus biomass. Enzyme Microb Technol 17(9):791–796 Cai P, Huang QY, Zhang XW (2006) Microcalorimetric studies of the effects of MgCl2 concentrations and pH on the adsorption of DNA on montmorillonite, kaolinite and goethite. Appl Clay Sci 32(1–2):147–152 Cao Y, Wei X, Cai P, Huang Q, Rong X, Liang W (2011) Preferential adsorption of extracellular polymeric substances from bacteria on clay minerals and iron oxide. 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FEMS Microbiol Rev 33(5):917–941 Pierre G, Zhao JM, Orvain F, Dupuy C, Klein GL, Graber M, Maugard T (2014) Seasonal dynamics of extracellular polymeric substances (EPS) in surface sediments of a diatom-dominated intertidal mudflat (Marennes–Oléron, France). J Sea Res 92:26–35 Sari A, Tuzen M (2014) Cd(II) adsorption from aqueous solution by raw and modified kaolinite. Appl Clay Sci 88–89:63–72 Son YO, Wang L, Poyil P, Budhraja A, Hitron JA, Zhang Z, Lee JC, Shi X (2012) Cadmium induces carcinogenesis in BEAS-2B cells through ROS-dependent activation of PI3 K/AKT/GSK-3β/β-catenin signaling. Toxicol Appl Pharmacol 264(2):153–160 Tang WF, Gu XY, Zhang S, Yuan HF, Jiang Y, Zhao JR (2015) Preparation and characterization of kaolinite-potassium dihydrogen phosphate intercalation composite. Spectrosc Spectr Anal (Chin J) 35:462–465 Volesky B, Holan ZR (1995) Biosorption of heavy metals. Biotechnol Prog 11(3):235–250 Wang L, Yang J, Chen Z, Liu X, Ma F (2013) Biosorption of Pb(II) and Zn(II) by extracellular polymeric substance (Eps) of Rhizobium Radiobacter: equilibrium, kinetics and reuse studies. Arch Environ Prot 39(2):129–140 Wu Y, Li L, Gan N, Zheng L, Ma H, Shan K, Liu J, Xiao B, Song L (2014) Seasonal dynamics of water bloom-forming Microcystis morphospecies and the associated extracellular microcystin concentrations in large, shallow, eutrophic Dianchi Lake. J Environ Sci 26(9):1921–1929 Xu H, Cai H, Yu G, Jiang H (2013) Insights into extracellular polymeric substances of cyanobacterium Microcystis aeruginosa using fractionation procedure and parallel factor analysis. Water Res 47(6):2005–2014 Ye W, Liu X, Tan J, Li D, Yang H (2009) Diversity and dynamics of microcystin—producing cyanobacteria in China's third largest lake, Lake Taihu. Harmful Algae 8(5):637–644 The experiments were conceived and designed by JS and JG. The experiments were performed by XK, SL and LP. The reagents/materials/analysis tools were provided by JS and GW. The manuscript was written by JS. All the authors read and approved the final manuscript. The work was supported by the National Natural Science Foundation of China (No. 31470511); the Foundation of National Water Science and Technology Projects of China (2014ZX07206001-03); Foundation from Education Department of Hunan Province (14B084). College of Resources and Environment, Hunan Agricultural University, Changsha, 410128, People's Republic of China Xiaolin Kuang, Jihai Shao, Anwei Chen, Si Luo, Liang Peng & Genyi Wu Hunan Provincial Key Laboratory of Farmland Pollution Control and Agricultural Resources Use, Hunan Agricultural University, Changsha, 410128, People's Republic of China Ji-Dong Gu Laboratory of Environmental Microbiology and Toxicology, School of Biological Sciences, The University of Hong Kong, Hong Kong SAR, People's Republic of China Xiaolin Kuang Jihai Shao Anwei Chen Si Luo Liang Peng Genyi Wu Correspondence to Jihai Shao. Kuang, X., Shao, J., Chen, A. et al. Effects of bloom-forming cyanobacterial extracellular polymeric substances on the adsorption of cadmium onto kaolinite: behaviors and possible mechanisms. SpringerPlus 5, 542 (2016). https://doi.org/10.1186/s40064-016-2191-8 Received: 14 October 2015 Extracellular polymeric substances	CommonCrawl
When taken as prescribed, Modafinil is safer than Adderall with fewer side effects. Smart pill enthusiasts find a heightened sense of alertness and motivation with Modafinil. In healthy individuals, Modafinil will reliably boost energy levels. If you find that it gives you headaches, add a choline supplement to your stack. With that said, you should only use Modafinil in moderation on an as-needed basis. Smart Pill is a dietary supplement that blends vitamins, amino acids, and herbal extracts to sustain mental alertness, memory and concentration. One of the ingredients used in this formula is Vitamin B-1, also known as Thiamine, which sustains almost all functions present in the body, but plays a key role in brain health and function. A deficiency of this vitamin can lead to several neurological function problems. The most common use of Thiamine is to improve brain function; it acts as a neurotransmitter helping the brain prevent learning and memory disorders; it also provides help with mood disorders and offers stress relief. But when aficionados talk about nootropics, they usually refer to substances that have supposedly few side effects and low toxicity. Most often they mean piracetam, which Giurgea first synthesized in 1964 and which is approved for therapeutic use in dozens of countries for use in adults and the elderly. Not so in the United States, however, where officially it can be sold only for research purposes. It is not because of the few thousand francs which would have to be spent to put a roof [!] over the third-class carriages or to upholster the third-class seats that some company or other has open carriages with wooden benches. What the company is trying to do is to prevent the passengers who can pay the second class fare from traveling third class; it hits the poor, not because it wants to hurt them, but to frighten the rich. And it is again for the same reason that the companies, having proved almost cruel to the third-class passengers and mean to the second-class ones, become lavish in dealing with first-class passengers. Having refused the poor what is necessary, they give the rich what is superfluous. "There seems to be a growing percentage of intellectual workers in Silicon Valley and Wall Street using nootropics. They are akin to intellectual professional athletes where the stakes and competition is high," says Geoffrey Woo, the CEO and co-founder of nutrition company HVMN, which produces a line of nootropic supplements. Denton agrees. "I think nootropics just make things more and more competitive. The ease of access to Chinese, Russian intellectual capital in the United States, for example, is increasing. And there is a willingness to get any possible edge that's available." There are seven primary classes used to categorize smart drugs: Racetams, Stimulants, Adaptogens, Cholinergics, Serotonergics, Dopaminergics, and Metabolic Function Smart Drugs. Despite considerable overlap and no clear border in the brain and body's responses to these substances, each class manifests its effects through a different chemical pathway within the body. First was a combination of L-theanine and aniracetam, a synthetic compound prescribed in Europe to treat degenerative neurological diseases. I tested it by downing the recommended dosages and then tinkering with a story I had finished a few days earlier, back when caffeine was my only performance-enhancing drug. I zoomed through the document with renewed vigor, striking some sentences wholesale and rearranging others to make them tighter and punchier. A similar pill from HQ Inc. (Palmetto, Fla.) called the CorTemp Ingestible Core Body Temperature Sensor transmits real-time body temperature. Firefighters, football players, soldiers and astronauts use it to ensure that they do not overheat in high temperatures. HQ Inc. is working on a consumer version, to be available in 2018, that would wirelessly communicate to a smartphone app. A rough translation for the word "nootropic" comes from the Greek for "to bend or shape the mind." And already, there are dozens of over-the-counter (OTC) products—many of which are sold widely online or in stores—that claim to boost creativity, memory, decision-making or other high-level brain functions. Some of the most popular supplements are a mixture of food-derived vitamins, lipids, phytochemicals and antioxidants that studies have linked to healthy brain function. One popular pick on Amazon, for example, is an encapsulated cocktail of omega-3s, B vitamins and plant-derived compounds that its maker claims can improve memory, concentration and focus. Do you start your day with a cup (or two, or three) of coffee? It tastes delicious, but it's also jump-starting your brain because of its caffeine content. Caffeine is definitely a nootropic substance—it's a mild stimulant that can alleviate fatigue and improve concentration, according to the Mayo Clinic. Current research shows that coffee drinkers don't suffer any ill effects from drinking up to about four cups of coffee per day. Caffeine is also found in tea, soda, and energy drinks. Not too surprisingly, it's also in many of the nootropic supplements that are being marketed to people looking for a mental boost. Take a look at these 7 genius brain boosters to try in the morning. It is a known fact that cognitive decline is often linked to aging. It may not be as visible as skin aging, but the brain does in fact age. Often, cognitive decline is not noticeable because it could be as mild as forgetting names of people. However, research has shown that even in healthy adults, cognitive decline can start as early as in the late twenties or early thirties. Armodafinil is sort of a purified modafinil which Cephalon sells under the brand-name Nuvigil (and Sun under Waklert20). Armodafinil acts much the same way (see the ADS Drug Profile) but the modafinil variant filtered out are the faster-acting molecules21. Hence, it is supposed to last longer. as studies like Pharmacodynamic effects on alertness of single doses of armodafinil in healthy subjects during a nocturnal period of acute sleep loss seem to bear out; anecdotally, it's also more powerful, with Cephalon offering pills with doses as low as 50mg. (To be technical, modafinil is racemic: it comes in two forms which are rotations, mirror-images of each other. The rotation usually doesn't matter, but sometimes it matters tremendously - for example, one form of thalidomide stops morning sickness, and the other rotation causes hideous birth defects.) As professionals and aging baby boomers alike become more interested in enhancing their own brain power (either to achieve more in a workday or to stave off cognitive decline), a huge market has sprung up for nonprescription nootropic supplements. These products don't convince Sahakian: "As a clinician scientist, I am interested in evidence-based cognitive enhancement," she says. "Many companies produce supplements, but few, if any, have double-blind, placebo-controlled studies to show that these supplements are cognitive enhancers." Plus, supplements aren't regulated by the U.S. Food and Drug Administration (FDA), so consumers don't have that assurance as to exactly what they are getting. Check out these 15 memory exercises proven to keep your brain sharp. Another common working memory task is the n-back task, which requires the subject to view a series of items (usually letters) and decide whether the current item is identical to the one presented n items back. This task taxes working memory because the previous items must be held in working memory to be compared with the current item. The easiest version of this is a 1-back task, which is also called a double continuous performance task (CPT) because the subject is continuously monitoring for a repeat or double. Three studies examined the effects of MPH on working memory ability as measured by the 1-back task, and all found enhancement of performance in the form of reduced errors of omission (Cooper et al., 2005; Klorman et al., 1984; Strauss et al., 1984). Fleming et al. (1995) tested the effects of d-AMP on a 5-min CPT and found a decrease in reaction time, but did not specify which version of the CPT was used. By which I mean that simple potassium is probably the most positively mind altering supplement I've ever tried…About 15 minutes after consumption, it manifests as a kind of pressure in the head or temples or eyes, a clearing up of brain fog, increased focus, and the kind of energy that is not jittery but the kind that makes you feel like exercising would be the reasonable and prudent thing to do. I have done no tests, but feel smarter from this in a way that seems much stronger than piracetam or any of the conventional weak nootropics. It is not just me – I have been introducing this around my inner social circle and I'm at 7/10 people felt immediately noticeable effects. The 3 that didn't notice much were vegetarians and less likely to have been deficient. Now that I'm not deficient, it is of course not noticeable as mind altering, but still serves to be energizing, particularly for sustained mental energy as the night goes on…Potassium chloride initially, but since bought some potassium gluconate pills… research indicates you don't want to consume large amounts of chloride (just moderate amounts). Because these drugs modulate important neurotransmitter systems such as dopamine and noradrenaline, users take significant risks with unregulated use. There has not yet been any definitive research into modafinil's addictive potential, how its effects might change with prolonged sleep deprivation, or what side effects are likely at doses outside the prescribed range. Enhanced learning was also observed in two studies that involved multiple repeated encoding opportunities. Camp-Bruno and Herting (1994) found MPH enhanced summed recall in the Buschke Selective Reminding Test (Buschke, 1973; Buschke & Fuld, 1974) when 1-hr and 2-hr delays were combined, although individually only the 2-hr delay approached significance. Likewise, de Wit, Enggasser, and Richards (2002) found no effect of d-AMP on the Hopkins Verbal Learning Test (Brandt, 1991) after a 25-min delay. Willett (1962) tested rote learning of nonsense syllables with repeated presentations, and his results indicate that d-AMP decreased the number of trials needed to reach criterion. Cost-wise, the gum itself (~$5) is an irrelevant sunk cost and the DNB something I ought to be doing anyway. If the results are negative (which I'll define as d<0.2), I may well drop nicotine entirely since I have no reason to expect other forms (patches) or higher doses (2mg+) to create new benefits. This would save me an annual expense of ~$40 with a net present value of <820 ($); even if we count the time-value of the 20 minutes for the 5 DNB rounds over 48 days (0.2 \times 48 \times 7.25 = 70), it's still a clear profit to run a convincing experiment. the larger size of the community enables economies of scale and increases the peak sophistication possible. In a small nootropics community, there is likely to be no one knowledgeable about statistics/experimentation/biochemistry/neuroscience/whatever-you-need-for-a-particular-discussion, and the available funds increase: consider /r/Nootropics's testing program, which is doable only because it's a large lucrative community to sell to so the sellers are willing to donate funds for independent lab tests/Certificates of Analysis (COAs) to be done. If there were 1000 readers rather than 23,295, how could this ever happen short of one of those 1000 readers being very altruistic? Both nootropics startups provide me with samples to try. In the case of Nootrobox, it is capsules called Sprint designed for a short boost of cognitive enhancement. They contain caffeine – the equivalent of about a cup of coffee, and L-theanine – about 10 times what is in a cup of green tea, in a ratio that is supposed to have a synergistic effect (all the ingredients Nootrobox uses are either regulated as supplements or have a "generally regarded as safe" designation by US authorities) As I am not any of the latter, I didn't really expect a mental benefit. As it happens, I observed nothing. What surprised me was something I had forgotten about: its physical benefits. My performance in Taekwondo classes suddenly improved - specifically, my endurance increased substantially. Before, classes had left me nearly prostrate at the end, but after, I was weary yet fairly alert and happy. (I have done Taekwondo since I was 7, and I have a pretty good sense of what is and is not normal performance for my body. This was not anything as simple as failing to notice increasing fitness or something.) This was driven home to me one day when in a flurry before class, I prepared my customary tea with piracetam, choline & creatine; by the middle of the class, I was feeling faint & tired, had to take a break, and suddenly, thunderstruck, realized that I had absentmindedly forgot to actually drink it! This made me a believer. With so many different ones to choose from, choosing the best nootropics for you can be overwhelming at times. As usual, a decision this important will require research. Study up on the top nootropics which catch your eye the most. The nootropics you take will depend on what you want the enhancement for. The ingredients within each nootropic determine its specific function. For example, some nootropics contain ginkgo biloba, which can help memory, thinking speed, and increase attention span. Check the nootropic ingredients as you determine what end results you want to see. Some nootropics supplements can increase brain chemicals such as dopamine and serotonin. An increase in dopamine levels can be very useful for memory, alertness, reward and more. Many healthy adults, as well as college students take nootropics. This really supports the central nervous system and the brain. Exercise and nutrition also play an important role in neuroplasticity. Many vitamins and ingredients found naturally in food products have been shown to have cognitive enhancing effects. Some of these include vitamins B6 and B12, caffeine, phenethylamine found in chocolate and l-theanine, found in green tea, whose combined effects with caffeine are more extensively researched. At this point, I began thinking about what I was doing. Black-market Adderall is fairly expensive; $4-10 a pill vs prescription prices which run more like $60 for 120 20mg pills. It would be a bad idea to become a fan without being quite sure that it is delivering bang for the buck. Now, why the piracetam mix as the placebo as opposed to my other available powder, creatine powder, which has much smaller mental effects? Because the question for me is not whether the Adderall works (I am quite sure that the amphetamines have effects!) but whether it works better for me than my cheap legal standbys (piracetam & caffeine)? (Does Adderall have marginal advantage for me?) Hence, I want to know whether Adderall is better than my piracetam mix. People frequently underestimate the power of placebo effects, so it's worth testing. (Unfortunately, it seems that there is experimental evidence that people on Adderall know they are on Adderall and also believe they have improved performance, when they do not5. So the blind testing does not buy me as much as it could.) Nootropics are a great way to boost your productivity. Nootropics have been around for more than 40 years and today they are entering the mainstream. If you want to become the best you, nootropics are a way to level up your life. Nootropics are always personal and what works for others might not work for you. But no matter the individual outcomes, nootropics are here to make an impact! It is at the top of the supplement snake oil list thanks to tons of correlations; for a review, see Luchtman & Song 2013 but some specifics include Teenage Boys Who Eat Fish At Least Once A Week Achieve Higher Intelligence Scores, anti-inflammatory properties (see Fish Oil: What the Prescriber Needs to Know on arthritis), and others - Fish oil can head off first psychotic episodes (study; Seth Roberts commentary), Fish Oil May Fight Breast Cancer, Fatty Fish May Cut Prostate Cancer Risk & Walnuts slow prostate cancer, Benefits of omega-3 fatty acids tally up, Serum Phospholipid Docosahexaenonic Acid Is Associated with Cognitive Functioning during Middle Adulthood endless anecdotes. However, when I didn't stack it with Choline, I would get what users call "racetam headaches." Choline, as Patel explains, is not a true nootropic, but it's still a pro-cognitive compound that many take with other nootropics in a stack. It's an essential nutrient that humans need for functions like memory and muscle control, but we can't produce it, and many Americans don't get enough of it. The headaches I got weren't terribly painful, but they were uncomfortable enough that I stopped taking Piracetam on its own. Even without the headache, though, I didn't really like the level of focus Piracetam gave me. I didn't feel present when I used it, even when I tried to mix in caffeine and L-theanine. And while it seemed like I could focus and do my work faster, I was making more small mistakes in my writing, like skipping words. Essentially, it felt like my brain was moving faster than I could. It was a productive hour, sure. But it also bore a remarkable resemblance to the normal editing process. I had imagined that the magical elixir coursing through my bloodstream would create towering storm clouds in my brain which, upon bursting, would rain cinematic adjectives onto the page as fast my fingers could type them. Unfortunately, the only thing that rained down were Google searches that began with the words "synonym for"—my usual creative process. the rise of IP scofflaw countries which enable the manufacture of known drugs: India does not respect the modafinil patents, enabling the cheap generics we all use, and Chinese piracetam manufacturers don't give a damn about the FDA's chilling-effect moves in the US. If there were no Indian or Chinese manufacturers, where would we get our modafinil? Buy them from pharmacies at $10 a pill or worse? It might be worthwhile, but think of the chilling effect on new users. An entirely different set of questions concerns cognitive enhancement in younger students, including elementary school and even preschool children. Some children can function adequately in school without stimulants but perform better with them; medicating such children could be considered a form of cognitive enhancement. How often does this occur? What are the roles and motives of parents, teachers, and pediatricians in these cases? These questions have been discussed elsewhere and deserve continued attention (Diller, 1996; Singh & Keller, 2010). Some supplement blends, meanwhile, claim to work by combining ingredients – bacopa, cat's claw, huperzia serrata and oat straw in the case of Alpha Brain, for example – that have some support for boosting cognition and other areas of nervous system health. One 2014 study in Frontiers in Aging Neuroscience, suggested that huperzia serrata, which is used in China to fight Alzheimer's disease, may help slow cell death and protect against (or slow the progression of) neurodegenerative diseases. The Alpha Brain product itself has also been studied in a company-funded small randomized controlled trial, which found Alpha Brain significantly improved verbal memory when compared to adults who took a placebo. If you could take a pill that would help you study and get better grades, would you? Off-label use of "smart drugs" – pharmaceuticals meant to treat disorders like ADHD, narcolepsy, and Alzheimer's – are becoming increasingly popular among college students hoping to get ahead, by helping them to stay focused and alert for longer periods of time. But is this cheating? Should their use as cognitive enhancers be approved by the FDA, the medical community, and society at large? Do the benefits outweigh the risks? While the primary effect of the drug is massive muscle growth the psychological side effects actually improved his sanity by an absurd degree. He went from barely functional to highly productive. When one observes that the decision to not attempt to fulfill one's CEV at a given moment is a bad decision it follows that all else being equal improved motivation is improved sanity. Though their product includes several vitamins including Bacopa, it seems to be missing the remaining four of the essential ingredients: DHA Omega 3, Huperzine A, Phosphatidylserine and N-Acetyl L-Tyrosine. It missed too many of our key criteria and so we could not endorse this product of theirs. Simply, if you don't mind an insufficient amount of essential ingredients for improved brain and memory function and an inclusion of unwanted ingredients – then this could be a good fit for you. We'd want 53 pairs, but Fitzgerald 2012's experimental design called for 32 weeks of supplementation for a single pair of before-after tests - so that'd be 1664 weeks or ~54 months or ~4.5 years! We can try to adjust it downwards with shorter blocks allowing more frequent testing; but problematically, iodine is stored in the thyroid and can apparently linger elsewhere - many of the cited studies used intramuscular injections of iodized oil (as opposed to iodized salt or kelp supplements) because this ensured an adequate supply for months or years with no further compliance by the subjects. If the effects are that long-lasting, it may be worthless to try shorter blocks than ~32 weeks. (In particular, I don't think it's because there's a sudden new surge of drugs. FDA drug approval has been decreasing over the past few decades, so this is unlikely a priori. More specifically, many of the major or hot drugs go back a long time. Bacopa goes back millennia, melatonin I don't even know, piracetam was the '60s, modafinil was '70s or '80s, ALCAR was '80s AFAIK, Noopept & coluracetam were '90s, and so on.) Because smart drugs like modafinil, nicotine, and Adderall come with drawbacks, I developed my own line of nootropics, including Forbose and SmartMode, that's safe, widely available, and doesn't require a prescription. Forskolin, found in Forbose, has been a part of Indian Ayurvedic medicine for thousands of years. In addition to being fun to say, forskolin increases cyclic adenosine monophosphate (cAMP), a molecule essential to learning and memory formation. [8]	CommonCrawl
Claremont Topology Seminar Fall, 2012 special days, times or locations are in red Date Speaker Title and Abstract Organizational Meeting Dave Bachman Pitzer College Title: Double covers of strongly irreducible surfaces Abstract: We show that double covers of strongly irreducible surfaces are topologically minimal. This is a first step in the confirmation of two larger conjectures, which together give a purely topological proof of the virtually Haken theorem. This is joint work with Yoav Moriah. Helen Wong Carlton College Title: A Quantum Trace Map For a surface S, we describe two seemingly unrelated combinatorial objects, the Kauffman skein algebra K(S) and the quantum Teichmuller space T(S). One, the Kauffman skein algebra K(S), was inspired by the Jones polynomial of knots and links, whereas the other, the quantum Teichmuller space T(S), is a non-commutative version of a well-studied object from hyperbolic geometry. In this talk, we'll describe an injective ``quantum trace'' map from K(S) and T(S) and also mention why such a map might be useful. This work is joint with Francis Bonahon. Sam Nelson Claremont McKenna College Title: Quantum Enhancements of Birack Counting Invariants Abstract: A quantum enhancement of the birack counting invariant is a quantum invariant of birack-labeled knots and links. We will examine various schemes for finding such enhancements and using the results to enhance the birack counting invariant. Grace Kennedy UCSB Title: A Diagrammatic Multivariate Alexander Invariant of Tangles Abstract: I will present my multivariate Alexander polynomial, which also generalizes to a tangle invariant. I'll discuss the algorithm and proof that our algorithm is in fact the multivariate Alexander polynomial defined by Conway in 1970. This multivariate calculation generalizes Professor Stephen Bigelow's diagrammatic method for calculating the single variable Alexander polynomial of a knot or link. Emille Davie Lawrence University of San Francisco Title: The sigma-ordering of the braid groups Abstract: The braid groups have been an interesting field of study in low-dimensional topology and algebra since Emil Artin introduced the notion of a braid in the 1920s. Over the years, it has been discovered that the braid groups play a useful role in knot theory, robotics, theoretical physics, and a variety of other areas. In 1992 Patrick Dehornoy proved that the braid groups were left-orderable, providing a long overdue merger between braid groups and orderable. We will give an introduction to the braid groups and discuss a new distinguished form for 3-braids. We will also define Dehornoy's sigma-ordering of the braid groups, and show how our distinguished form allows us in most cases to determine positivity in this ordering. Fall Break David Rose USC Title: Quantum link invariants and (higher) representation theory via skew Howe duality Abstract: Quantum link invariants (e.g. the Jones polynomial) arise due to structures on the category of finite-dimensional representations of quantum groups. These categories often have diagrammatic descriptions which give the skein-theoretic definitions of the link invariants. We will discuss the relation between the diagrammatic framework and skew Howe duality, a representation-theoretic construction which is intimately connected to link invariants. Time permitting, we'll also discuss recent work of the speaker (joint with A. Lauda and H. Queffelec) where we sort out the categorified version of this picture, showing that Khovanov homology is a 2-representation of the categorified quantum group. Zhongtao Wu California Institute of Technology Title: An introduction to the rational genus of a knot Abstract: What is the "simplest" knot in a given three-manifold $Y$? We know that the answer is the unknot when $Y=S^3$, as the unknot happens to be the only knot in the three-sphere with the smallest genus (=0). In this talk, we will discuss the more general notion of the rational genus of knots. In particular, we will show that the simple knots are really the "simplest" knots in the lens spaces in the sense of being a genus minimizer in its homology class. This is a joint work with Yi Ni. Hans Boden McMaster University Title: Metabelian SL(n,C) representations of knot groups Abstract: This talk will focus on applications of group representation theory in low-dimensional topology. We will focus attention on metabelian representations into SL(n,C), and we report on joint work with S. Friedl on the classification problem of such representations (up to conjugacy) and on the problem of constructing deformations within the larger space of all SL(n,C) representations. We use this approach to establish the existence of large families of irreducible SL(n,C) representations under certain mild conditions on the knot which are easily expressed in terms of its (twisted) Alexander polynomial. Carlton College The Kauffman Skein Algebra and hyperbolic geometry The Kauffman skein algebra of a surface $S$ was originally defined as a generalization of the Jones polynomial, but it was later found to have connections with hyperbolic geometry. Here, we'll describe how it is related both to the character variety, consisting of homomorphisms from $\pi_1 S$ to $\mathrm{SL}_2 \mathbb C$, and to a quantizations thereof. If time permits, we will also discuss ways this might be exploited, for instance to interpret quantum invariants of 3-manifolds in terms of hyperbolic geometry. This work is joint with Francis Bonahon. UC Riverside Title: Advanced Positions of Knots in the Three Sphere Abstract: In this talk, we introduce the notion of advanced position of a knot on a Heegaard surface and present several examples. This is joint work with Jesse Johnson and Alice Stevens. Rena Levitt Pomona College Title: Graphs and Geometry: A Combinatorial Version of Area and Perimeter Abstract: First introduced by Leonhard Euler to solve the famous Bridges of Konigsberg Problem in 1736, graphs have emerged as an important concept in modern mathematics. We use graphs to model everything from links among websites, to bonds between atoms in molecules, or the evolutionary relationships among related species. In this talk I will introduce the notion of a graph, and present some applications of graph theory. I will then introduce combinatorial versions of length and area that allow us to add geometric structure to an abstract graph. Later in the talk, I will focus on the class of bridged graphs, and show that the area of a disk in a bridged graph is bounded quadratically by the length of its perimeter. This is joint work with my students from the Fletcher Jones Fellowship Summer Research Program: Nicholas Bosviel, Gillian Grindstaff, Lingge Li, Patrick Meehan, and Matthew Owen. Danny Ruberman Brandeis University Title: Embeddings of non-orientable surfaces in 4-manifolds Abstract: Two-dimensional surfaces are classified by two characteristics: their orientability, and their genus (a non-negative integer). Low dimensional topology has long centered around the problem of finding the least complicated (meaning lowest genus) oriented surface carrying a given 2-dimensional integral homology class in a 4-manifold. The Thom conjecture about homology classes in complex projective space, solved by Kronheimer-Mrowka using Seiberg-Witten gauge theory, was the most famous such problem. I will discuss joint work with Adam Levine and Saso Strle about embeddings of non-orientable surfaces in 4-manifolds of the form (3-manifold x I). Chad Musick Nagoya University Title: A method of encoding generalized link diagrams Abstract: We describe a method of encoding various types of link diagrams, including those with classical, flat, rigid, welded, and virtual crossings. We show that this method may be used to encode link diagrams, up to equivalence, in a notation whose length is a cubic function of the number of 'riser marks'. For classical knots, the minimal number of such marks is twice the bridge index, and a classical knot diagram in minimal bridge form with bridge index b may be encoded in order b^2 integers. A set of moves on the notation is defined. Some uses of the notation are discussed. Ryo Nikkuni Tokyo Women's Christian University Title: A homotopy classification of two-component spatial graphs up to neighborhood equivalence Abstract: A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to neighborhood homotopy by the elementary divisor of a linking matrix with respect to the first homology group of each of the connected components. This also leads a kind of homotopy classification of 2-component handlebody-links. This is a joint work with Atsuhiko Mizusawa. Pitzer College Title: Normalizing Topologically Minimal surfaces Abstract: Topologically minimal surfaces generalize several well-studied classes of surfaces in 3-manifolds, and provide a topological analogue to geometrically minimal surfaces. We will discuss recent progress in obtaining a normal form for any such surface with respect to a fixed triangulation. This provides striking analogues with results of Colding and Minicozzi, and establishes finiteness results which are crucial to understanding how Heegaard splittings are effected by Dehn surgery. Cal Tech TITLE: Representation volume of 3-manifolds ABSTRACT: In this talk we discuss volume of 3-manifold arise from representations into PSL(2,C) and \widetilde{SL}_2(R). Recent techniques of Przytycki and Wise allows us to construct certain interesting representations after passing to a finite index subgroup of the fundamental group. In particular, one can show the virtual representation volume to be positive if a corresponding geometric piece presents. This is joint work with Pierre Derbez and Shicheng Wang. Scott Carter University of South Alabama Title: Braiding branched covers of spheres over knots Classical theorems (Alexander, Hilden, Montesinos) indicate that any 3-manifold can be realized as a 3-fold branched covering of the 3-sphere with branched set a knot or link. By generalizing Kamada's braid charts to one higher dimension, we show how to embed and immerse these coverings in $S^3 \times D^2$ such that the projection onto the first factor is the covering. Similarly, every 4-manifold is a 5-fold branched cover of $S^4$ with branched set an embedded or linked surface. In some cases, we can also construct analogous embeddings and immersions in $S^4 \times D^2$. The methods for doing so are very detailed. Lots of examples will be given. Emily Hamilton Cal Poly SLO Title: Separability of Double Cosets and Conjugacy Classes in 3-Manifold Groups Abstract: A subset $X$ of a group $\Gamma$ is {\it separable} in $\Gamma$ if for every element $\gamma \in \Gamma - X$ there is a homomorphism $\phi$ from $\Gamma$ to a finite group such that $\phi(\gamma) \notin \phi(X)$. A group $\Gamma$ is {\it residually finite} if the trivial subgroup is separable, {\it subgroup separable} if every finitely generated subgroup of $\Gamma$ is separable, and {\it conjugacy separable} if every conjugacy class in $\Gamma$ is separable. Separability has applications in group theory and geometric topology. If a finitely presented group $\Gamma$ is residually finite, then there exists an algorithm to decide if a given word in the presentation of $\Gamma$ is trivial. If $G$ is subgroup separable, then one can solve more generalized word problems. In the context of geometric topology, subgroup separability has been used to solve immersion to embedding problems. For example, in $3$-manifold topology it is well known that subgroup separability allows passage from immersed incompressible surfaces to embedded incompressible surfaces in finite covers. In this talk we consider separability of double cosets and conjugacy classes in $3$-manifold groups. Let $M = {\Bbb H}^3 / \Gamma$ be a hyperbolic $3$-manifold of finite volume. We show that if $H$ and $K$ are abelian subgroups of $\Gamma$ and $g \in \Gamma$, then the double coset $HgK$ is separable in $\Gamma$. As a consequence, we prove that if M is a closed, orientable Haken $3$-manifold and the fundamental group of every hyperbolic piece of the torus decomposition of $M$ is conjugacy separable then so is the fundamental group of $M$. Invoking recent work of Agol and Wise, it follows that if $M$ is a compact, orientable $3$-manifold, then $\pi_1(M)$ is conjugacy separable. Katie Walsh UC San Diego Title: Patterns in the Coefficients of the Colored Jones Polynomial The colored Jones polynomial assigns to each knot a sequence of Laurent polynomials. We will discuss the various ways of calculating the colored Jones polynomial and formulas that allow us to calculate many of the polynomials in the sequence for certain knots. These formulas allow us to look at patterns in the coefficients. A few conjectures relating these coefficients to the hyperbolic volume conjecture will be discussed. Danny Stoll Oakland Technical High School Cliff Stoll Acme Klein Bottle Title: Low Dimensional Topology for Fun and Profit 17 ways to Extract Lucre from R4 Space The Bad Pants Homology Abstract: For over a decade, Acme Klein Bottle has supplied nonorientable manifolds to math folk. Like much of mathematics, it's marginally profitable, but endlessly entertaining. There are thousands of computer models of the Klein Bottle and its bounded friend, the Moebius loop. But physical models are rarely made. So how do you turn a set of parameterized equations for a manifold into a glass Klein Bottle? When you immerse a manifold into R3, what's lost? How about glass models of the projective plane, Boy's surface, the torus, and other manifolds? Recently, Kahn and Markovic have used the good pants homology to prove the Ehrenpreis conjecture. Inspired by this, we have developed the bad pants homology to create a certain nonorientable Riemannian manifold. As a door prize, we will give away a Hausdorffian, unbounded, affine, closed, rustproof, self-intersecting, compact, microwave-safe borosilicate manifold that's locally Euclidean and homeomorphic to a sphere with two crosscaps. Matt Owen Pitzer College Title: Construction between partially-ordered sets and CAT(0) cube complexes Abstract: Hyperplanes in a cube complex X allow us a nice way of inducing the order of inclusion on the vertices of X. We first provide an introduction to cube complexes and partially-ordered sets (posets). We then examine a construction under which one can build CAT(0) cube complexes from posets, and posets from CAT(0) cube complexes. We conclude by considering consequences of this construction, such as its domain and range, how the dimension of the cube complex is affected, what the degree of the fixed vertex implies. No Seminar	CommonCrawl
How does a classical computer simulate nonclassical correlations? This may be a dumb question, if so please forgive me, it is late at night. I have learned that a classical computer can simulate a quantum computer in exponential time and space, but classical computers are bound to non-quantum phenomenon. How then, would one be able to simulate say CHSH, which produces fundamentally quantum probabilities that cannot be explained locally/classically? Am I misinterpreting the meaning of simulate? In general, how could a classical computer simulate quantum phenomena that cannot be explained classically (such as the dynamics of more than a single particle)? I would think that one could not generate random numbers violating any of Bell's inequalities, i.e. necessarily quantum correlations are off limits. entanglement simulation classical-computing games non-locality PhysMathPhysMath $\begingroup$ related: quantumcomputing.stackexchange.com/q/1/55 $\endgroup$ Quantum phenomena cannot be "explained classically" only when locality is taken into consideration. In other words, classical phenomena cannot reproduce (some types of) quantum correlations provided that we don't allow for certain types of correlations. As a concrete example, consider a standard CHSH scenario. We can compute the outcome probability distributions for each measurement setting (it's what you do when you study the protocol), therefore you can trivially write some code to "simulate" the results of an experiment, meaning to draw a possible sequence of measurement outcomes you would find in an experiment. But this is clearly not the same as observing nonlocality with a classical computer: you would just be crunching some numbers that you know, in some situations, can be interpreted as markers of nonclassical correlations. Put in another way, you can always sample from an arbitrary probability distribution $p(ab\|xy)$. Whether such a distribution is "nonclassical" is only meaningful in relation to some imposed restriction (e.g. defining "classical" when it can be written as $p(ab\|xy)=\sum_\lambda p_\lambda p_\lambda(a\|x) p_\lambda(b\|y)$). When you simulate such a distribution on a computer, you don't need to respect such restrictions, so there is no problem. In general, how could a classical computer simulate quantum phenomena that cannot be explained classically Aside from locality constraints, such as those described above, quantum mechanics does not predict output probability distributions that are incompatible with classical physics. The difference is in how those outputs can be obtained: quantum mechanic can produce output probability distributions in a radically different way than what classical physics allows for, and in some cases these new behaviours are more efficient. glS♦glS There are two definitions of simulation that are commonly used in this context. We consider a quantum computation to be: 1. loading an input 2. performing some processing 3. doing a measurement This defines a distribution on possible measurement outcomes for each input. Weak Simulation would be a classical randomised algorithm that could sample from these distributions, given a suitable description of the quantum computation as defined above. Strong Simulation is the ability to approximately calculate individual probabilities. A naive simulation algorithm that uses exponential time and space is to store the state as a big vector (of length $2^n$) and then multiply it by the matrices for each of the gates (size $2^n \times 2^n$). Then measurement probabilities can also be calculated by finding the eigenspaces for the measurement operator, and projecting the final state vector onto the one of interest. This doesn't violate any laws of quantum physics, because it is simulating the whole system, not simulating each qubit locally Simon CraneSimon Crane Not the answer you're looking for? Browse other questions tagged entanglement simulation classical-computing games non-locality or ask your own question. Can a Turing machine simulate a quantum computer? Can a quantum computer simulate a normal computer? How to simulate quantum entanglement variation in different quantum gates? Are correlations stronger than those allowed by quantum mechanics possible? Does a classical computer really require $2^n$ complex numbers to represent the state of $n$ qubit quantum computer? How is a quantum simulator able to simulate a quantum mechanical properties on a classical computer? Role of convexity in proof of Monogamy of Bell correlations Classical versus quantum correlations and partial traces	CommonCrawl
Problem I IXth Problem Emily recently learned about the Roman Empire and its civilization at school. One aspect that was especially fascinating to her is the number system that they used, the Roman numerals. The Roman number system uses seven distinct digits, each representing a different value and denoted by a letter, where I is $1$, V is $5$, X is $10$, L is $50$, C is $100$, D is $500$ and M is $1\, 000$. Multiples of $1$, $10$, $100$ and $1\, 000$ are then written according to the following table: $\times $ $1$ LXX LXXX $100$ $1\, 000$ Most of the numerals in this table are formed additively, i.e. by summing the values of the digits. For example, LXX is $50+10+10=70$. Columns $4$ and $9$, however, use so-called subtractive notation, where IV is read as $5-1$, IX is read as $10-1$, and so on. Each number from $1$ to $3\, 999$ is written as a combination of numerals from the table, using at most one numeral from each row and going from bottom to top. For instance, $2\, 021$ is MMXXI and $594$ is DXCIV. Note that in this number system it is not possible to write numbers greater than $3\, 999$ and also that subtractive notation can only be used in the six cases above (e.g. IC is not considered a valid Roman numeral). Emily found a bunch of old Scrabble sets in her attic. She threw out all the tiles with letters other than the Roman digits and started forming Roman numerals from the remaining tiles. It is easy to form valid numerals from the tiles by using just one tile per numeral, but what is the minimal number of numerals that can be formed while still using all the available tiles? One line with seven integers $m$, $d$, $c$, $\ell $, $x$, $v$ and $i$ ($0 \le m,d,c,\ell ,x,v,i \le 10^{18}$), which respectively are the number of M, D, C, L, X, V and I tiles that must be used. There is at least one tile, that is $m+d+c+\ell +x+v+i \ge 1$. Output an integer $n$, the minimal possible number of Roman numerals that can be formed while using all of the tiles in the input. Then output an optimal solution in the following format. An integer $k$, the number of distinct Roman numerals used in this solution. $k$ pairs of a Roman numeral and a positive integer indicating how often this numeral is used in this solution. The solution must consist of exactly $n$ numerals in total and must use exactly the specified number of each letter. The $k$ Roman numerals in the solution must be distinct. You do not need to minimize $k$. If there is more than one optimal solution, any one of them will be accepted. MMDCCCLXX 1 MMCCCXCVIII 1 0 0 0 300 2000 1000 2100 XXVIII 700 LXXV 300 Problem ID: ixthproblem CPU Time limit: 1 second Authors: Paul Wild and Antti Laaksonen	CommonCrawl
Erdös-Ginzburg-Ziv theorem From Encyclopedia of Mathematics EGZ theorem If $m$ is a positive integer and $a_1,\ldots,a_{2m-1}$ is a sequence of elements from the cyclic group $\mathbb{Z}_m$, then there exists a set $I\subseteq \{1,\ldots,2m-1\}$ of cardinality $m$ such that $\sum_{i\in I}a_i=0$. This theorem was first shown in [a5]. 1 Related theorems. 2 Outline of developments. 3 Proofs. 4 Generalizations and analogues. 4.1 Conjecture 1. 5 Zero-sum Ramsey theory. Related theorems. Looking at a sequence of $ m - 1 $ zeros and $ m - 1 $ ones one sees that $ 2m - 1 $ cannot be replaced by a smaller number. This motivates the definition of the Erdös–Ginzburg–Ziv constant for an arbitrary Abelian group, as follows. If $ G $ is an Abelian group, then $ { \mathop{\rm EGZ}\nolimits} ( G ) $ is the minimum integer $ e $ such that every sequence $ a _{1} \dots a _{e} $ of elements from $ G $ contains a subsequence of cardinality $ o ( G ) $, the order of $ G $, that adds up to $ 0 $. It can be proven that $ { \mathop{\rm EGZ}\nolimits} ( G ) \leq {2o ( G ) - 1} $ and equality holds if and only if $ G = \mathbf Z _{m} $. This result and the observation above led to the following two directions of investigation: i) To find bounds, or possibly determine, $ { \mathop{\rm EGZ}\nolimits} ( G ) $ for groups other than $ \mathbf Z _{m} $ in terms of $ o ( G ) $ and other group invariants. Recent results in this direction were obtained by Y. Caro and Weidong Gao. ii) To find or estimate the minimum integer $ e = e ( G,k ) $ such that every sequence $ a _{1} \dots a _{e} $ of elements from $ G $ contains a subsequence of cardinality $ o ( G ) $ that adds up to $ 0 $, provided one knows that there are at least $ k $ distinct elements in the sequence. Recent results in this direction are due to A. Bialostocki, P. Dierker, Y.O. Hamidoune, and M. Lotspeich. A breakthrough in this direction was achieved after the recent proof of the long standing Erdös–Heilbronn conjecture (cf. also Erdös–Heilbronn problem). Along a different line, J.E. Olson extended the definition of the $ { \mathop{\rm EGZ}\nolimits} ( G ) $ constant to non-Abelian groups and proved that $ { \mathop{\rm EGZ}\nolimits} ( G ) \leq {2o ( G ) - 1} $ still holds. Outline of developments. There are several reasons why this theorem has recently (1996) drawn much attention. Quite unexpectedly, N. Alon and M. Dubiner [a1] have shown that the theorem follows from several deeper results in algebra and number theory, establishing interesting links. The theorem has many possible generalizations, some of which have been proved and others are easy to state as fundamental open problems, see [a4] and the conjectures below. The theorem motivated the development of what is called a zero-sum Ramsey theory: If the sequence in the theorem consists only of the elements $ 0 $ and $ 1 $, then its proof follows from the pigeon hole principle (cf. Dirichlet principle), hence the theorem can be viewed as a generalization of this principle. Consequently, since Ramsey theory (cf. also Ramsey theorem) is a development of the pigeon hole principle, there is a clear motivation to develop from the EGZ theorem a zero-sum Ramsey theory along the lines of traditional Ramsey theory. While in Ramsey theory one looks for monochromatic configurations, in zero-sum Ramsey theory the colours are elements of a group and one looks for zero-sum configurations. Zero-sum Ramsey theory generalizes many results of the traditional Ramsey theory and leaves many open problems. Proofs. In [a1] five proofs for the EGZ theorem have been given. In all these proofs it is assumed that $ m $ is a prime number, since the transition to a non-prime is a simple induction. The original proof is based on the Cauchy–Davenport theorem from elementary additive number theory; two other proofs use the Fermat little theorem, along with a counting argument and a lemma concerning permanents, respectively. A fourth proof uses the Chevalley–Warning theorem about zeros of polynomials over a finite field. Most interesting is the proof that uses knowledge of the Davenport constant of an Abelian $ p $- group, determined by Olson. Let $ G $ be a finite Abelian group. The Davenport constant of $ G $, denoted by $ D ( G ) $, is the minimal $ d $ such that every sequence of $ d $ elements from $ G $ contains a subsequence that adds up to $ 0 $. Generalizations and analogues. Clearly, if $ G $ is cyclic of order $ m $, then $ D ( G ) = m $. An interesting relation between $ D ( G ) $ and the EGZ theorem is Weidong's generalization of the EGZ theorem: Let $ a _{1} \dots a _{s} $ be a sequence of elements from an Abelian group $ G $. If $ s = o ( G ) + D ( G ) - 1 $, then there exists a set $ I \subseteq \{ 1 \dots s \} $ of cardinality $ o ( G ) $ such that $ \sum _ {i \in I} a _{i} = 0 $. The following two conjectures are other possible generalizations of the EGZ theorem. Conjecture 1. Let $ m $ and $ s $ be positive integers. If $ a _{1} \dots a _{s} $ is a sequence of elements from the cyclic group $ \mathbf Z _{m} $, then it contains at least $ \binom{ {\lceil {s/2} \rceil}}{m} + \binom{ {\lfloor {s/2} \rfloor}}{m} $ subsequences of $ m $ elements that add up to $ 0 $. If one takes $ s = 2m - 1 $ in this conjecture, then the EGZ theorem follows. Let $ m $ be a positive integer and let $ b _{1} \dots b _{m} $ be a sequence of elements from the cyclic group $ \mathbf Z _{m} $ whose sum is $ 0 $. If $ a _{1} \dots a _ {2m - 1} $ is a sequence of elements from $ \mathbf Z _{m} $, then it contains a subsequence $ a _ {k ( 1 )} \dots a _ {k ( m )} $ such that the sequence $ b _{1} \dots b _{m} $ can be reordered $ b _ {j ( 1 )} \dots b _ {j ( m )} $ such that $ \sum ^{m} _ {i = 1} a _ {k ( i )} b _ {j ( i )} = 0 $. If one takes $ b _{i} = 1 $, $ i = 1 \dots m $, in this conjecture, then the EGZ theorem follows. Conjecture 1 was proven by M. Kisin for $ m = p ^ \alpha $ and $ m = p ^ \alpha q $, where $ p $ and $ q $ are distinct prime numbers and $ \alpha \geq1 $. In [a7], Z. Füredi and D.J. Kleitman confirmed Conjecture 1 asymptotically for every positive integer $ m $. Conjecture 2 can be easily proven for $ m $ prime. Both conjectures illustrate the general difficulty that exists in this area for handling the non-prime case. There are many related problems to the EGZ theorem. The following conjecture was raised by H. Harborth and some progress was made by Alon and Dubiner. It illustrates that certain problems are open, even for primes. If $ p $ is a prime and $ a _{1} \dots a _ {4p - 3} $ is a sequence of elements from the group $ \mathbf Z _{p} \oplus \mathbf Z _{p} $, then there exists a subsequence of $ p $ elements whose elements add up to $ ( 0,0 ) $. A sequence containing only the elements $ ( 0,0 ) $, $ ( 0,1 ) $, $ ( 1,0 ) $, and $ ( 1,1 ) $, where each element appears $ p - 1 $ times, implies that $ 4p - 3 $ can not be replaced by a smaller number. Zero-sum Ramsey theory. This theory was first introduced in [a3]. Today it includes many results on zero-sum Ramsey numbers for graphs. Recent developments by Bialostocki, P. Erdös, H. Lefmann, and D. Schaal deal with zero-sum solutions to systems of equations and inequalities over the integers. Surveys of this can be found in [a2] and [a4]. The following theorem from zero-sum Ramsey theory, proved in [a6] and [a8], generalizes in the sense of the EGZ theorem the folkloristic fact that in every $ 2 $- colouring of the edges of a complete graph there is always a monochromatic spanning tree: If each edge $ e $ of the complete graph $ K _ {m + 1} $( cf. also Graph theory) is assigned an element from the cyclic group $ \mathbf Z _{m} $, say $ c ( e ) $, then there exists a spanning tree $ T $ of $ K _ {m + 1} $ with edges $ e _{1} \dots e _{m} $ such that $ \sum ^{m} _ {i = 1} c ( e _{i} ) = 0 $. [a1] N. Alon, M. Dubiner, "Zero-sum sets of prescribed size" D. Miklós (ed.) V.T. Sós (ed.) T. Szönyi (ed.) , Combinatorics, Paul Erdös is Eighty , Bolyai Society Mathematical Studies , 1 , Keszthely (Hungary) (1993) pp. 33–50 [a2] A. Bialostocki, "Zero-sum trees: a survey of results and open problems" N.W. Sauer (ed.) R.E. Woodrow (ed.) B. Sands (ed.) , Finite and Infinite Combinatorics in Sets and Logic , Nato ASI Ser. , Kluwer Acad. Publ. (1993) pp. 19–29 [a3] A. Bialostocki, P. Dierker, "Zero-sum Ramsey theorems" Congressus Numerantium , 70 : 1 (1990) pp. 19–130 [a4] Y. Caro, "Zero-sum problems: a survey" Discrete Math. , 152 (1996) pp. 93–113 [a5] P. Erdös, A. Ginzburg, A. Ziv, "A theorem in additive number theory" Israel Research and Development Nat. Council Bull., Sect. F , 10 (1961) pp. 41–43 [a6] Z. Füredi, D. Kleitman, "On zero trees" J. Graph Th. , 16 (1992) pp. 107–120 [a7] Z. Füredi, D. Kleitman, "The minimal number of zero sums" D. Miklós (ed.) V.T. Sós (ed.) T. Szönyi (ed.) , Combinatorics, Paul Erdös is Eighty , Bolyai Society Mathematical Studies , 1 , Keszthely (Hungary) (1993) pp. 159–172 [a8] L. Schrijver, P. Seymour, "A simpler proof and generalization of the zero-trees theorem" J. Combin. Th. A , 58 (1991) pp. 301–305 Erdös-Ginzburg-Ziv theorem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Erd%C3%B6s-Ginzburg-Ziv_theorem&oldid=44351 This article was adapted from an original article by A. Bialostocki (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article Retrieved from "https://encyclopediaofmath.org/index.php?title=Erdös-Ginzburg-Ziv_theorem&oldid=44351" TeX done	CommonCrawl
Evaluation of fluralaner as an oral acaricide to reduce tick infestation in a wild rodent reservoir of Lyme disease Jérôme Pelletier1,2,3, Jean-Philippe Rocheleau2,4, Cécile Aenishaenslin1,2,3, Francis Beaudry5, Gabrielle Dimitri Masson1,2, L. Robbin Lindsay6, Nicholas H. Ogden2,7, Catherine Bouchard2,7 & Patrick A. Leighton1,2,3 Parasites & Vectors volume 13, Article number: 73 (2020) Cite this article Lyme disease (LD) is an increasing public health threat in temperate zones of the northern hemisphere, yet relatively few methods exist for reducing LD risk in endemic areas. Disrupting the LD transmission cycle in nature is a promising avenue for risk reduction. This experimental study evaluated the efficacy of fluralaner, a recent oral acaricide with a long duration of effect in dogs, for killing Ixodes scapularis ticks in Peromyscus maniculatus mice, a known wildlife reservoir for Borrelia burgdorferi in nature. We assigned 87 mice to 3 fluralaner treatment groups (50 mg/kg, 12.5 mg/kg and untreated control) administered as a single oral treatment. Mice were then infested with 20 Ixodes scapularis larvae at 2, 28 and 45 days post-treatment and we measured efficacy as the proportion of infesting larvae that died within 48 h. At each infestation, blood from 3 mice in each treatment group was tested to obtain fluralaner plasma concentrations (Cp). Treatment with 50 mg/kg and 12.5 mg/kg fluralaner killed 97% and 94% of infesting larvae 2 days post-treatment, but no significant effect of treatment on feeding larvae was observed 28 and 45 days post-treatment. Mouse Cp did not differ significantly between the two tested doses. Mean Cp decreased from 13,000 ng/ml in the 50 mg/kg group and 4000 ng/ml in the 12.5 mg/kg group at Day 2 to < 100 ng/ml in both groups at Day 45. We provide the first evidence that fluralaner is effective for killing immature ticks in Peromyscus mice, a first step in evaluating its potential for treating wild rodents as a public health intervention to reduce LD risk in endemic areas. Lyme disease (LD), caused by the spirochete Borrelia burgdorferi [1], is the most important tick-borne disease in Europe and North America [2]. In the USA, the annual incidence rate was 7.2 reported cases per 100,000 people with 33,000 reported cases in 2018 alone [3]. In southern Canada, Lyme borreliosis is currently emerging, associated with the northward spread of the tick Ixodes scapularis, with the number of annual reported cases increasing from 144 in 2010 to 2025 in 2017 [4,5,6]. Because LD is a significant burden for public health, different strategies have been developed to prevent disease transmission to humans, including promoting the adoption of personal preventive measures and reducing tick density in the environment. Tick control measures include the direct application of acaricides in the environment or the treatment of the main tick hosts, such as the white-tailed deer, with oral or topical acaricides [7]. Another potential intervention approach is to treat key reservoirs of B. burgdorferi, such as Peromyscus spp. mice, to decrease the density of ticks in the environment and/or the prevalence of infection in questing ticks, both of which contribute to the density of infected ticks in the environment which is the main measure of the acarological risk of LD [7,8,9]. Oral vaccination of mice against B. burgdorferi's outer surface protein A (OspA) is reported in the literature as an effective way to reduce the prevalence of the spirochete among host seeking ticks [10, 11]. The application of topical acaricides to wild rodents using treatment stations has also been used to effectively reduce tick density in the environment [12,13,14,15,16]. In 2014, a novel ectoparasiticide family called isoxazolines reached the veterinary drug market. Isoxazolines are non-competitive inhibitors of y-aminobutyric acid (GABA)- and l-glutamate-gated chloride channels (GABACl and GluCl), a target that they share with other ectoparasiticides like fipronil, dieldrin and avermectins [17, 18]. More specifically, isoxazolines mostly act on the GABACl channel by blocking ion channel opening [17,18,19,20]. Isoxazolines, like sarolaner and afoxolaner, have been shown to kill adult ticks and prevent B. burgdorferi transmission in dogs [21, 22]. Fluralaner, another member of this new family, is noted for its ability to kill ticks rapidly and for its long efficacy period following a single oral administration, when used in dogs [23, 24]. Wengenmayer et al. [24] showed that, in dogs, fluralaner (BravectoTM chewable formulation) killed 98% of infesting adult Ixodes ricinus ticks within 24 hours following a single oral administration up to 12 weeks post-treatment. A pharmacology study in dogs supported the clinical observations of a long duration effect by measuring a fluralaner half-life of 12–15 days and a quantifiable plasmatic concentration for up to 112 days [25]. These two characteristics, high efficacy and long duration of effect, are attractive features for treatment of wildlife where providing an effective dose to a significant proportion of the host population can be both difficult and costly. In addition, isoxazolines have been shown to be safe when applied at many times the recommended dose in both mammals (dogs and rats [26,27,28]) and birds (chickens [29, 30]). Some toxicological data about fluralaner and related compounds like afoxolaner and sarolaner exist for laboratory mice (Mus musculus) but they are limited to genotoxicity and mutagenicity [20, 29, 31]. Despite the potential of rodent-targeted interventions for reducing LD risk in the environment and the unique pharmacological properties of fluralaner and other isoxazolines, there are currently no data on the efficacy of this product in mice, and specifically in wild mice of the genus Peromyscus. Peromyscus mice are considered to be the primary wildlife reservoirs for Borrelia burgdorferi in much of North America [32, 33]. In the present study, we administered fluralaner to Peromyscus mice and then infested mice with larval Ixodes scapularis ticks in a controlled trial in a laboratory environment as a first step to evaluate the potential of fluralaner, and more broadly the new isoxazoline family of ectoparasiticide drugs, to kill ticks on wild rodents as a public health intervention. Eighty-seven healthy Peromyscus maniculatus mice from Rocky Mountain Laboratory (Hamilton, MT, USA) were used in this experiment. Peromyscus maniculatus is a competent reservoir for B. burgdorferi and permissive host for I. scapularis, and closely phylogenetically related to P. leucopus the primary reservoir for LD in many parts of North America [32]. The group was composed of 40 male and 47 female adult mice (> 1 year-old) with an average weight (± standard deviation, SD) of 20.1 ± 2.7 g. Mice were individually housed in cages with 580 cm2 floors, environmental enrichment, commercial food (Charles River rodent diet, Charles River Laboratory, Wilmington, MA, USA) and tap water during the entire experimentation period. All animals were housed in the same room at a temperature between 22–25 °C, a relative humidity between 50–70%, and a 12:12 h light/dark photocycle. Behaviour was visually assessed daily, and mouse weight was assessed during each manipulation. Mice were euthanized at the end of the experiment or when limit points were reached. Mice were randomly allocated to three equal groups of 29 animals: one control group and two treatment groups. Each mouse received a 250 mg peanut butter bait: fluralaner (BravectoTM chewable formulation, Merck Animal Health, Madison, NJ, USA) was mixed with peanut butter baits in the two treatment groups, while pure peanut butter was given to the control group. The first treatment group received a dose of 50 mg/kg, which is 2 times the minimal targeted treatment dose used for dogs, and the second treatment group received a dose of 12.5 mg/kg, which is half the minimal targeted treatment dose for dogs [23, 24]. The 50 mg/kg dose was chosen since we anticipated more rapid clearance of the molecule by Peromyscus mice compared to dogs. The 12.5 mg/kg dose was included to evaluate the potential clinical effect of a dose below the targeted range, which is likely to occur under field conditions. Each mouse received their treatment and access to regular food was maintained during the period when baits were deposited in the cages to mimic the context of a natural environmental intervention with food competition. Bait consumption was verified after 24 h to ensure the entire bait had been consumed. Infestations To evaluate treatment efficacy, each mouse was infested with 20 unfed I. scapularis larvae at three time points: 2, 28 and 45 days post-treatment. The larvae were hatched from eggs 2 to 3 months before the start of the study and displayed typical host-seeking behaviours at the time of experimental infestations. Groups of mice were infested with larvae of the same age. Infestation was performed by placing larvae on the ears and fur using fine-tipped forceps. To maximise larval attachment, mice were anesthetized (isoflurane 2%) for 1 h during infestation with heater carpets as thermal support and with an injection of subcutaneous fluid (0.5 ml of NaCl 0.9%). At 12, 24 and 48 h post-infestation, mice were visually inspected under anesthesia for a duration of 5 min to count attached larvae. To visually inspect mice, observers followed a systematic inspection procedure: (i) inspection of the ears, head and face; (ii) inspection of the back; and (iii) inspection of the stomach, legs and tail. Observers were blinded to the treatment in order to prevent bias. At 48 h, a sample of remaining attached larvae was removed from each mouse and observed under a binocular microscope to classify them as dead or alive. Larvae showing movement of the legs, movement of the palps and mouthparts, or midgut pulsation were considered alive and larvae expressing none of these behaviours were considered dead. Larvae with no mouthpart during the observation were excluded because the sampling technique was assumed to be the cause of death. The proportion of attached larvae that died was obtained from the observations of larvae and was used to calculate the number of attached living larvae. Statistical models Three generalized linear models (GLMs) were used to analyze the data. The dependent variable for Model 1 was the number of attached larvae. The dependent variable for Model 2 was the number of attached living larvae. Both models 1 and 2 used a negative binomial distribution to account for overdispersion. Independent variables for Models 1 and 2 were the treatment dose, the time elapsed (h) between infestation and larva count, the time elapsed (days) between treatment administration and larva count and mouse sex. Mouse ID was included in both models as a random factor to account for repeated measures. For Model 3, the dependent variable was the proportion of attached larvae on each mouse that were dead at 48 h for each infestation, hereafter termed "mortality proportion", modelled using a binomial distribution. The independent variables were the treatment dose, the time elapsed (days) between treatment administration and larvae count, mouse sex and mouse ID as random factor. Sex was added as a covariate in all models because a link exists between this factor and the number of ticks infesting small mammals [33]. Model fit was evaluated using Pearson residual plots. Statistical analyses were performed using R version 3.5.1 with glmmADMB, lme4 and ggplot2 packages [34,35,36,37,38]. Efficacy assessment Efficacy was defined as the proportion of larvae killed due to the treatment and was calculated based on the number of attached living larvae according to Abbott's formula [39] $${\text{Efficacy }}\left( \% \right) = \frac{{{\text{Mc}} - {\text{Mt}}}}{\text{Mc}} \times 100$$ where Mc is the arithmetic mean of the number of attached living larvae in the control group and Mt is the arithmetic mean of the number of attached living larvae in treatment groups. For all experimental groups, detached larvae were assumed to be dead. Concentration of fluralaner in blood Mouse blood was sampled under anesthesia from the lateral femoral vein on 3 mice in each treatment group on each infestation day, i.e. at Day 2, 28 and 45 post-treatment. Following sampling, the blood was centrifuged at 3000×g for 15 min to extract the plasma. Two hundred µl of internal standard solution (100 ng/ml of reserpine in methanol) was added to 50 µl of plasma samples. The sample was quickly vortexed, left to stand for a period of 10 min and then centrifuged at 12,000×g for 10 min. The supernatant was transferred into an injection vial for HPLC-MS analysis. The HPLC system was a Vanquish Flex UHPLC system (Thermo Fisher Scientific, San Jose, CA, USA). The chromatography was achieved using a gradient mobile phase along with a microbore column Thermo BioBasic Phenyl (Thermo Fisher Scientific) 50 × 1 mm with a particle size of 5 μm. The initial mobile phase condition consisted of acetonitrile and water (both fortified with 0.1% formic acid) at a ratio of 5:95. From 0 to 1 minute, the ratio was maintained at 5:95. From 1 to 5 min, a linear gradient was applied up to a ratio of 20:80 and maintained for 3 min. The mobile phase composition ratio was reverted at the initial conditions and the column was allowed to re-equilibrate for 7 min for a total run time of 15 min. The flow rate was fixed at 75 µl/min and 2 µl of samples were injected. A Q Exactive Orbitrap Mass Spectrometer (Thermo Fisher Scientific) was interfaced with a UltiMate 3000 Rapid Separation UHPLC system (Thermo Fisher Scientific), using a pneumatic assisted heated electrospray ion source. MS detection was performed in positive ion mode, operating in high-resolution accurate-mass (HRAM) scan mode. Nitrogen was used for sheath and auxiliary gases and were set at 10 and 5 arbitrary units. The heated ESI probe was set to 4000 V and the ion transfer tube temperature was set to 300 °C. The scan range was set to m/z 500–700. Data were acquired at a resolving power of 140,000 (FWHM) using an automatic gain control target of 3.0 × 106 and maximum ion injection time of 200 msec. Targeted drug quantification was performed by MS detection using specific precursor masses based on monoisotopic masses (i.e. [M+H]+ ions). Quantification was performed by extracting specific precursor ions using a 5 ppm mass window. Instrument calibration was performed prior to all analysis and mass accuracy was notably below 1 ppm using PierceTM LTQ Velos ESI positive ion calibration solution (Thermo Fisher Scientific) and automated instrument protocol. Fluralaner quantification was performed using peak-area ratio of fluralaner, and the internal standard reserpine and concentrations were determined by interpolating unknowns from the calibration curve constructed with a standard prepared in mouse plasma. The observed precision and accuracy were < 15%. Plasmatic concentrations were statistically analyzed for each time point with the non-parametric Mann-Whitney-Wilcoxon test. Animals and bait consumption Eight mice died or were euthanized according to the protocol limit points before the completion of the experiment (Table 1). All mice completely consumed the 250 mg bait within the first 24 h after administration. Table 1 Number of attached larvae on mice 48 hours post-infestation for each experimental group at Day 2, Day 28 and Day 45 after treatment administration Attached larvae (Model 1) The number of attached larvae decreased over the course of the 48 h post-infestation observation period in both treatment and control groups. During the first infestation (Day 2 post-treatment), the number of attached larvae in the two treatment groups significantly decreased from a mean (± standard error, SE) of 7.3 ± 0.4 to a mean of 4.0 ± 0.3 attached larvae between 12 and 48 h post-infestation (GLM, Wald-test, P < 0.001). In the control group, the mean number of attached larvae slightly decreased from 8.3 ± 0.5 (SE) to 7.6 ± 0.6 (SE) (GLM, Wald-test, P = 0.58). The reduction in the number of attached larvae was significantly higher in the two treatment groups than in the control group (GLM, Wald-test, P = 0.001) (Fig. 1). Both treatment groups showed similar reductions of the number of attached larvae (GLM, Wald-test, P = 0.92). The treatment effect on the mean number of attached larvae was no longer significant for the Day 28 (GLM, Wald-test, P = 0.57) and Day 45 (GLM, Wald-test, P = 0.33) infestations (Fig. 2a). Mean number of attached larvae 12, 24 and 48 h following infestation carried out 2 days after administration of fluralaner treatment. Mice were infested with 20 larvae at time 0 and ticks were counted at 12, 24 and 48 h post-infestation. Error bars are ± 1 SE. Key: Circle, 0 mg/kg; square, 50 mg/kg; triangle, 12.5 mg/kg; , a statistically significant difference compared with the 0 mg/kg group (GLM, Wald-test, P < 0.01) Effect of fluralaner treatment 48 h following infestations carried out at Day 2, 28 and 45 post-treatment. a Mean number of attached larvae at 48 h obtained by mouse visual inspections. b Mortality proportion of larvae at 48 h post-infestation. A sample of the remaining attached larvae was collected at 48 h and observed under microscope to evaluate if they were dead or alive. c Mean number of attached living larvae at 48 h calculated from the number of attached larvae and the larvae mortality proportion. d Fluralaner Cp arithmetic mean obtained from blood samples of three mice from each treatment group. Error bars represent ± 1 SE in a, b and c, and ± 1 SD in d. Key: black, 0 mg/kg; dark grey, 12.5 mg/kg; light grey, 50 mg/kg; , a statistically significant difference compared with the control group (0 mg/kg) (GLM, Wald-test, P < 0.01) Mortality proportion (Model 3) A larger number of attached ticks, dead and alive, was collected in the control group (n = 151) in comparison to both treatment groups at Day 2: 92 in the 50 mg/kg group and 70 in the 12.5 mg/kg group. This difference was less pronounced at Day 28: 155 in the control group; 138 in the 50 mg/kg group; and 145 in the 12.5 mg/kg group (Table 1). In total the proportion of attached larvae that died was 93%, 87% and 8% for the 50 mg/kg, the 12.5 mg/kg and the control groups, respectively, at Day 2 after treatment administration. Treatment administration was significantly associated with a high larval mortality proportion (GLM, Wald-test, P < 0.001). Mortality proportion decreased significantly over time (GLM, Wald-test, P < 0.001) and became statistically non-significant at Day 45 post-treatment (Fig. 2b). The most substantial reduction in mortality proportion occurred between Day 2 and Day 28 (GLM, Wald-test, P < 0.001) with no statistical difference between Day 28 and Day 45 (GLM, Wald-test, P = 0.2). Attached living larvae (Model 2) and efficacy On Day 2, both treatment groups showed a significantly greater reduction in the number of attached living larvae compared to the control group (GLM, Wald-test, P = 0.001). In the 50 mg/kg and the 12.5 mg/kg group the mean number of attached living larvae increased with time since treatment: respectively 0.2 ± 0.1 (SE) and 0.4 ± 0.2 (SE) when ticks attached on Day 2, but 8.0 ± 0.6 (SE) and 7.9 ± 0.6 (SE) when ticks attached on Day 28 (Fig. 2c). On Day 2, fluralaner treatment efficacy was 97% and 94% for the 50 mg/kg and the 12.5 mg/kg groups, respectively. Efficacy decreased at Day 28 to 3% for the 50 mg/kg dose and 4% for the 12.5 mg/kg dose (Table 2). Table 2 Fluralaner dose efficacy at Day 2, Day 28 and Day 45 after treatment administration At Day 2, the plasmatic concentration (Cp) arithmetic mean (± standard deviation, SD) was 13,815 ± 11,585 ng/ml in the 50 mg/kg group and 4594 ± 6995 ng/ml in the 12.5 mg/kg. Nevertheless, given the great variability in the Cp of tested individuals, Cp were not statistically different between the two groups (Mann-Whitney U-test, U(6) = 7, P = 0.4). At Day 28, the differences in Cp between treatments decreased with 579 ± 885 (SD) ng/ml in the 50 mg/kg group and 208 ± 277 (SD) ng/ml in the 12.5 mg/kg group (Mann-Whitney U-test, U(6) = 7, P = 0.4). Plasmatic concentration became roughly the same at Day 45 (Mann-Whitney U-test, U(6) = 0, P = 0.1) with 46.7 ± 0.5 (SD) ng/ml and 52 ± 1 (SD) ng/ml, respectively (Fig. 2d). To the best of our knowledge, this study provides the first evidence that fluralaner is effective at killing larval I. scapularis ticks feeding upon Peromyscus mice. Efficacy two days post-treatment was greater than 90% for both tested doses, suggesting that fluralaner delivered orally using voluntarily-consumed baits has the potential to kill a significant proportion of immature ticks infesting small mammals, thus disrupting the B. burgdorferi transmission cycle in nature. While fluralaner did not provide the same duration of high efficacy as seen in dogs, the achieved efficacy of 94% at Day 2 with a 12.5 mg/kg treatment dose indicates that fluralaner provides effective short-term protection in Peromyscus mice at a dose 4 times lower than 50 mg/kg and 2 times than 25 mg/kg. Overall, our results suggest that regular administration of fluralaner baits to small mammals during the peak season for immature ticks has the potential to provide a promising new approach for localized reduction of LD risk in North America. We found that, 2 days post-treatment, fluralaner reduced the mean number of attached larvae on Peromyscus mice (Figs. 1, 2a). This suggests that fluralaner treatment at the two doses tested affected larval viability enough to cause them to fall off. This may be associated with an increased susceptibility to host grooming behavior, which is a major factor in explaining mouse ectoparasite infestation rates [40,41,42,43], although hard ticks are somewhat resistant to grooming due to their tough cuticles and feeding behaviour which causes them to be anchored to the skin [44]. However, treatment did not bring the number of attached larvae to zero (Fig. 1), even though many attached larvae were in fact dead. The fact that treatment may be effective without causing ticks to detach is an important consideration for the evaluation of treatment efficacy in the absence of a direct evaluation of the viability of larvae. A similar observation was made by Fisara and Webster [45] in their clinical controlled trial of BravectoTM efficacy in dogs against Ixodes holocyclus ticks, in which the authors noted that the presence of attached ticks on dogs could be perceived as a treatment failure but they observed that the remaining ticks were killed by the treatment. We were able to confirm treatment efficacy by documenting significant tick mortality in attached larvae, which brought the infestation rate based on attached living larvae close to zero in both treatment groups. The significant difference in the proportion of dead larvae was the main observation supporting treatment efficacy at Day 2 post-treatment and was the only significant difference between treatment and control groups at Day 28 (Fig. 2b, c). Unlike a study of fluralaner efficacy against adult I. ricinus ticks on dogs, the treatment did not result in an efficacy of 100% within 2 days of treatment administration [24]. This difference could be explained by variability in attachment and the feeding speed of the larvae depending on their ability to bite at the time of infestation, resulting in a delay in the treatment effect [46]. Previously published studies used adult ticks, and the difference in the volume of the blood meals of larvae and adults, could also explain the different results observed in this study [47]. We found that clinical effect of fluralaner bait in mice declined rapidly over time, showing only a marginally greater tick mortality proportion compared to controls, with a limited impact on the attached living larva infestation rate 28 days post-treatment (Fig. 2). This differs from previous findings reported in dogs where fluralaner efficacy against adult ticks remained high for more than 2 months post-treatment [23, 24, 45, 48]. Pharmacokinetics in dogs showed that fluralaner clearance is mainly via the hepatobiliary pathway [25, 27]. Systemic clearance of the molecule should be related to hepatic clearance, which is linked to hepatic blood flow [49]. Hepatic blood flow in mice is three times higher (129.6 l/kg/day) than in dogs (44.5 l/kg/day). So this difference, along with other physiological and metabolic differences between dogs and mice may explain the more rapid decline of treatment efficacy observed in the present study [25, 50]. At Day 2 after treatment, Cp values in mice for the dose of 50 mg/kg and the dose of 12.5 mg/kg were higher than those seen in dogs at the same doses and the same time point. In contrast, at day 28, mice had a mean Cp lower than what Kilp et al. [25] observed in dogs. While faster drug clearance appears to reduce the duration of effect in mice, it may also reduce fluralaner toxicity in mice and increase its therapeutic index in this species. The Cp concentration was highly variable in both treatment groups, particularly shortly following treatment, likely due in part to the oral self-administration of the treatment bait. By 45 days post-treatment, fluralaner concentration decreased below 100 ng/ml (Fig. 2d) also supporting the hypothesis of faster drug clearance in mice than in dogs. In dogs, Kilp et al. [25] measured Cp values below the 100 ng/ml threshold just before 60 days or 2 months post-treatment. Similarly, Becskei et al. [48] observed a reduction of the BravectoTM formulation efficacy in dogs after 60 days. In contrast, we observed the greatest efficacy reduction between day 2 and day 28 post-treatment, with only a marginal effect at 28 days when mean Cp values were 578 ng/ml for the 50 mg/kg group and 207 ng/ml for the 12.5 mg/kg group. The absence of difference in clinical effect between 12.5 mg/kg and 50 mg/kg treatment doses is similar to the study of Kilp et al. [25] who found no significant difference in Cp area under the curve (AUC) between 12.5 mg/kg and 50 mg/kg doses in dogs. The present study shows no statistical difference in Cp for the same dose range at Day 2, 28 and 45 after a single oral administration even with large Cp differences between the two groups at Day 2 (Fig. 2d). While this observation correlates with clinical effect, it remains preliminary given the high variability in the Cp data and limited statistical power. It is also possible that an efficacy differential between the two doses develops in the shorter term, i.e. somewhere between Day 2 and Day 28 post-treatment, but a greater observation frequency would be required to evaluate this. The infestation method used in this study resulted in significant loss of larvae between infestation and the observation time points in both treated and control group (Fig. 1). This phenomenon occurred at all infestations and resulted in a low infestation rate at 48 hours for all groups even in the absence of a significant treatment effect (Table 1, Fig. 2a). Grooming behaviour could partly explain this observation as Peromyscus mice are reported to be effective at removing and damaging infesting larvae [43]. Larval loss could also be partially explained by the variable attachment ability of larvae related to variation in larval activity during the infestation period and in varying capacity of individual larvae to attach to and feed on mice. Nilsson and Lundqvist [46] reported that ticks that do not find suitable feeding sites can actively leave the host or passively fall off due to host movements and larval attachment rates of less than 50% on mice are not uncommon in the literature [51]. A low rate of larval attachment could be explained by the fact that no device or procedure was used to restrain mouse movements or grooming behavior, potentially decreasing the attachment success of larvae post-anesthesia [52, 53]. Visual inspection of mice could also have underestimated the number of attached larvae as ticks may have attached in locations where it was hard to see them (e.g. in the dense fur on their backs or between their toes). Nevertheless, the low rate of attachment does not affect the conclusion of this study, given that the application of the same infestation technique in each group, and of a standardized observation method, ensured that control and treatment groups remained comparable. This study showed that fluralaner is effective at killing I. scapularis ticks that infest Peromyscus mice, a natural reservoir host of LD. This is a first step towards potential use of fluralaner in baits to treat wild rodents as an intervention to reduce LD risk in North America. However, more research is needed to better understand duration of efficacy, pharmacokinetics and toxicology of fluralaner in wild rodents in order to evaluate treatment efficacy, safety and predictability. The efficacy of smaller and shorter treatments when determining a treatment dose and refilling frequency for baits targeting wild rodents like Peromyscus mice in an intervention setting should also be considered. Further pharmacological research on mice in the laboratory setting and field trials in wildlife could help address some of these questions. The datasets generated during and/or analysed during the current study are available from the corresponding author upon reasonable request. AUC: plasma concentration generalized linear model LD: Steere AC, Grodzicki RL, Kornblatt AN, Craft JE, Barbour AG, Burgdorfer W, et al. 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The authors would like to thank all the interns who helped during the study and all the employees from the Cégep de Saint-Hyacinthe for taking care of and housing the mice during the experiment. This study was funded by the Université de Montréal, the Institute National de Santé Publique du Québec (INSPQ), the Public Health Agency of Canada (PHAC) and a Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery grant to PL. The mass spectrometry analyses were performed using an infrastructure funded by the Canadian Foundation for Innovation (CFI) and the Fonds de Recherche du Québec (FRQ), Gouvernement du Québec (F. Beaudry CFI Johns R. Evans Leaders grant no 36706). Département de pathologie et microbiologie, Faculté de médecine vétérinaire, Université de Montréal, Saint-Hyacinthe, QC, Canada Jérôme Pelletier, Cécile Aenishaenslin, Gabrielle Dimitri Masson & Patrick A. Leighton Groupe de recherche en épidémiologie des zoonoses et santé publique, Faculté de médecine vétérinaire, Université de Montréal, Saint-Hyacinthe, QC, Canada Jérôme Pelletier, Jean-Philippe Rocheleau, Cécile Aenishaenslin, Gabrielle Dimitri Masson, Nicholas H. Ogden, Catherine Bouchard & Patrick A. Leighton Centre de recherche en Santé Publique, Université de Montréal, Montréal, QC, Canada Jérôme Pelletier, Cécile Aenishaenslin & Patrick A. Leighton Département de santé animale, CÉGEP de Saint-Hyacinthe, Saint-Hyacinthe, QC, Canada Jean-Philippe Rocheleau Groupe de recherche en pharmacologie animale, Département de biomédecine vétérinaire, Faculté de médecine vétérinaire, Université de Montréal, Saint-Hyacinthe, QC, Canada Francis Beaudry Zoonotic Diseases and Special Pathogens Division, National Microbiology Laboratory, Public Health Agency of Canada, Winnipeg, MB, Canada L. Robbin Lindsay Public Health Risk Sciences Division, National Microbiology Laboratory, Public Health Agency of Canada, Saint-Hyacinthe, QC, Canada Nicholas H. Ogden & Catherine Bouchard Jérôme Pelletier Cécile Aenishaenslin Gabrielle Dimitri Masson Nicholas H. Ogden Catherine Bouchard Patrick A. Leighton JP, JPR, CA, NHO, LRL, CB and PAL participated in the study design and protocol. JP, JPR and GDM conducted the experiment. FB designed and conducted the mass spectrometry analysis. JP conducted statistical analysis and wrote the manuscript. All authors revised the manuscript. All authors read and approved the final manuscript. Correspondence to Jérôme Pelletier. All animal experiments were performed in agreement with the Canadian Council on Animal Care (CCAC) regulation and with the ethical approval of the institutional animal ethics committee of Université de Montréal (16-Rech-1845) and of CÉGEP de Saint-Hyacinthe (ENS-LYME-2017-HY). Pelletier, J., Rocheleau, JP., Aenishaenslin, C. et al. Evaluation of fluralaner as an oral acaricide to reduce tick infestation in a wild rodent reservoir of Lyme disease. Parasites Vectors 13, 73 (2020). https://doi.org/10.1186/s13071-020-3932-7 Isoxazolines Fluralaner Peromyscus spp.	CommonCrawl
Three-dimensional scanless holographic optogenetics with temporal focusing (3D-SHOT) Nicolas C. Pégard ORCID: orcid.org/0000-0003-2868-71181,2 na1, Alan R. Mardinly ORCID: orcid.org/0000-0001-9891-67191 na1, Ian Antón Oldenburg ORCID: orcid.org/0000-0002-7356-104X1, Savitha Sridharan1, Laura Waller ORCID: orcid.org/0000-0003-1243-23562 & Hillel Adesnik ORCID: orcid.org/0000-0002-3796-86431,3 Nature Communications volume 8, Article number: 1228 (2017) Cite this article Optogenetics Optical methods capable of manipulating neural activity with cellular resolution and millisecond precision in three dimensions will accelerate the pace of neuroscience research. Existing approaches for targeting individual neurons, however, fall short of these requirements. Here we present a new multiphoton photo-excitation method, termed three-dimensional scanless holographic optogenetics with temporal focusing (3D-SHOT), which allows precise, simultaneous photo-activation of arbitrary sets of neurons anywhere within the addressable volume of a microscope. This technique uses point-cloud holography to place multiple copies of a temporally focused disc matching the dimensions of a neuron's cell body. Experiments in cultured cells, brain slices, and in living mice demonstrate single-neuron spatial resolution even when optically targeting randomly distributed groups of neurons in 3D. This approach opens new avenues for mapping and manipulating neural circuits, allowing a real-time, cellular resolution interface to the brain. Optical manipulation of neural circuits is one of the most powerful approaches for revealing causal links between neural activity and behavior1, 2. Optogenetics enables rapid and reversible control of genetically defined cell types by employing photo-sensitive microbial opsins that either generate or suppress neuronal activity in response to light2,3,4. In principle, optogenetics offers high spatiotemporal precision, yet the vast majority of optogenetics studies primarily leverage genetic specificity rather than high resolution spatial control due to the difficulties of accurately focusing light in brain tissue. However, since many neural computations and behaviors rely on populations of neurons that are genetically similar but spatially intermixed5,6,7,8, new methods are needed to enable precise three-dimensional (3D) targeting of custom neuron ensembles within the brain. Several methods have been developed for optogenetic photostimulation; however none are capable of simultaneous single-neuron spatial resolution9, 10 across a large volume without compromising temporal precision. The simplest approach, one-photon optogenetics, uses absorption in the visible spectrum to activate the opsin, yet strong optical aberrations and scattering through brain tissue severely degrade spatial resolution, even when using adaptive optics11. Two-photon (2P) excitation partially addresses the issue of optical scattering12, dramatically improving axial resolution and depth penetration of the illumination patterns13, 14. The most common approach employed for two-photon excitation is to focus a femtosecond-pulsed infrared laser beam into a single diffraction-limited spot which is scanned in two-dimensions (2D) or three dimensions (3D)14, 15. For optogenetic applications, a raster16, 17 or spiral5, 18, 19 pattern is scanned across the cell body of each targeted opsin-expressing neuron. Since two-photon absorption is nonlinear, photoexcitation is confined to a small spot, enabling single neuron spatial resolution at appropriate power levels16, 18. However, photosensitive opsins such as ChR2 deactivate rapidly, making it difficult to quickly achieve the photocurrent needed for fast and reliable action potential initiation by activating the opsin point by point in each neuron18. While newly engineered opsins with slow deactivation kinetics overcome this problem17, they necessarily degrade temporal resolution, making it difficult to trigger action potentials with precise timing16, 19. Computer generated holography (CGH)20,21,22,23 is a scanless solution for two-photon optogenetics9, 24,25,26,27,28,29, which significantly increases temporal precision of photostimulation. CGH relies on a spatial light modulator (SLM) to distribute a laser beam into multiple targets with custom 3D shapes20, 21; unlike scanning approaches, CGH wide-area holograms matched to the dimensions of each neuron's soma should enable simultaneous, flash-based activation of large numbers of opsin molecules yielding photocurrents with fast kinetics10. However with CGH, spatial resolution along the optical axis is entirely determined by the rate by which wave propagation attenuates the power density on either side of the targeted area. Thus, CGH favors high numerical aperture (NA) objectives with small addressable volumes. CGH, and even point scanning methods10, 18, often result in significant undesired photoexcitation above and below the object target. In practice, physiological spatial resolution is highly power dependent, and single neuron spatial resolution (a Gaussian fit axial full-width at half-maximum (FWHM) of ~30 µm9, 10) is generally impossible across large volumes. Temporal Focusing (TF)30 eliminates the trade-off between the target size in the lateral (x,y) plane and axial (z) resolution30, 31. TF relies on a diffraction grating placed in the image plane to decompose femtosecond pulses into separate colors, such that the different wavelengths components within the original pulse propagate along separate light paths. Each component of the decomposed pulse is broadened in time, which dramatically reduces peak intensity and prevents two-photon absorption until the original pulse constructively interferes at the conjugate image plane of the diffraction grating30, 31. This strategy introduces a secondary axial confinement mechanism that restricts the two-photon response to a thin layer around the focal plane. Since the thickness of this layer no longer depends on the dimensions of the targeted area, but rather on the bandwidth of the pulse, this property has been successfully applied for depth-selective two-photon fluorescence imaging32, 33, and has been implemented with mechanical scanning34 and with random-access volume sampling of functional fluorescence35. For two-photon photostimulation applications, TF activates opsins over a wide area matching the neuron's shape in the focal plane, without compromising depth specificity10, 36. TF also mitigates the effects of light scattering37, 38 even through thick layers of brain tissue39, 40. Although multiphoton CGH with TF can achieve wide field photostimulation with cellular resolution and high temporal precision, most implementations only enable excitation within a single 2D plane10, 36, 41. Thus, neurons located above or below the focal plane are not addressable, a necessary condition for many experiments designed to interface with neural circuits in vivo, where neurons are located continuously in 3D. Multi-level temporal focusing has been shown with holograms tiled into clusters that can be individually defocused in space by applying digital lens patterns on a second SLM. However, this strategy is limited to at most 4–5 depth levels before in-plane resolution is degraded, severely constraining the neuronal population that is simultaneously addressable with optical stimuli42. In most brain structures, neurons are distributed in 3D, not in discrete layers. Therefore, the inability of scanless optogenetics approaches to target neurons at any arbitrary set of axial planes simultaneously is a major obstacle for large-scale optogenetic interrogation of neural circuits. To overcome this outstanding challenge, we developed 3D scanless holographic optogenetics with temporal focusing (3D-SHOT), a new holographic photostimulation technique that combines CGH and temporal focusing to enable single-shot in vivo photo-activation of custom neuron ensembles with single neuron spatial resolution, without limits on the number of addressable target planes. Our strategy benefits from the large accessible volume of conventional holographic microscopy, yet takes advantage of temporal focusing to further confine the two-photon photoexcitation in the axial dimension. Here we present the theoretical design and empirically validate the ability of 3D-SHOT to target neurons in an arbitrary number of axial planes with high spatial precision. We further demonstrate its functionality for in vivo optogenetics applications in mice, validating 3D-SHOT's utility as a new technology for scanless optical manipulation of neural activity in the intact brain. Designing a TF system for arbitrary 3D targeting 3D-SHOT operates by replicating identical copies of a temporally focused disc of light, termed the custom temporarily focused pattern (CTFP), at arbitrary 3D positions. Here, the dimensions of the CTFP were chosen to match the characteristic size of a layer 2/3 cortical pyramidal neuron35, (Supplementary Table 1) and may be easily adjusted for different applications (Supplementary Table 2). The CTFP is designed by separating a patterned laser beam (characterized by its phase and intensity) into spectral components with a diffraction grating as in a conventional TF system. The beam intensity profile determines the dimensions of the CTFP, while phase, a previously unused degree of freedom, is engineered to make 3D holography and temporal focusing compatible. To ensure good diffraction efficiency of all spectral components by the SLM, we used lens L c to apply a small spherical phase pattern. The focal length was adjusted so that each spectral component of the pulse spans across the short axis of the SLM in the Fourier domain (Supplementary Figs. 1, 2). Besides experimental simplicity, the spherical phase mask imposed by lens L c yields convenient analytical expressions for simulation purposes (Supplementary Notes 1−3). We note, however, that alternate phase masks (for instance generated with a secondary SLM), could also be employed as long as they expand the spectral components to cover enough area of the SLM to enable holography. The fundamental principle of 3D-SHOT (see Methods section) is to make temporal focusing compatible with 3D CGH by placing the SLM after the diffraction grating. This design forgoes the ability to synthesize custom shapes for each neuron, but represents an acceptable trade-off for many optogenetic applications. The resulting experimental set-up operates an all-optical convolution product given by: $${{{A_{\rm{E}}}(x,y,z,\Delta k) = {A_{\rm{C}}}\left( {\frac{{{f_4}x}}{{{f_5}}},\frac{{{f_4}y}}{{{f_5}}},\Delta k} \right) \otimes \left[ {{\rm{F}}\left[ {{e^{i\varphi }}} \right]\left( {\frac{x}{{{\lambda f_5}}},\frac{y}{\lambda {f_5}}} \right) \otimes h\left( {x,y,z} \right)} \right],}}$$ where ⊗ denotes the convolution product. The CTFP, A C (x,y,∆k), adjusted to the characteristic dimensions of a neuron after demagnification, can then be placed on demand at the desired locations by an all-optical convolution with a 3D hologram corresponding to the phase mask, φ, displayed on the SLM (Fig. 1). To simultaneously place identical copies of the CTFP at n neurons located in positions (x i ,y i ,z i ) in space, we computed a hologram optimized so that the Fresnel propagation, h, of F[e iφ] best approximates a cloud of points located at the desired targets with weighted intensities that can be adjusted for each targeted neuron. A demagnified copy of the CTFP was then recreated at each point of the cloud in the resulting field. Simplified experimental set-up for 3D-SHOT. a A spherical phase mask is applied to a Gaussian femtosecond laser pulse incident on a blazed diffraction grating. After the grating, the direction of propagation of the first-order beam is wavelength-specific, decomposing the pulse in the temporal domain. Temporal focusing and the associated nonlinear response thus only happens across a disc-shaped area at depth planes corresponding to images of the diffraction grating (dashed, green). We call this 3D intensity distribution a Custom Temporally Focused Pattern (CTFP). b We then copied this temporally focused disc pattern to different areas in 3D by computer generated holography (CGH). To do so, a spatial light modulator (SLM) in Fourier space (dashed, red) generates a point-cloud hologram that replicates the CTFP at each target point in the volume image. The resulting field is demagnified again before impinging on the sample to create custom 3D positioning of the temporally focused disk, each targeted at a particular neuron Here, our primary goal was not to render a visually accurate hologram but instead to increase contrast for two-photon excitation at selected locations while avoiding inadvertent photo-activation of non-targeted areas, and we implemented a modified version of the multilevel Gerchberg−Saxton (GS)20 algorithm that emphasizes precise control of the intensity at the desired targets. Quantitative 3D characterization of two-photon absorption To evaluate the capabilities of 3D-SHOT and quantify how two-photon absorption is spatially distributed in 3D, we placed a flat phase mask on the SLM, $\varphi \left( {x,y} \right) = 0$, so that the convolution product in Equation (1) reduces to the simplest case of requesting a single copy of the CTFP to be placed at the center of the operating volume, defined in x = y = z = 0 (that is, the system's zero-order). We then placed a thin fluorescent film on a microscope slide under the excitation objective and recorded the corresponding two-photon fluorescence with a sub-stage objective coupled to a camera (Fig. 2a). We recorded z-stack images by moving the excitation objective along the z-axis by 1 µm increments. The resulting data correspond to a quantitative 3D measurement of two-photon absorption induced by the CTFP. In the specific case of a flat phase pattern on the SLM, we have also derived an analytical expression for the instantaneous two-photon absorption, ${\left\| {{A_{\rm{F}}}\left( {x,y,z,\Delta t} \right)} \right\|^4}$(Supplementary Fig. 3), which we used to predict and visualize the CTFP in space and time, and also to compare simulation and experiments. Optical characterization of the spatial resolution of CGH vs. 3D-SHOT. a We used a fluorescent calibration slide and an inverted microscope to compare two-photon absorption patterns in 3D. b For conventional holography, we consider a 10 µm diameter disk target, and show (from top to bottom) example projection views of two-photon absorption in the (x,y), (z,y), and (z,x) planes. With 3D-SHOT, the CTFP was adjusted to a 10 µm diameter target and the same projection views were recorded c experimentally, and d rendered with simulation. e Simulation additionally provides space-time projections (Supplementary Notes 1−3). The primary focus (green arrow) at z = 0 displays the characteristic depth-sectioned properties of temporal focusing, with a perceived femtosecond pulse line object rapidly swept along the x-axis. The secondary focus (pink arrow), a static line along the x-axis in y = 0, is a geometric projection of the spherical phase pattern induced by lens L c. The pulse duration at the secondary focus is stretched in time (~1000 fs) which minimizes nonlinear response We first compared 3D-SHOT to conventional 3D holography (Fig. 2b). Using CGH, we computed a 10 µm disk image target at z = 0 where we imposed a high-frequency speckle pattern to maximize spatial confinement along the z-axis. Projection views of two-photon absorption along the x, y, and z axes show how even in an optimized hologram unwanted photostimulation remains above and below a neuron targeted with this method. When the 10 µm CGH pattern is replaced by a 3D-SHOT CTFP of equal size, experimental results (Fig. 2c) and simulations (Fig. 2d−e) show that temporal focusing significantly enhances spatial confinement along the z-axis. Scanless two-photon optogenetics using 3D-SHOT We evaluated the spatial resolution of 3D-SHOT via optogenetic stimulation of opsin-expressing Chinese Hamster Ovary (CHO) cells and mouse neurons in acute brain slices and in vivo. We evaluated the spatial resolution (or physiological point spread function (PPSF)) by recording the photocurrent response to multiphoton photostimulation as a function of the displacement between the holographic target and the patched cell (Fig. 3a, e). The set-up is fitted with a pair of mirrors on a sliding stage to rapidly swap between CGH and 3D-SHOT (Supplementary Fig. 1). The two optical paths are aligned so that the centers of the CTFP (3D-SHOT path) and the disc illumination (CGH path) are co-aligned along all 3D. This allows both methods to be tested on individual cells without any realignment. 3D-SHOT generates axially confined photo-activation. a A photostimulation pattern generated with CGH was mechanically stepped along the optical z-axis and passed through a cell expressing opsin. Photocurrents were recorded in the whole-cell voltage clamp configuration. b−f The response profile for CGH with a 10 µm disk target and different power levels on CHO cells for CGH b or 3D-SHOT f (n = 12 cells, data points are a representative example cell). d The FWHM of the characteristic response profile for both methods at various power levels on CHO cells (n = 12 cells, data represent mean ± s.e.m.). e As in a, but in mouse brain slices. c, g as in b, f, but in mouse brain slices (n = 11 neuron, data points are a representative example neuron). h The FWHM of the characteristic response profile for both methods at various power levels in mouse brain slices (n = 11 neurons, data represent mean ± s.e.m.) Since power levels needed for photostimulation vary across cells due to differences in opsin expression and excitability, we compared the spatial confinement of 3D-SHOT and CGH photo-excitation as a function of laser power density. With conventional holography, we observed substantial photocurrents 25–50 µm above and below the target, indicating that photo-activation of non-targeted neurons is likely to occur (Fig. 3b, c). As predicted by simulations (Supplementary Fig. 3), temporal pulse stretching significantly enhanced spatial resolution with 3D-SHOT, as photocurrents were more significantly attenuated above and below the primary focus (Fig. 3f, g). In neurons and CHO cells, axial resolution with 3D-SHOT was significantly improved relative to CGH, even when using several orders of magnitude more laser power (Fig. 3d, h). This implies that one may increase excitation light to generate action potentials without compromising spatial confinement. 3D-SHOT photostimulation with single-neuron resolution We next quantified the physiological spatial resolution of CGH and 3D-SHOT in neurons by measuring the spiking probability along the lateral (x,y) and axial (z) dimensions. Experimental results show similar spatial resolution with both methods in the lateral direction in the focal plane, with a FWHM of 10 ± 2 µm for holography, and 9 µm ± 1.3 for 3D-SHOT, (p = 0.57, Mann−Whitney U-test) consistent with the dimensions of the disc and CTFP (Fig. 4a). With CGH, the spike probability along the z-axis does not permit single-cell resolution (FWHM = 78 ± 6 µm). In contrast, 3D-SHOT provides far superior resolution (FWHM = 28 ± 0.7 µm, p = 0.006, Mann−Whitney U-test, Fig. 4b, c) compatible with single-cell resolution in 3D, in that the FWHM of spike probability is on par with the typical dimensions of a cortical neuron and their inter-somatic spacing. 3D-SHOT also has a secondary focus that is sheared off-axis relative to the linear (x,y,z) dimensions (Fig. 2). Although, we did not predict significant two-photon excitation to occur at the secondary geometric focus, we tested the spatial resolution by photo-stimulating a 3D grid pattern (50 × 50 × 100 µm3 x,y,z). This experiment revealed that the neuron was photo-activated only when the disc image was targeted to the cell body (Fig. 4d). 3D-SHOT provides high spatial resolution photo-activation of neurons in vitro and in vivo. a Spatial profile of two-photon evoked spiking of a L2/3 pyramidal neuron in a mouse brain slice in the radial dimension. (CGH: black, n = 12 neurons; 3D-SHOT: red, n = 14 neurons; p = 0.56 Mann−Whitney U-test. Data represent mean ± s.e.m). b As in a) but along the axial dimension (CGH n = 11 neurons, 3D-SHOT n = 5 neurons, p = 0.006). c Quantification of the FWHM comparing CGH and 3D-SHOT (data represent mean and s.e.m.). d Full volumetric assessment of photostimulation resolution using 3D-SHOT. Points throughout the volume were tested, but only points that elicited spike probability greater than zero are shown (data represent mean of n = 7 neurons). e−g As in a−c but for neurons recorded via in vivo 2P guided patch: radial: p = 0.46; axial: p = 0.004, CGH (n = 6 neurons), and 3D-SHOT (n = 6 neurons). h as in d, but in vivo cell-attached patch using 3D-SHOT (data represent mean of n = 5 neurons) To demonstrate 3D-SHOT's single-neuron spatial resolution under in vivo conditions, we quantified the PPSF for L2/3 pyramidal neurons using 3D-SHOT and CGH in living mice. We obtained two-photon guided loose patch recordings from opsin-expressing neurons in anesthetized mice, generated action potentials in targeted neurons with light pulses, and measured the PPSF for CGH and 3D-SHOT by digitally displacing the holographic target. As in brain slices, CGH and 3D-SHOT exhibited similar spatial resolution in the lateral (x,y) dimensions (lateral FWHM: CGH: 15 ± 4 µm, 3D-SHOT: 11 ± 2 µm, p = 0.46, Mann−Whitney U-test, Fig. 4e). However, along the z-axis, 3D-SHOT achieved significantly better spatial confinement than CGH (Axial FWHM: CGH: 70 ± 16 µm, 3D-SHOT: 29 ± 3 µm, p = 0.004, Mann−Whitney U-test, Fig. 4f, g). Measuring spike probability in response to 3D-SHOT stimulation throughout a 3D 50 × 50 × 100 µm3 grid revealed no off-axis excitation by the secondary focus (Fig. 4h). Together, these data validate 3D-SHOT as a novel scanless optogenetic stimulation paradigm that can achieve single-neuron spatial resolution during optogenetic stimulation in the mouse brain in vivo. Spatially precise remote control with 3D-SHOT Since the major advantage of 3D-SHOT is the ability to target multiple neurons arbitrarily in 3D, it is vital that 3D-SHOT can activate neurons with high spatial resolution even when digitally focusing light far from the zero-order of the optical system. Therefore we next evaluated the accessible depth within the volume by measuring the activation and spatial resolution as a function of the distance from the holographic natural focus plane. Toward this end, we recorded photocurrents in CHO cells via a voltage clamp and then measured spike probability in neurons via a current clamp in mouse brain slices (Fig. 5a, e). To test whether the CTFP can be digitally displaced along the z-axis, we systematically moved the digital focus of the hologram, and accordingly corrected the mechanical position of the objective by the same distance (δz Digital = −δz Mechanical). This test showed that 3D-SHOT effectively photostimulates cells at locations distal to the zero-order, as photocurrent and spike-probability were not affected by digital offset in z (Fig. 5b, CHO cells p = 0.39, Fig. 5f, neurons p = 0.2, Kruskal−Wallis). 3D-SHOT provides cellular resolution photostimulation in a large volume through digital focusing. a To quantify the spatial resolution of 3D-SHOT as a function of hologram target depth, we recorded photocurrents in CHO cells while digitally targeting varying positions along the optical axis (z), and measuring resolution by mechanically sweeping the objective over the entire (z) range and measuring the response at each point. b Normalized photocurrent in CHO cells while targeting the same cell from different axial displacements (n = 5 cells; p = 0.39, Kruskal−Wallis test with multiple comparisons correction, data are mean and s.e.m.). c Axial photocurrent resolution as a function of digital displacement—shaded green colors denote mechanical sweeps across the optical axis for different digital displacements. d Quantification of the FWHM for the axial fit of photocurrents in CHO cells as a function of digital defocus from the focal plane (n = 5 cells, p = 0.07, data are mean and s.e.m.). e−h As in a−d, but spike probability recorded in mouse brain slices via current clamp instead of photocurrent in CHO cells recorded in voltage clamp (f: p = 0.2; h: p = 0.17, n = 3 neurons) We next asked if the axial resolution of stimulation was constant when stimulating away from the natural focal plane at z = 0. For this we measured the FWHM of the axial PPSF as a function of digital defocus. As before, we digitally moved the holographic target along the z-axis, but instead of matching the digital and mechanical offset, we stepped the objective across the entire range of the z-axis and measured the physiological response at each location. This allowed us to measure the axial resolution of photostimulation from locations distributed on either side of the optical axis. Results show that 3D-SHOT effectively confines excitation to the desired depth range throughout the 180 µm range that we sampled, as the FWHM of stimulation did not change as a function of digital defocus in z (Fig. 5c-d, CHO cells p = 0.07, neurons, Fig. 5g-h. p = 0.17, Kruskal−Wallis test). These experiments show that 3D-SHOT retains axial confinement capabilities compatible with single-cell resolution for photocurrents and spike probability while targeting neurons at any depth within the accessible volume defined by the SLM and the microscope assembly (Supplementary Fig. 4, Supplementary Note 4). Selective photostimulation of vertically stacked neurons We next considered the particularly challenging scenario of activating two vertically stacked neurons without activating a neuron located between them. To test this scenario, we computed holograms that simultaneously target two axially aligned targets vertically separated by about 80 µm along the optical z-axis, either two disc patterns with conventional 3D CGH or two copies of the CTFP target made with 3D-SHOT and a two-point hologram. We then compared the photo-induced response in a single patched cell (CHO cells and neurons). Since the typical size of a L2/3 cortical pyramidal neuron is 15–20 µm in the axial dimension (plus additional strong photocurrent contributions from an apical dendrite oriented along the optical axis)43, without an (x,y) offset we expect that two pyramidal neurons would rarely be packed closer than 80 µm in z with a third neuron positioned between them44,45,46. Thus this scenario represents a challenging, yet physiologically relevant test case. As in the previous experiment, a CHO cell or neuron was patched to record photocurrent and/or spike probability as a function of the respective displacement between the cell and the photostimulation pattern with two targets on the optical axis (Fig. 6a). With conventional holography and two disk targets, we observed a significant amount of photocurrent when the cell is located between the two targets (Fig. 6b, c), where no photocurrent is desired. Conversely, with 3D-SHOT and two similarly axially separated copies of the CTFP, no photocurrent was observed at the intermediate location, and thus spatial resolution was significantly improved (Fig. 6b, c). In neurons, the added non-linearity introduced by the cell's action potential threshold further enhanced the axial contrast in terms of spike probability (Fig. 6d, Supplementary Fig. 5, Supplementary Note 5). Single-neuron resolution with simultaneous photostimulation of two targets along the axial dimension. a Using CGH or 3D-SHOT we simultaneously photostimulated two targets separated by 80 µm along the optical z-axis. The photocurrent was recorded as a function of the respective displacement Δz between one patched cell and the volume hologram in an example CHO cell (b, n = 11 cells) or in an example cortical neuron (c, n = 5 neurons), with conventional holography (black) and with 3D-SHOT (red). d As in c, but recording spike probability instead of photocurrent for 3D-SHOT Addressing arbitrary 3D locations with precise power control Our results so far establish that 3D-SHOT allows optogenetic activation of neurons with high spatial precision in vivo and can arbitrarily target light in 3D with high spatial resolution. However the major advantage of 3D-SHOT over existing approaches is its ability to simultaneously illuminate many regions of interest located throughout a volume, each at a different axial z-depth. To demonstrate the ability of 3D-SHOT to simultaneously target disc images to 50 unique z-planes, we computed a phase-mask corresponding to a point-cloud hologram with 50 targets placed in a spiral pattern, each with a unique z-position. We measured the two-photon absorption in the vicinity of each targeted spot and in 3D with a sub-stage camera (as in Fig. 2, but repeatedly near each target), demonstrating that 3D-SHOT can illuminate this complex set of 50 targets at 50 separate axial depths (Fig. 7a). Power corrected 3D-SHOT simultaneously illuminates 50 spots. a Uncorrected simultaneous 3D-SHOT with a hologram targeting 50 spots in a spiral pattern, occupying 50 individual z-planes. Spots are color coded by normalized 2P absorption in each spot (measured with a sub-stage camera). b Correction factor computed for each spot via 3D power interpolant. c Measurements of 2P-induced fluorescence with 3D-SHOT, and a power-corrected hologram targeting the same locations as in a. d Mean intensity images of power-corrected 50 spot spiral hologram showing (z,y) (top left), (z,x) (bottom left), or (x,y) (right) projection views. e Box plots showing the variance in normalized 2P absorption from each spot within the corresponding hologram before and after power correction (p < 1 × 10−12, F-test of equality of variances, error bars correspond to range, red line is median, n = 50 spots) However, we note that while each spot in this 50 region of interest hologram clearly displays a replica image of the CTFP at each targeted point, the total two-photon energy deposited from target to target exhibits a high variance (27%). Precise power control on each target represents a critical challenge for 3D-SHOT, since both the neuronal response and the spatial resolution are related to the stimulation power (Fig. 3). In holographic optical systems such as 3D-SHOT, spatial non-uniformities in the distribution of power are related not only to well-known photon losses throughout the optical system, but also to the SLM's diffraction efficiency and its ability to accurately render specific CGH patterns. For precise control of the power distribution across multiple targets, we have developed a model of the diffraction efficiency as a function of target location, and we relied on simulations during hologram computation to compensate for the known spatial dependence of the SLM's diffraction efficiency. As for additional physical losses through the optical system, we measured the difference between expected and actual received power at 15,000 discrete points randomly distributed throughout our addressable volume (Supplementary Fig. 6). We then generated a 3D interpolant to adjust the weights for each spot in multi-target holograms (Fig. 7b). By combining simulation and experimental calibration data, our system compensates for non-uniform power distributions (Supplementary Note 6). To test the performance of this approach, we re-computed a phase mask targeting the same 50 spots with power compensation and measured 2P absorption as before. The results show a dramatic reduction in the variance (down to 9%) of the 2P absorption in each spot (Fig. 7c−e, p < 1 × 10−12 F-test), validating that 3D-SHOT used in combination with our power correction algorithm can deposit equivalent amounts of energy and achieves spatially precise 2P excitation in at least 50 distinct axial planes. Control of large volumes with high spatial resolution To test the ability of 3D-SHOT to accurately target large numbers of spots in a large volume, we measured 3D-SHOT spatial resolution in numerous contexts. We characterized individual spots within multi-target holograms as a function of increasing the numbers of targets, decreasing the distance between targets, propagation through scattering medium, and (x,y,z) position of the target. We generated holograms targeting 20–750 spots spaced 17–135 µm apart, and imaged them through 0–800 µm thick brain slices using high-dynamic range imaging with a sub-stage camera. Using principle component analysis (Supplementary Notes 7, 8), we defined which of these parameters affected the resolution of individual spots within multi-target 3D-SHOT holograms. The limiting factor for deep brain photostimulation is propagation through brain tissue, where absorption, optical aberrations, and scattering degrade spatial resolution even when operating in the infrared wavelength range. We quantified the effects of optical aberrations on the FWHM by measuring two-photon absorption in 3D through various depths of mouse brain tissue (Supplementary Figs. 7, 8). The effect of scattering on axial resolution was statistically significant after 400 µm (no scatter: 18.1 ± 5.1 µm, 400 µm brain tissue: 19 ± 5.5 µm, p = 7.34 × 10−4, Kruskal−Wallis with multiple comparisons), but the degradation of the PSF did not exceed 1 µm until 600 µm of mouse brain (600 µm brain tissue: 25.2 ± 66 µm). We also observed that performance loss was not only due to a gradual degradation of spatial resolution in deeper layers of the brain, but also to unwanted deposition of energy outside of the desired volume after passing through about 500 µm of brain tissue. This result defines the maximal operating depth for 3D-SHOT and is similar to other two-photon technologies operating in mouse brain tissue with temporal focusing47. To identify the influence of spatial location and target number on spatial resolution independently of the predominant effect of scattering, we conducted additional experiments without scattering tissue. Increasing the number of spots did not significantly degrade the axial resolution until 750 spots were simultaneously illuminated (Fig. 8a, d: 500 spots vs. 600 spots, p = 0.9, 600 spots vs. 750 spots, p < 3 × 10−5, Kruskal−Wallis with multiple comparisons). However, we observed a gradually increasing level of off-target two-photon absorption for holograms containing more than 400 targets (Fig. 8d). Since the physical location of each target is known a priori, we computed the contrast ratio by quantifying the amount of two-photon absorption in the targeted neuron-sized volumes, divided by the total two-photon absorption in the entire volume of interest. We estimated that the maximal number of targets in a single hologram to be 380–500, assuming 1–5% background illumination. Contrast further degraded as the number of targets was further increased (Fig. 8e). Notably, this decrease in resolution is not a feature of 3D-SHOT per se, but relates to the overall quality of point cloud holograms, which is limited by the pixel density of the SLM that we employed. Using an SLM with a higher pixel count should allow more targets to be encoded before significant loss of contrast occurs. Spatial resolution with simultaneous targets throughout a large volume. a−b Example 3D renderings from tomographic images of two-photon absorption from single-shot holograms targeting increasing numbers of randomly distributed spots. The FWHMs of the two-photon response was computed for each target, c radially, and d axially. Results show that spatial resolution and axial confinement are not significantly degraded by increasing the number of simultaneous targets in any given hologram. e The contrast ratio of the holograms was quantified as a function of the number of targets, and shows that contrast, rather than resolution determines the total number of targets that can be photostimulated in a single hologram. f 3D recordings of various scaling of the same point cloud were made to evaluate density as a possible factor affecting spatial resolution (error bars correspond to range, red line is median) Furthermore, we also observed that the FWHM depends on the physical location of targets (Supplementary Fig. 9, Supplementary Note 9). We identified target location along the optical axis to be the dominant factor, d(FWHM)/dz = 1.8 × 10−2, which corresponds to known asymmetric geometrical aberrations and magnification properties when attempting to focus light on either side of the natural focal plane of the microscope objective. We did not observe significant changes in resolution for multi-target holograms as a function of (x,y) position, or as a function of the spacing of spots within a hologram (radial p = 0.17, axial p = 0.29, Kruskal−Wallis with multiple comparisons, Fig. 8f, Supplementary Fig. 9b, d). This independence is bounded by the limiting case in which spots are targeted within one spot-size (specified by the CTFP) of each other, whereupon they constructively interfere and form a continuous area of excitation. Overall, as with CGH, the performance of 3D-SHOT is limited by either the SLM, the total available laser power, or the microscope system. Altogether, these determine the accessible volume (Supplementary Fig. 4) and the number of neurons that can be simultaneously illuminated with the desired spatial resolution. Here, using an SLM with 600 × 800 pixels, we characterized single shot photostimulation of up to 750 targets (limited by laser power) with degradation of resolution within a 0.034 mm3 volume (350 × 350 × 280 µm, Fig. 8), and improvement of an order of magnitude over previous work using multi-level TF42. Volumetric optogenetics at high spatial resolution We next tested the ability of 3D-SHOT to stimulate ensembles of cells distributed in a volume with high spatial resolution. To quantify the PPSF in the context of ensemble stimulation, we generated holograms simultaneously targeting multiple regions of interest distributed throughout the addressable volume and obtained whole-cell recordings from CHO cells while mechanically displacing the multi-target hologram (Fig. 9a). Consistent with direct measurements of 2P absorption, we observed no changes in the lateral (Fig. 9b) or axial (Fig. 9c) PPSF photocurrent FWHM even when simultaneously stimulating 50 regions of interest (p = 0.64 Kruskal−Wallis). Spatially precise volumetric optogenetics with 3D-SHOT. a Schematic demonstrating 3D-SHOT stimulation of a CHO cell with a single spot in a hologram targeting multiple spots in the volume. The objective was moved to measure the physiological point spread function via voltage clamp recordings. b Normalized photocurrent and quantification of FWHM as a function of radial displacement for holograms targeting 1–50 spots (data represent mean ± s.e.m. of n = 3 cells, p = 0.39, Kruskal−Wallis test with multiple comparison correction). c As in b but axially (n = 3 cells, p = 0.64). d Schematic showing whole cell recordings in brain slices while stimulating multiple targets. To measure spatial resolution of 3D-SHOT, a series of new holograms was computed that displaced only the center target while holding all other spots stationary. e Photocurrent measurements from brain slices for radial digital offset of a center spot at several stimulation powers (colors, 0.5–2 W), quantification of FWHM as a function of stimulation power through the objective (data are mean ± s.e.m. of n = 5 neurons, p = 0.69, Kruskal−Wallis test with multiple comparison). f As in e but axially (p = 0.11). g As in d, but for in vivo loose patch recordings; example image of a 2P guided patch of a L2/3 pyramidal neuron expressing ST-ChrimsonR-mRuby2 (scale bar = 50 µm). h Radial and axial physiological point spread functions showing resolution of 3D-SHOT while targeting an ensemble of 21 neurons while only the center spot was moved (data represent mean and s.e.m. from an example neuron). i Bar graph showing mean ± s.e.m. of the radial and axial PPSFs from targeted in vivo patch while stimulating 21 cells (n = 17 radial and n = 18 axial). j Scatter plot showing axial FWHM vs. the depth below the cortical surface of individual neurons (axial PPSF is from experiments with 1 or 21 holograms, n = 24). Red dot indicates the mean values, and the black line is the line of best fit—within this range, cortical depth can explain none of the variance in axial FWHM (R 2 = −0.03) We next tested volumetric optogenetics resolution in neurons by eliciting photocurrents with a single hologram targeting 21 spots, each in a unique z-plane. Instead of mechanically displacing the objective, we computed holograms where only one target was digitally displaced, and the others held in place (Fig. 9d). This approach directly tests the spatial resolution of the target spot while accounting for contamination from non-target spots. These experiments revealed that off-target spots or general loss of contrast do significantly affect photocurrents (Fig. 9e−f). We repeated this experiment for various average power levels, demonstrating that 3D-SHOT is capable of distributing even very high levels of two-photon light (up to 2 Watts of average power) into spatially confined packets distributed in true 3D throughout a large volume (Fig. 9e−f), and simultaneously (Supplementary Fig. 10). To validate spatially precise ensemble stimulation in vivo, we used two-photon targeted loose patch in anesthetized mice. As before, we generated holograms that targeted 21 random spots placed throughout a 250 × 250 × 200 µm3 volume, and used the SLM to digitally displace the spot targeting the patched neuron while holding the other spots stationary. In this context, we measured a radial spiking PPSF of 13 ± 2 µm and an axial PPSF of 29 ± 5 µm (n = 18). These values are very similar to measurements obtained with only one hologram (Fig. 4), and are narrower than the resolution recorded in brain slices due to the additional non-linearity of the action potential threshold (Fig. 9g−i). As predicted from measurements of PSFs through scattering brain slices, there was no relationship between the axial resolution and the depth of the neurons from which we recorded (113–323 µm below the pial surface, Fig. 9j). Finally, we used a simple model (Supplementary Note 9) to assess expected off-target activation during ensemble stimulation using 3D-SHOT. We randomly placed neurons throughout a 400 × 400 × 400 µm3 volume of brain tissue at physiological density48 and superimposed 3D Gaussian fits of our PPSF on randomly selected target neurons. This model revealed that even while targeting 500 neurons, on average, non-target neurons are unlikely to be activated (Supplementary Fig. 11a, b). The number of non-target neurons predicted to be active was only a small fraction of the target number, and increasing the number of spots linearly increased the number of activated non-target neurons, indicating that contrast should remain high past 500 spots (Supplementary Fig. 11c). Finally, most of the expected off-target spikes evoked by volumetric 3D-SHOT stimuli resulted from neurons with low spike probabilities, indicating that few off-target neurons should reliably follow repetitive stimulation of a particular neuronal ensemble (Supplementary Fig. 11d). In this study, we have demonstrated and validated 3D-SHOT, a method that enables holography and temporal focusing to operate in full 3D with a single SLM. This technology is the first to offer simultaneous targeting of custom neuronal ensembles located anywhere within a large operating volume at cellular resolution, and with simultaneous photo-activation of the entire neuron's soma. We have demonstrated the ability of 3D-SHOT to target neurons at high resolution in vivo in mouse brains, and we have shown optogenetic control in a large volume corresponding to the width of multiple cortical columns in mice with single neuron spatial resolution. Our technology relies on a custom temporally focused pattern (CTFP), which is a fixed-size temporally focused pattern, engineered to enable simultaneous illumination of the entire neuronal cell body, yet confined in a small enough volume to prevent inadvertent photostimulation of non-targeted neurons. We have also engineered the CTFP's phase, which was so far an unused degree of freedom in temporal focusing systems. By patterning the phase, here with a lens (L C), we made holography and temporal focusing compatible by improving the diffraction efficiency at the SLM in a way that allows simultaneous processing of all spectral components of the pulsed light source with a single SLM frame. Spatial resolution in the lateral plane is mostly limited by the numerical aperture of the objective, as in conventional microscopy systems49. This criterion is not a significant limiting factor for wide-area targeting of neurons and most future applications in neuroscience. With conventional holography, defocusing (by simple propagation) is the only available mechanism to attenuate light intensity and confine the nonlinear response near the desired target20. Axial resolution being inverse proportional to NA2, depth selectivity requires high-NA objectives, and generally permits single neuron spatial resolution only in small operating volumes28. With 3D-SHOT, temporal focusing eliminates this trade-off between spatial resolution and operating volume: cellular resolution along the z-axis is made possible even with less expensive lower NA objectives, and with smaller magnifications enabling much larger fields of view. The CTFP stretches pulses in time above or below the primary focus, and the nonlinear response decreases with depth regardless of the dimensions of the targeted area in the focal plane. Attenuation of photostimulation away from the targeted neurons is now made possible by the combined effects of physical defocusing and temporal pulse stretching, which are two independent effects, mutually contributing to improving spatial resolution and power stability. As predicted by simulations and recordings of two-photon absorption in the CTFP, our experiments in CHO cells and neurons show that the physiological spatial resolution, measured in terms of photocurrent, is not only narrower for 3D-SHOT than for conventional holography, but its FWHM is also less sensitive to power variations. This convenient property of the CTFP enables the user to consider conservative estimations of the required power levels to ensure action potentials can be triggered without sacrificing spatial resolution. Indeed, one ultimate goal for multiphoton photostimulation in brain tissue is to elicit action potentials in many individual neurons with single-cell resolution simultaneously. Recording in voltage clamp, photocurrents linearly reflected the location of the holographic stimuli. When recording action potentials in brain slices or in vivo, the physiological response of a targeted neuron is subject to a non-linearity imposed by action potential threshold. In vivo loose patch recordings and measurement of axial confinement through scattering brain tissue confirm that 3D-SHOT remains efficacious and spatially precise when operating in mouse brains. Using 3D-SHOT, we reliably measured in vivo spiking point spread functions of less than 30 µm axially and about 10 µm radially, even when stimulating up to 21 neurons. As these values closely match the physical size of the soma and proximal dendrites of cortical L2/3 pyramidal neurons, axial PPSFs of about 30 µm have previously been considered consistent with achieving single-neuron spatial resolution9, 26. However, while the spatial resolution of patterned optogenetic photostimulation is determined by the optical point spread function, it is also specified by other factors like the subcellular location of opsin on a neuron50, 51, the density of opsin-expressing neurons, and stimulation frequency and duration convolved with variation in intrinsic neuronal excitability and opsin expression levels. Therefore, in future studies it will be useful to consider single-cell spatial resolution not as a binary switch, but rather, as a continuous variable defined by the probability of generating off-target spikes given by the three-axis physiological point spread function, the number and physical location of other opsin-expressing neurons, and the distributions of opsin-expression and intrinsic excitability. Modeling studies with our physiological point spread function show that even with several hundred targets, while the targeted population is reliably photo-stimulated on each trial, the off-target activated neurons would be similar to very slightly elevated background activity. Notably, this form of analysis of spatial resolution is also relevant for other forms of patterned optogenetic photostimulation. For photostimulation applications, the current limiting factor for the number of neurons 3D-SHOT can simultaneously control is available laser power and opsin sensitivity, both of which are likely to improve in the future. However, we were able to characterize performance via recordings of two-photon induced fluorescence with a sensitive fluorescent monolayer and camera allowing us to predict that with more powerful laser technology, the current technique will be able to simultaneously activate up to 300–600 neurons per SLM frame with minimal off-target activation, depending on the acceptable levels of contrast between targeted and background volumes. This number is limited by the resolution of the SLM, currently at 600 × 800 pixels for 3D hologram synthesis in our system, but higher density SLMs are commercially available with tradeoffs between speed, resolution and diffraction efficiency. The SLM can be chosen to meet the demands of specific neurobiological applications. In this study, we chose a lens for the CTFP for simplicity, but also because a spherical phase mask provides an analytical expression for the CTFP in space and time. The CTFP dimensions may be adjusted for specific neuronal cell types for brain areas to match the characteristic dimensions of neurons. In specific instances when a circuit is composed of neurons with very different diameters (for example, the cerebellar cortex) a second SLM could be used not only to apply other types of phase patterns to the CTFP to further improve the diffraction efficiency, but also to rapidly change the CTFP dimensions and create custom target shapes in any number of desired 3D locations. However, even with a second SLM, the CTFP will be identical for all stimulation targets at any given moment in time. In the future, the implementation of 3D-SHOT in combination with functional imaging of neural activity will enable real-time manipulation of functionally defined neural ensembles with high specificity in both space and time, paving the way for a new class of experiments aimed at understanding the neural code. All animal experiments were performed in accordance with the guidelines and regulations of the Animal Care and Use Committee of the University of California, Berkeley. Two-photon absorption characterization CGH and 3D-SHOT characterization experiments were performed by recording two-photon induced fluorescence on a calibration slide with an inverted microscope. We used a Basler ACa2500 camera, and a Leitz 6.3X Objective to map the entire operational range of the SLM on the camera sensor. We placed two infrared filters along the light-path to eliminate the remaining laser light, leaving only the fluorescence signal in the visible range to be recorded by the camera sensor. For power characterization, we used thick autofluorescent plastic slides (Chroma) to simultaneously collect fluorescence light within the entire volume of excitation from a single focused image. For more precise 3D characterization of two-photon absorption, we used a custom made thin film of fluorescent paint (Tamiya Color TS-36 fluorescent red) sprayed on a microscope glass slide. Here, by mechanically displacing the image acquisition set-up and the photo-excitation pattern (either from CGH or 3D-SHOT), we recorded two-photon absorption in 3D by digitally assembling slice images captured at various depth levels (with micro-metric mechanical increments). The imaging system was calibrated spatially to confirm the effective magnification of the imaging system, and with single target recordings at known power levels to account for non-uniformity in optical transmission across the field of view of the camera. Up to three recordings at various laser power were made to digitally increase the effective dynamic range of the acquisition process. The FWHM was computed first by identifying isolated targets (threshold-based detection) within multi-target holograms, then by computing projections along any axis of interest and by fitting Gaussian profiles to the resulting data. Biological samples preparation The cation channelrhodopsins ChrimsonR and Chronos52; accession: KF992040.1 generated by gene synthesis (Genewiz, South Plainfield, NJ) and anion opsin GtACR153, provided by Dr. John Spudich, University of Texas Health Science Center, Houston) were fused to mRuby2 at the C-terminus at a NotI site (Chronos) or AgeI site (GtACR1) and subcloned into the pCAGGS expression vector between KpnI and XhoI restriction sites by In-Fusion cloning (Clontech, Mountain View, CA). In order to target the opsins to the soma and proximal dendrites of neurons, the sequence encoding the proximal restriction and clustering domain of the Kv2.1 voltage-gated potassium channel consisting of amino acids 536–60050, 51, 54 was codon optimized, synthesized (Integrated DNA Technologies, Coralville, IA) and inserted at the C-terminus of mRuby2 between BsrGI and XhoI restriction sites by In-Fusion cloning. Chinese hamster ovary (CHO) cells were maintained in Ham's F-12 medium with l-glutamine (Thermo Fisher Scientific, Waltham, MA) containing 10% fetal bovine serum in a humidified incubator at 37 °C and 5% CO2. One day prior to transfection, cells were plated on coverglass (Carolina Biological Supply, Burlington, NC) coated with poly-D-lysine (Sigma-Aldrich, St. Louis, MO) so as to reach a confluence of about 80% and transfected with the expression plasmid encoding either Chronos or GtACR1 using Fugene HD (Promega Corporation, Madison, WI) and recorded 24–48 h post transfection. In utero electroporations Electroporations were performed on pregnant CD1 (ICR) mice (E15, Charles River ca. SC:022). For each surgery, the mouse was initially anesthetized with 5% isoflurane and maintained with 2.5% isoflurane. The surgery was conducted on a heating pad, and warm sterile PBS was intermittently perfused over the pups throughout the procedure. A micropipette was used to inject ~2 µl of recombinant DNA at a concentration of 2 µg/µl and into the left ventricle of each neonate's brain (typically DNA encoding opsins were doped with plasmids expressing GFP or mRuby3 at a concentration of 1:20 to facilitate screening for expression). Fast-green (Sigma-Aldrich) was used to visualize a successful injection. Following successful injection, platinum-plated 5 mm Tweezertrodes (BTX Harvard Apparatus ca. 45-0489) were positioned along the frontal axis across the head of the neonate with the positive electrode of the tweezers positioned against the left side of the head. An Electro Square Porator (BTX Harvard Apparatus ca. 45-0052) was used to administer a train of 5 × 40 mV pulses with a 1 s delay. After the procedure, the mouse was allowed to recover and come to term, and the delivered pups were allowed to develop normally. Neonatal injections were performed as described55. P0-4 EMX1-Cre mice were injected with AAV9-CAG-flexed-ST-ChrimsonR-mRuby2 obtained from the UC Berkeley Vision Science Core Gene Delivery Module. Viral aliquots were loaded into a Drummond Nanoject injector. Neonates were briefly cryo-anesthetized and placed in a head mold. With respect to the lambda suture coordinates for S1 injections were 2.0 mm AP, 3.0 mm L, 0.3 mm DV. Slice electrophysiology We used radial slices from the somatosensory barrel cortex cut along the thalamo-cortical plane or coronal cortical sections. The hemisphere was trimmed on both the anterior and posterior side of barrel cortex with coronal cuts, placed on its anterior side and a cut was made with a scalpel so that much of barrel cortex lay in a plane parallel to cut. The surface of this last cut was glued to the slicer tray. The preparation was aided by the use of epifluorescent goggles to visualize the expressing area. Two to three 300–500 µm slices were prepared. Cortical slices (400 µm thick) were prepared56 from the transfected hemispheres of both male and female mice aged P15−P40 using a DSK Microslicer in a reduced sodium solution containing (in mM) NaCl 83, KCl 2.5, MgSO4 3.3, NaH2PO4 1, glucose 22, sucrose 72, CaCl2 0.5, and stored submerged at 34 °C for 30 min, then at room temperature for 1–4 h in the same solution before being transferred to a submerged recording chamber maintained at 30–32 °C by inline heating in a solution containing (in mM) NaCl 119, KCl 2.5, MgSO4 1.3, NaH2PO4 1.3, glucose 20, NaHCO3 26, CaCl2 2.5. CHO cells were recorded in the same media, but with the addition of 5–10 μM all-trans-retinal (Sigma-Aldrich, St. Louis, MO). Recordings were performed in either a Cs+ based internal for voltage clamp recordings (CsMeSO4 135 mM, NaCl 8 mM, HEPES 10 mM, Na3GTP 0.3 mM, MgATP 4 mM, EGTA 0.3 mM, QX-314-Cl 5 mM, TEA-Cl 5 mM) or a potassium gluconate based internal for current clamp recordings (k-gluconate 135 mM, NaCl 8 mM, HEPES 10 mM, Na3GTP 0.3 mM, MgATP 4 mM, EGTA 0.3 mM). In most experiments, Alexa Fluor 488 or 594 (Thermo-Fisher) was dissolved into the internal solution to enable morphological recovery. Data were analyzed from recordings in which series resistance remained stable and below 30 MΩ. For measuring photocurrent, cells were included if they had holographic currents > 100 pA; for measurements of action potentials cells were included if holographic stimuli could induce spiking within 200 ms. Data were acquired and filtered at 2.2 kHz using a Multiclamp 700B Amplifier (Axon Instruments) and digitized at 20 kHz (National Instruments). All data were acquired using custom written MATLAB (Mathworks) software. In vivo patch Two-photon guided patch recordings were performed from adult both male and female (35 days or older) wild-type (WT) electroporated adult mice or neonatally injected EMX1-Cre mice (Jackson Labs # 005628). Mice were anesthetized with isofluorane and a custom steel headplate was surgically implanted over the region of interest. A large (2–4 mm diameter) craniotomy was made over the expression site, washed with HEPES ACSF (in mM: NaCl 125, KCl 3, HEPES 10, glucose 10, MgSO4×7 H2O2, CaCl2×2 H2O2, set to 300–310 mOsm and pH 7.4) and covered with agarose gel (1%) maintained at 45 °C prior to application. Mice were anesthetized with 1.5 g/kg urethane and 2 µg/kg chlorprothexane before being transferred to recording rig. Body temperature was maintained with a thermal heating pad (FHC) at 37 °C throughout the experiment. Supplementary isofluorane (0–1%) was used to maintain an even level of sedation during recordings, and additional urethane and chlorprothexane was administered every 2–4 h as needed. Cells were identified under a Sutter MOM 2P microscope. Data were acquired using a Multiclamp 700B Amplifier (Axon Instruments) and digitized at 20 kHz (National Instruments). Data was digitally band pass filtered 0.5–2.2 kHz for identification of spikes. All data were acquired using custom written MATLAB (Mathworks) software. Cells were included for analysis if they were spontaneously active and those spikes were sufficiently larger than the noise (>4 Standard deviations of the noise). Furthermore, cells had to pass a 1 P expression check by firing action potentials in response to brief 1 P LED illumination (Lumencore, Sola SE). Cells were holographically stimulated with increasing stimulus durations and laser power until action potentials were reliably generated at 1 Hz stimulation frequency. Spike probability or normalized firing rate was calculated by normalizing the number of action potentials evoked by each stimulus as a function of target position. For in vivo experiments, the minimum number of spikes that occurring during stimulation was subtracted to account for the spontaneous firing rate of the cell. Holographic replication of the CTFP by 3D optical convolution Let ${\rm{F}}:A\left( {x,y} \right) \to \widetilde A\left( {{k_x},{k_y}} \right)$ denote the 2D Fourier transform operator, and (x,y) the lateral coordinates. The relationship between the CTFP field A C (Supplementary Fig. 1), and the field at the input face of the SLM for each component of the spectrum $\Delta k$ is given by: $${A_{\rm{C}}}\left( {x,y,\Delta k} \right) = {\rm{F}}[A_{\rm{D}}^ - ]\left( {\frac{x}{{\lambda {f_4}}},\frac{y}{{\lambda {f_4}}},\Delta k} \right)$$ We adjusted the phase pattern (focal length of lens L C) at the diffraction grating so that the dimensions of the beam $A_{\rm{D}}^ -$ matched the dimensions of the SLM's short axis to optimize the number of pixels that can be used for holography (Supplementary Fig. 2). The SLM applies a phase mask, φ, and the reflected beam becomes: $$A_{\rm{D}}^ + \left( {x,y,\Delta k} \right) = A_{\rm{D}}^ - \left( {x,y,\Delta k} \right){e^{i\varphi \left( {x,y} \right)}}$$ Hence: $${\rm{F}}\left[ {A_{\rm{D}}^ + } \right] = {\rm{F}}\left[ {A_{\rm{D}}^ - } \right] \otimes {\rm{F}}\left[ {{e^{i\varphi }}} \right]$$ where ⊗ represents the 2D convolution product, and F represents the Fourier transform in the (x,y) plane. Lens L 5 applies another optical Fourier transform to build the corresponding hologram, which is further demagnified with the tube lens L 6 and the microscope objective L 7 to form the final hologram into the brain. The field A E is given by: $${A_{\rm{E}}}\left( {x,y,\Delta k} \right) = {\rm{F}}[A_{\rm{D}}^ + ]\left( {\frac{x}{{\lambda {f_5}}},\frac{y}{{\lambda {f_5}}},\Delta k} \right){e^{i\varphi \left( {x,y} \right)}}$$ By combining Equations 2, 4, and 5 we find: $${A_{\rm{E}}}\left( {x,y,\Delta k} \right) = {A_{\rm{C}}}\left( {\frac{{{f_4}x}}{{{f_5}}},\frac{{{f_4}y}}{{{f_5}}},\Delta k} \right) \otimes {\rm{F}}[{e^{i\varphi }}]\left( {\frac{x}{{\lambda {f_5}}},\frac{y}{{\lambda {f_5}}}} \right)$$ We deduce the field in 3D by applying Fresnel propagation to each component of the pulse spectrum: $${A_{\rm{E}}}\left( {x,y,z,\Delta k} \right) = {A_{\rm{E}}}\left( {x,y,\Delta k} \right) \otimes h\left( {x,y,z} \right)$$ where $h\left( {x,y,z} \right) = {e^{ikz}}{e^{\frac{{ik}}{{2z}}\left( {{x^2} + {y^2}} \right)}}$ is the Fresnel propagation kernel. The associativity of the convolution product yields the 3D-SHOT principle where the field to be demagnified and imaged into the sample, ${A_{\rm{E}}}\left( {x,y,z,\Delta k} \right)$, is a convolution of the CTFP, ${A_{\rm{C}}}( {\frac{{{f_4}x}}{{{f_5}}},\frac{{{f_4}y}}{{{f_5}}},\Delta k} )$, and the 3D point cloud hologram object, ${\rm{F}}[ {{e^{i\varphi }}} ]( {\frac{x}{{\lambda {f_5}}},\frac{y}{{\lambda {f_5}}}} ) \otimes h( {x,y,z} )$, corresponding to the phase mask, $\varphi ,$ placed on the SLM. $${A_{\rm{E}}}\left( {x,y,z,\Delta k} \right) = {A_{\rm{C}}}\left( {\frac{{{f_4}x}}{{{f_5}}},\frac{{{f_4}y}}{{{f_5}}},\Delta k} \right) \otimes \left[ {{\rm{F}}\left[ {{e^{i\varphi }}} \right]\left( {\frac{x}{{\lambda {f_5}}},\frac{y}{{\lambda {f_5}}}} \right) \otimes h\left( {x,y,z} \right)} \right]$$ Identification of factors affecting the FWHM by principal component analysis To identify the hologram and brain tissue properties affecting spatial resolution, we used a simple form of principal component analysis (PCA), (Supplementary Notes 7, 8). We consider a diverse data set of multiple holograms for which we gather for each target relevant parameters such as x,y,z location, total number of other targets, brain tissue depth, and distance to the nearest neighbor in a p by k+1 matrix, A, (a last column of ones is used to account for a constant offset). From volume recordings of all the holograms, we record either the radial or axial FWHM in a p by 1 data matrix D. We then compute k+1 by 1 matrix X that minimizes \|\|D-AX\|\|2. With a diverse enough data set, A×A is invertible and the optimal solution is given by X = (A×A)−1A×D, The components of X represents the respective contributions of each parameter to the FWHM, with the last one being the constant offset. All statistical analysis was performed with Matlab (Mathworks). The tests performed were Mann−Whitney U-test for two-sample comparisons, Kruskal−Wallis test with multiple comparisons for multiple sample comparison, and F-test of equality of variances. 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H.A. is a New York Stem Cell Foundation Robertson Investigator and acknowledges support from the Arnold and Mabel Beckman Foundation, the New York Stem Cell Foundation, and from the NIH core grant P30 EY003176. A.M. acknowledges support by NINDS of the NIH under award number F32NS095690-01. I.O. acknowledges the support of the Simon's Foundation Collaboration for the Global Brain award 415569. This work was supported by National Institutes of Health BRAIN R21 Grant EY027597-01 and Defense Advanced Research Projects Agency Contract No. N66001-17-C-4015 to H.A. and L.W. Nicolas C. Pégard and Alan R. Mardinly contributed equally to this work. Department of Molecular and Cell Biology, 205 Life Science Addition, University of California, Berkeley, CA, 94720, USA Nicolas C. Pégard, Alan R. Mardinly, Ian Antón Oldenburg, Savitha Sridharan & Hillel Adesnik Department of Electrical Engineering and Computer Science, 514 Cory Hall, University of California, Berkeley, CA, 94720, USA Nicolas C. Pégard & Laura Waller Helen Wills Neuroscience Institute, 132 Barker Hall #3190, University of California, Berkeley, CA, 94720, USA Hillel Adesnik Nicolas C. Pégard Alan R. Mardinly Ian Antón Oldenburg Savitha Sridharan Laura Waller N.C.P., L.W., and H.A. developed the principle of 3D-SHOT. N.C.P. assembled experimental device, and performed experimental recordings and simulations for two-photon absorption. A.R.M. and H.A. designed and performed electrophysiology experiments in mouse brain slice and CHO cells. A.R.M. designed and performed in vivo electrophysiology experiments. N.C.P., A.R.M., and I.A.O., wrote code and helped developed software for experimental control. S.S. performed cell culture and transfections. N.C.P., A.R.M., and H.A. wrote the manuscript. Correspondence to Hillel Adesnik. Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Pégard, N.C., Mardinly, A.R., Oldenburg, I.A. et al. Three-dimensional scanless holographic optogenetics with temporal focusing (3D-SHOT). Nat Commun 8, 1228 (2017). https://doi.org/10.1038/s41467-017-01031-3 Probing neural codes with two-photon holographic optogenetics Lamiae Abdeladim Nature Neuroscience (2021) Nonmechanical parfocal and autofocus features based on wave propagation distribution in lensfree holographic microscopy Agus Budi Dharmawan Shinta Mariana Andreas Waag Dual-comb hyperspectral digital holography Edoardo Vicentini Zhenhai Wang Nathalie Picqué Nature Photonics (2021) A database and deep learning toolbox for noise-optimized, generalized spike inference from calcium imaging Peter Rupprecht Stefano Carta Rainer W. Friedrich Functional ultrasound imaging of the spreading activity following optogenetic stimulation of the rat visual cortex M. Provansal G. Labernède F. 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Image Enhancement by S-Shaped Curves Using Successive Approximation for Preserving Brightness Damian Tohl, Jim Li For image contrast enhancement, an S-shaped transfer function has been developed to better match the human vision system with an associated median brightness subtraction and addition method to preserve the median brightness of an image. However, this median brightness preservation method will cause clipping of the dynamic range of images resulting in a loss of contrast. Moreover, preserving the mean or median image brightness will sometimes produce a different result without a consistent preference. In this letter, we have developed a method to preserve either the mean or median image brightness by shifting the intersection point of S-shaped curves along the ${\mathbf y=x}$ line by successive approximation. To improve computational efficiency, two newly derived equations have been proposed to reduce the number of optimum control parameters from four to two for solving the S-shaped curves. In addition, our proposed method can alter the image brightness without causing clipping at either ends of the intensity range. Our proposed brightness preservation method can also be applied to a video sequence to change its brightness without causing any flickering. It has been shown that our proposed method can produce visually pleasing enhanced images and videos. https://doi.org/10.1109/LSP.2017.2718018 Brightness preservation image and video enhancement S-shaped curve 10.1109/LSP.2017.2718018 Fingerprint Dive into the research topics of 'Image Enhancement by S-Shaped Curves Using Successive Approximation for Preserving Brightness'. Together they form a unique fingerprint. Image enhancement Engineering & Materials Science Luminance Engineering & Materials Science Flickering Engineering & Materials Science Computational efficiency Engineering & Materials Science Transfer functions Engineering & Materials Science Tohl, D., & Li, J. (2017). Image Enhancement by S-Shaped Curves Using Successive Approximation for Preserving Brightness. IEEE SIGNAL PROCESSING LETTERS, 24(8), 1247-1251. [7954739]. https://doi.org/10.1109/LSP.2017.2718018 Tohl, Damian ; Li, Jim. / Image Enhancement by S-Shaped Curves Using Successive Approximation for Preserving Brightness. In: IEEE SIGNAL PROCESSING LETTERS. 2017 ; Vol. 24, No. 8. pp. 1247-1251. @article{9ae2dc27bf1a4cb991f4a0e8f0bc91f2, title = "Image Enhancement by S-Shaped Curves Using Successive Approximation for Preserving Brightness", abstract = "For image contrast enhancement, an S-shaped transfer function has been developed to better match the human vision system with an associated median brightness subtraction and addition method to preserve the median brightness of an image. However, this median brightness preservation method will cause clipping of the dynamic range of images resulting in a loss of contrast. Moreover, preserving the mean or median image brightness will sometimes produce a different result without a consistent preference. In this letter, we have developed a method to preserve either the mean or median image brightness by shifting the intersection point of S-shaped curves along the ${\mathbf y=x}$ line by successive approximation. To improve computational efficiency, two newly derived equations have been proposed to reduce the number of optimum control parameters from four to two for solving the S-shaped curves. In addition, our proposed method can alter the image brightness without causing clipping at either ends of the intensity range. Our proposed brightness preservation method can also be applied to a video sequence to change its brightness without causing any flickering. It has been shown that our proposed method can produce visually pleasing enhanced images and videos.", keywords = "Brightness preservation, image and video enhancement, S-shaped curve, successive approximation", author = "Damian Tohl and Jim Li", doi = "10.1109/LSP.2017.2718018", journal = "IEEE SIGNAL PROCESSING LETTERS", Tohl, D & Li, J 2017, 'Image Enhancement by S-Shaped Curves Using Successive Approximation for Preserving Brightness', IEEE SIGNAL PROCESSING LETTERS, vol. 24, no. 8, 7954739, pp. 1247-1251. https://doi.org/10.1109/LSP.2017.2718018 Image Enhancement by S-Shaped Curves Using Successive Approximation for Preserving Brightness. / Tohl, Damian; Li, Jim. In: IEEE SIGNAL PROCESSING LETTERS, Vol. 24, No. 8, 7954739, 08.2017, p. 1247-1251. T1 - Image Enhancement by S-Shaped Curves Using Successive Approximation for Preserving Brightness AU - Tohl, Damian AU - Li, Jim N2 - For image contrast enhancement, an S-shaped transfer function has been developed to better match the human vision system with an associated median brightness subtraction and addition method to preserve the median brightness of an image. However, this median brightness preservation method will cause clipping of the dynamic range of images resulting in a loss of contrast. Moreover, preserving the mean or median image brightness will sometimes produce a different result without a consistent preference. In this letter, we have developed a method to preserve either the mean or median image brightness by shifting the intersection point of S-shaped curves along the ${\mathbf y=x}$ line by successive approximation. To improve computational efficiency, two newly derived equations have been proposed to reduce the number of optimum control parameters from four to two for solving the S-shaped curves. In addition, our proposed method can alter the image brightness without causing clipping at either ends of the intensity range. Our proposed brightness preservation method can also be applied to a video sequence to change its brightness without causing any flickering. It has been shown that our proposed method can produce visually pleasing enhanced images and videos. AB - For image contrast enhancement, an S-shaped transfer function has been developed to better match the human vision system with an associated median brightness subtraction and addition method to preserve the median brightness of an image. However, this median brightness preservation method will cause clipping of the dynamic range of images resulting in a loss of contrast. Moreover, preserving the mean or median image brightness will sometimes produce a different result without a consistent preference. In this letter, we have developed a method to preserve either the mean or median image brightness by shifting the intersection point of S-shaped curves along the ${\mathbf y=x}$ line by successive approximation. To improve computational efficiency, two newly derived equations have been proposed to reduce the number of optimum control parameters from four to two for solving the S-shaped curves. In addition, our proposed method can alter the image brightness without causing clipping at either ends of the intensity range. Our proposed brightness preservation method can also be applied to a video sequence to change its brightness without causing any flickering. It has been shown that our proposed method can produce visually pleasing enhanced images and videos. KW - Brightness preservation KW - image and video enhancement KW - S-shaped curve KW - successive approximation UR - http://ieeexplore.ieee.org/document/7954739/ U2 - 10.1109/LSP.2017.2718018 DO - 10.1109/LSP.2017.2718018 JO - IEEE SIGNAL PROCESSING LETTERS JF - IEEE SIGNAL PROCESSING LETTERS Tohl D, Li J. Image Enhancement by S-Shaped Curves Using Successive Approximation for Preserving Brightness. IEEE SIGNAL PROCESSING LETTERS. 2017 Aug;24(8):1247-1251. 7954739. https://doi.org/10.1109/LSP.2017.2718018	CommonCrawl
Change in speed of a satellite Suppose there's some satellite orbiting the earth in circular motion. Suppose there's an asteroid that hits the satellite in the same direction as the instant velocity vector of the satellite. The collision causes the satellite to move faster. And here are my 2 questions: 1) Why will the satellite start moving in an elliptical orbit? Is it because its speed has increased, but the centripetal acceleration hasn't? It seems intuitively right for me, because then the satellite covers larger path before the centripetal acceleration causes the change in the velocity vector direction. 2) However, what confuses me is the fact that the centripetal acceleration is dependent on the velocity ($v^2/r$). On the other hand, since the force of gravity exerted on the satellite by the earth, hasn't changed after the hit (if we neglect asteroid's mass or suppose it just fell down after the hit), because there was no change in the radius (i suppose) of the circular path, there was no change in the centripetal acceleration. So these two arguments contradict each other. Where am I wrong? What I miss here? newtonian-mechanics newtonian-gravity acceleration satellites centripetal-force Bzazz grjj3grjj3 If an object is moving in a circular motion, its velocity $\vec{v}$ changes. The centripetal acceleration is just a formula that gives you the length of the derivative $\frac{d\vec{v}}{dt}$ which is the acceleration. It must be caused by some force, according to Newton's second law. If you are holding the object with a rope, then it is the tension of the rope, if it is a satelite on a circular orbit, then the force is of gravitational nature. When the asteroid hits the satellite, $\vec{v}$ changes, while the gravitional force remains the same. So, the force now creates the same acceleration, but now it does not coincide with 'centripetal acceleration' for this speed (which is just a number characterizing the orbit, not the object). This simply means that the object will leave the circular orbit, because its acceleration and speed now correspond to a different trajectory. This trajectory happens to be elliptic/parabolic/hyperbolic depending on the speed. These cases can be distinguished by total energy -- $E<0$, $E=0$, $E>0$ respectively. Peter KravchukPeter Kravchuk $\begingroup$ Thank you. So basically, my mistake was that I thought that $v^2 / r$ is what determines the force, but this only holds for a circular motion. And if the "boost" in the speed is not caused by a force, it can't describe the force itself/doesn't influence the force. Thank you very much, zemlyak! $\endgroup$ – grjj3 Apr 28 '13 at 20:11 $\begingroup$ @grjj3 You are welcome.) "Boost" is caused by a force created by the asteroid, but yes, this force is unrelated to gravity. $\endgroup$ – Peter Kravchuk Apr 28 '13 at 20:17 Not the answer you're looking for? Browse other questions tagged newtonian-mechanics newtonian-gravity acceleration satellites centripetal-force or ask your own question. Centripetal issue when considering gravity Centrifugal force affecting satellite How does centripetal acceleration produce the tangential velocity? Which force is required by a satellite revolving around the earth? Principle of launching satellites into orbit Why normal acceleration doesn't bring a change in speed? How can centripetal acceleration not change speed? Wrong derivation of centripetal acceleration's direction in uniform circular motion? Do internal forces cause change in velocity? Kinematics and dynamics of a crashing satellite	CommonCrawl
History of Science and Mathematics Stack Exchange is a question and answer site for people interested in the history and origins of science and mathematics. It only takes a minute to sign up. What are examples of serendipity in the history of the sciences and math? Cosmic microwave background radiation was discovered after Penzias & Wilson couldn't get rid of the noise generated by their horn. In fact, the noise was their discovery. The strings in string theory were introduced in the context of the strong interaction to make the back-then newly discovered interaction between quarks visible. The strings turned out to be applicable (in closed form) even to gravity, certainly not what they were intended for. What are other examples of serendipity in the sciences? (If someone has a tag suggestion it is welcome) Deschele Schilder Deschele SchilderDeschele Schilder $\begingroup$ Invention of vulcanized rubber? Or is that a myth? $\endgroup$ – davidbak $\begingroup$ @davidbak No, it is not. $\endgroup$ – José Carlos Santos $\begingroup$ @davidbak One day in 1839, when trying to mix rubber with sulfur, Goodyear accidentally dropped the mixture in a hot frying pan. To his astonishment, instead of melting further or vaporizing, the rubber remained firm and, as he increased the heat, actually became harder. Goodyear quickly worked out a consistent system for this hardening, which he called vulcanization because of the heat involved. Serendipity indeed. Luckily he didnt eat it. $\endgroup$ – Deschele Schilder $\begingroup$ Oh well, I know plenty of sources say that Goodyear discovered vulcanized rubber by accidently dropping some glop in a hot frying pan and observing the results. But, really, doesn't that shout "urban myth" to you? Maybe if any one of these secondary sources had a reference to some writing of Goodyear's where he claims it that would suffice. But, e.g., Wikipedia does not provide such evidence, neither in the article on vulcanized rubber nor in the one on Goodyear himself. $\endgroup$ $\begingroup$ BTW, this book of Goodyear's, though it does not claim he discovered it by accident (or make any claims on how it was discovered at all) is fascinating in that it contains over 300 pages of uses of vulcanized rubber! $\endgroup$ Teflon (Polytetrafluoroethylene) was discovered by Roy Plunkett while working on new refrigerant. There was a residue at the bottom of the bottle he was using, a bottle which should have been emptied of gas and yet still registered extra weight. He discovered that the milky new substance was stable and extremely slippery and, voila, we can no longer use metal implements on our non-stick pans! Roy J Plunkett; Science History Institute Another example is the discovery in 2006 that tarantulas have silk-producing spinnerets on their feet which they use for traction. Adam Summers, a research assistant at University of California, Irvine normally placed tarantulas on a glass plate tilted at an angle to store them temporarily. Tarantulas have a fear of falling and would simply cling to the glass without moving, a fact long-established. One day he noticed that there were trails of web from the tarantulas' feet where the tarantulas had been slowly sliding down the angled glass plate. Prior to this observation, it was not known, apparently, that any spiders possessed spinnerets on their feet, a fact with evolutionary implications. A chance observation led to the discovery. Tarantulas Produce Silk From Feet, Science Daily JohnHuntJohnHunt $\begingroup$ That tarantula discovery is fascinating. Could it have evolved because of their weight, and smaller spiders wouldn't have needed the extra help? $\endgroup$ – GammaGames $\begingroup$ @GammaGames; The thinking seems almost to be the other way round and that all spinnerets evolved from sensory organs (which they still resemble) into the later development of webbing-specific organs. The size factor might explain why the tarantulas retained the older function. .en.wikipedia.org/wiki/Spinneret $\endgroup$ – JohnHunt In 1961, Edward Lorenz was running a numerical simulation of weather systems. To restart a run half-way, he copied the initial values from a previous printout — but saw that the simulation began to diverge from the previous run. This turned out to be the result of the printout showing values that were rounded to 3 decimal places, without the full precision used in the calculations. He expected the resulting errors to stay small; but instead, they grew exponentially, doubling roughly every four simulated days, until after two simulated months the weather scenario was completely different. He thus encountered what is now known as the butterfly effect. giddsgidds One famous example is that of Alexander Fleming. He left a cup of staphylococci on his desk and later discovered that it was contaminated with some fungus. Instead of disposing this cup, he started to investigate and the result was the discovery of penicillin, the first antibiotic. This is how he later described this himself: One sometimes finds, what one is not looking for. When I woke up just after dawn on September 28, 1928, I certainly didn't plan to revolutionize all medicine by discovering the world's first antibiotic, or bacteria killer. But I suppose that was exactly what I did. Alexandre EremenkoAlexandre Eremenko $\begingroup$ It helps if you rise just after dawn! $\endgroup$ – PatrickT $\begingroup$ It seems that the antibiotic properties of penicillin were known long before that. See en.wikipedia.org/wiki/… and en.wikipedia.org/wiki/Ernest_Duchesne for example $\endgroup$ $\begingroup$ @Joseph_Jaroslaw: Nevertheless, the article you refer to calls Flemings discovery a "breakthrough", and this is correct. $\endgroup$ – Alexandre Eremenko $\begingroup$ Indeed it was a breakthrough! $\endgroup$ One example is radioactivity. In 1896, Henri Becquerel was working on an experiment involving a uranium-enriched crystal. He believed that sunlight was the reason that the crystal would burn its image on a photographic plate. But then, on a day, the weather was bad, with dark clouds blocking the light from the Sun. Becquerel packed up his stuff and decided to continue his research on another sunny day. Some few days later, he retrieved the crystal from a darkened drawer, but the image burned on the plate was, as he described, "fogged." The crystal emitted rays that fogged a plate, but were dismissed as weaker rays compared to William Roentgen's X-rays. Becquerel wouldn't go on to put a name to the phenomenon. He left that for a couple of fellow scientists: Pierre and Marie Curie. José Carlos SantosJosé Carlos Santos $\begingroup$ So he discovered radioactivity without knowing that it was radioactivity? What kind of radioactivity was it? $\endgroup$ $\begingroup$ It's the result of uranium decaying. The result is the emission of either $\alpha$ particles (helium nucleus) or $\beta$ particles (fast energetic electrons or positrons). $\endgroup$ $\begingroup$ While he thought it was electromagnetic radiation (X-rays)? Did he think sunlight was refracted by the crystal, and that that burned the plate (like with a looking glass)? $\endgroup$ $\begingroup$ Perhaps that, at first, Becquerel thought that these were X_rays. I don't know the answer to the other question. $\endgroup$ $\begingroup$ The idea was that the crystals were absorbing and re-emitting photons. The discovery was that the crystal itself produced photons without any external input. $\endgroup$ – chepner It was well known that when you iterate $x\mapsto \lambda x(1-x)$, the following happens: when $\lambda$ is small, $x=0$ is an attracting fixed point; as $\lambda$ grows, at some moment $\lambda_1$ the attracting point becomes repelling, but an attracting $2$-cycle is born nearby. ($2$-cycle is an fixed point of $f\circ f$). As $\lambda$ grows further, this attracting cycle becomes repelling at $\lambda_2>\lambda_1$, but a new attracting $4$-cycle is born nearby, so we have a sequence of "doubling bifurcations" $\lambda_1<\lambda_2<\ldots$, and this sequence converges to some $\lambda_\infty$. In 1978, Mitchell Feigenbaum studied this sequence using a hand calculator. He used Newton method to compute $\lambda_k$. Newton's method requires a good initial guess. Since the computation was slow, Feigenbaum started to think what the best initial guess will be, that is how to extrapolate the obtained sequence one step further. And he discovered that the ratio $(\lambda_{n}-\lambda_{n-1})/(\lambda_{n+1}-\lambda_{n})$ tends to a constant. To his great surprise, when he tried another function, $x\mapsto \lambda\sin x$, he found that this ratio tends to the SAME constant! This great discovery is called the Feigenbaum Universality, and the constant Feigenbaum constant. It is a universal mathematical constant (like $\pi$), and it is approximately equal to 4.669201609102990671853203820466... He said himself once, that the discovery was made because he had no programmable calculator at his disposal. $\begingroup$ Great one! Especially his remark about the calculator. Im not sure which answer to accept. They are all nice examples. But this is the nicest so far. In my eyes that is. $\endgroup$ The subject of Graph Theory in mathematics, via the Seven Bridges of Königsberg and involving Euler of all people! "The theory of graphs is one of the few fields of mathematics with a definite birth date." -Oystein Ore, graph theorist & number theorist Namely, that birthdate is in 1736 when Leonard Euler refers to "geometry of position" that we've come to know and love as Graph Theory. Quotes below are from Chapter 3 of Graphs & Digraphs, 5th Edition, by Chartrand, Lesniak, and Zhang: Early in the 18th century, the East Prussian city of Konigsberg (now called Kaliningrad and located in Russia) occupied both banks of the River Pregel and the island of Kneiphof, lying in the river at a point where it branches into two parts. There were seven bridges that spanned various sections of the river. A popular puzzle, called the Konigsberg Bridge Problem, asked whether there was a route that crossed each of these bridges exactly once. Although such a route was long thought to be impossible, the first mathematical verification of this was presented by the famed mathematician Leonhard Euler (1707–1783) at the Petersburg Academy on 26 August 1735. Euler's proof was contained in a paper that would turn out to be the beginning of graph theory. This paper appeared in the 1736 volume of the proceedings of the Petersburg Academy. Euler's paper, written in Latin, started as follows (translated into English): "In addition to that branch of geometry which is concerned with magnitudes, and which has always received the greatest attention, there is another branch, previously almost unknown, which Leibniz first mentioned, calling it the geometry of position. This branch is concerned only with the determination of position and its properties; it does not involve measurements, nor calculations made with them. It has not yet been satisfactorily determined what kind of problems are relevant to this geometry of position, or what methods should be used in solving them. Hence, when a problem was recently mentioned, which seemed geometrical but was so constructed that it did not require the measurement of distances, nor did calculation help at all, I had no doubt that it was concerned with the geometry of position – especially as its solution involved only position, and no calculation was of any use. I have therefore decided to give here the method which I have found for solving this kind of problem, as an example of the geometry of position. Euler goes on to say (see an excerpt from this amazing lecture on Euler's genius): "...this solution bears little relationship to mathematics, and I do not understand why to expect a mathematician to produce it, rather than anyone else, for the solution is based on logic alone." I guess I find this story so serendipitous, because you had to have so many things fall into place: the rivers naturally flowing in a unique way people to settle and build just the right bridges in just the right places to make the underlying problem unsolvable an arbitrary human constraint to want to cross bridges exactly once on a Sunday afternoon walk petitioning one of the most prolific and insightful minds of mathematics for all time (Euler)... ...who proceeded to solve it despite the fact that he didn't think it had any applications in math, nor did he think a mathematician was needed to solve this problem! I find it hard to believe Graph Theory would not have been developed eventually by someone else for another of its many applications, but to think that this was the fashion that it was introduced makes me consider it a serendipitous outcome. Xoque55Xoque55 There's always Archimedes ''eureka' moment, sitting in a bath tub and realizing that a given volume of a material will displace the same amount of water when fully submerged regardless of the object's shape. SoronelHaetirSoronelHaetir $\begingroup$ You can now research whether this is believed to be a true incident. $\endgroup$ – Gerald Edgar José Carlos Santos' answer mentions X-rays but not their discovery. Nature 53,–276 (1896) By W. C. Röntgen. Translated by Arthur Stanton from the Sitznngsbcrichte der Würzburger Physik-medic. Gesellschaft, 1895: On a New Kind of Rays The Guardian has interesting background and mentions this google doodle as well Google doodle celebrates 115 years of X-rays From the American Physical Society's This Month in Physics History; November 8, 1895: Roentgen's Discovery of X-Rays: Roentgen's scientific career was one beset with difficulties. As a student in Holland, he was expelled from the Utrecht Technical School for a prank committed by another student. His lack of a diploma initially prevented him from obtaining a position at the University of Würzburg even after he received his doctorate, although he eventually was accepted. From History of Medicine: Dr. Roentgen's Accidental X-Rays: Wilhelm Roentgen, Professor of Physics in Wurzburg, Bavaria, discovered X-rays in 1895—accidentally—while testing whether cathode rays could pass through glass. His cathode tube was covered in heavy black paper, so he was surprised when an incandescent green light nevertheless escaped and projected onto a nearby fluorescent screen. Through experimentation, he found that the mysterious light would pass through most substances but leave shadows of solid objects. Because he did not know what the rays were, he called them 'X,' meaning 'unknown,' rays. From X-ray; Discovery by Röntgen: On November 8, 1895, German physics professor Wilhelm Röntgen stumbled on X-rays while experimenting with Lenard tubes and Crookes tubes and began studying them. He wrote an initial report "On a new kind of ray: A preliminary communication" and on December 28, 1895 submitted it to Würzburg's Physical-Medical Society journal. This was the first paper written on X-rays. Röntgen referred to the radiation as "X", to indicate that it was an unknown type of radiation. The name stuck, although (over Röntgen's great objections) many of his colleagues suggested calling them Röntgen rays. They are still referred to as such in many languages, including German, Hungarian, Ukrainian, Danish, Polish, Bulgarian, Swedish, Finnish, Estonian, Turkish, Russian, Latvian, Lithuanian, Japanese, Dutch, Georgian, Hebrew and Norwegian. Röntgen received the first Nobel Prize in Physics for his discovery. The principle of the microwave oven was discovered by accident. In 1946, the engineer Dr. Percy LeBaron Spencer, who worked for the Raytheon Corporation, was working on magnetrons. One day at work, he had a candy bar in his pocket, and found that it had melted. He realized that the microwaves he was working with had caused it to melt. After experimenting, he realized that microwaves would cook foods quickly - even faster than conventional ovens that cook with heat. Zoom Inventors and Inventions BarmarBarmar $\begingroup$ That's a nice story. Unfortunately, it's entirely false: radio heating was known at least as far back as 1930, and a microwave oven was demonstrated at the 1933 World's Fair. $\endgroup$ $\begingroup$ @Mark The 1930 device (operating at wavelengths of 10s of meters) was not microwave oven. The cavity magnetron which is the essential component of all practical microwave ovens was indeed invented during WWII (but not by American engineers) and its heating effect discovered by accident. In fact, the design of the cavity magnetron was given free to the USA by the UK when the USA entered WWII. (Of course without centimeter-band radars using magnetrons, the US Air Force would not have been able contribute much anyway) $\endgroup$ – alephzero $\begingroup$ @alephzero the Tizard mission actually occurred over a year before the US entered the war $\endgroup$ – llama $\begingroup$ @alephzero, an impractical microwave oven is still a microwave oven. $\endgroup$ $\begingroup$ @Mark I think the distinction being made is between short-wave RF and microwaves. Although it does seems weird that if they knew about short-wave cooking, it took this serendipitous discovery to come up with microwave ovens. $\endgroup$ Alfred Wilm discovered the age hardening effect of aluminium, after delaying his testing of some freshly annealed samples (I believe to take the weekend off to go sailing). This is now used in the design of aluminum alloys with applications from aircraft to bicycles to keychain bottle openers, with his alloy used in "Duralinium". https://www.researchgate.net/publication/279898292_Aluminium_Alloys_-_A_Century_of_Age_Hardening notAlfredwilmnotAlfredwilm The eponymous Serendipity elements used in the finite element method for solving PDEs fit the bill. These elements ignore the internal nodes (unlike their Lagrange counterparts), reducing the number of degrees of freedom of the system while (and this is the key) retaining the same element order. Serendipity elements are therefore less computationally expensive than Lagrange elements but just as accurate and herein lies the "happy chance". thomj1332thomj1332 Thanks for contributing an answer to History of Science and Mathematics Stack Exchange! Not the answer you're looking for? Browse other questions tagged physics or ask your own question. Proof by "accident" When was the vector notation in physics and other sciences first introduced? What is the history of the energy concept and its measurement? What are the major flaws of the "caloric" theory of heat? What is the history of electric current and resistance? Math development and under-appreciation of Maxwell's Equations What is the ancient cosmic canon of proportion and its role in the history of science? What is the explanation of rope's strength in Galileo's Two New Sciences? What are some historical examples in physics of heuristic proofs of mathematical results? What are the earliest inventions to store and release energy (e.g. fly wheels)?	CommonCrawl
Cyclic orbit codes and stabilizer subfields AMC Home Information--bit error rate and false positives in an MDS code May 2015, 9(2): 169-176. doi: 10.3934/amc.2015.9.169 Close values of shifted modular inversions and the decisional modular inversion hidden number problem Igor E. Shparlinski 1, Department of Pure Mathematics, University of New South Wales, Sydney, NSW 2052, Australia Received September 2013 Published May 2015 We give deterministic polynomial time algorithms for two different decision version the modular inversion hidden number problem introduced by D. Boneh, S. Halevi and N. A. Howgrave-Graham in 2001. For example, for one of our algorithms we need to be given about $1/2$ of the bits of each inversion, while for the computational version the best known algorithm requires about $2/3$ of the bits and is probabilistic. Keywords: small solutions., hidden number problem, Shifted inversion, congruences. Mathematics Subject Classification: Primary: 11T71; Secondary: 11D85, 94A6. Citation: Igor E. Shparlinski. Close values of shifted modular inversions and the decisional modular inversion hidden number problem. Advances in Mathematics of Communications, 2015, 9 (2) : 169-176. doi: 10.3934/amc.2015.9.169 A. Akavia, Solving hidden number problem with one bit oracle and advice,, in Adv. Crypt. - CRYPTO 2009, (2009), 337. doi: 10.1007/978-3-642-03356-8_20. Google Scholar D. Boneh, S. Halevi and N. A. Howgrave-Graham, The modular inversion hidden number problem,, in Adv. Crypt. - ASIACRYPT 2001, (2001), 36. doi: 10.1007/3-540-45682-1_3. Google Scholar D. Boneh and R. Venkatesan, Hardness of computing the most significant bits of secret keys in Diffie-Hellman and related schemes,, in Adv. Crypt. - CRYPTO '96, (1996), 129. doi: 10.1007/3-540-68697-5_11. Google Scholar D. Boneh and R. Venkatesan, Rounding in lattices and its cryptographic applications,, in Proc. 8th Annual ACM-SIAM Symp. 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AEER Home Advances in Environmental and Engineering Research (AEER) is an international peer-reviewed Open Access journal published quarterly online by LIDSEN Publishing Inc. This periodical is devoted to publishing high-quality peer-reviewed papers that describe the most significant and cutting-edge research in all areas of environmental science and engineering. Work at any scale, from molecular biology through to ecology, is welcomed. Main research areas include (but are not limited to): Atmospheric pollutants Air pollution control engineering Ecological and human risk assessment Environmental management and policy Environmental impact and risk assessment Environmental microbiology Ecosystem services, biodiversity and natural capital Control and monitoring of pollutants Remediation of polluted soils and water Fate and transport of contaminants Water and wastewater treatment engineering Advances in Environmental and Engineering Research publishes a range of papers (original research, review, communication, opinion, study protocol, comment, conference report, technical note, book review, etc.). We encourage authors to be succinct; however, authors should present their results in as much detail as necessary. Reviewers are expected to emphasize scientific rigor and reproducibility. Rapid publication: manuscripts are undertaken in 12 days from acceptance to publication (median values for papers published in this journal in 2021, 1-2 days of FREE language polishing time is also included in this period). Current Issue: 2023 Archive: 2022 2021 2020 Open Access Original Research Degree-hours and Degree-days in Coastal Mediterranean Cities, Patras and Kalamata, Greece Panagiotis Kyriakopoulos 1 , Athanassios Giannopoulos 1 , Yannis G. Caouris 1,* , Manolis Souliotis 2 , Mattheos Santamouris 3 Department of Mechanical Engineering & Aeronautics, University of Patras, 26504 Patras, Greece Department of Chemical Engineering, University of Western Macedonia, Kozani, 50132, Greece School of Built Environment, University of New South Wales, Sydney, 2052, Australia * Correspondence: Yannis G. Caouris Academic Editor: Anthony Brazel Special Issue: Urban Heat Island Effect Received: September 04, 2021 \| Accepted: November 17, 2021 \| Published: December 06, 2021 Adv Environ Eng Res 2021, Volume 2, Issue 4, doi:10.21926/aeer.2104032 Recommended citation: Kyriakopoulos P, Giannopoulos A, Caouris YG, Souliotis M, Santamouris M. Degree-hours and Degree-days in Coastal Mediterranean Cities, Patras and Kalamata, Greece. Adv Environ Eng Res 2021; 2(4): 032; doi:10.21926/aeer.2104032. The hourly ambient air temperature information was analyzed for two Greek coastal Mediterranean cities: Patras (for the entire 2018 year) with ten urban and one rural stations, and Kalamata (for the entire 2019 and 2020 years) with eight urban and two rural stations. The heating and cooling Degree Hours (DH) and Degree Days (DD) were calculated, for base temperatures of 18 °C and 26 °C, respectively. The urban heating degree hours for the cities of Patras and Kalamata were observed to be 19.2% and 24%, respectively, lower than that of the rural areas. Similarly, the urban cooling degree hours for the two cities were 9% and 22% higher than that of rural areas. These findings indicate a distinct urban heat island effect in both the cities, with greater effects in Kalamata than in Patras. Following comparisons with historical data from reliable sources, it could be observed that summers are trending warmer and winters are trending milder. Heating degree-hours; Heating degree-days; Cooling degree-hours; Cooling degree-days; Urban heat island; Kalamata; Patras. Various techniques, including simple steady-state models to comprehensive dynamic simulation approaches, have been successfully used for assessing the energy demands to heat or cool a building. Most of the dynamic simulation tools available in the market are often challenging to operate [1] since they demand a significant number of various input parameters such as analytical meteorological data, lighting profiles, the quantity and schedule of occupants, and so on [2]. These factors make them inappropriate for widespread applications, especially in preliminary evaluation of the energy requirements of buildings [3]. Conversely, simple steady-state models require minimal data (typically only hourly or daily weather data) and maintain satisfactory accuracy in estimating the energy consumption of buildings, as long as the building usage and the efficiency of heating ventilation and air conditioning system are maintained constant. The traditional and variable-base degree-day (DD) or degree-hour (DH) techniques are the most recognized methods of these steady-state models [1]. The thermal and cooling energy consumption of buildings has been estimated primarily by the DD approach [4], which is a basic and easy method for preliminary energy audits, providing acceptable accuracy in the estimation of energy consumption of a building [5,6]. DD refers to the difference between the outdoor mean temperature during 24 hours and a specific base temperature (Tb) [7]. The latter represents the outdoor air temperature at which heating or cooling systems are not required to satisfy people. The calculated DD is regarded as heating degree day (HDD), when the mean daily ambient air temperature is less than heating base temperature, and as Cooling Degree Day (CDD) when it is greater than the cooling base temperature. As a reason, the indoor/outdoor air exchange through windows and doors and the total heat gains from inhabitants, lighting, equipment, and solar radiation should be considered to determine base temperature [6,8,9]. The anticipated outputs can be applied to enhance the overall energy efficiency of buildings and identify the most effective solutions to minimize the energy consumption of buildings [10]. The Technical Guideline (TG) of the Technical Chamber of Greece (TCG) adopts base temperatures of 18 °C and 26 °C for calculating HDD and CDD, respectively [11], which correspond to acceptable comfort temperatures during winter and summer in Greece [8,11,12]. For areas with hourly temperature data, the degree-hour (DH) approach can be used to estimate the energy requirements of a building more precisely rather than the DD method. The DH method is defined as identical to the DD method. When the mean hourly ambient air temperature is less than the heating base temperature, the estimated DH is heating degree hour (HDH). In contrast, when it is greater than the cooling base temperature, it is called cooling degree hour (CDH) [11,13]. Aside from estimating the energy demand of a building, DDs and DHs are frequently employed as climatic indicators for assessing climate change impacts, especially the increasing outdoor temperature [9]. Although these methodologies are obsolete, they are nevertheless widely applied to predict the energy consumption of buildings and climate change trends. Harvey (2020) [8] examined the application of HDD and CDD methods to estimate heating and cooling loads of buildings and proposed acceptable reference temperatures. Spinoni et al. (2018) [14] a lso applied HDD-CDD indicators to investigate whether energy demands for cooling and heating of buildings are projected to rise or fall due to climate change. Similarly, Andrade et a l. (2021) [15] also investigated climate change scenarios in Portugal using HDD-CDD indicators. Ramon et al. (2020) calculated the HDD and CDD in the context of the recent past and near future high-end climate change scenario (RCP 8.5) in Belgium. Many researchers have reported the Mediterranean region as one of the most vulnerable areas to the projected climate change [14,15,16,17,18,19,20]. The current climate projections predict extreme weather events in the region in response to the warmer and drier periods in the near future. Hence, it is critical to research the climate conditions of metropolitan areas with frequent heatwaves. The coastal cities are highly influenced by climate due to their proximity to the sea and are unique. The current study examines the urban and rural values of HDHs CDHs, HDDs, and CDDs for two coastal Mediterranean cities, Patras and Kalamata. Both cities have high levels of urban heat island intensity (UHI), with higher levels in Kalamata. The variable-base DD or DH approaches are applied here as an extension of the classic approach, and the results are compared with relevant information from past years. The monthly DDs and DHs for most Greek cities are reported by TG 20701–3/2010 (2014) of TCG [11] and Papakostas et al. a,b [21,22]. In the former study, HDDs and CDHs statistics are published for 62 and 30 Greek cities, respectively, whereas HDDs and CDDs for 50 Greek cities are reported in the latter. The mean monthly ambient temperature was used to formulate an equation for the estimation of HDD (equation 9 in section 2) and mean hourly ambient temperatures of each monthly mean day were used to formulate the equation to estimate CDHs (equation 11 in section 2) [11]. Papakostas et al. a,b [21,22] calculated HDDs and CDDs for 48 cities, including Patras and Kalamata by Erb's method [23], using the monthly average ambient temperature of several years. The authors used a statistical algorithm with the accuracy of 5% ÷ 10.5% for calculations of HDDs [21] and 0.1% ÷ 11% for CDDs [22]. 2. Methods of Calculation Various techniques for estimating HDDs, CDDs, HDHs, and CDHs have been proposed, with the hourly method being the most accurate, which requires hourly temperature data. This method estimates the degree-hours by adding the differences between base temperature and hourly average ambient air temperature. The daily HDHs and CDHs can be defined by equations (1) and (2), respectively. \[ H D H_{d}=\sum_{i=1}^{24}\left(T_{b}-T_{i}\right)^{+} \tag{1} \] \[ C D H_{d}=\sum_{i=1}^{24}\left(T_{i}-T_{b}\right)^{+} \tag{2} \] Where 'Tb' is the base temperature, and 'Ti' is the ambient air temperature at the ith hour of the day. Similarly, the number of daily HDDs and CDDs can be defined by equations (3) and (4), respectively. $H D D_{d}=\frac{\sum_{i=1}^{24}\left(T_{b}-T_{i}\right)^{+}}{24} \tag{3} $ $C D D_{d}=\frac{\sum_{i=1}^{24}\left(T_{i}-T_{b}\right)^{+}}{24} \tag{4} $ The number of monthly heating and cooling DHs/DDs can be calculated by adding the daily DDs/DHs over a specific period of time and can be defined by equations (5) and (6), respectively. The number of annual heating and cooling DHs/DDs is calculated by summing up the monthly DHs/DDs over the period and can be defined by equations (7) and (8), respectively. \[ D H_{m}=\sum_{j=1}^{N} D H_{d, j} \tag{5} \] \[ D D_{m}=\sum_{j=1}^{N} D D_{d, j} \tag{6} \] Where 'N' denotes the number of days per month and '$DH_{d, j}$' and '$DD_{d, j}$' represent the daily DHs and DDs of the jth day of the month. \[ D H_{a}=\sum_{k=1}^{12} D H_{m, k} \tag{7} \] \[ D D_{a}=\sum_{k=1}^{12} D D_{m, k} \tag{8} \] Where $' D H_{m, k}$ ' and $' D D_{a}^{\prime}$ represent the monthly DHs and DDs of the kth month of the year. In areas where hourly temperature data is unavailable, the calculation of the HDHs or HDDs of a month can be carried out using equation (9) [11], which is given below. \[ H D D_{m}=\sum\left[N_{m}\left(T_{b}-T_{m}\right)^{+}\right] \tag{9} \] Where 'Nm', 'Tb' and 'Tm' represent is the number of days in a month, base temperature (18 °C) and the mean monthly ambient air temperature, respectively. Similarly, the monthly CDDs can be calculated using the equation (10) and CDHs can be calculated, as per the guidelines [11] using the equation (11), and are as follows. \[ C D D_{m}=\sum\left[N_{m}\left(T_{m}-T_{b}\right)^{+}\right] \tag{10} \] \[ C D H_{m}=\sum\left[N_{m} \sum_{i}\left(T_{b}-T_{i m}\right)^{+}\right] \tag{11} \] Where 'Tb' is the base temperature (26 °C), and 'Tim' is the mean hourly ambient air temperature in the mth month of the year. Only positive parameters are used in these equations (1, 2, 3, 4, 9, 10, 11) which is indicated by a '+' power. 3. Description of the Cities and Measuring Networks Patras (38° 15´ N, 21° 45´ E) is the capital of Western Greece and is a medium-sized city with a population of over 200,000 people. With a population of about 70,000 people, Kalamata (37° 2′ N, 22° 7′ E) is the second populous city in the Peloponnese area. The relative locations of the two cities are shown in the following Figure 1. Figure 1 Locations of Patras and Kalamata cities (terrain view by Google Earth 2021). As part of the study, suitable sites were identified in both the cities to install twenty-one temperature monitoring and logging stations, among which ten were in the urban areas of Patras, one in the rural area of Patras (Agios Vasileios ~10 km from the city center), eight in the urban area of Kalamata and the remaining two in the rural areas of Antikalamos (inland, ~5 km from the city center) and Verga (near seashore, ~5.5 km from the city center). The stations in the two study sites were placed at 4 ÷ 4.5 m and 4÷5 m respectively from the ground. A general view of Patras and Kalamata and the locations of monitoring stations are shown in Figure 2 and Figure 3, respectively. The devices were placed inside white cages (radiation shields), with lateral gaps (similar to the Stevenson screen), to protect them from solar or thermal radiation and rain. Figure 2 General view of Patras city. Red circles mark the locations of the ten urban monitoring stations and green rectangle the rural monitoring station (terrain view by Google Earth 2021). Figure 3 General view of Kalamata city. Red asterisks mark the locations of the eight urban monitoring stations. The inland and near sea stations are marked with green and cyan rectangles, respectively (terrain view by Google Earth 2021). The temperature measurements were recorded for every hour. The period of data collection for Patras was the year 2018 and that for kalamata was 2019 and 2020 full years Functional range of devices installed in Patras was −40 °C to + 85 °C, with sensor accuracy of ±0.2 °C, (range from 0°C to 70 °C) and resolution of 0.4 °C. Similarly, the devices used in Kalamata city had a functional range from -30 to 70 °C with a sensor accuracy of ±0.5 °C and resolution of 0.1 °C. The hourly recorded temperature data were used to compute the monthly HDHs and CDHs of each station for the base temperatures of 18 °C and 26 °C, respectively, using equation 5. The urban values are calculated as the average value of all urban stations, and the rural values for Kalamata represent the average value of the two rural stations and are shown in Tables 4 and 6. The estimated results of HDHs, HDDs, CDHs, and CDDs for Patras and Kalamata for different years are presented in separate Tables 1, 2, 3, 4, 5, and 6. Table 1 The monthly HDHs, HDDs, CDHs, and CDDs of the urban areas of Patras for the year 2018. HDHs CDHs CDDs Table 2 The monthly HDHs, HDDs, CDHs, and CDDs of the rural stations of Patras for the year 2018. Table 3 The monthly HDHs and HDDs of the urban areas of Kalamata for the years 2019 and 2020. Average 2019–2020 Avg. Yearly Table 4 The monthly HDHs and HDDs of the rural area of Kalamata for the years 2019 and 2020. Average 2019─2020 Table 5 The monthly CDHs and CDDs of the urban area of Kalamata for the years 2019 and 2020. Table 6 The monthly CDHs and CDDs for the rural areas of Kalamata for the years 2019 and 2020. The hourly recorded temperatures of each monitoring station for base temperatures of 18 °C and 26 °C were used to calculate the monthly HDHs and CDHs, respectively, using equation (5). The HDHs and CDHs for the urban areas are calculated from the average HDHs, and CDHs collected from corresponding urban stations. The HDDs and CDDs are calculated by dividing HDHs and CDHs by 24 (equations 3, 4). The urban zones of Patras are observed to have 5,495.89 HDHs lesser than the rural areas approximating a 19.2% reduction (Tables 1 and 2), which is close to the early estimate of 22.3% by Caouris et al. [24]. Similarly, the CDHs in the urban areas are also 9% higher than those in the rural areas, indicating the UHI effect. Table 7 clearly shows that January is the coldest month, and this finding is substantiated by previous studies [11,21]. As shown in Table 7, the findings suggest that July is the warmest month, which contradicts the findings provided by AUTh [22], which reports August month as the warmest. However, the CDHs or CDD statistics for Patras city are not reported by TCG [11]. Figure 4 Average daily (24 h) ambient air temperatures (°C) for each month for Patras and their standard deviation. Figure 5 Yearwise average daily (24 h) ambient air temperature (°C) for Kalamata for each month and their standard deviation. The coldest month for Kalamata city is January, as evident from Tables 3 and 4. This observation is also supported by the findings reported by TCG [11] and AUTh [21]. The comparison of the current study results with the findings of TCG [11] and AUTh [21] is shown in Table 8. It is also noted that 2019 was cooler than 2020 throughout the warmer months. The urban area of Kalamata has 5,178.14 HDHs lesser than the rural areas, accounting for a reduction of 24% (Table 3 and 4) and 1,489.86 CDHs greater than the rural areas accounting for an increase of 22% (Table 5 and 6). These figures show the presence of a UHI effect in Kalamata, which is stronger than in Patras. August tends to be the warmest month in agreement with TCG [11] and in contrast with AUTh [22], which records July as the warmest month (Table 9). During the cooling phase, it was also noticed that 2019 was warmer than 2020. Figures 4 and 5 show the average daily (24 h) ambient air temperatures for each month and their standard deviations for Patras and Kalamata, respectively, providing a clear depiction of the typical air temperature conditions prevailing in the study area. From Table 3, 4, 5, and 6, it appears that 2020 was warmer during the heating phase and colder during the cooling phase when compared with 2019. The difference in HDHs and CDHs between the urban and rural areas of the two cities reflect an index of energy consumption. However, these differences may not be real, as it depends on the characteristics of each building, such as type of use, operation schedules, number of people, etc., and the variation profiles of ambient temperature. 4.1 Comparisons with Records from Other Sources As part of the study, the estimated data were compared with the findings reported by TCG and AUTh [11,21,22]. The AUTh [21,22] provides HDD and CDD monthly average values based on mean monthly temperature data for Patras and Kalamata during a range of consecutive years spanning from 1955 to 1997 in Patras and 1956 to 1997 in Kalamata. TCG [11] reported HDD values for both the cities and CDH values for only the Kalamata city. Historical data has been included with ambiguous sources and temporal periods, particularly before 2003. Temperature data were procured from the Hellenic National Meteorological Service (HNMS) [25], and its surface stations for Patras and Kalamata are WMO 689 (Lat. 38° 15'N; Long. 21° 44'E; Elevation 3 m) and WMO 726 (Lat. 37° 04'N; Long. 22° 01'E; Elevation 8 m), respectively. The surface station in Kalamata is located at the airport, in a distinctly rural inland area ~4 km from the inland rural reference station and ~5 km from the coastline. The surface station in Patras is situated at the central jetty of the old port, directly along the coastline and near to the city center. The station receives a positive influence due to its direct proximity to the sea. Table 7 Comparisons of estimated HDDs and CDDs for Patras with other source data [11,21,22]. P.W.-U P.W.-R Table 8 Comparisons of estimated HDDs for Kalamata with other source data [11,21]. Source/ Table 9 Comparisons of CDDs and CDHs for Kalamata with other source data [11,22]. Any positive or negative estimates cannot be based on the agreement or disagreement between the observed and published findings in the study area. Data from several recent years must be processed to accomplish this, even though certain complications may arise. Tables 10, 11, and 12 show the associations derived from the observed values in the present study and the values for urban areas, rural areas, an average of urban as well as rural areas, values from the AUTh [21,22] and TCG [11] are represented in the tables as PW, PWU, PWR, PWUR, AUTh, and TCG respectively. For Patras city, the associations derived for annual values are given in Table 10. Table 10 The associations derived for the annual values for the Patras city. HDDPWU = 0.85HDDAUTh HDDPWU = 0.96HDDTCG HDDPWR = 1.05HDDAUTh HDDPWR = 1.18HDDTCG HDDPWUR = 0.95HDDAUTh HDDPWUR = 1.07HDDTCG CDDPWU = 2.23CDDAUTh CDDPWR = 2.03CDDAUTh CDDPWUR = 2.13CDDAUTh A considerable variation could be observed in the CDDs estimated in the present study and those reported by TCG and AUTh [11,22]. CDDPW is found to be more than double those of the TCG and AUTh. However, this deviation could not be observed for HDD values, instead considered normal. The AUTh values were extracted from the HNMS station, and hence HDDPWR values are slightly higher (relation (C3)) due to the positive influence of coastline to the HNMS station. The same fact explains the relation (C4) if TCG values are extracted from HNMS data stations as AUTh, but for different years. However, the values of CDDPWU and CDDPWR (more than twice of AUTh value), relations (C7) and (C8) are difficult to explain due to the impact of the sea on the HNMS measurement station. For Kalamata city, the association derived for annual values is shown in Table 11 and 12. Table 11 The associations derived for the annual values of HDD for the Kalamata city. HDDPWU = 0.6HDDAUTh HDDPWUR = 0.7HDDAUTh HDDPW is always smaller than HDDAUTh and HDDTCG, with fluctuations of 60% and 89%. Table 12 The associations derived for the annual values of CDD and CDH for the Kalamata city. CDDPWU = 3CDDAUTh CDHPWU = 2.83CDHTCG CDHPWR = 2.32CDHTCG CDHPWUR = 2.57CDHTCG CDDPW is significantly higher than CDDAUTh, attaining a value three times that of CDDAUTh and a similar principle applies to CDHPW to a lesser extent. The following observations are established after the abovementioned analysis and the fact that AUTh and TCG are used as major sources of the recent historical data in this study. Comparisons with TCG sources are not taken into account, as the measurement reference stations are unknown. As the HNMS measurement station in the Kalamata city is situated in rural area, the data collected from this station are compared with the results obtained from the local rural stations considered for this study. The same will be done for Patras due to the positive influence of the sea on the data collected by HNMS station even though it is located close to the city. It should also be noted that no extreme weather events could be observed in the study area during the years 2018, 2019, and 2020 [25]. The comparably higher observed CDDPWR values for Patras and Kalamata as compared to the CDDAUTh (relations (C8), (C17)) indicate a warmer summer trend. In addition, the lower HDDPWR values for Kalamata compared to the HDDAUTh (relation (C12)) indicate a modest tendency for warmer winters. As previously demonstrated and confirmed by the relations (C1) and (C5), the slightly opposite conclusion of the relation (C3) seems to have no effect on the depiction. Furthermore, the inclusion of two rural stations in different places helps to clarify the comparisons made in the Kalamata city. These findings are consistent with the conclusions of Spinoni et al. [14] and other Mediterranean-related research. However, the constraint that an update of DHs and DDs, for the entire country and separately for each urban and rural area appears to be required. The hourly ambient air temperature data of Patras city were collected annually for 2018, and that of Kalamata city were collected for the years 2019 and 2020. For both these cities, data has been compiled to determine the heating and cooling degree hours. The conclusions derived from the results of this study are as follows. 5.1 For Patras City The urban and rural HDHs in Patras city amount to 23,109.51 and 28,605.40, respectively, with a reduction of 19.2% in urban HDHs relative to rural HDHs. Similarly, the urban and rural CDHs amount to 6,677.33 and 6,078.10, respectively, with an increase of 9% in urban areas compared to the rural areas. 5.2 For Kalamata City The urban and rural HDHs amount to 16,357.80 and 21,535.94, with a 24% reduction in urban HDHs relative to rural HDHs. Similarly, the urban and rural CDHs amount to 8,271.51 and 6,781.65, respectively, a 22% rise in the urban zones. In both the cities, a UHI effect could be observed with more intensity reported in Kalamata. The observed data were compared with the findings published by other researchers [11,21,22]. There is a slight tendency towards milder winters and warmer summers, which needs more extensive investigation. More precise data collection methods and devices are required due to climate change and the discrepancies among the supplied by different sources [11,21,22]. There are several reliable weather stations at a reasonable price available nowadays, which can be installed in urban, suburban, and rural areas to gather accurate meteorological data (hourly at least). Data collected for several years may be used in comprehensive and simplified energy calculation approaches for independently treating urban, suburban, and rural areas. P. Kyriakopoulos has collected and elaborated the data for Kalamata. Also, he has written a part of this work. A. Giannopoulos has collected and elaborated the data for Patras. Y. Caouris has supervised this work. M. Souliotis and M. 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Caouris YG, Giannopoulos A, Santamouris M. Heating demands differences between central and surrounding areas in the coastal town of Patras. In: Proceedings of the International Conference Passive and Low Energy Cooling 2005. Santorini: Heliotopos Conferences; 2005. pp.139-143. Hellenic National Meteorological Service. Homepage [Internet]. Elliniko: Hellenic National Meteorological Service. Available from: http://www.emy.gr/. To receive the table of contents of newly released issues of Advances in Environmental and Engineering Research, add your e-mail address in the box below, and click on subscribe.	CommonCrawl
Diagnostic and Prognostic Research Evaluation of microcapillary culture method for the isolation of Leishmania aethiopica parasites from patients with cutaneous lesions in Ethiopia Lensa Aberra1, Adugna Abera2Email authorView ORCID ID profile, Tariku Belay3, Amha Kebede2, Endalamaw Gadisa1 and Geremew Tasew2 Diagnostic and Prognostic Research20193:4 https://doi.org/10.1186/s41512-019-0051-z Accepted: 30 January 2019 In addition to direct slide microscopy, traditional culture method (TCM) has long been considered as a gold standard method for the diagnosis of cutaneous leishmaniasis (CL). However, TCM is relatively expensive and time-consuming compared to the newly introduced microculture method (MCM), which has shown to be sensitive and rapid diagnostic method elsewhere for different Leishmania parasite species other than Leishmania (L.) aethiopica. The objective of this study was to evaluate the diagnostic performance of MCM for the diagnosis of CL caused by L. aethiopica. One hundred forty-three lesion aspirates were collected from 124 suspected CL patients prospectively based on their consecutive series. Portion of the aspirates were cultured in duplicate in TCM with modified Novy-MacNeal-Nicolle (NNN) in tissue culture flask and microcapillary tubes containing RPMI 1640 with 10% fetal bovine serum (FBS) for MCM. Smears on glass slides from the remaining portion of the aspirate were used for direct microscopy to detect the parasite after stained with Giemsa staining solution. Up on a consensus, positive result in any two of the three tests was used as a reference standard to analyze sensitivity. As per consensus standard criteria, 52 of the lesions were qualified to evaluate MCM versus TCM. Forty-eight lesion samples were positive by MCM, 36 by TCM, and 37 by smear microscopy. The representative DNA from parasite culture isolates revealed the causative Leishmania parasite was L. aethiopica by ITS1 polymerase chain reaction-restriction fragment length polymorphism (PCR-RFLP). Culturing L. aethiopica in vitro by MCM is more sensitive (92.3%) than by TCM (69.2%), P = 0.003. The median time for L. aethiopica promastigotes emergence in the culture was 3 days for MCM and 6 days for TCM, P < 0.001. Our finding indicated that MCM is a sensitive and a rapid culturing method for the isolation of L. aethiopica than TCM and smear microscopy. Traditional culture method ITS1-PCR-RFLP Diagnosis of CL Leishmaniasis is a vector-borne disease caused by various species of Leishmania parasites which are transmitted to mammalian host by the bite of female sand fly. The disease is expressed by various clinical manifestations ranging from self-healing cutaneous lesions to potentially fatal visceral form [1]. Cutaneous leishmaniasis (CL) is a disfiguring skin disease, with the potential of long-term psychological and social consequences, especially in young women [2]. In Ethiopia, the CL form of the disease has got three clinical forms such as localized (LCL), mucocutaneous (MCL), and diffuse CL (DCL) [3]. Cutaneous leishmaniasis is the commonest form of leishmaniasis in Ethiopian highland which is predominantly caused by Leishmania (L). aethiopica. It is becoming a growing public health concern with increased number of cases and new outbreaks in areas of previously not known to be endemic [4]. It is a zoonotic disease in which the parasites in the ecological system is maintained by rock hyraxes species of Procavia capensis and Heterohyrax brucei, that have been incriminated as the only known reservoir hosts of L. aethiopica [5]. The diagnosis of CL in endemic areas can be made on the basis of clinical and epidemiological data. However, due to potential toxicity associated with standard pentavalent antimonial therapy, identification of the parasites in the clinical specimens is important. Thus, timely and definitive diagnosis is important for the appropriate management of CL. The definitive diagnosis of CL includes visualization of the amastigotes by microscopic examination of Giemsa stained smears or in histological sections and in vitro culture of the parasite [6]. Although microscopic examination is rapid, cheap, and easy to perform, it lacks sensitivity due to the generally low number of parasites found in tissue samples [7]. In vitro cultures obtained from aspirates, biopsies, or from skin scrapings are reported to be more sensitive than microscopy, but the sensitivity is variable and the differences are based on various factors as for example, the viability of collected parasites, the strain and the media used, the presence of super infection, and the expertise of the investigator [8]. Polymerase chain reaction (PCR) is considered as the most sensitive method for the diagnosis of CL [9–13]. However, this method is not yet available outside of the research setting and still remains expensive for field operation. The microculture method (MCM) is reported to be sensitive and has less promastigote emergence time than traditional culture method (TCM) for the diagnosis of CL as described elsewhere [11–16] for CL caused other than L. aethiopica. Cutaneous leishmaniasis induced by L. aethiopica is clinically diverse and pleotropic with high genetic diversity as well as resistant to most standard anti-leishmaniasis drugs [17]. Due to such diversity, diagnostic tools working out for other CL may or may not work for the detection of CL due to L. aethiopica. Therefore, the objective of this work was to evaluate MCM for isolation of L. aethiopica parasite from cutaneous lesions in Ethiopia. Study area and period The study was conducted in three health centers (Ankober, Kela, and Kibet) and at All African Leprosy, Tuberculosis and Rehabilitation Training (ALERT) Hospital from April 2012 to February 2013. Ankober health center is located in Amhara Regional State, which serves for 3 towns and 19 administrative kebeles (lowest administrative unit). Kela and Kibet health centers are located in Southern People Nations and Nationalities Regional State. ALERT Hospital is located in Addis Ababa at 7 km southwest. Cutaneous leishmaniasis patients are referred to this hospital from almost all over the country in which they get diagnosis as well as treatment services both at the outpatient and inpatient departments. Study population Patients who were referred to the health center or hospital for suspected CL had a clinical indication for skin scraping or aspirate and were able to provide informed consent before included into the study. Children less than 5 years of age, patients with lesions indicative of inter-current bacterial or fungal super-infection and patients on active treatment for CL were excluded from the study. The operational definition for CL was fulfilled when clinical description that involves appearance of one or more lesions with duration of > 2 weeks, typically on uncovered parts of the body such as the face, neck, arms, and legs were enrolled [5]. Consensus reference standard: defined when a lesion was positive by any two of the three tests (MCM, TCM, and smear microscopy). These tests were served as "reference" standard against which an index test was compared. Sample size calculation Sample size was determined as described previously [11]. The sensitivity and the median time of positivity of TCM and MCM were estimated to be 56% (5.6 + 0.5 days) and 75% (3.5 + 0.5 days) respectively. In order to detect increment in sensitivity of MCM and significant difference in time of positivity, α = 0.05 and power of 80% was assumed to calculate the number of lesions using two population proportion formulas as follows: z1 − α= standard normal z values corresponding to the selected alpha z1 − β= standard normal z values corresponding to the selected beta P= simple average of the expected proportions P1 and P2= expected sensitivity of each method (TCM and MCM) n= number of lesions required in each groups $$ n=\frac{{\left\{{z}_{1-\upalpha}\sqrt{\left[2P\left(1-P\right)\right]}+{\mathrm{z}}_{1\hbox{-} \upbeta}\sqrt{\left[P1\left(1-P1\right)+P2\left(1-P2\right)\right]}\right\}}^2}{\left(P1-P2\right)2}=\frac{{\left[1.65\sqrt{\left[2\times 0.65(0.35)\right]}+0.84\sqrt{\left[0.56(0.44)+0.75(0.25)\right]}\right]}^2}{\left(0.75-0.56\right)2}+10\%\mathrm{of}\ n=99 $$ Given the above assumptions, the total number of lesions required was calculated to be 99. However, we have collected samples from a total of 143 lesions to compensate for those lesions which were difficult to collect all the three samples specified. Clinical sample collection Each cutaneous lesion of study participants were physically examined by dermatologist for proper identification of the lesion and exclusion of super infection. The lesion aspirates were collected by experienced nurse from individuals who were clinically suspected for CL. Aseptically, lesion aspirates were collected using a 25-gauge needle and disposable syringe containing 0.5 ml of sterile saline (85% NaCl, pH = 7) which was inserted intra-dermally into the outer border of the lesion. The syringe was rotated, and then tissue fluid was gently aspirated into the needle as it is withdrawn. The aspirated fluid was placed in sterile cryotubes which was transported to Armauer Hansen Research Institute (AHRI) Leishmaniasis laboratory from the field sites within cold chain. The aspirated material was divided equally under sterile condition which was then inoculated in TCM or MCM within 5–10 h after collection. Portion of the aspirate at the edge of the needle was used to make a smear on clean glass slide for direct microscopy. Direct amastigote detection Air dried smear on glass slide were fixed by methanol and stained with 10% Giemsa for 25 min. Slides were examined under light microscopy with × 100 objective for detection and quantification of the burden of amastigotes form based on Chulay and Bryceson method [18]. All slides were examined prior to the knowledge of the culture results to avoid subjective interpretation of results and 10% of the slides were confirmed by independent laboratory personnel as part of quality control. Traditional culture method was performed by using Novy-MacNeal-Nicolle (NNN) medium and Locke's solution as an overlay media. Whereas for MCM, a commercially available liquid media RPMI 1640 medium (Sigma Chemical Co.) was used with 2 mM L-glutamine and 25 mM Hepes (Sigma Chemical Co.) which was supplemented with 15–20% fetal bovine serum (FBS) (Sigma Chemical Co.) and 100 U/100 μg/ml penicillin-streptomycin (Sigma Chemical Co.). The pH solution was adjusted to 7.2 and filtered through 0.2 μm pore size diameter filter. Culturing techniques Aspirated fluid was inoculated in TCM and the MCM in duplicate and parallel inside bio-safety cabinet under sterile condition. For TCM, 150–200 μL aspirated fluid was inoculated on NNN media immediately after the 3 ml of Locke's solution was dispensed in the media. The inoculated culture flasks were incubated at 25–26 °C. Whereas MCM was performed by mixing 150–200 μL lesion aspirates with equal volume of complete RPMI 1640 medium in sterile cryo-tube. The mixture was then loaded 2/3 length of 1 × 75 mm non-heparinized microhematocrit capillary tubes (Heinz, Germany) using 1 ml syringe as described previously [19]. The ends of the capillary tubes were sealed and incubated horizontally at 25–26 °C temperature. All inoculated culture flasks and microcapillary tubes were examined every day under an inverted microscope (Leitz-Wetzlar, Germany) with × 20 and × 40 objectives for observation of motile promastigotes in the culture. Cultures were considered positive when a motile promastigote was observed and negative if there was no motile promastigote after being examined for 30 days. The isolates grown to late exponential growth phase were used for DNA extraction and subsequent PCR-RFLP species identification. DNA extraction and species typing The genomic DNA was extracted from culture isolates using commercial kit (QIAamp DNA Mini Kit; Qiagen, Chatsworth, CA, USA) in accordance with the manufacturer's instructions. Species typing was done using the internal transcriber spacer-1 (ITS1)-RFLP as described by Schonian et al. [20] and Gadisa et al. [21]. Data processing and statistical analysis Descriptive statistics was calculated for continuous variables. Categorical variables were quantified by proportions, and statistical analyses were performed using STATA version 11 (StataCorp LP, College Station, TX). The sensitivity, specificity, positive, and negative predictive values of the tests was calculated by using the consensus standard (positive results of any two of three tests) as the "reference standard." Differences in time to culture positivity were compared between groups by using one-way analysis of variance. Differences in sensitivities were compared using the z test. The agreement between two tests was assessed by kappa value, and the level of significance was set as a P < 0.05. To check the quality of culture media, positive control cultures was inoculated and treated as the same manner as the clinical isolates. Culture medium with no clinical sample was also used as negative controls. Reference strains (L. aethiopica (MHOM/ET/72/L100), L. donovani (MHOM/IN/80/DD8), L. chagasi (MHOM/BR/00/1669), L. infantum (MHOM/FR/LEM-75), L. tropica (MHOM/SU/74/K27), and L. major (MHOM/ SU/73/5-ASKH) were used as positive controls for species identification and PCR amplification. A total of 124 suspected CL cases, of which 38, 33, 38, and 15 of the CL patients were recruited from ALERT Hospital, Ankober, Kela, and Kibet health centers respectively (Fig. 1). Seventy-eight of the study participants were males. From these 124 suspected CL cases, 143 suspected skin lesions were collected and considered as unit of analysis. Flow diagram for diagnostic evaluation of MCM for isolation of L. aethiopica from CL lesions in Ethiopia The median duration of lesion was 9 months (range 1 month to 20 years). Clinical observation revealed that out of the 143 lesions, 95 (66.4%) were suspected to be LCL, whereas the rest 37 (25.9%) and 11 (7.7%) were assumed to be MCL and DCL respectively. Seventy-six (53.1%) of the 143 lesions were ulcerated while the rest 67 (46.9%) were nodular lesions. Considering the consensus standard criteria as a reference standard, 52 out of 143 lesions fulfilled the criteria for the diagnosis of CL. Sixty-three lesion samples were positive by at least one of the three tests and 25 were positive by three tests. Of the 52 lesions that were positive by standard criteria, all of them were culture positive by MCM and/or TCM. From these, 48 of the lesions were positive by MCM and 36 of the lesions were positive by TCM, while 37 lesions were positive by direct microscopy (Table 1). Clinical characteristics of confirmed CL lesions (n = 52) among 143 suspected lesions by CL types, appearance, and lesion duration Clinical characteristics Total no. of lesion Positive parasitological methods CL lesions, n (%) MCM, n (%) TCM, n (%) Microscopy, n (%) CL types 40 (76.9)** 11 (7.7) CL appearance Ulcerative Non ulcerative 32 (61.5)* Lesion duration < 12 months > 12 months *P < 0.001 and P < 0.01. DCL, diffuse cutaneous leishmaniasis; MCL, mucocutaneous leishmaniasis; LCL, localized cutaneous leishmaniasis From the standard consensus criteria, 76.9% of positive lesions were clinically suspected for LCL (P < 0.001), of which 90% were also positive by MCM. When results are compared across lesion appearance, majority of positive lesions were non-ulcerative and the difference was statistically significant (p = 0.013). The overall sensitivity and specificity of MCM was 92.3% (95% [CI] = 84.8–99.8%) and 97.8% respectively. The sensitivity and specificity of TCM was 69.2% (95% [CI] = 54.1–84.3%) and 98.9% respectively (P = 0.003) (Table 2). The agreement between MCM and TCM was 83.9% with kappa value of 0.642 (P < 0.001). From Table 1 above, it is clear that isolation of L. aethiopica parasite from non-ulcerative LCL with lesion duration less than 12 months were best recovered by MCM than TCM and direct microscopy. Comparison of performance of three methods for diagnosis of CL from suspected lesions against consensus standard (gold standard, positive = 52, negative = 91) Diagnostic method No. of positive No. of negative Sensitivity (%) Specificity (%) PPV (%) NPV (%) Direct microscopy 92.3+† +P = 0.003 versus TCM by z test, †P = 0.0018 versus direct microscopy by z test When individual patient was used as unit of analysis, the sensitivity of MCM and TCM was 91.1% and 71.1% respectively, while specificity for both MCM and TCM was 98.6%; which did not change substantially from the per-lesion analysis and remained statistically significant (P = 0.013). Thirty-seven lesions were positive by direct microscopy which yielded a sensitivity of 71.2% (95% [CI] = 54.5–80%). There was a moderate agreement (kappa = 0.430) between smear and TCM whereas a substantial agreement (kappa = 0.671) was found between smear and MCM (P = 0.0018). Even though MCM was more sensitive (92.3%) than TCM (69.2%) and direct microscopy (71.2%) in isolation of L. aethiopica, all the three tests have similar specificity (Table 2). The three methods have similar in respective of positive predictive value, but MCM (95.7%) has more negative predictive value than the other two methods (Table 2). Amastigote to promastigotes transformation is faster in MCM than in TCM The median time to culture positivity for MCM was 3 days (range 2–11 days) and 6 days for TCM (3–17 days) (P < 0.001). When the individual patient was used as unit of analysis, median time to culture positivity did not change substantially from the per-lesion analysis and remained statistically significant (median = 3, range 2–10) while it was 5.5 (range = 3–17) by TCM (Table 3). Time to transformation of amastigotes to promastigotes by culture methods Culturing method Time to positivity in days (per lesion analysis) Time to positivity in days (per patient analysis) Mean + SD 3.7 + 1.9 5.8 + 2.6 *P < 0.001 by median test We also compared the costs of MCM and TCM in terms of media consumption per test; sheep blood requirement, autoclaving, and requirement for distilled water. As indicted in Table 4, MCM uses 75 μL of medium per test compared to TCM which uses 4000 μL sheep blood and 2000 μL Locke's medium per test. The cost for 100 ml of complete RPMI medium is approximately 4.5 USD and the cost of 100 ml Locke's semi-solid medium is approximately 1 USD. From this comparison, the cost of MCM is at least 5.9 times cheaper than that of TCM. Comparison of MCM and TCM media in terms of costs Cost of 100 ml sheep blood Filtration through 0.22 mm Required for Locke's solution Media required/test 75 μL complete media 4 ml sheep blood and 2 ml Locke's solution Cost of Locke's solution/100 ml The data for comparison was collected from store records, local shops, pharmacy, and laboratories Species typing by PCR-RFLP confirms that the infecting parasites were L. aethiopica Amplification by the ITS-1 primer pairs produced PCR product of about 328 bp (Fig. 2a). When the PCR product was digested by Hha I enzyme, L. aethiopica reference strain and the DNA isolates from cultured promastigotes formed similar bands approximately 162 bp size (Fig. 2b). This confirms the infecting Leishmania parasites were L. aethiopica. L. major on the other hand yielded two bands of about 88 bp and 240 bp while, L. infantum, L. donovani, L. chagasi, and L. tropica gave single band size of 328 bp. a PCR products of ITS-1 from promastigote DNA extract, 1. 100 bp ladder, 2. Negative control, 3. L. donovani, 4. L. aethiopica, 5. L. tropica, 6. L. major, 7. L. infantum, 8. L. chagasi, 9–12 clinical isolates. b PCR-ITS1-RFLP of the amplicon with Hha I, 1. 100 bp ladder, 2. L. donovani, 3. L. aethiopica, 4. L. tropica, 5. L. major, 6. L. infantum, 7. L. chagasi, 8–12 clinical isolate The conventional CL diagnostic methods currently employed in Ethiopia are slide microscopy and cultivation of Leishnamia parasite using TCM. However, utilization of slide microscopy is compromised by lesser sensitivity while TCM is not considered applicable in regional laboratories due to logistic and infrastructure barriers. In present study, we have set a consensus standard criteria in which any two positive tests out of the three tests were considered as a gold standard against which each individual method is compared [22]. In isolation of Leishmania promastigotes from CL lesions in the present study, MCM was shown to be more sensitive (92.3%) than the TCM (69.2%) and smear microscopy (71.1%). Microculture method is offering a simpler, cost-effective, and sensitive alternative to TCM and smear microscopy in the diagnosis of CL. In the previous studies, the sensitivity of TCM shown to be varied with parasites load [12], culture media used [16], Leishmania species [23] duration, and appearance of lesions [15]. In contrast, the sensitivity of MCM was shown not to be affected by CL clinical categories [15]. The higher sensitivity of MCM in the present report is in agreement with the previous finding (83.3–97%) by Allahverdiyev et al., who also explained the reason to be due to the capillary tube ability to concentrate the sample material and provide microaerophilic conditions favorable for transformation of the amastigotes to promastigotes. In addition, higher partial CO2 (pCO2) in MCM was reported in the same study which corresponds with the reduction in pO2 and pH also favoring the survival of promastigotes [12]. Nevertheless, other studies in Peru reported lesser MCM sensitivity than our finding which is 71.7% [11] and 78.3% [15]. This variation could be attributed to the difference in Leishmania species involved in which in Peru the characterized parasite was L. (V.) braziliensis complex, different from ours, L. aethiopica. However, the lesser median time of MCM positivity reported in our case was in agreement with previous studies, and there is no considerable difference was observed among species [15]. MCM have been shown to be rapid and easy for transportation, and characterization of microcapillary cultivated promastigotes of L. donovani [19], L. tropica, and L. infantum [24]. In the present study, eight MCM (two from each study sites) were mass cultured and characterized by ITS1-RFLP which were identified to be L. aethiopica. Since there is no safe procedure for extraction of cultured promastigotes, we have adapted our own techniques which involve breaking the capillary tubes with care and withdrawing the fluid with fine needle. However, such maneuver has to be evaluated further with care to minimize the risks of laboratory acquired leishmania infection. In terms of medium consumption, MCM uses 75 μL of medium per test compared to TCM which uses 2000 μL medium per test. Similarly, the costs of MCM is at least 5.9 times cheaper than that of TCM, since the cost of 100 ml of complete RPMI medium is approximately 4.5 USD and the cost of 100 ml Locke's semi-solid medium is approximately 1 USD. A 100 ml sheep blood and 50 ml of Locke's overlay solution could be used for 20–25 tests at a total cost of 10.5 USD. Whereas, a 100 ml of complete media could be used for approximately 1333 tests at a total cost of 4.5 USD [25]. Microculture method could not occupy much space in the incubator and easy to transport from place to place compared to TCM. One of the most advantages of MCM is that it can utilize light microscope which could be available at all district levels compared to TCM which utilizes inverted microscope which is only available at higher institutions. Rapid isolation of CL causative organism in Ethiopia will also facilitate more rapid species identification in institutions where molecular diagnostic capabilities exist. Because the experience from other countries shows that species identification becomes increasingly important due to species variation in response to therapy [26] and in a region where leishmainasis/HIV co-infection is considered high [27]. Inter-specific variability in response to standard anti-leishmaniasis drugs, such as amphotericin B, miltefosine, pentamidine, and paromomycin, has been observed among other species of Leishmania parasites somewhere else [26]. In respective of these views, prompt diagnosis and rapid isolation with species identification of CL in Ethiopia are so clinically helpful for dermatologists to treat CL and may contribute in the control and prevention of the disease. Our finding indicated that MCM is a sensitive CL diagnostic method than TCM and smear microscopy. As it was consistently shown in other studies, MCM also proved to be economical and rapid culturing technique in our finding as well. Thus, this report depicted the value of MCM for the isolation of L. aethiopica promastigotes from lesions of CL patients in Ethiopia. Armauer Hansen Research Institute All Africa Leprosy, Tuberculosis and Rehabilitation Training CL: Cutaneous leishmaniasis DCL: Diffuse cutaneous leishmaniasis FBS: Fetal bovine serum ITS-1: Internal transcriber spacer-1 LCL: Localized cutaneous leishmaniasis MCL: Mucocutaneous leishmaniasis MCM: Microculture method NNN: Novy-MacNeal-Nicolle RFLP: Restriction fragment length polymorphism RPMI: Roswell Park Memorial Institute The authors acknowledge World Health Organization country office for Ethiopia for financing the study and the Armauer Hansen Research Institute (AHRI) for provision of laboratory reagents and consumables for this work. This study was supported by the World Health Organization country office for Ethiopia through Ethiopian Public Health Institute (EPHI); project number AF/ETH/AAC/000/RB/08 AMS CODE: 2123883, and the Armauer Hansen Research Institute (AHRI) core budget. Availability of data and materials The datasets generated and analyzed during this study are available from the corresponding author upon reasonable request. No potential conflict of interest was reported by the authors. Ethics and consent For children 6–18 years of age, the informed consent was obtained from their parents or guardians. An assent was obtained from 12–17 year old children in addition to the consent obtained from their parents or guardians. For all suspected CL cases, laboratory diagnosis and treatment were given free of charge and all results were kept confidentially. All authors read and approved the final version of the manuscript. GT and EG conceived the study. GT generated the idea. AA and LA performed the field and laboratory experiments, analyzed the data, and prepared the paper. AA and GT drafted the manuscript. LA, EG, TB, AK, and GT participated on proposal development. This study was ethically approved by Scientific and ethical review Office of Ethiopian Public Health Institute (EI/SERO/SERC/45/2002) and AHRI/ALERT Ethics (PO07/12) committee. Written consent was obtained from all study participants. Armauer Hansen Research Institute, Malaria and Neglected Tropical Diseases Research Directorate, P. O. Box 1005, Addis Ababa, Ethiopia Ethiopia Public Health Institute, Malaria and Neglected Tropical Diseases Research Team, P. O. Box 1242, Addis Ababa, Ethiopia College of Public and Medical Health, Department of Medical Laboratory and Pathology, Jimma University, P. O. Box 378, Jimma, Ethiopia Alvar J, Vélez ID, Bern C, Herrero M, Desjeux P, Cano J, et al. Leishmaniasis Worldwide and Global Estimates of Its Incidence. 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Physics And Astronomy (71) Annals of Human Genetics (4) International Astronomical Union Colloquium (4) Journal of Fluid Mechanics (4) Transactions of the International Astronomical Union (3) Zygote (3) Symposium - International Astronomical Union (2) AI EDAM (1) Cardiology in the Young (1) Journal of Applied Probability (1) Microscopy Today (1) The Journal of Asian Studies (1) Ryan Test (4) Applied Probability Trust (1) The Association for Asian Studies (1) Towards a finite-time singularity of the Navier–Stokes equations. Part 2. Vortex reconnection and singularity evasion H. K. Moffatt, Yoshifumi Kimura Journal: Journal of Fluid Mechanics / Volume 870 / 10 July 2019 Published online by Cambridge University Press: 07 May 2019, R1 In Part 1 of this work, we have derived a dynamical system describing the approach to a finite-time singularity of the Navier–Stokes equations. We now supplement this system with an equation describing the process of vortex reconnection at the apex of a pyramid, neglecting core deformation during the reconnection process. On this basis, we compute the maximum vorticity $\unicode[STIX]{x1D714}_{max}$ as a function of vortex Reynolds number $R_{\unicode[STIX]{x1D6E4}}$ in the range $2000\leqslant R_{\unicode[STIX]{x1D6E4}}\leqslant 3400$ , and deduce a compatible behaviour $\unicode[STIX]{x1D714}_{max}\sim \unicode[STIX]{x1D714}_{0}\exp [1+220(\log [R_{\unicode[STIX]{x1D6E4}}/2000])^{2}]$ as $R_{\unicode[STIX]{x1D6E4}}\rightarrow \infty$ . This may be described as a physical (although not strictly mathematical) singularity, for all $R_{\unicode[STIX]{x1D6E4}}\gtrsim 4000$ . Pulmonary hypertension during respiratory syncytial virus bronchiolitis: a risk factor for severity of illness Dai Kimura, Isabella F. McNamara, Jiajing Wang, Jay H. Fowke, Alina N. West, Ranjit Philip Journal: Cardiology in the Young / Volume 29 / Issue 5 / May 2019 Print publication: May 2019 Respiratory syncytial virus infection is the most frequent cause of acute lower respiratory tract disease in infants. A few reports have suggested that pulmonary hypertension is associated with increased severity of respiratory syncytial virus infection. We sought to determine the association between the pulmonary hypertension detected by echocardiography during respiratory syncytial virus bronchiolitis and clinical outcomes. We retrospectively reviewed 154 children admitted with respiratory syncytial virus bronchiolitis who had an echocardiography performed during the admission. The association between pulmonary hypertension and clinical outcomes including mortality, intensive care unit (ICU) admission, prolonged ICU stay (>10 days), tracheal intubation, and need of high frequency oscillator ventilation was evaluated. Echocardiography detected pulmonary hypertension in 29 patients (18.7%). Pulmonary hypertension was observed more frequently in patients with congenital heart disease (CHD) (n = 11/33, 33%), chronic lung disease of infancy (n = 12/25, 48%), prematurity (<37 weeks gestational age, n = 17/59, 29%), and Down syndrome (n = 4/10, 40%). The presence of pulmonary hypertension was associated with morbidity (p < 0.001) and mortality (p = 0.02). However, in patients without these risk factors (n = 68), pulmonary hypertension was detected in five patients who presented with shock or poor perfusion. Chronic lung disease was associated with pulmonary hypertension (OR = 5.9, 95% CI 2.2–16.3, p = 0.0005). Multivariate logistic analysis demonstrated that pulmonary hypertension is associated with ICU admission (OR = 6.4, 95% CI 2.2–18.8, p = 0.0007), intubation (OR = 4.7, 95% CI 1.8–12.3, p = 0.002), high frequency oscillator ventilation (OR = 8.4, 95% CI 2.95–23.98, p < 0.0001), and prolonged ICU stay (OR = 4.9, 95% CI 2.0–11.7, p = 0.0004). Pulmonary hypertension detected by echocardiography during respiratory syncytial virus infection was associated with increased morbidity and mortality. Chronic lung disease was associated with pulmonary hypertension detected during respiratory syncytial virus bronchiolitis. Routine echocardiography is not warranted for previously healthy, haemodynamically stable patients with respiratory syncytial virus bronchiolitis. Towards a finite-time singularity of the Navier–Stokes equations Part 1. Derivation and analysis of dynamical system Journal: Journal of Fluid Mechanics / Volume 861 / 25 February 2019 The evolution towards a finite-time singularity of the Navier–Stokes equations for flow of an incompressible fluid of kinematic viscosity $\unicode[STIX]{x1D708}$ is studied, starting from a finite-energy configuration of two vortex rings of circulation $\pm \unicode[STIX]{x1D6E4}$ and radius $R$ , symmetrically placed on two planes at angles $\pm \unicode[STIX]{x1D6FC}$ to a plane of symmetry $x=0$ . The minimum separation of the vortices, $2s$ , and the scale of the core cross-section, $\unicode[STIX]{x1D6FF}$ , are supposed to satisfy the initial inequalities $\unicode[STIX]{x1D6FF}\ll s\ll R$ , and the vortex Reynolds number $R_{\unicode[STIX]{x1D6E4}}=\unicode[STIX]{x1D6E4}/\unicode[STIX]{x1D708}$ is supposed very large. It is argued that in the subsequent evolution, the behaviour near the points of closest approach of the vortices (the 'tipping points') is determined solely by the curvature $\unicode[STIX]{x1D705}(\unicode[STIX]{x1D70F})$ at the tipping points and by $s(\unicode[STIX]{x1D70F})$ and $\unicode[STIX]{x1D6FF}(\unicode[STIX]{x1D70F})$ , where $\unicode[STIX]{x1D70F}=(\unicode[STIX]{x1D6E4}/R^{2})t$ is a dimensionless time variable. The Biot–Savart law is used to obtain analytical expressions for the rate of change of these three variables, and a nonlinear dynamical system relating them is thereby obtained. The solution shows a finite-time singularity, but the Biot–Savart law breaks down just before this singularity is realised, when $\unicode[STIX]{x1D705}s$ and $\unicode[STIX]{x1D6FF}/\!s$ become of order unity. The dynamical system admits 'partial Leray scaling' of just $s$ and $\unicode[STIX]{x1D705}$ , and ultimately full Leray scaling of $s,\unicode[STIX]{x1D705}$ and $\unicode[STIX]{x1D6FF}$ , conditions for which are obtained. The tipping point trajectories are determined; these meet at the singularity point at a finite angle. An alternative model is briefly considered, in which the initial vortices are ovoidal in shape, approximately hyperbolic near the tipping points, for which there is no restriction on the initial value of the parameter $\unicode[STIX]{x1D705}$ ; however, it is still the circles of curvature at the tipping points that determine the local evolution, so the same dynamical system is obtained, with breakdown again of the Biot–Savart approach just before the incipient singularity is realised. The Euler flow situation ( $\unicode[STIX]{x1D708}=0$ ) is considered, and it is conjectured on the basis of the above dynamical system that a finite-time singularity can indeed occur in this case. Hungry in Japan: Food Insecurity and Ethical Citizenship Aya H. Kimura Journal: The Journal of Asian Studies / Volume 77 / Issue 2 / May 2018 Published online by Cambridge University Press: 16 March 2018, pp. 475-493 In addition to other forms of precarity, food insecurity—citizens not having access to nutritious food—is an issue of growing concern in contemporary Japan. This article explores societal responses and documents a strong growth of volunteerism in the form of food banks and kodomo shokudō (children's cafeterias) that offer cheap or free meals to children in need. Both types of programs have become more common since the mid-2000s and are filling a void left by the government. This article explores the tensions in these private programs by drawing on the concept of ethical citizenship, which suggests that volunteerism is entrenched in neoliberalization. The programs are constructed in terms of moral matters, such as creating ibasho (space) for citizens' mutual help and reducing food loss by "bringing back mottainai" (wasting nothing). This championing of community power risks masking the fact that food insecurity is in part a result of the failure of public safety nets. A tent model of vortex reconnection under Biot–Savart evolution Yoshifumi Kimura, H. K. Moffatt Journal: Journal of Fluid Mechanics / Volume 834 / 10 January 2018 Published online by Cambridge University Press: 17 November 2017, R1 Print publication: 10 January 2018 Vortex reconnection under Biot–Savart evolution is investigated geometrically and numerically using a tent model consisting of vortex filaments initially in the form of two tilted hyperbolic branches; the vortices are antiparallel at their points of nearest approach. It is shown that the tips of these vortices approach each other, accelerating as they do so to form a finite-time singularity at the apex of the tent. The minimum separation of the vortices and the maximum velocity and axial strain rate exhibit nearly self-similar Leray scaling, but the exponents of the velocity and strain rate deviate slightly from their respective self-similar values of $-1/2$ and $-1$ ; this deviation is associated with the appearance of distinct minima of curvature leading to cusp structures at the tips. The writhe and twist of each vortex are both zero at all times up to the instant of reconnection. By way of validation of the model, the structure of the eigenvalues and eigenvectors of the rate-of-strain tensor is investigated: it is shown that the second eigenvalue $\unicode[STIX]{x1D706}_{2}$ has dipole structure around the vortex filaments. At the tips, it is observed that $\unicode[STIX]{x1D706}_{2}$ is positive and the corresponding eigenvector is tangent to the filament, implying persistent stretching of the vortex. Crystallization Processes of Amorphous GeSn Thin Films by Heat Treatment and Electron Beam Irradiation T. Kimura, M. Ishimaru, M. Okugawa, R. Nakamura, H. Yasuda Diffraction Contrast Tomography in the Laboratory – Applications and Future Directions C. Holzner, L. Lavery, H. Bale, A. Merkle, S. McDonald, P. Withers, Y. Zhang, D. Juul Jensen, M. Kimura, A. Lyckegaard, P. Reischig, E.M. Lauridsen Journal: Microscopy Today / Volume 24 / Issue 4 / July 2016 Individual differences in the distribution of sperm acrosome-associated 1 proteins among male patients of infertile couples; their possible impact on outcomes of conventional in vitro fertilization K. Kishida, H. Harayama, F. Kimura, T. Murakami Journal: Zygote / Volume 24 / Issue 5 / October 2016 The aims of this study were to show the existence of individual differences in the distribution of sperm acrosome-associated 1 (SPACA1) among male patients of infertile couples and to examine their possible impact on the outcomes of conventional in vitro fertilization (IVF). The spermatozoa were collected from male patients of infertile couples, washed by centrifugation, collected by the swim-up method, and then used for clinical treatments of conventional IVF. The surplus sperm samples were fixed and stained with an anti-SPACA1 polyclonal antibody for the immunocytochemistry. In the clinical IVF treatments, fertilization rates and blastocyst development rates were evaluated. The immunocytochemical observations revealed that SPACA1 were localized definitely in the acrosomal equatorial segment and variedly in the acrosomal principal segment. Specifically, the detection patterns of SPACA1 in the acrosomal principal segment could be classified into three categories: (A) strong, (B) intermediate or faint, and (C) almost no immunofluorescence. The SPACA1 indexes were largely different among male patients with the wide range from 13 to 199 points. The SPACA1 indexes were significantly correlated with developmental rates of embryos to blastocysts (r = 0.829, P = 0.00162), although they were barely associated with fertilization rates at 19 h after insemination (r = 0.289, P = 0.389). These results suggest that the distribution of SPACA1 in sperm affects the outcomes of conventional IVF. In conclusion, this study provides initial data to promote large-scale clinical investigation to demonstrate that the SPACA1 indexes are valid as molecular biomarkers that can predict the effectiveness of conventional IVF of infertile couples. Development of a Monochromated and Aberration-Corrected Low-Voltage (S)TEM Masaki Mukai, Shigeyuki Morishita, Atsushi Kimura, Akihiro Ikeda, Kazunori Somehara, Hidetaka Sawada, Luiz H. G. Tizei, Yung-Chang Lin, Koji Kimoto, Kazu Suenaga Published online by Cambridge University Press: 23 September 2015, pp. 351-352 Enhancement of glass-forming ability and plasticity of Cu-rich Cu–Zr–Al bulk metallic glasses by minor addition of Dy B.W. Zhou, L. Deng, X.G. Zhang, W. Zhang, H. Kimura, A. Makino Journal: Journal of Materials Research / Volume 29 / Issue 12 / 28 June 2014 Published online by Cambridge University Press: 04 July 2014, pp. 1362-1368 (Cu0.47Zr0.45Al0.08)100–xDyx (x = 0, 1, 2, 3, 4; at.%) metallic glasses with greatly enhanced glass-forming ability (GFA) and plasticity were synthesized based on microalloying technique. The structure, thermal stability, and elastic properties of the BMG samples were studied by x-ray diffraction (XRD), differential scanning calorimetry (DSC), and ultrasonic measurements, respectively. With addition of minor dysprosium (Dy), fully metallic glassy rods with diameters exceeding 20 mm could be successfully fabricated by copper mold casting. In addition, the Cu–Zr–Al–Dy BMGs exhibit good mechanical properties under a compressive deformation mode, i.e., high yield strength of 1735–1906 MPa, Young's modulus of 85–100 GPa, and distinct plastic strain up to 4.02%. The strength and plasticity show remarkable correlations with glass transition temperature and Poisson's ratio, respectively. The role of minor Dy addition in enhancement in GFA and mechanical property of the Cu-rich BMGs is also discussed. Reconnection of skewed vortices Y. Kimura, H. K. Moffatt Based on experimental evidence that vortex reconnection commences with the approach of nearly antiparallel segments of vorticity, a linearised model is developed in which two Burgers-type vortices are driven together and stretched by an ambient irrotational strain field induced by more remote vorticity. When these Burgers vortices are exactly antiparallel, they are annihilated on the strain time-scale, independent of kinematic viscosity $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\nu $ in the limit $\nu \rightarrow 0$ . When the vortices are skew to each other, they are annihilated under this action over a local extent that increases exponentially in the stretching direction, with clear evidence of reconnection on the same strain time-scale. The initial helicity associated with the skewed geometry is eliminated during the process of reconnection. The model applies equally to the reconnection of weak magnetic flux tubes under the action of a strain field, when Lorentz forces are negligible. The Design and Performance of a Double Wien Filter Monochromator for Application in TEM A. Kirkland, J. Warner, J.S. Kim, P. Nellist, M. Mukai, H. Sawada, T. Kaneyama, K. Omoto, A. Kimura, A. Ikeda, J. Zhou Published online by Cambridge University Press: 09 October 2013, pp. 310-311 Extended abstract of a paper presented at Microscopy and Microanalysis 2013 in Indianapolis, Indiana, USA, August 4 – August 8, 2013. Intestinal mast cells and eosinophils in relation to Strongyloides ratti adult expulsion from the small and large intestines of rats Y. SHINTOKU, T. KADOSAKA, E. KIMURA, H. TAKAGI, S. KONDO, M. ITOH Journal: Parasitology / Volume 140 / Issue 5 / April 2013 Mucosal mast cells (MMC) play a crucial role in the expulsion of Strongyloides ratti adults from the small intestine of mice. We reported the large intestinal parasitism of S. ratti in rats, and there has been no report on MMC in the large intestine of the natural host. We studied kinetics of MMC, together with eosinophils, in the upper and lower small intestines, caecum and colon of infected rats. Two distinct phases of mastocytosis were revealed: one in the upper small intestine triggered by stimulation of 'ordinary' adults, and the other in the colon stimulated by 'immune-resistant' adults that started parasitizing the colon around 19 days post-infection. In all 4 intestinal sites, the MMC peaks were observed 5–7 days after the number of adult worms became the maximum and the height of MMC peaks appeared to be dependent on the number of parasitic adults, suggesting an important role played by worms themselves in the MMC buildup. Prevalence and epidemiological traits of HIV infections in populations with high-risk behaviours as revealed by genetic analysis of HBV Y. KOJIMA, T. KAWAHATA, H. MORI, K. FURUBAYASHI, Y. TANIGUCHI, A. IWASA, K. TANIGUCHI, H. KIMURA, J. KOMANO Journal: Epidemiology & Infection / Volume 141 / Issue 11 / November 2013 Published online by Cambridge University Press: 25 January 2013, pp. 2410-2417 The prevalence and epidemiological traits of human immunodeficiency virus (HIV)/hepatitis B virus (HBV) infections in high-risk populations (HRPs) remained unclarified in Japan. We determined the prevalence of HIV, HBV and Treponema pallidum (TP) and the viral genotypes in HRPs who attended primary sexually transmitted infection (STI) clinics in Osaka province during 2006–2011. Of 7898 specimens, 133 (1·7%) were HIV positive, which was significantly higher than the figures reported by Japanese Red Cross (0·0019%) and public health centres (0·27%) in Japan. The frequency of HIV-1 subtype B was 88·7%, followed by CRF01_AE (2·3%) and C (0·8%), which were almost identical to the national trend. HBV seroprevalence was surprisingly high in the HIV-positive group (63·2%), which was significantly higher than that in the HIV-negative group (25·6%). By contrast, there was no statistical correlation between HIV and TP infection. Interestingly, the distinct HBV genotypes Ae and G were prevalent in the HIV-positive population (60·0% and 20·0%, respectively), although both were rarely detected during nationwide surveillance. The transmission of HIV and HBV appeared to occur largely within a closed community early in life. Of note, about one-quarter of HIV-positive cases would have remained untested if health professionals had not motivated individuals to undergo HIV testing. This is the first evidence-based assessment of HIV positivity and HIV/HBV co-infection in HRPs at primary STIs in Japan and the effect of the involvement of health professionals in the diagnosis of HIV infections in asymptomatic carriers. The genotyping of HBV provided valuable information for understanding HIV epidemical traits. Effect of estradiol during culture of bovine oocyte–granulosa cell complexes on the mitochondrial DNA copies of oocytes and telomere length of granulosa cells M. Endo, K. Kimura, T. Kuwayama, Y. Monji, H. Iwata Journal: Zygote / Volume 22 / Issue 4 / November 2014 During the development of oocytes from early antral follicles (EAFs) to antral follicles (AFs), the mitochondrial DNA copy number (Mt DNA number) increases, and granulosa cells markedly proliferate. This study examined the effect of supplementation of culture medium with estradiol-17β (E2) on the in vitro growth of oocytes, and increases in the Mt DNA number, and telomere length during the in vitro culture of oocytes derived from EAFs (0.4–0.7 mm in diameter). The E2 supplementation improved antrum formation and the ratio of oocytes reaching the metaphase II (MII) stage, and there was a significant difference in these values between addition E2 concentrations of 10 μg/ml and 0.1 μg/ml. When the oocytes were cultured in the medium containing 10 μg/ml E2, the Mt DNA number determined by real-time polymerase chain reaction (PCR) significantly increased, and the ratio of the Mt DNA number at the end of culture to the Mt DNA number at the beginning of the culture was greatly different among cows, and could be predicted by the degree of the difference between the Mt DNA number of oocytes derived from EAFs and that of oocytes derived from AFs (3–6 mm in diameter). When oocytes were cultured for 16 days in a medium containing 10 μg/ml E2 or 0.1 μg/ml E2, the Mt DNA number of oocytes grown in vitro did not differ, but the telomere length of the granulosa cells was significantly greater in the 10 μg/ml E2 group than in the 0.1 μg/ml group. In conclusion, E2 supplementation in culture medium improved the growth of oocytes derived from EAFs, and a high E2 concentration increased the telomere length of the granulosa cells. Fabrication and analytical modeling of transverse mode piezoelectric energy harvesters Seon-Bae Kim, Jung-Hyun Park, Seung-Hyun Kim, Hosang Ahn, H. Clyde Wikle, Dong-Joo Kim Journal: MRS Online Proceedings Library Archive / Volume 1397 / 2012 Published online by Cambridge University Press: 25 May 2012, mrsf12-1397-p09-47 A transverse (d 33) mode piezoelectric cantilever was fabricated for energy harvesting. Various dimensions of interdigital electrodes (IDE) were deposited on a piezoelectric layer to examine the effects of electrode design on the performance of energy harvesters. Modeling was performed to calculate the output power of the devices. The estimation was based on Roundy's analytical modeling derived for a d 31 mode piezoelectric energy harvester (PEH). In order to apply the Roundy's model to d 33 mode PEH, the IDE configuration was converted to the area of top and bottom electrodes (TBE). The power conversion in d 33 mode PEH was commonly estimated by the product of piezoelectric layer's thickness and finger electrode's length. In addition, the spacing between fingers was regarded as gap between top and bottom electrodes. However, the output power in a transverse mode PEH increases continuously with the increase of finger spacing, which does not correspond to experimental results. In this research, the dimension of IDE was converted to that of TBE using conformal mapping, and variation of power of PEH was remodeled. The modified model suggests that the maximum power in a transverse mode PEH is obtained when the finger spacing is identical with effective finger spacing. The output power then decreases when finger spacing is larger than effective finger spacing. The decrease of efficiency may result from insufficient degree of poling and increased charged defect with increasing finger spacing. Microstructures in Pb(In1/2Nb1/2)O3 with the Perovskite B-site Randomness S. Mori, K. Kurushima, K. Kobayashi, H. Ohwa, N. Yasuda, K. Ohwada Published online by Cambridge University Press: 29 February 2012, mrsf11-1397-p09-32 We have investigated microstructures in both the antiferroelectric (AFE) and relaxor states of Pb(In1/2Nb1/2)O3 (PIN) with the perovskite structure by a transmission electron microscopy (TEM). Electron diffraction (ED) experiments revealed that the AFE state is characterized as the modulated structure with the modulation vector of q =1/4 1/4 0. High-resolution TEM images clearly show the coexistence of two types of domains consisting of the modulated and the nonmodulated structures with the 100 ∼ 200 nm size. On the other hand, in the relaxor state there appear two types of diffuse scatterings in the ED patterns. One is diffuse spots at the 1/2 1/2 0-type reciprocal positions and the other is diffuse streaks elongating along the <110> direction around the fundamental spots. The real-space TEM images clearly demonstrate the presence of nanodomains with the average size of ∼ 5 nm. These nanodomains in the relaxor state should be responsible for the characteristic dielectric properties. Mechanically Stable Free-Standing Bilayer Lipid Membranes in Microfabricated Silicon Chips Azusa Oshima, Ayumi Hirano-Iwata, Yasuo Kimura, Michio Niwano Published online by Cambridge University Press: 21 February 2012, mrsf11-1415-ii03-08 In this paper, we will discuss our recent approaches for improving the mechanical stability of free-standing bilayer lipid membranes (BLMs) by combining with BLM formation and microfabrication techniques. BLMs were prepared across a microaperture fabricated in a silicon (Si) chip and their mechanical stability and electric properties were investigated. BLMs suspended in a thin Si3N4 septum showed a dramatic improvement of BLM stability. The BLMs were resistant to voltage of ±1 V and the membrane lifetime was 15- ~40 h with and without incorporated channels. The membrane containing gramicidin channel exhibited tolerance to repetitive solution exchanges. At first, electric properties of the BLMs, such as noise level and current transient, were necessary to be improved. However, after coating the chip with insulator layers of Teflon and SiO2, total chip capacitance was reduced, leading to noise reduction (1-2 pA in peak-to-peak after low-pass filtering at 1 kHz) and elimination of current transients (< 0.5 ms). Since the vicinity of the aperture edge was remained uncoated, the BLMs formed in the Si chips still showed high mechanical stability after the insulator coatings. The mechanically stable BLMs having electric properties suitable for recording activities of biological channels will open up a variety of applications including high-throughput analysis of ion-channel proteins. Three-Step Deposition Method for Improvement of the Dielectric Properties of BST Thin Films H. Liu, V. Avrutin, C. Zhu, J.H. Leach, E. Rowe, L. Zhou, D. Smith, Ü. Özgür, H. Morkoç Epitaixal Ba0.5Sr0.5TiO3 (BST) thin films were grown on SrTiO3 (STO) and DyScO3 substrates by radio-frequency magnetron sputtering system using three-step method which involves a relatively low-temperature (573-773 K) growth of a BST interlayer sandwiched between two BST layers deposited at a high substrate temperature of 1068 K. X-ray diffraction measurement showed different strains on the films with interlayers grown at different temperatures. Post-growth thermal treatment reduced film strain to a great extent (the film strain of a tri-layer film with a 773 K grown interlayer is only -0.001). Comparing with the control films grown at high temperature, three-step technique improved the dielectric properties, especially increased dielectric constant by 60% for BST/STO and 31% for BST/DyScO3, respectively. High dielectric constant of 1631.4 and its tuning of 36.7% were achieved on the BST/STO with an interlayer grown on 773 K. Strongyloides ratti: transplantation of adults recovered from the small intestine at different days after infection into the colon of naive and infection-primed Wistar rats, and the effect of antioxidant treatment on large intestinal parasitism Y. SHINTOKU, H. TAKAGI, T. KADOSAKA, F. NAGAOKA, S. KONDO, M. ITOH, S. HONDA, E. KIMURA Journal: Parasitology / Volume 138 / Issue 8 / July 2011 Strongyloides ratti (Nagoya strain) is unique in that a portion of adults parasitizing the small intestine withstands 'worm expulsion', which starts at around day 8 post-infection (p.i.) by host immunity, and establishes in the large intestine after day 19 p.i. To investigate the mechanism, adults obtained from the small intestine at day 7 or 19 p.i. were transplanted into the colon of infection-primed immune rats. Adults obtained at day 7 p.i. were rejected quickly, whereas those obtained at day 19 p.i. could establish infection. Moreover, the body length and the number of intrauterine eggs increased in the large intestine. In a separate experiment, large intestinal parasitism was abolished by the treatment of host rats with an anti-oxidant, butylated hydroxyanisole. These results indicate that small intestinal adults between days 7 and 19 p.i. acquired the ability to parasitize the large intestine of immune rats, and that free radicals produced by the host may have played a significant role in the process.	CommonCrawl
Asymptotic properties of delayed matrix exponential functions via Lambert function DCDS-B Home Detecting features of epileptogenesis in EEG after TBI using unsupervised diffusion component analysis January 2018, 23(1): 145-160. doi: 10.3934/dcdsb.2018009 Sensitivity of combined chemo-and antiangiogenic therapy results in different models describing cancer growth Marzena Dolbniak , Malgorzata Kardynska and Jaroslaw Smieja , Systems Engineering Group, Silesian University of Technology, Akademicka 16, Gliwice, 44-100, Poland * Corresponding author: Jaroslaw Smieja Received November 2016 Revised June 2017 Published January 2018 Fund Project: This work was supported by the NCN grant DEC-2013/11/B/ST7/01713 Full Text(HTML) Figure(11) / Table(3) This paper is concerned with analysis of two anticancer therapy models focused on sensitivity of therapy outcome with respect to model structure and parameters. Realistic periodic therapies are considered, combining cytotoxic and antiangiogenic agents, defined on a fixed time horizon. Tumor size at the end of therapy and average tumor size calculated over therapy horizon are chosen to represent therapy outcome. Sensitivity analysis has been performed numerically, concentrating on model parameters and structure at one hand, and on treatment protocol parameters, on the other. The results show that sensitivity of the therapy outcome highly depends on the model structure, helping to discern a good model. Moreover, it is possible to use this analysis to find a good protocol in case of heterogeneous tumors. Keywords: Chemotherapy, antiangiogenic therapy, sensitivity. Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35. Citation: Marzena Dolbniak, Malgorzata Kardynska, Jaroslaw Smieja. Sensitivity of combined chemo-and antiangiogenic therapy results in different models describing cancer growth. 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Reynolds, Anti-angiogenic therapy for cancer: Current progress, unresolved questions and future directions, Angiogenesis, 17 (2014), 471-494. doi: 10.1007/s10456-014-9420-y. Google Scholar J. Welti, S. Loges, S. Dimmeler and P. Carmeliet, Recent molecular discoveries in angiogenesis and antiangiogenic therapies in cancer, The Journal of Clinical Investigation, 8 (2013), 3190-3200. doi: 10.1172/JCI70212. Google Scholar J. Zalevsky, A. K. Chamberlain, H. M. Horton, S. Karki, I. W. Leung, T. J. Sproule, G. A. Lazar, D. C. Roopenian and J. R. Desjarlais, Enhanced antibody half-life improves in vivo activity, Nature Biotechnology, 28 (2010), 157-159. doi: 10.1038/nbt.1601. Google Scholar Figure 1. Parameter sensitivity ranking calculated with first-order sensitivity functions for the model (2). Sensitivity indices for parameters were normalized to the maximum value Figure Options Download full-size image Download as PowerPoint slide Figure 2. Parameter sensitivity rankings calculated with first-order sensitivity functions for different treatment protocols and the model (2): chemotherapy administered every (a) 2 days, (b) 4 days, (c) 10 days; antiangiogenic agents administered every (a) 10 days, (b) 13 days, (c) 20 days. Sensitivity indices for parameters were normalized to the maximum value to facilitate comparison of the rankings Figure 3. The heatmap representing sensitivity of the treatment outcome, defined as the number of cancer cells at the end of treatment (right) and two sample solutions that illustrate its meaning (left) Figure 4. Evaluation of various treatment protocols for the models (a, b) (2) and (c, d) (3); taking into account: low drugs toxicity (a, c) and high drugs toxicity (b, d). Axes are labeled by the number of days between consecutive doses of respective drugs Figure 5. An example of the model (2) response for treatment protocol selected on the basis of J Figure 6. Changes in therapy outcome caused by different administration times of the same total doses for the models (a, b) (2) and (c, d) (3). Left and right columns represent indices given by the tumor volume at the end of treatment and mean tumor volume during the treatment, respectively Figure 7. Changes in therapy outcome for model (2) due to changes in parameter $\beta$: (a, b) increased by 50%; (c, d) decreased by 50%. Left and right columns represent indices given by the tumor volume at the end of treatment and mean tumor volume during the treatment, respectively Figure 8. Changes in therapy efficiency caused by variability in parameters for model (2). Maximum change is presented. (a, b) $\beta$, (c, d) $\gamma$, (e, f) $\lambda$. Left and right columns represent indices given by the tumor volume at the end of treatment and mean tumor volume during the treatment, respectively Figure 9. Changes in therapy efficiency caused by variability in parameters for model (2). Mean change is presented. (a, b) $\beta$, (c, d) $\gamma$, (e, f) $\lambda$. Left and right columns represent indices given by the tumor volume at the end of treatment and mean tumor volume during the treatment, respectively Figure 10. Changes in therapy efficiency caused by variability in parameters for model (3). Max change is presented. (a, b) $\beta$, (c, d) $\gamma$, (e, f) $\lambda$. Left and right columns represent indices given by the tumor volume at the end of treatment and mean tumor volume during the treatment, respectively Figure 11. Changes in therapy efficiency caused by variability in parameters for model (3). Mean change is presented. (a, b) $\beta$, (c, d) $\gamma$, (e, f) $\lambda$. Left and right columns represent indices given by the tumor volume at the end of treatment and mean tumor volume during the treatment, respectively Table 1. Nominal values of parameters Par. Values Description Model (2) Model (3) $N_0$ $10^6$ $10^6$ Initial no. of cancer cells $[mm^3]$ $K_0$ $N_0 \cdot 10 $ $N_0 \cdot 10 $ Initial no. of endothelial cells $[mm^3]$ $\beta$ $1.92 \cdot 10^{-1}$ $1.92 \cdot 10^{-1}$ Tumor growth parameter $[day^{-1}]$ $\gamma$ $1.755 \cdot 10^{1}$ $1.755 \cdot 10^{1}$ Endothelial stimulation parameter $[day^{-1}]$ $\lambda$ $8.73 \cdot 10^{-5}$ $8.73 \cdot 10^{-5}$ Endothelial inhibition parameter $[day^{-1} mm^{-\frac{2}{3}}]$ $\mu$ 0 0 Natural mortality of endothelial cells $[day^{-1}]$ $\psi$ $1.17 \cdot 10^{-2}$ - Cytostatic killing parameter (for cancer cells) $[mg^{-1} m^2]$ $\psi * $ - $1.17 \cdot 10^{-2}$ Maximum value of cytostatic killing parameter (for cancer cells) -$[mg^{-1} m^2]$ $\eta$ $1.17 \cdot 10^{-4}$ $1.17 \cdot 10^{-4}$ Cytostatic killing parameter (for endothelial cells) $[mg^{-1} m^2]$ $\xi$ $1.75 \cdot 10^{-2}$ $5.25 \cdot 10^{-2}$ Anti-angiogenic killing parameter $[mg^{-1} kg]$ $\sigma$ - $3.5\cdot 10^{-1}$ Parametr used in the efficacy curve of the drug $\rho_{opt}$ - 2 $\frac{K}{N}$ ratio, for which the most effective functionality of vasculature is observed Table Options Download as excel Table 2. Pharmacokinetics parameters Parameter $k_u$ $k_v$ $T_{u1/2}$ $T_{v1/2}$ Model (2) $0.0117$ $0.0175$ 12[h] 3.5[days] $u$ -chemotherapy $v$ -antiangiogenic therapy Table 3. Performance index parameters for models (2) and (3) Case (ⅰ) (ⅱ) Parameter $r_1$ $r_2$ $r_3$ $r_1$ $r_2$ $r_3$ Value $1$ $0.1 \cdot 10^4$ $0.05 \cdot 10^4$ $1$ $0.5 \cdot 10^5$ $0.25 \cdot 10^5$ Cristian Morales-Rodrigo. A therapy inactivating the tumor angiogenic factors. Mathematical Biosciences & Engineering, 2013, 10 (1) : 185-198. doi: 10.3934/mbe.2013.10.185 Ismail Abdulrashid, Abdallah A. M. Alsammani, Xiaoying Han. Stability analysis of a chemotherapy model with delays. Discrete & Continuous Dynamical Systems - B, 2019, 24 (3) : 989-1005. doi: 10.3934/dcdsb.2019002 Jan Poleszczuk, Marek Bodnar, Urszula Foryś. New approach to modeling of antiangiogenic treatment on the basis of Hahnfeldt et al. model. Mathematical Biosciences & Engineering, 2011, 8 (2) : 591-603. doi: 10.3934/mbe.2011.8.591 Baba Issa Camara, Houda Mokrani, Evans K. Afenya. Mathematical modeling of glioma therapy using oncolytic viruses. Mathematical Biosciences & Engineering, 2013, 10 (3) : 565-578. doi: 10.3934/mbe.2013.10.565 Manuel Delgado, Cristian Morales-Rodrigo, Antonio Suárez. Anti-angiogenic therapy based on the binding to receptors. Discrete & Continuous Dynamical Systems - A, 2012, 32 (11) : 3871-3894. doi: 10.3934/dcds.2012.32.3871 Danthai Thongphiew, Vira Chankong, Fang-Fang Yin, Q. Jackie Wu. An on-line adaptive radiation therapy system for intensity modulated radiation therapy: An application of multi-objective optimization. Journal of Industrial & Management Optimization, 2008, 4 (3) : 453-475. doi: 10.3934/jimo.2008.4.453 Urszula Ledzewicz, Heinz Schättler. Drug resistance in cancer chemotherapy as an optimal control problem. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 129-150. doi: 10.3934/dcdsb.2006.6.129 Urszula Ledzewicz, Heinz Schättler. Controlling a model for bone marrow dynamics in cancer chemotherapy. Mathematical Biosciences & Engineering, 2004, 1 (1) : 95-110. doi: 10.3934/mbe.2004.1.95 Craig Collins, K. Renee Fister, Bethany Key, Mary Williams. Blasting neuroblastoma using optimal control of chemotherapy. Mathematical Biosciences & Engineering, 2009, 6 (3) : 451-467. doi: 10.3934/mbe.2009.6.451 Urszula Ledzewicz, Behrooz Amini, Heinz Schättler. Dynamics and control of a mathematical model for metronomic chemotherapy. Mathematical Biosciences & Engineering, 2015, 12 (6) : 1257-1275. doi: 10.3934/mbe.2015.12.1257 Urszula Ledzewicz, Heinz Schättler, Shuo Wang. On the role of tumor heterogeneity for optimal cancer chemotherapy. Networks & Heterogeneous Media, 2019, 14 (1) : 131-147. doi: 10.3934/nhm.2019007 Piotr Bajger, Mariusz Bodzioch, Urszula Foryś. Singularity of controls in a simple model of acquired chemotherapy resistance. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2039-2052. doi: 10.3934/dcdsb.2019083 Tao Yu. Measurable sensitivity via Furstenberg families. Discrete & Continuous Dynamical Systems - A, 2017, 37 (8) : 4543-4563. doi: 10.3934/dcds.2017194 Caglar S. Aksezer. On the sensitivity of desirability functions for multiresponse optimization. Journal of Industrial & Management Optimization, 2008, 4 (4) : 685-696. doi: 10.3934/jimo.2008.4.685 Jianjun Paul Tian. Finite-time perturbations of dynamical systems and applications to tumor therapy. Discrete & Continuous Dynamical Systems - B, 2009, 12 (2) : 469-479. doi: 10.3934/dcdsb.2009.12.469 Urszula Ledzewicz, Helen Moore. Optimal control applied to a generalized Michaelis-Menten model of CML therapy. Discrete & Continuous Dynamical Systems - B, 2018, 23 (1) : 331-346. doi: 10.3934/dcdsb.2018022 Rachid Ouifki, Gareth Witten. A model of HIV-1 infection with HAART therapy and intracellular delays. Discrete & Continuous Dynamical Systems - B, 2007, 8 (1) : 229-240. doi: 10.3934/dcdsb.2007.8.229 Ben Sheller, Domenico D'Alessandro. Analysis of a cancer dormancy model and control of immuno-therapy. Mathematical Biosciences & Engineering, 2015, 12 (5) : 1037-1053. doi: 10.3934/mbe.2015.12.1037 Harsh Vardhan Jain, Avner Friedman. Modeling prostate cancer response to continuous versus intermittent androgen ablation therapy. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 945-967. doi: 10.3934/dcdsb.2013.18.945 Avner Friedman, Xiulan Lai. Antagonism and negative side-effects in combination therapy for cancer. Discrete & Continuous Dynamical Systems - B, 2019, 24 (5) : 2237-2250. doi: 10.3934/dcdsb.2019093 PDF downloads (33) HTML views (80) Marzena Dolbniak Malgorzata Kardynska Jaroslaw Smieja	CommonCrawl
Is there any formal foundation to ultrafinitism? Ultrafinitism is (I believe) a philosophy of mathematics that is not only constructive, but does not admit the existence of arbitrarily large natural numbers. According to wikipedia, it has been primarily studied by Alexander Esenin-Volpin. On his opinions page, Doron Zeilberger has often expressed similar opinions. Wikipedia also says that Troelstra said in 1988 that there were no satisfactory foundations for ultrafinitism. Is this still true? Even if so, are there any aspects of ultrafinitism that you can get your hands on coming from a purely classical perspective? Edit: Neel Krishnaswami in his answer gave a link to a paper by Vladimir Sazonov (On Feasible Numbers) that seems to go a ways towards giving a formal foundation to ultrafinitism. First, Sazonov references a result of Parikh's which says that Peano Arithmetic can be consistently extended with a set variable $F$ and axioms $0\in F$, $1\in F$, $F$ is closed under $+$ and $\times$, and $N\notin F$, where $N$ is an exponential tower of $2^{1000}$ twos. Then, he gives his own theory, wherein there is no cut rule and proofs that are too long are disallowed, and shows that the axiom $\forall x\ \log \log x < 10$ is consistent. lo.logic mathematical-philosophy ultrafinitism constructive-mathematics PyRulez Michael O'ConnorMichael O'Connor $\begingroup$ Edward Nelson is another well-known exponent of untrafinitism. He has many essays about it on his webpage here : math.princeton.edu/~nelson/papers.html $\endgroup$ – Andy Putman Oct 30 '10 at 2:45 $\begingroup$ Winking emoticons aside, it's probably good to have people like Nelson and Zeilberger around, to test received opinions and keep people on their toes. $\endgroup$ – Todd Trimble♦ Oct 30 '10 at 12:53 $\begingroup$ I hope everyone has heard the story told by Harvey Friedman: "I have seen some ultrafinitists go so far as to challenge the existence of 2^100 as a natural number, in the sense of there being a series of 'points' of that length. There is the obvious 'draw the line' objection, asking where in 2^1, 2^2, 2^3, … , 2^100 do we stop having 'Platonistic reality'? Here this … is totally innocent, in that it can be easily be replaced by 100 items (names) separated by commas. I raised just this objection with the (extreme) ultrafinitist Yesenin-Volpin during a lecture of his." (cont...) $\endgroup$ – Todd Trimble♦ Oct 30 '10 at 22:37 $\begingroup$ "He asked me to be more specific. I then proceeded to start with 2^1 and asked him whether this is 'real' or something to that effect. He virtually immediately said yes. Then I asked about 2^2, and he again said yes, but with a perceptible delay. Then 2^3, and yes, but with more delay. This continued for a couple of more times, till it was obvious how he was handling this objection. Sure, he was prepared to always answer yes, but he was going to take 2^100 times as long to answer yes to 2^100 then he would to answering 2^1. There is no way that I could get very far with this." $\endgroup$ – Todd Trimble♦ Oct 30 '10 at 22:38 $\begingroup$ @Zsban,Daniel: Those are real numbers, not integers. Perhaps we know their values to less than 100 bits of accuracy... $\endgroup$ – Gerald Edgar May 23 '11 at 21:05 There are no foundations for ultrafinitism as satisfactory for it as (say) intuitionistic logic is for constructivism. The reason is that the question of what logic is appropriate for ultrafinitism is still an open one, for not one but several different reasons. First, from a traditional perspective -- whether classical or intuitionistic -- classical logic is the appropriate logic for finite collections (but not K-finite). The idea is that a finite collection is surveyable: we can enumerate and look at each element of any finite collection in finite time. (For example, the elementary topos of finite sets is Boolean.) However, this is not faithful to the ultra-intuitionist idea that a sufficiently large set is impractical to survey. So it shouldn't be surprising that more-or-less ultrafinitist logics arise from complexity theory, which identifies "practical" with "polynomial time". I know two strands of work on this. The first is Buss's work on $S^1_2$, which is a weakening of Peano arithmetic with a weaker induction principle: $$A(0) \land (\forall x.\;A(x/2) \Rightarrow A(x)) \Rightarrow \forall x.\;A(x)$$ Then any proof of a forall-exists statement has to be realized by a polynomial time computable function. There is a line of work on bounded set theories, which I am not very familiar with, based on Buss's logic. The second is a descendant of Bellantoni and Cook's work on programming languages for polynomial time, and Girard's work on linear logic. The Curry-Howard correspondence takes functional languages, and maps them to logical systems, with types going to propositions, terms going to proofs, and evaluation going to proof normalization. So the complexity of a functional program corresponds in some sense to the practicality of cut-elimination for a logic. IIRC, Girard subsequently showed that for a suitable version of affine logic, cut-elimination can be shown to take polynomial time. Similarly, you can build set theories on top of affine logic. For example, Kazushige Terui has since described a set theory, Light Affine Set Theory, whose ambient logic is linear logic, and in which the provably total functions are exactly the polytime functions. (Note that this means that for Peano numerals, multiplication is total but exponentiation is not --- so Peano and binary numerals are not isomorphic!) The reason these proof-theoretic questions arise, is that part of the reason that the ultra-intuitionist conception of the numerals makes sense, is precisely because they deny large proofs. If you deny that large integers exist, then a proof that they exist, which is larger than the biggest number you accept, doesn't count! I enjoyed Vladimir Sazonov's paper "On Feasible Numbers", which explicitly studies the connection. I should add that I am not a specialist in this area, and what I've written is just the fruits of my interest in the subject -- I have almost certainly overlooked important work, for which I apologize. Neel KrishnaswamiNeel Krishnaswami $\begingroup$ Thanks! That Sazonov paper (which is available not through Springer here: csc.liv.ac.uk/~sazonov/papers/lcc.ps) seems quite interesting. It makes me think the correct answer to my original question might be "yes"! $\endgroup$ – Michael O'Connor Oct 30 '10 at 17:53 $\begingroup$ Taking cut away is really brutal, though -- it's mathematics with no lemmas allowed! This is where linear logic shines: it lets you bound the size of the expansion from the abbreviation power of lemmas. $\endgroup$ – Neel Krishnaswami Oct 30 '10 at 18:21 $\begingroup$ I don't understand the "weaker induction principle" you mention. It seems that you can use it to prove that for all x: x=0. $\endgroup$ – Sune Jakobsen Oct 31 '10 at 8:51 $\begingroup$ @Sune: This is a flooring division, so $x/2$ gives the largest integer less than or equal to $\frac{x}{2}$ For example, $3/2 = 1$. In particular, this means that in general we only have $2 \times x/2 \leq x$. $\endgroup$ – Neel Krishnaswami Oct 31 '10 at 10:12 $\begingroup$ A clarification: Buss's polynomial induction schema is equivalent to usual induction. It only gets weak when you severely restrict the class of formulas allowed in the schema, and this works for usual induction too. When the schemata are restricted to a class of formulas not closed under bounded quantification, the two schemata are no longer equivalent, hence both are used to axiomatize different theories of bounded arithmetic (such as $S^1_2$). However, what makes these theories weak is the restriction on formula complexity, not the form of the induction schema. $\endgroup$ – Emil Jeřábek Jun 7 '11 at 14:51 I've been interested in this question for some time. I haven't put any serious thought into it, so all I can offer is a further question rather than an answer. (I'm interested in the answers that have already been given though.) My question is this. Is there a system of logic that will allow us to prove only statements that have physical meaning? I don't have a formal definition of "physically meaningful" so instead let me try to illustrate what I mean by an example or two. Consider first the statement that the square root of 2 is irrational. What would be its physical meaning? A naive suggestion would be that if you drew an enormous grid of squares of side length one centimetre and then measured the distance between (0,0) and (n,n) for some n, then the result would never be an integer number of centimetres. But this isn't physically meaningful according to my nonexistent definition because you can't measure to infinite accuracy. However, the more finitistic statement that the square root of 2 can't be well approximated by irrationals has at least some meaning: it tells us that if n isn't too large then there will be an appreciable difference between the distance from (0,0) to (n,n) and the nearest integer. As a second example, take the statement that the sum of the first n positive integers is n(n+1)/2. If n is too huge, then there is no hope of arranging a huge triangular array and counting how many points are in it. So one can't check this result experimentally once n is above a certain threshold (though there might be ingenious ways of checking it that are better than the obvious method). This shows that we can't apply unconstrained induction, but there could be a principle that said something like, "If you keep on going for as long as is practical, then the result will always hold." One attitude one might take is that this would be to normal classical mathematics as the use of epsilons and deltas is to the mathematics of infinities and infinitesimals. One could try to argue that statements that appear to be about arbitrarily large integers or arbitrarily small real numbers (or indeed any real numbers to an arbitrary accuracy) are really idealizations that are a convenient way of talking about very large integers, very small real numbers and very accurate measurements. If I try to develop this kind of idea I rapidly run into difficulties. For example, what is the status of the argument that proves that the sum of the first n integers is what it is because you can pair them off in a nice way? In general, if we have a classical proof that something will be the case for every n, what do we gain from saying (in some other system) that the conclusion of the proof holds only for every "feasible" n? Why not just say that the classical result is valid, and that this implies that all its "feasible manifestations" are valid? Rather than continue with these amateur thoughts, I'd just like to ask whether similar ideas are out there in a better form. Incidentally, I'm not too fond of Zeilberger's proposal because he has a very arbitrary cutoff for the highest integer -- I'd prefer something that gets fuzzier as you get larger. Edit: on looking at the Sazonov paper, I see that many of these thoughts are in the introduction, so that is probably a pretty good answer to my question. I'll see whether I find what he does satisfactory. gowersgowers $\begingroup$ In this system of logic, should the Poincare recurrence theorem be provable? In some way it contradicts the second law of thermodynamics... $\endgroup$ – Łukasz Grabowski Nov 4 '10 at 18:16 $\begingroup$ If I am not making a mistake, the mathematical philosophy you are referring to is called actualism. I also think finite model theory is relevant here, they use rational languages (no function symbols like + and .) to avoid forcing the models to be infinite. $\endgroup$ – Kaveh Nov 9 '10 at 23:51 Here is an ultrafinitist manifesto (link) I have co-written a few years ago: http://arxiv.org/pdf/cs/0611100v1 It is absolutely not a finished paper (there are a few inaccuracies, and many parts are sloppy), but it contains a brief history of ultrafinitistic ideas from the early greeks all the way to present time, a number of refs, as well as a sketch of a programme towards a model theory and a proof theory of ultrafinitistic mathematics. You may also want to google the FOM list on "ultrafinitism", there are a few posts by Podnieks, Sazonov, myself, and a few others pro and contra ultrafinitism. Mirco A. MannucciMirco A. Mannucci $\begingroup$ The most recent on FOM being the thread I started in March cs.nyu.edu/pipermail/fom/2011-March/015326.html and the subsequent replies and links. $\endgroup$ – Daniel Mehkeri May 24 '11 at 2:03 $\begingroup$ I added a link to the arXiv abstract page $\endgroup$ – David Roberts May 24 '11 at 2:26 One could take ETCS - which is a finite, first order axiomatisation of the category of sets - and remove the axiom that guarantees the existence of a natural numbers object. Then in this set up one can prove the existence of sets of finite cardinality, but not the existence of a set with cardinality $\geq \aleph_0$. Moreover one could weaken this to a finitist version of Palmgren's constructive, predicative version of ETCS, which would be a well-pointed $\Pi$-pretopos with enough projectives. This latter version minus function sets (the '$\Pi$' in $\Pi$-pretopos) would perhaps be closer to Nelson's idea, because at one point he expresses doubts about the finiteness of $n^m := \{1,\ldots,n\}^{\{1,\ldots,m\}}$ for large $n$ and $m$. EDIT: I should say that in a formal setting this would translate to the unprovability of the statement "$n^m$ is finite", which would be the case in a model of a "finite set theory" without function sets. Or one can just work with Nelson's arithmetic, which is the most ultrafinitist thing I know. For example, exponentiation is not a total function in his theory. David RobertsDavid Roberts $\begingroup$ A Π-pretopos still has exponentials, which means that $n^m$ will still exist. So I think you want a non-Π pretopos if you want to exclude exponentials. $\endgroup$ – Mike Shulman Nov 1 '10 at 0:30 $\begingroup$ Ah, thanks. I'll edit the answer to reflect that. $\endgroup$ – David Roberts Nov 1 '10 at 0:46 $\begingroup$ Still a minor error: you identify the "Π" "Π-pretopos" as power sets, but it's actually function sets (exponentials). Palmgren's theory, being (weakly) predicative, already lacks power sets (and it's possible to have function sets without power sets because of the intuitionistic logic). $\endgroup$ – Toby Bartels Sep 9 '11 at 22:24 $\begingroup$ Hm, ok. Would it be ok if I just changed it to 'latter version minus function sets (the '$\Pi$'..' $\endgroup$ – David Roberts Sep 9 '11 at 23:14 $\begingroup$ Yes, that would be correct. $\endgroup$ – Toby Bartels Nov 28 '12 at 6:23 I've always thought that assuming a formalist position (i.e., mathematics is merely the manipulation of symbols) easily allows for an ultrafinitist position. The formalist may easily grant that $b=10^{10^{10^{10}}}$ is a formal number, in the sense that it is permissible in the grammar, (e.g., $\log_{10}(10^{10^{10^{10}}})>10^{9^8}$ is TRUE) without it being an ontological number (case and point: there is no string of characters which is $10^{10^{10}}$ long, the length of would-be decimal representation of $b$). Similarly, axioms which fool us into thinking they are about infinity are happily read as finite strings, from which point they may be perfectly acceptable. From this point of view, the entities which might otherwise be numbers, but will be rejected here, are not those which are expressible in a few characters or even a few pages of characters, but those for which no human will ever come close to expressing, calculating with, etc. I am not advocating formalism here, but it seems to make ultrafinitism philosophically defensible. As I have put it, it also makes ultrafinitism inconsequential, except as a philosophical point. AndrewLMarshallAndrewLMarshall $\begingroup$ to manipulate symbols you need to accept something like finitism. Remember that Hilbert himself was fine with finitism, the goal of his formalism was reducing higher stuff to finitism. $\endgroup$ – Kaveh Sep 28 '11 at 11:20 Just my personal opinion, as a non-specialist in this area, is that ultrafinitism cannot be formalized for the same reason that the straw which breaks the camel's back cannot be formalized. We know that a healthy camel can carry one kilogram, but not 10 tons. So there must be some point at which the camel cannot carry another straw, but it is impossible to define. In practice, various things would start to go wrong with the camel as the limit is reached. In the same way, we cannot list all of the elements of the von Neumann universe 6th stage, which contains $2^{65536}$ elements, which are the sets that you can construct from the empty set alone in ZF set theory up to a nesting depth of 6. However, it is not possible to say exactly what the bounds are for the representation of sets and numbers. There is some $n$ for which a truly random sequence of $2^n$ decimal digits cannot be written down. There are only finitely many atoms in the universe, one assumes, which means that there must be a bound on how large an integer can be written down. But things would just start to go badly wrong as we approach the limit. For example, we might run out of trees to make paper with, or we might run out of silicon to make memory chips with, and so forth. My own personal solution to this problem is to divide all numbers into dark numbers, which include those real numbers which are truly random and therefore impossible to write as a finite formula as one would do for $\pi$, and grey numbers, which are clearly impossible to represent with all of the atoms in the universe, and then the bright numbers which we use every day, like 3. The problem with this classification is that there is no clear-cut boundary between the bright numbers and grey numbers. And in my opinion, there never will be, just as we will never be able to formalize how many straws will break the camel's back. The best approach, I think, is to acknowledge philosophically that there are limits, but to not worry about them in practice. Because in practice, we will never go over the limit. Alan U. KenningtonAlan U. Kennington There is this argument against Nelson's predicative arithmetic which basically says that the assumption that exponentiation is not total, which is in some sense the whole reason to start predicative arithmetic, implies the inconsistency of the predicative arithmetic. Stefan GeschkeStefan Geschke I would suggest the following axiomatization to my ultrafinitist friends. Let Nx mean "x is a natural number", Sxy mean "y succeeds x", and 0 to be "zero". The Peano Axioms are: 1/ N0 2/ S is into N 3/ S is total on N (every number has a successor) 4/ S is a function 5/ S is one-to-one 6/ 0 is not in the image of S 7/ Induction Remove Axiom 3. Then the models of these axioms are: the standard model (if it exists) and the initial segments. {0} for instance is a model. One can work either in second-order logic and define sequences as second-order entities (http://www.andrewboucher.com/papers/arith-succ.pdf) or work in first-order logic and add sequences directly as first-order entities, with some additional axioms (http://www.andrewboucher.com/papers/fpa.pdf). With sequences one can make the usual recursive definitions of addition, multiplication, and exponentiation, and then towers of powers. It will not, of course, be able to prove any of them total. So the ultrafinitist who has any particular idea which numbers are permissible and which are not can simply add in the axioms he wants, such as E/ "the product of 100 and 100 exist" and F/ "a tower of 10 powers of 2 does not exist". IMHO, these assumptions are not of any mathematical interest, since the system without Axiom 3 is capable of proving many mathematical theorems (Quadratic Reciprocity...), and adding any axioms such as E or F only adds trivial capabilities to prove additional theorems. So it is better, mathematically at least (and IMHO philosophically), to be agnostic about the successor axiom, rather than an atheist or a theist. The question in the title suggests that there already is a formal foundation (call it $\mathcal F$) for finitism. Maybe ZFC minus Axiom of Infinity would be such a foundation. It might then make sense to argue philosophically that $\mathcal F$ is really a formal foundation for ultra-finitism, after all. According to Wittgenstein, the meaning of a word or phrase is encapsulated by its use. Now consider a natural number $n_0$ that is so large that no use, or even mention, of this specific number could possibly be made by humans, either directly or indirectly. Then $n_0$ does not really have any meaning. And so what ZFC-Inf really "means", is ultra-finitism. Bjørn Kjos-HanssenBjørn Kjos-Hanssen $\begingroup$ This is not totally unreasonable, but my understanding is that we are easily able to express numbers which an ultrafinitist would view with disdain, such as $10^{10^{10}}$ (recalling that a googol exceeds our current estimates of the number of fermions in the universe). $\endgroup$ – Niel de Beaudrap Oct 30 '10 at 13:33 $\begingroup$ ZFC-Infinity can prove the totality of $<\epsilon_0$-recursive functions. This goes a long way beyond even the Ackermann function, which is already very, very far from ultrafinitism. Proper ultrafinitists don't believe in factorial! $\endgroup$ – Daniel Mehkeri Nov 1 '10 at 1:17 $\begingroup$ @Bjørn: Maybe, but there are other ways out of the "first non-feasible number" problem. It does not follow from mathematical induction that all inhabited subsets of the natural numbers have a first element - that requires classical logic, so non-constructive, so presumably, a fortiori, non-ultrafinitist. Plus an ultrafinitist can also deny full mathematical induction (which is the essence of bounded arithmetic for example). $\endgroup$ – Daniel Mehkeri Nov 1 '10 at 16:53 $\begingroup$ I do not think ZF MINUS Infinity is a foundation for ultrafinitism, way too "infinitary". People with an interest in ultrafinite themes (like myself) have problems not only with actual infinity, but with potential infinity as well. This is not a place for a philosophical discussions, but in my "manifesto" quoted in my answer above you will find some perspectives on this specific issue $\endgroup$ – Mirco A. Mannucci Jun 1 '11 at 16:32 $\begingroup$ ZFC-Inf (which is essentially PA) is not even a foundation for finitism, let alone ultra-finitism. People have argued that finitism is captured by PRA. Finitists have issues with quantification over infinite sets, so an unbounded quantifier is problematic. $\endgroup$ – Kaveh Sep 28 '11 at 11:27 Not the answer you're looking for? Browse other questions tagged lo.logic mathematical-philosophy ultrafinitism constructive-mathematics or ask your own question. Are there any good nonconstructive "existential metatheorems"? Single logic foundation vs. multi-logic foundation Are there any mathematical objects that exist but have no concrete examples? Is there a finite-dimensional vector space whose dimension cannot be found? Variable-centric logical foundation of calculus What is the status of irrational numbers within finitism/ultrafinitism? Does there exist a non-trivial Ultrafinitist set theory? Formal/rigorous treatment of (im)predicativity/predicativism Does foundation/regularity have any categorical/structural consequences, in ZF? Is there any physical or computational justification for non-constructive axioms such as AC or excluded middle?	CommonCrawl
Quasi-convex Hamilton-Jacobi equations posed on junctions: The multi-dimensional case Blow-up phenomena and travelling wave solutions to the periodic integrable dispersive Hunter-Saxton equation December 2017, 37(12): 6437-6470. doi: 10.3934/dcds.2017279 Global solution in critical spaces to the compressible Oldroyd-B model with non-small coupling parameter Ruizhao Zi , School of Mathematics and Statistics & Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China Corresponding author: Ruizhao Zi Received April 2017 Published August 2017 This paper is dedicated to the global well-posedness issue of the compressible Oldroyd-B model in the whole space $\mathbb{R}^d$ with $d≥2 $. By exploiting the intrinsic structure of the system, we prove that if the initial data is small enough (depending on the coupling parameter), this set of equations admits a unique global solution in a certain critical Besov space. 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