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Bacterial Resistance to Aminoglycoside Antibiotics
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Aminoglycoside (AG) antibiotics (Box [1](#BX1){ref-type="boxed-text"}) have not been an exception to the fact that after their introduction in clinical practice, resistance has been recorded ([@B85]). In fact, the three classes of aminoglycoside-modifying enzymes, aminoglycoside acetyltransferases (AACs), aminoglycoside phosphotransferases (APHs), and aminoglycoside nucleotidyltransferases (ANTs), have been widely detected in most pathogenic bacteria as a major determinant of resistance; in these bacteria the presence of aminoglycoside-modifying enzymes correlated with patterns of AG susceptibility ([@B76]). The modified AG (either by acetylation, phosphorylation or nucleotidylation) fails to inhibit their bacterial target, the 30S ribosomal subunit ([@B76]). Most genes encoding aminoglycoside-modifying enzymes are plasmid-located (indicative of a potential acquisition by horizontal gene transfer processes) and confer the bacterial hosts with high levels of AG resistance ([@B19]).
**Box 1.** Aminoglycosides: origins, structure, mode of action, resistance and clinical use.
Most aminoglycoside antibiotics are produced by bacterial species of the genus *Streptomyces*, such as the antitubercular streptomycin that is produced by *S. griseus* being the first antibiotic identified from bacteria. Other genera producing aminoglycosides are *Micromonospora* and *Bacillus*. Many semi-synthetic aminoglycosides, such as amikacin, have also been produced ([@B55]; [@B51]; [@B74]).
Structurally, aminoglycosides are formed by an aminocyclitol (commonly, 2-deoxystreptamine) with additional amino sugars bound by glycosidic bonds. There are two large families of 2-deoxystreptamine aminoglycosides, those carrying substitutions at positions 4 and 5 of the 2-deoxystreptamine ring (including neomycin, paromomycin, lividomycin, ribostamycin and butirosin) and those being substituted at positions 4 and 6 of the 2-deoxystreptamine (including kanamycin, amikacin, tobramycin, dibekacin, arbekacin, gentamicin, isepamicin, sisomicin, and netilmicin). The carbon atoms in the sugar bound to position 4 of the 2-deoxystreptamine ring are named with primed numbers ('), and those in the sugar bound to positions 5 or 6 of the 2-deoxystreptamine ring are named with double-primed numbers ("). Other aminoglycosides contain aminocyclitols distinct to 2-deoxystreptamine (this is the case of streptomycin or apramycin) or are formed by fused amino sugar rings (i.e., spectinomycin) ([@B51]; [@B74]). The following figure shows the structure of kanamycin A, an example of 4,6 di-substituted 2-deoxystreptamine aminoglycoside antibiotic.
{#d35e349}
The bacterial target of aminoglycosides is the 30S small ribosomal subunit, and their global effect is the interference with protein synthesis. In bacterial cells, translation is initiated when the 30S ribosomal subunit binds the Shine-Dalgarno sequence (because of sequence complementarity between the Shine-Dalgarno sequence and the 16S rRNA molecule of the 30S ribosomal subunit), which is normally present in the 5′ untranslated region of mRNAs. Next, initiation factors and fMet-tRNA will join the complex that finally will recruit the 50S ribosomal subunit in order to start translation. Aminoglycoside binding to the 30S subunit does not affect the binding of mRNA and the large 50S subunit, so translation can proceed. However, aminoglycosides differ in their binding site at the 30S subunit, hence affecting the protein production at different levels. Whereas spectinomycin blocks translocation (hence being bacteriostatic), streptomycin and most 2-deoxystreptamine aminoglycosides lock the ribosome in a conformation that is prone to introducing erroneous aminoacyl-tRNAs. The accumulation of aberrant proteins in the bacteria results in cell death ([@B19]; [@B51]; [@B73]).
Resistance to aminoglycosides may be due to several mechanisms ([@B19]; [@B51]). Reduced uptake (which can be a consequence of alterations in the composition of bacterial membrane or to metabolic conditions like anaerobiosis) or the action of efflux pumps can lead to limited intracellular concentration of aminoglycosides, hence causing resistance. Mutations in 16S ribosomal RNA or certain ribosomal proteins such as S12 (encoded by *rpsL* gene) lead to aminoglycoside resistance through target modification; this is also achieved after the action of methyltransferases, which introduce methyl groups in guanine or adenine nucleotides of 16S ribosomal RNA. The presence of aminoglycoside-modifying enzymes is, however, the most prevalent mechanism of aminoglycoside resistance; there are three types of aminoglycoside-modifying enzymes: aminoglycoside *N*-acetyltransferases (AAC), *O*-phosphotransferases (APH), and *O*-nucleotidyltransferases (ANT). Aminoglycoside-modifying enzymes are named by using the aforementioned abbreviations, followed by a number in brackets indicating the site of modification in the aminoglycoside molecule (as explained above), a Roman numeral related with substrate profile, and a lower-case letter for differentiating isoenzymes, i.e., AAC(2′)-Ib.
Clinically, due to their oto- and nephrotoxicity and the rising prevalence of resistance, aminoglycosides are commonly reserved as a second line of treatment of serious infections. Due to their low absorption when given orally, aminoglycosides need to be administered through injections. Streptomycin was a first-line drug in the treatment of tuberculosis, and in our days, kanamycin and amikacin are listed as second line drugs against this disease. Spectinomycin is used against *Neisseria gonorrhoeae* infections ([@B78]). *Pseudomonas aeruginosa* infections in cystic fibrosis patients, septicemia, endocarditis and several other infections caused by non-tuberculous mycobacteria, Gram-positive or Gram-negative bacteria can be treated efficiently by using aminoglycosides, either alone or in combinations with other antibacterials such as the beta-lactam antibiotics ([@B55]; [@B51]; [@B9]).
In mycobacteria, however, resistance to AGs resulted mainly from mutations of the ribosome components that prevent the drugs from inhibiting its function ([@B43]; [@B93]; [@B72]). This is due to the fact that most mycobacterial species have either one (like *Mycobacterium. tuberculosis*) or two (like *Mycobacterium fortuitum*) ribosomal operons, hence making dominant those mutations acquired in their components ([@B51]; [@B74]). The presence of aminoglycoside-modifying enzymes, mostly AAC, in mycobacterial species has been reported over the years (as detailed in the following sections), and the role of such AACs has been explored, originally for their contribution to AG resistance, and more recently for their role in other bacterial processes, which has resulted in the interest of developing inhibitors of these enzymes ([@B40]; [@B46]). In this review, we will summarize major findings on two mycobacterial AACs, the AAC(2′)-I and Eis enzymes, that have resulted in a Copernican turn for AACs in mycobacteria, from being putative drug resistance mechanisms, to reach the status of novel drug targets.
Aacs in Non-Tuberculous Mycobacteria
====================================
The first detection of AACs in mycobacteria ([@B39]) was reported in a group of *M. fortuitum* isolates, an opportunistic fast-growing mycobacteria. Biochemical assays of crude extracts from *M. fortuitum* strains revealed the presence of AAC activity, strongly acetylating gentamicin and kanamycin A, along with other AGs. This substrate profile was consistent with that of AAC(3) enzymes that had been previously described in *Pseudomonas* and *Enterobacteriaceae* ([@B7]), although confirmation at the genetic or molecular levels were not done at that time. Surprisingly, the AG susceptibility profile of *M. fortuitum* could not be correlated with the activity of AACs, indicating that in this species AACs were not the major responsible for AG resistance; it was neither correlated with the presence of plasmids, hence suggesting a chromosomal location ([@B39]). In fact, the frequency of resistant mutants to kanamycin and amikacin in *M. fortuitum* and the related species *Mycobacterium chelonae* ranged between 10^-4^ and 10^-7^ ([@B86]). This relatively high frequency of mutations, along with the fact that AAC activity was detected at similar levels between susceptible and resistant strains, led the authors to suggest that ribosome alterations were the main factor responsible of AG resistance in these species ([@B86]). In another study ([@B82]), altered transport or permeability of AGs was identified as a contributor to AG resistance in *M. fortuitum*, since ribosomes from a clinical isolate were inhibited by one tenth of the MIC of AGs: for example, the MIC of kanamycin for *M. fortuitum* was 50 μg/ml, and in cell-free systems, 5 μg/ml of kanamycin reduced the activity of ribosomes to 13% in comparison with drug-free controls; similar results were obtained when using gentamicin or paromomycin ([@B82]).
The biochemical analysis of crude extracts from other non-tuberculous mycobacteria such as *Mycobacterium smegmatis, Mycobacterium phlei, Mycobacterium vaccae*, and *Mycobacterium kansasii*, from both clinical and environmental origins, revealed similar characteristics to those found in *M. fortuitum*: crude extracts from all strains contained AAC enzymatic activity, but no correlation with AG susceptibility profile could be established ([@B80]; [@B35]). In other mycobacterial species such as *Mycobacterium avium* and *Mycobacterium intracellulare*, however, AAC activity could not be detected ([@B35]). In a recent study, using cell-free translation assays, ribosomes of *Mycobacterium abscessus* and *M. smegmatis* were inhibited by both AGs having a 2′-amino group (tobramycin, dibekacin, and kanamycin B) and by those having a 2′-hydroxyl group (amikacin, and kanamycin A). However, in *M. abscessus*, those AGs having a 2′-amino group (tobramycin, dibekacin, and kanamycin B) were less efficient in killing the cells and inhibiting its ribosomes, which is consistent with the presence of a highly active AAC(2′) activity in this species. These findings suggested that in *M. abscessus*, AACs could somewhat mitigate the bactericidal effect of its AGs substrates ([@B52]).
Interestingly, when characterizing the enzymatic activity of crude extracts, early reports detected that substrates such as amino sugars, malonyl-CoA, propionyl-CoA or butyryl-CoA inhibited the enzymatic activity of AACs from mycobacterial species. Such effect of non-acetyl CoA donors had never been described for the AAC(3) enzymes from other bacteria ([@B80]). Altogether, these findings strongly suggested for the very first time that, in mycobacteria, AACs could have important metabolic functions, and their contribution to AG resistance could be marginal ([@B81]).
Aac(2′), a New Enzyme Comes Into Scene
======================================
In *Providencia stuartii*, a Gram-negative species, phylogenetically distant from mycobacteria, a novel class of AAC was identified as AAC(2′), because of its acetylating activity against gentamicin and lack of enzymatic activity against kanamycin A. The gene encoding AAC(2′)-Ia was cloned from *P. stuartii* ([@B66]) and found to be present in the chromosome of all isolates of this bacteria. In *P. stuartii*, the expression of the *aac(2′)-Ia* gene was controlled by several transcriptional regulators ([@B50]), suggesting that this enzyme could play an important role, beyond its contribution to drug resistance ([@B22]). In fact, AAC(2′)-Ia contributes to *O*-acetylation of peptidoglycan affecting cell morphology and the expression of autolysins, and can use acetylated peptidoglycan precursors as donors of acetyl groups, another indication about the role of this enzyme beyond resistance ([@B61], [@B62]; [@B15]; [@B60]).
AAC(2′) in Mycobacteria
-----------------------
Given the high AG acetylating activity against gentamicin, tobramycin, netilmicin and its derivatives 2′-*N*-ethyl- and 6′-*N*-ethyl-netilmicin, kanamycin A and kanamycin B found in *M. fortuitum* ([@B39]; [@B3]), we launched a molecular approach aimed at characterizing the determinant of AG resistance in this species. A genomic library of *M. fortuitum* was transformed in *M. smegmatis*, and characterization of AG resistant clones allowed the identification of a *M. fortuitum* gene showing sequence similarity to *aac(2′)-Ia* of *P. stuartii*. The enzyme of *M. fortuitum* was named AAC(2′)-Ib ([@B3]) and was capable of acetylating gentamicin, but not kanamycin A, hence indicating that another AAC enzyme should be present in *M. fortuitum*. Similarly to *P. stuartii*, the *aac(2′)-Ib* gene was found in all strains of *M. fortuitum* regardless of the phenotype of AG resistance, suggesting other roles for the AAC(2′)-Ib in this species. Further studies (done by database searching or by southern blot analysis using the probe of *aac(2′)-Ib* gene) demonstrated the presence of *aac(2′)-I* genes in other mycobacterial species, including *M. tuberculosis* (the major pathogenic species in this genus), *Mycobacterium leprae*, and *M. smegmatis*, indicating thus that the presence of *aac(2′)-I* genes in mycobacteria could be universal ([@B4]). Interestingly, the expression of the *aac(2′)-Id* gene in *M. smegmatis* was driven from two promoters, and the strongest one produced a leaderless transcript having a GTG translation start codon at its 5′ end ([@B54]). Leaderless transcripts are those in which the transcription start site coincides with the translation start codon; although representing a rather unusual feature in the model organism *E. coli*, they are quite common in mycobacteria, where 25% of all transcripts are predicted to be leaderless ([@B73]); in fact, *eis* gene of *M. tuberculosis* (see the section "The Eis Protein Becomes a Novel Aminoglycoside Acetyltransferase," below) is transcribed also as a leaderless mRNA ([@B92]). In leaderless mRNAs, there is no Shine-Dalgarno sequence, and 70S ribosomes bind directly to the 5′-end of the mRNA in order to initiate translation ([@B73]).
New Roles for AAC(2′) in Mycobacteria
-------------------------------------
Two major evidences supported that in mycobacteria, AAC(2′)-I enzymes could have additional roles other than acetylation of AGs containing 2′-amino group: first, the capability of amino sugars and diverse acyl-CoA molecules to inhibit the acetylating activity of mycobacterial crude extracts ([@B81]); and second, the implication of AAC(2′)-Ia (an enzyme of the same class) in acetylation of cell wall substrates in *P. stuartii*. In a series of laboratory mutants of *P. stuartii* expressing *aac(2′)-Ia* gene at different levels, it was found that the extent of peptidoglycan acetylation correlated with the activity of AAC(2′)-Ia, hence suggesting a partial contribution of this enzyme (along with other enzymes) to peptidoglycan acetylation. Many bacterial pathogens acetylate their peptidoglycan as a way to resist the action of muramidase enzymes. Under *in vitro* conditions, AAC(2′)-Ia was able to acetylate tobramycin having acetylated peptidoglycan as donor of acetyl groups ([@B61], [@B62]; [@B60]).
We investigated the hypothesis of mycobacterial AAC(2′)-I enzymes having also a role in cell wall metabolism, and a gene knock-out mutant of *M. smegmatis* deleted in *aac(2′)-Id* gene was constructed. This mutant (named EP-10) defective in AAC(2′)-I activity was more susceptible to gentamicin, tobramycin, dibekacin, and netilmicin than the parental wild-type strain, and crude extracts of *M. smegmatis* EP-10 failed to acetylate 2′-amino group containing AGs, whereas wild-type strains of *M. smegmatis* readily acetylated such AGs ([@B4]; [@B52]). *M. smegmatis* EP-10 was also twofold more susceptible to lysozyme, a feature that has been associated with the extent of peptidoglycan acetylation ([@B4]). Hence, we concluded that in *M. smegmatis*, AAC(2′)-Id enzyme could also contribute to acetylation of peptidoglycan, since a less extensively acetylated peptidoglycan in the knock-out strain would be more susceptible to lysozyme degradation affecting cell viability.
Biochemical Analysis of Mycobacterial AAC(2′)-I Enzymes
-------------------------------------------------------
The presence of an AG (2′)-*N*-acetyltransferase gene in the genome of *M. tuberculosis* was intriguing. In this species, AAC activity had never been reported ([@B56]) and the expression of the *aac(2′)-Ic* gene \[annotated as Rv1258c gene in the *M. tuberculosis* H37Rv genome ([@B16])\] in the surrogate host *M. smegmatis* could not be associated with any change in the levels of susceptibility to AGs ([@B4]). We constructed a knock-out mutant of *M. tuberculosis* H37Rv deleted in the *aac(2′)-Ic* gene and observed that the mutant (named *M. tuberculosis* B1) was twofold more susceptible than the original wild-type strain to AGs containing a 2′-amino group such as gentamicin, tobramycin and dibekacin, and fourfold more susceptible to 6′-*N*-ethyl-netilmicin. This indicated that the *aac(2′)-Ic* gene was being expressed in *M. tuberculosis* although at a very low level, and that the AAC(2′)-Ic enzyme in *M. tuberculosis* would acetylate all these four AGs in the wild type strain; hence, acetylated AGs would bind less efficiently to the ribosome, and the AAC(2′)-Ic enzyme would contribute to basal AG resistance in this species.
In order to find the physiological role of this enzyme in *M. tuberculosis*, recombinant *E. coli*-produced AAC(2′)-Ic enzyme from *M. tuberculosis* was studied and found to efficiently acetylate AG antibiotics containing an amino group at the 2′ position (as expected; for example, *K*~m~ for kanamycin B was 1.4 μM), and surprisingly, it was also capable of acetylating (although to a much lesser extent) other AGs such as kanamycin A (*K*~m~ 320 μM) and amikacin (*K*~m~ 968 μM) that have a hydroxyl group in the 2′ position, hence suggesting this enzyme to be capable of both *N*- and *O*-acetylation ([@B34]; [@B20]). This residual activity of AAC(2′)-Ic against kanamycin A and amikacin does not affect their bactericidal activity, and these two antibiotics are used as second line drugs against drug resistant *M. tuberculosis* ([@B89]). The activity of *M. tuberculosis* AAC(2′)-Ic is dependent on metal ions, being inhibited by Cu^2+^ and Au^3+^ ([@B48]).
Another study consisted in binding covalently the AGs kanamycin A, tobramycin, neamine and neomycin B to an agarose matrix in order to quantify the extent of AG acetylation by AAC enzymes and their subsequent ability to bind an artificial probe mimicking the A-site of the ribosome ([@B8]). In such experimental model system, the AGs acetylated by *M. tuberculosis* AAC(2′)-Ic enzyme (only tobramycin, neamine and neomycin B) maintained their binding affinity with the probe mimicking A-site of the ribosome at detectable levels, maybe because the percent of AG acetylation by AAC(2′)-Ic was low. In contrast, these AGs were very efficiently acetylated by *E. coli* AAC(3) (at a different amino group) and had readily lost their affinity for binding this artificial probe. These experiments suggested that subtle differences in the structure of modified AGs (i.e., acetylation at the amino group in 2′ or 3 position) are sufficient to drastically affect their capability of binding to the A-site probe, and this would be expected to correlate with their activity as ribosome inhibitors. In consequence, in mycobacteria, AAC(2′)-I enzymes would not play a major role in resistance to these drugs ([@B8]). High resolution crystal structures of AAC(2′)-Ic complexed with AGs demonstrated that this enzyme is a member of the GNC5 acetyltransferase superfamily and suggested a role in the synthesis of mycothiol, a metabolite that has a key role in regulating redox potential in mycobacteria ([@B84], [@B83]).
In agreement with the preferential *N*-acetylating activity over the *O*-acetylating activity that was found in the *M. tuberculosis* enzyme ([@B34]; [@B20]), *M. abscessus* clinical isolates were found to be more susceptible to AGs containing a hydroxyl group at the 2′ position (such as amikacin and kanamycin A) than to AGs with a 2′-amino group (such as tobramycin, dibekacin and kanamycin B), as the latter group would be substrates of *M. abscessus* AAC(2′)-I enzyme ([@B52]). In fact, crude extracts of *M. abscessus* efficiently acetylated kanamycin B, whereas kanamycin A was not acetylated at detectable levels. In this species, deletion of the *aac(2′)-I* gene resulted in increased susceptibility to kanamycin B, tobramycin, dibekacin and gentamicin C (all of them containing a 2′-amino group) ([@B70]). These two reports demonstrate that in *M. abscessus*, the presence of an AAC(2′)-I enzyme contributes to decreased innate susceptibility to AGs containing a 2′-amino group ([@B49]).
Becoming a Drug Target: Developing Inhibitors of AAC(2′)-I
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The interest in developing inhibitors against AAC(2′)-I enzymes came from a study in the non-tuberculous species *M. abscessus* ([@B53]). It was found that AGs such as amikacin, gentamicin or tobramycin, which are normally bactericidal against *E. coli*, do not have such activity against *M. abscessus* or *M. smegmatis*. However, disruption of the chromosomally encoded *aac(2′)-I* gene in these species restored the bactericidal activity of these AGs ([@B53]). Given that AGs are used as second-line drugs in treatment of multidrug resistant (MDR) tuberculosis infections, and also in the treatment of other infections caused by non-tuberculous mycobacteria, the possibility of developing compounds that could enhance bactericidal activity of current antimycobacterial treatments became an interesting approach.
To date, the only putative inhibitor of *M. tuberculosis* AAC(2′)-Ic is andrographolide, a natural product that was identified in methanolic extracts of a plant that were capable of inhibiting growth of *M. tuberculosis* strains ([@B63]). *In silico* analysis predicted that this compound could potentially bind with a high affinity the AAC(2′)-Ic enzyme, as well as isocitrate lyase (a metabolic enzyme of the glyoxylate shunt, involved in persistence and virulence of *M. tuberculosis*) and other *M. tuberculosis* proteins ([@B63]). However, the specificity of this binding and the ability to really inhibit such putative target proteins were not tested. Given that the gene encoding AAC(2′)-Ic is not essential in *M. tuberculosis*, a direct link between AAC(2′)-Ic inhibition and bacterial growth inhibition could be discarded. Hence, the ability of plant extracts containing andrographolide to inhibit growth of *M. tuberculosis* could be due to the presence of additional compounds in the extract, or to multiple effects on *M. tuberculosis* cells. Other *in silico* analysis revealed that AAC(2′)-Ic enzyme from *M. tuberculosis* could interact with ten other proteins (including a protein of a putative RND-like efflux pump), suggesting that inhibition of AAC(2′)-Ic could also impact many other metabolic processes, hence conferring this enzyme with a relevant role in drug discovery of antituberculosis agents ([@B42]).
The Eis Protein Becomes a Novel Aminoglycoside Acetyltransferase
================================================================
Investigation of *M. tuberculosis* virulence factors lead to the identification of a protein, that was required for infecting and survival in human macrophages; this protein was named Eis for [e]{.ul}nhanced [i]{.ul}ntracellular [s]{.ul}urvival (Box [2](#BX2){ref-type="boxed-text"}) ([@B87]). Bioinformatic analysis revealed that Eis protein of *M. tuberculosis* was an acetyltransferase of the GCN-5 family ([@B71]).
**Box 2.** Discovery and characterization of enhanced intracellular survival (Eis) protein of *M. tuberculosis.*
A genome wide investigation of the ability of *M. tuberculosis* for infecting macrophages resulted in the identification of a coding sequence that, once cloned in the non-pathogenic *M. smegmatis* species, conferred capacity for infecting the human macrophage-like cell line U937. This gene was named *eis* (Rv2416c in the *M. tuberculosis* genome; [@B16]) for enhanced intracellular survival ([@B87]), and was detected only in pathogenic species of mycobacteria. The promoter of the *eis* gene is similar to consensus *E. coli* sigma-70 dependent promoters ([@B69]) and it is recognized by *M. tuberculosis* SigA sigma factor ([@B90]). The Eis protein was found to be mostly hydrophilic, but having a hydrophobic N-terminal end, so that it could be found in the cytosolic but also in other cell fractions such as the membrane, cell wall or among the secreted proteins of *M. tuberculosis* ([@B17]). In fact, antibodies against Eis could detect this protein in the sera of tuberculosis patients ([@B17]) and in the cytoplasm of infected macrophages ([@B71]). Also, it was found that Eis protein, directly added to cultures of human monocytes, modulated the secretion of pro-inflammatory cytokines in a similar way to that found in *M. tuberculosis* infected cells ([@B71]), hence suggesting a role of Eis as an effector protein. Further studies demonstrated that Eis inhibits the extra-cellular signal-regulated kinase 1/2 (ERK1/2) and JAK pathways, and in consequence it inhibited the production of TNF-alpha and IL-4, and stimulated the production of IFN-gamma and IL-10 ([@B47]). The effect of Eis in increasing production of IL-10 was found to be related to Eis-mediated acetylation of histone H3, which binds the promoter of the human IL-10 gene ([@B21]). Hence, by disturbing cross-regulation of T-cells and impairing TH1 and TH2 response, Eis could mediate *M. tuberculosis* pathogenicity ([@B47]). In fact, an isolate of the Beijing family (which are more transmissible and virulent than other *M. tuberculosis* genetic lineages ([@B33]) was found to contain elevated levels of Eis protein, mediated by increased expression of SigA ([@B90]). Other key factors in host immune response to tuberculosis are also mediated by Eis, which increased production of ROS and consequently modulated processes such as autophagy, inflammation, and cell death ([@B75]). These processes are started by Eis-dependent acetylation of dual-specificity phosphatase-16 (DUSP16)-mitogen-activated protein kinase phosphatase-7 (MKP-7), which dephosphorylates the JNK protein leading to its inactivation ([@B44]; [@B91]). Other studies have revealed the activity of Eis for acetylating arylalkylamines such as histamine, octopamine, or tyramine, suggesting novel roles for this protein in *M. tuberculosis* pathogenicity ([@B59]).
Later on, the analysis of kanamycin resistant *M. tuberculosis* laboratory and clinical strains revealed mutations in the -10 and -35 regions of the *eis* gene promoter, which resulted in increased levels of *eis* mRNA and Eis protein. These mutations were related to low-level resistance to kanamycin (MIC 25 μg/ml), but not to amikacin (MIC \< 4 μg/ml), whereas 16S rRNA mutations confer higher levels of resistance to kanamycin (MIC \> 80 μg/ml) and frequently cross-resistance to amikacin. These *eis* mutants also displayed increased levels of AAC activity, hence demonstrating that Eis was a novel class of AAC, highly divergent from all other previously known AACs. Eis is capable of acetylating kanamycin more efficiently than amikacin, and streptomycin was not found to be a substrate of Eis ([@B92]). From then on, detection of mutations in *eis* promoter has become a relevant assay in clinical microbiology laboratories for determining susceptibility to kanamycin ([@B27]); the diagnostic and clinical implications of these tests are beyond the scope of this review.
Formation of stable hexamers by Eis is required for its AAC activity ([@B23]; [@B6]), which can acetylate multiple amine groups of different AG antibiotics, including netilmicin, sisomicin, neamine, ribostamycin, paromomycin, neomycin B, kanamycin, amikacin, tobramycin and hygromycin, resulting in mono-, di-, tri, and tetraacetylated products ([@B12]; [@B37]), being able to use not only acetyl-CoA but also other acyl-CoA derivatives ([@B13]). The Eis protein works by a random-sequential bisubstrate mechanism of acetylation ([@B79]). Interestingly, Eis is also able to acetylate capreomycin, a polypeptide second-line antituberculosis drug commonly used in the treatment of MDR tuberculosis infections ([@B67]). Several metal ions such as Au^3+^, Cd^2+^ and Zn^2+^ inhibited Eis activity *in vitro* ([@B48]).
Other mycobacterial species such as *M. smegmatis* and *M. abscessus* have ortholog (and even paralog) *eis* genes, although the Eis proteins have distinct biochemical features and impact on AG susceptibility in comparison with Eis of *M. tuberculosis* ([@B14]; [@B70]). For example, *M. abscessus* has two *eis* genes, and the deletion of one (but not the other one) resulted in altered AG susceptibility ([@B70]; [@B49]). Consistently with these findings, mutational changes in the amino acid residues lining the substrate binding site of *M. tuberculosis* Eis altered its substrate specificity ([@B41]).
It is important to note that in *M. tuberculosis*, transcription of the *eis* gene is activated by the regulator WhiB7 ([@B67]). Mutations in the promoter of *whiB7* gene that led to increase in the mRNA of this gene resulted in increased expression of *eis* gene, along with other genes such as *rv1258c* (encoding the Tap efflux pump; [@B2]), hence resulting in cross resistance to several drugs including kanamycin (mediated by Eis protein) or streptomycin (mediated by Tap efflux pump). Similarly, in *M. abscessus*, WhiB7 controlled the expression of one of the two *eis* genes in this species and also that of the *erm(41)* gene, which encodes a ribosomal methyltransferase that by altering target structure is associated with resistance to macrolide antibiotics ([@B64]; [@B49]). Subinhibitory concentrations of clarithromycin induced the *whiB7* gene and consequently decreased Eis-mediated susceptibility to AGs, such as amikacin that is currently used in the treatment of *M. abscessus* infections ([@B64]).
Aminoglycosides and Beyond...
-----------------------------
The unusual properties of Eis acetyltransferase include its capability for acetylating peptides and proteins ([@B44]; [@B38]; [@B91]), in contrast with other AACs. The *M. tuberculosis* nucleoid-associated protein HU (encoded by Rv2986c gene) can be acetylated by Eis on multiple lysine residues, hence decreasing its ability to interact with DNA, and altering its DNA compactation activity ([@B28]; [@B31]). Overexpression of Eis led to a hyperacetylation of HU protein, and consequently, to a decompactation of the genome ([@B28]). The reverse effect (condensation of relaxed DNA) could be reached through the deacetylation of HU protein, which is mediated by a Sir2 family protein from *M. tuberculosis* encoded by the Rv1155c gene ([@B5]; [@B31]). Controlling the architecture of DNA is a key process in any bacteria, and so, the HU protein is essential for *M. tuberculosis*. In fact, inhibitors of HU have been discovered ([@B10]), which could act in synergy with potential inhibitors of Eis, as described in the next section.
Finding Inhibitors of Eis Protein
---------------------------------
The crystal structure of *M. tuberculosis* Eis protein was determined by several groups ([@B12]; [@B44]), which has been useful for determining docking properties of potential inhibitory compounds; also, its comparison with the crystal structure of *M. smegmatis* Eis protein revealed several distinct structural features that may account for the biochemical and substrate differences between the two proteins ([@B45]). A first screening of potential inhibitors of Eis from *M. tuberculosis* resulted in the identification of 25 molecules (including the antiseptic chlorhexidine) that inhibited Eis with IC~50~ values in the low micromolar range. In addition, this inhibition was specific to the *M. tuberculosis* Eis protein, since these molecules could not inhibit significantly AACs from AAC(2′), AAC(3), and AAC(6′) families ([@B32]), nor Eis protein from *Bacillus anthracis* ([@B29]). Later studies revealed the presence of *eis*-like genes in many pathogenic and non-pathogenic bacteria (remarkably, many mycobacterial species have two or even three paralogs of the *eis* gene), and chlorhexidine was capable of inhibiting (to different levels) all Eis proteins that were capable of acetylating AGs ([@B30]).
A second screening of a larger collection of small-molecule compounds resulted in the identification of several families of compounds capable of inhibiting Eis activity. These contained diverse chemical scaffolds ([@B24],[@B25], [@B26]; [@B88]; [@B57]). Besides, these inhibitors were highly selective for Eis, and did not inhibited AACs from other families ([@B25]). More importantly, as these inhibitors bound in the AG pocket of the Eis protein, they were able to reverse kanamycin resistance of a *M. tuberculosis* isolate ([@B25]; [@B88]; [@B57]). Some of these inhibitors, such as those based on a pyrrolo\[1,5-a\]pyrazine scaffold, also lacked any toxicity on mammalian cell lines ([@B26]).
Other Aminoglycoside-Modifying Enzymes in Mycobacteria
======================================================
Genome-wide analysis of *M. tuberculosis* genome identified only one other potential AAC (encoded by the Rv1347c gene), although such enzymatic activity could not be detected on the recombinant protein ([@B20]). Later studies related the product of the Rv1347c gene with a role in the synthesis of mycobactin, the mycobacterial siderophore ([@B11]).
Leaving apart AACs, only a few reports of other classes of aminoglycoside-modifying enzymes have been done in mycobacteria. An APH enzyme of the APH(3″) family, conferring resistance to the AG streptomycin only, has been characterized in *M. fortuitum* ([@B65]) and *M. abscessus* ([@B18]; [@B49]); the latter species encodes up to 11 additional putative APH enzymes ([@B68]). Furthermore, a putative APH of the APH(3′) class, encoded by the Rv3168 gene of *M. tuberculosis*, was identified and expressed as a recombinant enzyme in *E. coli*, being related to kanamycin phosphotransferase activity ([@B1]).
Back to the Start Point: Eis in *M. fortuitum*
==============================================
We started this review referring to previous work that has shown that crude extracts of *M. fortuitum* harbored AAC activity having gentamicin, tobramycin, netilmicin and its derivatives 2′-*N*-ethyl- and 6′-*N*-ethyl-netilmicin, kanamycin A and kanamycin B as substrates. So far, the only AG acetyltransferase identified in this species has been AAC(2′)-Ib ([@B3]), which cannot explain the acetyltransferase activity against kanamycin A and 2′-*N*-ethyl-netilmicin detected in *M. fortuitum* crude extracts. Later studies characterized Eis AAC in diverse mycobacterial species, but no report were been done on a putative Eis protein in *M. fortuitum*. In view of the universal presence of Eis proteins in mycobacteria, and its activity as AAC, we hypothesized that *M. fortuitum* could also have a putative Eis protein that would be responsible for the acetyltransferase activity against kanamycin A and 2′-*N*-ethyl-netilmicin detected in crude extracts of this species, as it was reported earlier ([@B39]; [@B3]).
Thus, we first ascertained the existence of an *eis* gene in the genome of *M. fortuitum* ([@B36]), which presented a 94% of identity with respect to the one reported in *M. tuberculosis;* the sequence of both Eis proteins from *M. tuberculosis* and *M. fortuitum* also presented high levels of identity ([Figure 1](#F1){ref-type="fig"}). We designed two oligonucleotides for amplifying specifically a DNA fragment from *M. fortuitum* genome containing *eis* gene. This DNA fragment was subsequently cloned in pMV261 vector ([@B77]), which expresses genes constitutively under the control of the *hsp60* gene promoter, resulting in plasmid pFS2. Given that this plasmid still contains the Tn*903*-derived aminoglycoside-3′-phosphotransferase (*aph*) gene (present in the original pMV261 cloning vector) conferring kanamycin resistance as selection marker, we anticipated that *M. smegmatis* strains harboring pMV261 vector or its derivatives would be intrinsically resistant to kanamycin A; this would prevent from determining whether this antibiotic is a substrate of the *M. fortuitum* Eis protein. Additionally, the selection marker could have cross-effect with other AGs and thus interfering with the resistance phenotype conferred by *eis* gene. To circumvent these problems, we generated a derivative of pFS2 through the disruption of the *aph* gene with the ampicillin resistance cassette (*bla* gene) from pGEM^®^-T easy (Promega). The resistance to 2′-*N*-ethylnetilmicin conferred by *eis* gene, as demonstrated for the parental plasmid pFS2 (see [Table 1](#T1){ref-type="table"}) was used as resistance marker for transformant selection and plasmid maintenance. This process resulted in plasmid pEAC which contains the *M. fortuitum eis* gene and no other determinant of AG resistance.
{#F1}
######
MICs (μg/ml) of antibiotics of different structural families in the *M. smegmatis* mc^2^ 155 strains that overexpress *eis* gene from *M. fortuitum*.
Strain *M. smegmatis* mc^2^ 155
------------------------- -------------------------- ------------ ------------ -------
Plasmid None pMV261 pFS2 pEAC
Marker gene on plasmid None *aph* *aph* *bla*
*M. fortuitum eis* gene -- -- \+ \+
Gentamicin 0.78-1.56 0.78 3.12 3.12
2′-*N*-ethyl netilmicin 6.25 3.12--6.25 50--100 50
6′-*N*-ethyl netilmicin 3.12 3.12 3.12--6.25 25
Kanamycin A 1.56 \>100 \>100 7.8
Kanamycin B 6.25 \>100 \>100 12.5
Hygromycin 15.6 15.6 31.2--62.5 62.5
Amikacin 0.39 0.39 0.39 0.39
Capreomycin 1.95 1.95 3.9 3.9
Streptomycin 0.25 0.25 0.25 0.25
Spectinomycin 62.5 31.2--62.5 62.5 62.5
The values separated by a dash indicate that growth was detected in both concentrations. The range of antibiotic concentrations spanned from 0.78
μ
g/ml to 100
μ
g/ml, and from 0.25
μ
g/ml to 125
μ
g/ml; a twofold difference in the MIC was not considered as significant. aph: aminoglycoside 3′-phosphotransferase from Tn903; bla: beta-lactamase.
The three plasmids \[original empty vector pMV261 as a control, and the two plasmids (pFS2 and pEAC) containing *M. fortuitum eis* gene\] were introduced in *M. smegmatis* mc^2^ 155 in order to over-express the ortholog *eis* gene from *M. fortuitum* and to elucidate its hypothetical implication in AG susceptibility. The antibiotic susceptibility assay was made, based on a double dilution protocol with the addition of resazurin dye ([@B58]).
We observed that plasmids pFS2 and pEAC produced detectable changes in AG susceptibility of *M. smegmatis* mc^2^ 155, which can be attributed to the expression of the plasmid-borne *M. fortuitum eis* gene. The major shift in the MICs was detected for 2′-*N*-ethylnetilmicin ([Table 1](#T1){ref-type="table"}), since the MIC increased from 3.12 to 6.25 μg/ml in the control strains to 50--100 μg/ml in the strains containing *M. fortuitum* Eis, accounting for a 8- to 32-fold increase; similar changes were observed for 6′-*N*-ethylnetilmicin (8-fold increase in the MIC). A moderate decrease in the susceptibility to kanamycin A (fivefold), hygromycin (twofold to fourfold) and gentamicin (twofold to fourfold) was also observed. Finally, slight changes (twofold) in the MICs were detected for kanamycin B and capreomycin; this finding is consistent with previous reports on the activity of *M. tuberculosis* Eis against capreomycin ([@B67]). The levels of susceptibility to the AGs amikacin, streptomycin and spectinomycin, and to other non-AG compounds tested (isoniazid, rifampicin, ethambutol, ciprofloxacin, tetracycline, chloramphenicol) were not altered significantly by the presence of the plasmid-encoded *eis* gene ([Table 1](#T1){ref-type="table"} and data not shown), suggesting that either these antimicrobials are not substrates of the Eis enzyme or the corresponding acetylations (if any) might just not affect antibacterial activity.
Concluding Remarks
==================
The presence and activity of AAC(2′)-I and Eis AACs in mycobacteria have clearly demonstrated that their primary role is little related with susceptibility to AGs.
In the case of AAC(2′)-I enzymes, its presence in phylogenetically distant genera as *Providencia* and *Mycobacterium* remains to be an evolutionary mystery. In contrast with this restricted distribution of AAC(2′)-I enzymes among bacteria, Eis enzymes seem to be more widely distributed, being present even in non-pathogenic and environmental species, which suggest a general function of Eis-like enzymes in bacterial metabolism, and virtually excludes any potential selection of *eis* genes due to the use of AGs, or its horizontal transfer from other species.
It is clear that in mycobacteria ribosomal modifications constitute the major mechanism of AG resistance, given that only one or two copies of ribosomal RNA operons are present in these species, hence making likely the acquisition of mutations conferring high levels of AG resistance. Then, AAC(2′)-I enzymes only contribute modestly to innate low level susceptibility to AGs, and despite other roles have been suggested in the literature for mycobacterial AAC(2′)-I enzymes, their relevance as potential drug targets is still modest, especially in comparison with Eis acetyltransferase. The contribution of Eis acetyltransferase to virulence of *M. tuberculosis*, and the finding that Eis is related with resistance to kanamycin (a second line drug for the treatment of tuberculosis) in clinical isolates has greatly attracted the attention and promoted the interest in developing Eis inhibitors. In some way, Eis inhibitors would fall into the class of anti-virulence and anti-resistance mechanisms compounds, which is a trending topic in the age of antimicrobial resistance. Globally, antimicrobial resistance is a major public health threat, and multi and extensively drug resistant (MDR, XDR) tuberculosis is a case of particular concern, so progress and major advances that can be expected from the coming years will be greatly welcomed.
Author Contributions
====================
JA, LR, and CM contributed to the conception and design of the study. FS-G, EA-C, AL, LR, and EP-H carried out the experimental work. FS-G, EA-C, and JA wrote the manuscript. All authors contributed to manuscript revision, read and approved the submitted version.
Conflict of Interest Statement
==============================
The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
**Funding.** FS-G and EA-C are recipients of FPU fellowships from the Spanish Ministry of Economy and Competitivity. JA acknowledges funding from the European Comission \[More Medicines for Tuberculosis (MM4TB) grant 260872\] and the Spanish Ministry of Economy and Competitivity (grants SAF-2013-48971-C2-2-R and SAF2017-84839-C2-1-R).
Dessi Marinova was acknowledged for critical reading of the manuscript.
[^1]: Edited by: Silvia Buroni, University of Pavia, Italy
[^2]: Reviewed by: Peter Sander, University of Zurich, Switzerland; Roland Brosch, Institut Pasteur, France
[^3]: ^†^Present address: Fernando Sanz-García, Departamento de Biotecnología Microbiana, Centro Nacional de Biotecnología, Consejo Superior de Investigaciones Científicas, Madrid, Spain; Esther Pérez-Herrán, GlaxoSmithKline, Tres Cantos Medicines Development Campus, Tres Cantos, Spain; Liliana Rodrigues, Unit of Medical Microbiology, Global Health and Tropical Medicine, Instituto de Higiene e Medicina Tropical, Universidade Nova de Lisboa, Lisbon, Portugal
[^4]: ^‡^These authors have contributed equally to this work
[^5]: This article was submitted to Evolutionary and Genomic Microbiology, a section of the journal Frontiers in Microbiology
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February 16, 1979
79-15 MEMORANDUM OPINION FOR ASSISTANT
ATTORNEY GENERAL, LANDS AND
NATURAL RESOURCES DIVISION
Federal Aviation Administration—Federal Airport
Act of 1946 (60 Stat. 170)—Airport and Airway
Development Act of 1970 (49 U.S.C. §§ 1716,
1723)—Conveyance of Federal Lands for Airport
Development
Mr. Harmon has asked me to respond to your memorandum requesting
this Office to initiate action to reinstate the authority initially conferred by
Executive Order No. 10536, but subsequently revoked by § 2 o f Executive
Order No. 12079. For the reasons expressed herein, we do not believe it
necessary to reinstate that authority. Rather, we conclude that the author
ity conferred by § 1 o f Executive Order No. 12079 is sufficient to meet
your concerns.
I. Background
You raise issues concerning the interrelationship of two separate but
related pieces o f legislation and the orders issued thereunder. The perti
nent portions o f the separate enactments relate both to the development of
public airports and to Federal assistance to such projects. The first enact
ment, the Federal Airport Act o f 1946, 60 Stat. 170 (hereinafter referred to
as the 1946 Act), required that, as a condition o f receiving Federal grants,
State and local public agencies submit airport development project appli
cations to the A dm inistrator o f the Federal Aviation Adm inistration. § 9(a),
60 Stat. 174. The Adm inistrator, before entering into any grant agreement,
was required to approve the project application. Numerous conditions
were to be met before approval could be given; one condition was that
No project shall be approved by the Adm inistrator with respect to
any airport unless a public agency holds good title, satisfactory
to the Adm inistrator, to the landing area o f such airport or the
95
site therefor, or gives assurance satisfactory to the Adm inistrator
that such title will be acquired. [Section 9(d), 60 Stat. 175.]
Another provision o f the same Act provided for the conveyance o f Federal
lands when the Adm inistrator determined that this was “ reasonably neces
sary for carrying out a project” under the Act. § 16(a), 60 Stat. 179. The
procedure for carrying out such a conveyance was as follows:
Upon receipt o f a request from the Adm inistrator under this sec
tion, the head o f the departm ent or agency having control o f the
lands in question shall determine whether the requested convey
ance is inconsistent with the needs o f the departm ent or agency,
and shall notify the A dm inistrator o f his determ ination within a
period o f four m onths after receipt o f the Adm inistrator’s re
quest. If such departm ent or agency head determines that the re
quested conveyance is not inconsistent with the needs o f that
departm ent or agency, such departm ent or agency head is hereby
authorized and directed, with the approval o f the President and
the A ttorney General o f the United States, and without any ex
pense to the United States, to perform any acts and to execute
any instruments necessary to make the conveyance requested;
but each such conveyance shall be made on the condition that the
property interest conveyed shall automatically revert to the
United States in the event that the lands in question are not
developed, or cease to be used, for airport purposes. [Section
16(b), 60 Stat. 179.]
In Executive Order No. 10536 o f June 9, 1954, the President authorized
the heads o f departm ents and agencies to execute conveyances under this
provision without the approval o f the President.
The second pertinent piece o f legislation, the Airport and Airway Devel
opm ent Act o f 1970, Pub. L. No. 91-258, 84 Stat. 219 (hereinafter re
ferred to as the 1970 Act), repealed the 1946 Act, but it also enacted provi
sions which, to a great extent, adhered to that A ct’s approach. As a condi
tion o f receiving Federal grants, public agencies once again had to obtain
approval o f project applications for airport development. 49 U.S.C.
§§ 1716(a), 1719. The conditions o f approval were largely the same as in
the 1946 Act, including that o f good title, 49 U .S.C . § 1716(c), but stricter
environmental standards were to be applied. See 49 U .S.C . § 1716(c)(4),
(d) and (e). A provision similar to that o f the 1946 Act was made for con
veyances o f Federal lands, except that certain parklands were exempted.
49 U.S.C. § 1723. In Executive O rder No. 12079, 3 CFR 224 (1979), the
President authorized the conveyances to be executed without his approval.
The repeal o f the 1946 Act soon gave rise to the question whether, where
grant agreements had been finalized under the 1946 Act, conveyances of
Federal land pursuant to those agreements might still be made and ap
proved under the authority o f the 1946 Act. In our opinion o f January 19,
1971, this Office answered the question affirmatively. The opinion relied
on § 52(c) o f the 1970 Act, 84 Stat. 219, 236, which explicitly continued in
96
effect “ all orders, determ inations, rules, regulations, permits, contracts,
certificates, licenses, grants, rights and privileges” which had taken effect
under the 1946 Act. The opinion also reasoned that, since a conveyance of
land was “ inextricably bound up with the grant agreem ent,” Congress
must have intended that the savings clause permitted conveyancing in ac
cordance with the 1946 Act.
Under this interpretation, conveyances continued to be made under the
1946 Act by reason o f Executive Order No. 10536, and were made without
the approval o f the President. Despite the significant lapse o f time since
the repeal o f the 1946 Act, it is our understanding that a num ber o f con
veyances, which could be approved without Presidential approval under
Executive Order No. 10536 and our previous opinion, have yet to be
made. However, since Executive Order No. 10536 has been revoked by Ex
ecutive Order No. 12079, the question is whether a new authorization must
be obtained in order to execute these conveyances without the approval o f
the President. As noted above, we do not believe this to be the case.
II. Discussion
Section 23 o f the 1970 Act, 49 U.S.C. § 1723, provides as follows:
(a) Requests for use.
Subject to the provisions o f subsection (c) o f this section,
whenever the Secretary determines that use o f any lands owned
or controlled by the United States is reasonably necessary for
carrying out a project for airport development under this part,
[part II], or for the operation o f any public airport, including
lands reasonably necessary to meet future development o f an air
port in accordance with the national airport system plan, he shall
file with the head o f the departm ent or agency having control of
the lands a request that the necessary property interests therein
be conveyed to the public agency sponsoring the project in ques
tion or owning or controlling the airport. The property interest
may consist o f the title to, or any other interest in, land or any
easement through or other interest in airspace.
(b) Execution o f conveyances.
Upon receipt o f a request from the Secretary under this sec
tion, the head o f the departm ent or agency having control o f the
lands in question shall determine whether the requested convey
ance is inconsistent with the needs o f the departm ent or agency,
and shall notify the Secretary o f his determ ination within a
period o f four m onths after receipt o f the Secretary’s request. If
the departm ent or agency head determines that the requested
conveyance is not inconsistent with the needs o f that departm ent
or agency, the departm ent or agency head is hereby authorized
and directed, with the approval o f the President and the
Attorney General o f the United States, and without any expense
to the United States, to perform any acts and to execute any
97
instruments necessary to make the conveyance requested. A con
veyance may be made only on the condition that, at the option of
the Secretary, the property interest conveyed shall revert to the
United States in the event that the lands in question are not
developed for airport purposes or used in a m anner consistent
with the terms o f the conveyance. If only a part o f the property
interest conveyed is not developed for airport purposes, or used
in a m anner consistent with the terms o f the conveyance, only
that particular part shall at the option o f the Secretary, revert to
the United States.
(c) Exemptions o f certain lands.
Unless otherwise specifically provided by law, the provisions
o f subsections (a) and (b) o f this section shall not apply with
respect to lands owned or controlled by the United States within
any national park, national m onum ent, national recreation area,
or similar area under the adm inistration o f the National Park
Service; within any unit o f the National Wildlife Refuge System
or similar area under the jurisdiction o f the Bureau o f Sport
Fisheries and Wildlife; or within any national forest or Indian
reservation.
Except for the language “ under this p art” in subsection (a), there is noth
ing in the section precluding its use in situations involving projects for air
port development conducted under the authority o f the 1946 Act. Rather,
the language o f the section is generally broad enough to encompass con
veyances contem plated in grants under the 1946 Act.
O f course, the phrase “ under this part” could be read to restrict the ap
plication o f § 23 to those airport development projects conducted under
the authority o f part II o f the 1970 Act. We do not believe, however, that
the phrase was meant to preclude the use o f § 23 in situations involving
grants under the 1946 Act. Since § 23 largely restates the analogous provi
sion o f the 1946 Act, Congress obviously wished to continue that A ct’s
purpose o f allowing Federal lands to be conveyed for carrying out airport
projects. This purpose would hardly be served by reading the language
“ under this part” to preclude the use o f § 23 in projects conducted under
the authority o f the 1946 Act. Rather, in light o f Congress’ purpose in en
acting § 23, and because part II o f the 1970 Act is largely a reenactment of
the 1946 Act, see H. Rept. 601, 91st Cong., 1st sess. 12-13 (1969), a more
reasonable assessment o f Congress’ intent would be to interpret the term
“ under this part” as including projects undertaken under the 1946 A c t.1
1 Indeed, the language “ under this p a rt” essentially tracks the language “ under this A ct”
in the analogous provision o f the 1946 A ct. This would suggest that it was not intended to
restrict § 23 with respect to the 1946 Act, but rather was simply a continuation o f the policy
o f the 1946 Act to allow Federal conveyances only for purposes o f aiding airport develop
ment projects.
98
Another aspect o f the statute supports our conclusion. As noted above,
§ 52 o f the 1970 Act provides that grants in effect at the time of the effec
tive date of the Act were to continue in effect. See 49 U .S.C . § 1701 note.
Moreover, as we explained in our January 19, 1971 opinion, grant agree
ments were inextricably bound up with conveyances o f Federal land. We
cannot believe that Congress would, on the one hand; act to preserve
grants under the 1946 Act that were dependent on such conveyances and,
on the other hand, restrict § 23 to preclude conveyances with respect to
these grants. Rather, since Congress wished to preserve existing grants, a
more likely interpretation o f § 23 would be that its authority is available to
effectuate those grants.2
The legislative history o f the 1970 Act supports this view. One com
mittee report states that land may be conveyed under § 23 “ for the pur
pose of carrying out projects for airport developm ent.” H. Rept. 601, 91st
Cong., 1st sess. 15 (1969). See also H. Rept. 1074, 91st Cong., 2d sess. 43
(1970). This general statement o f intent would appear to encompass p ro j
ects conducted not only under the 1970 Act, but also under the 1946 Act.
In addition, the Conference Report states that § 23 “ continues, with
minor modifications, the policy contained in existing law.” H. Rept. 1074,
91st Cong., 2d sess. 44 (1970). Since the existing law had allowed for
conveyances to aid projects under the 1946 Act, this statement would in
dicate Congress’ intent to allow for the same result to occur under § 23.
We thus conclude that, where grant agreements had been finalized
under the 1946 Act, conveyances o f land may be made pursuant to those
agreements under the authority conferred by § 23 o f the 1970 Act. By
reason o f Executive Order No. 12079, such conveyances may be made
without Presidential approval: There is thus no need to initiate action for-
reinstatement o f the authority, contained in the revoked Executive Order
No. 10536, in order to convey Federal lands without Presidential approval
under the 1946 Act.
The fear has been expressed that, if conveyances are made under § 23 o f
the 1970 Act, other requirements o f that Act would also have to be met.
As we have already noted, however, Congress in the 1970 Act continued in
force those grants under the 1946 Act that existed on the effective date o f
the 1970 Act. Even though the provisions o f the 1970 Act may impose ad
ditional or different requirements on grants, it seems clear to us that those
provisions do not apply to grants finalized before the 1970 Act became ef
fective. Moreover, we see no reason for § 23 to be deemed inapplicable to
1946 Act grants by requirements which, as Congress expressly provided,
2 We recognize that, in our January 19, 1971 opinion, we concluded that such conveyances
could go forward under the authority o f the 1946 Act. T hat opinion, however, did not deal
with the availability o f § 23 o f the 1970 Act; rather, it dealt only with the question whether
conveyances could be made under the revoked 1946 Act. While we have no occasion to ques
tion our prevous opinion's conclusion, we believe it more appropriate to proceed under the
authority o f § 23—which we believe to be applicable to projects under the 1946 A ct— rather
than under a provision in a repealed statute.
99
were not to apply to such grants. We have found nothing in § 23 or its
legislative history to suggest a contrary conclusion; rather, on the basis of
o ur previous discussion, we think that the language and the legislative
history o f § 23 indicate that Congress intended § 23 to permit conveyances
pursuant to those grant agreements entered into under the 1946 Act.
L eon U lman
D eputy Assistant A ttorney General
Office o f Legal Counsel
100
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No. 7 Mizzou Wrestling Makes History on Opening Weekend
WEST LAFAYETTE, IN -- After finishing off the 2011-12 campaign with the University's first Big 12Championship, the Tigers (2-0) have once again made history. In the team's first competition since last year's NCAA Championships, the Mizzou Wrestling squad opened up the year by not only shutting out the Old Dominion Monarchs, but by defeating them 35 to negative-1. In Mizzou Wrestling's 89-year history, they have never won a match where the opponent was in negative numbers. They followed that season opening performance with a 23-9 victory over host school Purdue.
The Tigers took on their new MAC rival Old Dominion early Saturday morning. Junior Alan Waters set the tone in the 125 pound class, winning by major decision over Rob Deutsch, 10-2. Possibly thebiggest matchup came at 141 pounds, when No. 14-ranked Nicholas Hucke rematched against No. 11 Justin LaValle, who had defeated Hucke in last year's NCAAs. Hucke had a huge third period against LaValle, handing him a reversal and a3-point near fall along with an escape to take the match, 8-4.
Sophomore Drake Houdashelt added another four team points at 149 pounds, winning his match in decisive fashion after finishing with 5:22 of riding time. Next up was Junior Kyle Bradley, who took a 3-1 lead into the 3rd period and held on over Old Dominion's No. 11 John Nicholson. Nicholson rejected Bradley's handshake following the 4-1 decision, which led to a misconduct penalty. By rule, a misconduct penalty in wrestling is also a forfeit of one team point. Tyler Prazma, Mike Larson, Todd Porter, Brent Haynes, and Dom Bradley each added 3 points of their own as well, and Mizzou was well on their way to a quick 1-0 start with a 35 to negative-1 win. This is the third time since January 29, 2012 that the Tigers have won all 10 matchups in a dual meet.
The Tigers didn't slow down for their afternoon meeting with Purdue. Again, Waters set the tone yet again, with an 11-2 major decision over No. 21 Camden Eppert. Waters solidified the major decision after a great takedown with four seconds remaining. Senior CaptainNathan McCormick followed up at 133 pounds with a 10-5 decision over true freshman Danny Sabatello, and at 141, Hucke came out on top once again. In another highly contested battle, Mizzou's 141-pound grappler took down his counterpart Brandon Nelson with one second left in the first, which proved to be a huge two points in a match that ended up as an 8-5 decision.
After three bouts, the Tigers had a comfortable 10-0 lead on the hosting Boilermakers from Purdue. But two overtime losses and a 7-3 win by decision for Pat Robinson against Mizzou's Prazma, and Purdue was within a point of the Tigers, 10-9.
Senior Todd Porter responded to Mizzou's three-match losing streak with a dominating 11-5 win, and the Tigers never looked back. After Mike Larson followed at 184 pounds with a 3-1 decision, Haynes outperformed Purdue's 197-pounder Braden Atwood to put the dual away. Atwood is ranked 16th in the nation among the 197-pounders, and the No. 6-Haynes accumulated two takedowns, a reversal, an escape, and an extra tally for riding time to go on and win 8-2.
Senior heavyweight Dom Bradley added his second win of the day over Purdue's Alex White, this time by major decision, 11-3. Bradley, who hadn't wrestled for Mizzou since 2010-11 due to an Olympic redshirt last year, controlled every minute of this grapple, with White's three points coming off of three escapes only.
The Tigers will follow up their 23-9 victory over Purdue with the team's home opener this Wednesday at 6:30 p.m. versus Baker University.
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I’m not denying this is territory I’ve covered before. There’s no disguising that I’m a fan of single-playing gaming over multiplayer. Finally it’s time to just say it. We need to stop avoiding the matter, stop not saying what everyone’s thinking. I’m the man brave enough to do this. I am a valiant man, and maybe I won’t be recognised within my own lifetime, but by God one day I shall be heralded as the prophet and man of integrity I truly am. But please, don’t think me immodest. I would hate that.
The very last thing I would want is to come off as snobbish. But I’d like to make the argument that multiplayer gaming is the going down to the pub to watch the “match”, to single-player gaming’s evening in with a glass of wine. What I’m trying to say is, I’ve had quite enough of loud, yobbish multiplayer gamers making noise outside my window as they drunkenly make their way home, because I have guests. I would like you all to keep it down please.
I remember the first time I played a multiplayer game. The internet had yet to find its ways into homes, and my friend Fred carried his PC to my house on his back. Setting them up in my father’s study, we linked the two together with something people back then called a serial cable, and with a fizz and a pop the two were connected. Their entities so entwined, when we each loaded up Doom by some sort of witchcraft we appeared on the other’s monitor. Dazzled, we found ourselves unable to look at only one screen, frantically swinging our heads back and forth to see how when we moved in our game, we moved at the same time in the other. It barely made sense.
But now, just as how the modern world has forgotten the value of a phone call now you no longer have to carry the coal from the bottom of the garden, multiplayer gaming falls too easily into the hands of the unwashed, and it becomes the grubby equivalent of teenagers comparing ringtones on a crowded train.
I stress again, I would hate it if I appeared pompous at all when I suggest that single-player gaming, ever-more the forgotten gem of our hobby, is for the more sophisticated, intellectual individual. It takes something more, a different kind of mind, a more educated, refined view, to understand and value the art of the single-player. Let me tell you why.
The worth of single-player comes in the form of narrative. As with any good novel, or a finely crafted film. It is the equivalent to literature. While multiplayer is an ill-informed argument. It has no direction, no beginning nor end, no meaning.
Games are made with intent. Like books, films and television, the finest examples among them are those that both exist to say something, but allow the player to create his own interpretation. And while of course there are any number of poor or stupid single-player games, there is no multiplayer that evenly closely matches the finest RPG or adventure.
Like I say, I would be just mortified if anyone interpreted these words to be snooty or condescending. I’m just saying people who prefer single player games are a better class than people who mostly opt for multiplayer.
But what about massively multiplayer games, one may ask. Well, it’s quite simple. When approached as a single-player game, with a world to explore, stories to be told, and a beginning, middle and end, they are firmly in the category of the more refined arts. Once they’ve descended into mindless raiding in an endless, empty pursuit of a trinket, looped for eternity, then they are something quite other.
I can hear those loutish grunts of protest. “Who are these ‘guests’ drinking your wine if you’re playing single-player?” they ask, thinking they’ve been so astute. Well, my generously foreheaded friend, they’re the characters in the game.
Yes, indeed, characters. Something of a mystery to our hooligan brethren. The closest they can understand would be the cartoons that accompany Team Fortress 2, pretending that these outlines of personalities have any effect on their Möbius strip of gaming. Meanwhile I am meeting people, people with lives, backgrounds, motivations and goals. People I can influence, and who can influence me, beyond temporarily making them be dead for a fifteen second wait.
My company in these single-player games does not berate me, nor shout racial and homophobic epithets after me. If I choose to play at my pace, on my terms, the cast of the game does not huff and grumble, nor question my parents. If I do extremely well they do not grow bitter, or question my methods. They play their parts, along a journey.
A journey with a goal, and ending, a purpose. Mine is a gaming infused with meaning. Mine is a simulacrum for life, a reflection on experience and a metaphor for understanding my existence. Multiplayer gamers emulate some Sisyphean torture, yet as the ball rolls back down the hill these creatures cheer and high five.
I do not argue that these people should be stopped, nor that their games should not be made. Of course not – they need their entertainment, and it’s best if they’re kept busy. Far better that they’re imagining progress within their 45,000th match of Modern Warfare 2 than out smashing windows or selling drugs in parks. But where I object is when the games that sate them become greater in number than those for the more discerning player.
I remember the days when every game had a multiplayer component bundled in with it, something to keep the children happy while the adults played the proper game. But this has now swung the other way, with single-player modes often a bot-based version of the multiplayer nothingness. This absolutely has to stop. The yobs cannot be allowed to dominate, or I would argue all of society can only be minutes from collapse.
So as I have said, coming across in any way as if I think myself superior is far from my intent. I apologise if anyone has gotten that impression. But let’s not let the multiplayer lot take over, eh?
|
{
"pile_set_name": "OpenWebText2"
}
|
Q:
What is the correct/ fastest way to update/insert a record in sql (Firebird/MySql)
I need some SQL to update a record in a database if it exists and insert it when it does not, looking around there looks to be several solutions for this, but I don't know what are the correct/ accepted ways to do this.
I would ideally like it to work on both Firebird 2 and MySQL 5 as the update will need to be ran against both databases, and it would be simpler if the same SQL ran on both, if it worked on more database that would be a plus.
Speed and reliability also factor in, reliability over speed in this case but it will potentially be used to update 1000's of records in quick succession (over different tables).
any subjections?
A:
In Firebird 2.1 you can use UPDATE OR INSERT for simple cases or MERGE for more complex scenarios.
A:
You should either use something like this:
BEGIN TRANSACTION
IF EXISTS (SELECT * FROM the_table WHERE pk = 'whatever')
UPDATE the_table SET data = 'stuff' WHERE pk = 'whatever'
ELSE
INSERT INTO the_table (pk, data) VALUES ('whatever', 'stuff')
COMMIT
Or this, but send them separately and ignore any errors from the INSERT about violating primary key constraints:
INSERT INTO the_table (pk, data) VALUES ('whatever', 'stuff')
UPDATE the_table SET data = 'stuff' WHERE pk = 'whatever'
|
{
"pile_set_name": "StackExchange"
}
|
#error "This file is just for the make check"
|
{
"pile_set_name": "Github"
}
|
// Copyright 2009 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.
// +build ignore
/*
Input to cgo -godefs. See README.md
*/
// +godefs map struct_in_addr [4]byte /* in_addr */
// +godefs map struct_in6_addr [16]byte /* in6_addr */
package unix
/*
#define KERNEL
#include <dirent.h>
#include <fcntl.h>
#include <poll.h>
#include <signal.h>
#include <termios.h>
#include <stdio.h>
#include <unistd.h>
#include <sys/param.h>
#include <sys/types.h>
#include <sys/event.h>
#include <sys/mman.h>
#include <sys/mount.h>
#include <sys/ptrace.h>
#include <sys/resource.h>
#include <sys/select.h>
#include <sys/signal.h>
#include <sys/socket.h>
#include <sys/stat.h>
#include <sys/time.h>
#include <sys/uio.h>
#include <sys/un.h>
#include <sys/utsname.h>
#include <sys/wait.h>
#include <net/bpf.h>
#include <net/if.h>
#include <net/if_dl.h>
#include <net/route.h>
#include <netinet/in.h>
#include <netinet/icmp6.h>
#include <netinet/tcp.h>
enum {
sizeofPtr = sizeof(void*),
};
union sockaddr_all {
struct sockaddr s1; // this one gets used for fields
struct sockaddr_in s2; // these pad it out
struct sockaddr_in6 s3;
struct sockaddr_un s4;
struct sockaddr_dl s5;
};
struct sockaddr_any {
struct sockaddr addr;
char pad[sizeof(union sockaddr_all) - sizeof(struct sockaddr)];
};
*/
import "C"
// Machine characteristics; for internal use.
const (
sizeofPtr = C.sizeofPtr
sizeofShort = C.sizeof_short
sizeofInt = C.sizeof_int
sizeofLong = C.sizeof_long
sizeofLongLong = C.sizeof_longlong
)
// Basic types
type (
_C_short C.short
_C_int C.int
_C_long C.long
_C_long_long C.longlong
)
// Time
type Timespec C.struct_timespec
type Timeval C.struct_timeval
// Processes
type Rusage C.struct_rusage
type Rlimit C.struct_rlimit
type _Gid_t C.gid_t
// Files
const ( // Directory mode bits
S_IFMT = C.S_IFMT
S_IFIFO = C.S_IFIFO
S_IFCHR = C.S_IFCHR
S_IFDIR = C.S_IFDIR
S_IFBLK = C.S_IFBLK
S_IFREG = C.S_IFREG
S_IFLNK = C.S_IFLNK
S_IFSOCK = C.S_IFSOCK
S_ISUID = C.S_ISUID
S_ISGID = C.S_ISGID
S_ISVTX = C.S_ISVTX
S_IRUSR = C.S_IRUSR
S_IWUSR = C.S_IWUSR
S_IXUSR = C.S_IXUSR
)
type Stat_t C.struct_stat
type Statfs_t C.struct_statfs
type Flock_t C.struct_flock
type Dirent C.struct_dirent
type Fsid C.fsid_t
// File system limits
const (
PathMax = C.PATH_MAX
)
// Sockets
type RawSockaddrInet4 C.struct_sockaddr_in
type RawSockaddrInet6 C.struct_sockaddr_in6
type RawSockaddrUnix C.struct_sockaddr_un
type RawSockaddrDatalink C.struct_sockaddr_dl
type RawSockaddr C.struct_sockaddr
type RawSockaddrAny C.struct_sockaddr_any
type _Socklen C.socklen_t
type Linger C.struct_linger
type Iovec C.struct_iovec
type IPMreq C.struct_ip_mreq
type IPv6Mreq C.struct_ipv6_mreq
type Msghdr C.struct_msghdr
type Cmsghdr C.struct_cmsghdr
type Inet6Pktinfo C.struct_in6_pktinfo
type IPv6MTUInfo C.struct_ip6_mtuinfo
type ICMPv6Filter C.struct_icmp6_filter
const (
SizeofSockaddrInet4 = C.sizeof_struct_sockaddr_in
SizeofSockaddrInet6 = C.sizeof_struct_sockaddr_in6
SizeofSockaddrAny = C.sizeof_struct_sockaddr_any
SizeofSockaddrUnix = C.sizeof_struct_sockaddr_un
SizeofSockaddrDatalink = C.sizeof_struct_sockaddr_dl
SizeofLinger = C.sizeof_struct_linger
SizeofIPMreq = C.sizeof_struct_ip_mreq
SizeofIPv6Mreq = C.sizeof_struct_ipv6_mreq
SizeofMsghdr = C.sizeof_struct_msghdr
SizeofCmsghdr = C.sizeof_struct_cmsghdr
SizeofInet6Pktinfo = C.sizeof_struct_in6_pktinfo
SizeofIPv6MTUInfo = C.sizeof_struct_ip6_mtuinfo
SizeofICMPv6Filter = C.sizeof_struct_icmp6_filter
)
// Ptrace requests
const (
PTRACE_TRACEME = C.PT_TRACE_ME
PTRACE_CONT = C.PT_CONTINUE
PTRACE_KILL = C.PT_KILL
)
// Events (kqueue, kevent)
type Kevent_t C.struct_kevent
// Select
type FdSet C.fd_set
// Routing and interface messages
const (
SizeofIfMsghdr = C.sizeof_struct_if_msghdr
SizeofIfData = C.sizeof_struct_if_data
SizeofIfaMsghdr = C.sizeof_struct_ifa_msghdr
SizeofIfAnnounceMsghdr = C.sizeof_struct_if_announcemsghdr
SizeofRtMsghdr = C.sizeof_struct_rt_msghdr
SizeofRtMetrics = C.sizeof_struct_rt_metrics
)
type IfMsghdr C.struct_if_msghdr
type IfData C.struct_if_data
type IfaMsghdr C.struct_ifa_msghdr
type IfAnnounceMsghdr C.struct_if_announcemsghdr
type RtMsghdr C.struct_rt_msghdr
type RtMetrics C.struct_rt_metrics
type Mclpool C.struct_mclpool
// Berkeley packet filter
const (
SizeofBpfVersion = C.sizeof_struct_bpf_version
SizeofBpfStat = C.sizeof_struct_bpf_stat
SizeofBpfProgram = C.sizeof_struct_bpf_program
SizeofBpfInsn = C.sizeof_struct_bpf_insn
SizeofBpfHdr = C.sizeof_struct_bpf_hdr
)
type BpfVersion C.struct_bpf_version
type BpfStat C.struct_bpf_stat
type BpfProgram C.struct_bpf_program
type BpfInsn C.struct_bpf_insn
type BpfHdr C.struct_bpf_hdr
type BpfTimeval C.struct_bpf_timeval
// Terminal handling
type Termios C.struct_termios
type Winsize C.struct_winsize
// fchmodat-like syscalls.
const (
AT_FDCWD = C.AT_FDCWD
AT_SYMLINK_NOFOLLOW = C.AT_SYMLINK_NOFOLLOW
)
// poll
type PollFd C.struct_pollfd
const (
POLLERR = C.POLLERR
POLLHUP = C.POLLHUP
POLLIN = C.POLLIN
POLLNVAL = C.POLLNVAL
POLLOUT = C.POLLOUT
POLLPRI = C.POLLPRI
POLLRDBAND = C.POLLRDBAND
POLLRDNORM = C.POLLRDNORM
POLLWRBAND = C.POLLWRBAND
POLLWRNORM = C.POLLWRNORM
)
// Uname
type Utsname C.struct_utsname
|
{
"pile_set_name": "Github"
}
|
#!/bin/sh
#
# Detects OS we're compiling on and outputs a file specified by the first
# argument, which in turn gets read while processing Makefile.
#
# The output will set the following variables:
# CC C Compiler path
# CXX C++ Compiler path
# PLATFORM_LDFLAGS Linker flags
# PLATFORM_LIBS Libraries flags
# PLATFORM_SHARED_EXT Extension for shared libraries
# PLATFORM_SHARED_LDFLAGS Flags for building shared library
# This flag is embedded just before the name
# of the shared library without intervening spaces
# PLATFORM_SHARED_CFLAGS Flags for compiling objects for shared library
# PLATFORM_CCFLAGS C compiler flags
# PLATFORM_CXXFLAGS C++ compiler flags. Will contain:
# PLATFORM_SHARED_VERSIONED Set to 'true' if platform supports versioned
# shared libraries, empty otherwise.
#
# The PLATFORM_CCFLAGS and PLATFORM_CXXFLAGS might include the following:
#
# -DLEVELDB_ATOMIC_PRESENT if <atomic> is present
# -DLEVELDB_PLATFORM_POSIX for Posix-based platforms
# -DSNAPPY if the Snappy library is present
#
OUTPUT=$1
PREFIX=$2
if test -z "$OUTPUT" || test -z "$PREFIX"; then
echo "usage: $0 <output-filename> <directory_prefix>" >&2
exit 1
fi
# Delete existing output, if it exists
rm -f $OUTPUT
touch $OUTPUT
if test -z "$CC"; then
CC=cc
fi
if test -z "$CXX"; then
CXX=g++
fi
if test -z "$TMPDIR"; then
TMPDIR=/tmp
fi
# Detect OS
if test -z "$TARGET_OS"; then
TARGET_OS=`uname -s`
fi
COMMON_FLAGS=
CROSS_COMPILE=
PLATFORM_CCFLAGS=
PLATFORM_CXXFLAGS=
PLATFORM_LDFLAGS=
PLATFORM_LIBS=
PLATFORM_SHARED_EXT="so"
PLATFORM_SHARED_LDFLAGS="-shared -Wl,-soname -Wl,"
PLATFORM_SHARED_CFLAGS="-fPIC"
PLATFORM_SHARED_VERSIONED=true
MEMCMP_FLAG=
if [ "$CXX" = "g++" ]; then
# Use libc's memcmp instead of GCC's memcmp. This results in ~40%
# performance improvement on readrandom under gcc 4.4.3 on Linux/x86.
MEMCMP_FLAG="-fno-builtin-memcmp"
fi
case "$TARGET_OS" in
CYGWIN_*)
PLATFORM=OS_LINUX
COMMON_FLAGS="$MEMCMP_FLAG -lpthread -DOS_LINUX -DCYGWIN"
PLATFORM_LDFLAGS="-lpthread"
PORT_FILE=port/port_posix.cc
;;
Darwin)
PLATFORM=OS_MACOSX
COMMON_FLAGS="$MEMCMP_FLAG -DOS_MACOSX"
PLATFORM_SHARED_EXT=dylib
[ -z "$INSTALL_PATH" ] && INSTALL_PATH=`pwd`
PLATFORM_SHARED_LDFLAGS="-dynamiclib -install_name $INSTALL_PATH/"
PORT_FILE=port/port_posix.cc
;;
Linux)
PLATFORM=OS_LINUX
COMMON_FLAGS="$MEMCMP_FLAG -pthread -DOS_LINUX"
PLATFORM_LDFLAGS="-pthread"
PORT_FILE=port/port_posix.cc
;;
SunOS)
PLATFORM=OS_SOLARIS
COMMON_FLAGS="$MEMCMP_FLAG -D_REENTRANT -DOS_SOLARIS"
PLATFORM_LIBS="-lpthread -lrt"
PORT_FILE=port/port_posix.cc
;;
FreeBSD)
PLATFORM=OS_FREEBSD
COMMON_FLAGS="$MEMCMP_FLAG -D_REENTRANT -DOS_FREEBSD"
PLATFORM_LIBS="-lpthread"
PORT_FILE=port/port_posix.cc
;;
GNU/kFreeBSD)
PLATFORM=OS_KFREEBSD
COMMON_FLAGS="$MEMCMP_FLAG -D_REENTRANT -DOS_KFREEBSD"
PLATFORM_LIBS="-lpthread"
PORT_FILE=port/port_posix.cc
;;
NetBSD)
PLATFORM=OS_NETBSD
COMMON_FLAGS="$MEMCMP_FLAG -D_REENTRANT -DOS_NETBSD"
PLATFORM_LIBS="-lpthread -lgcc_s"
PORT_FILE=port/port_posix.cc
;;
OpenBSD)
PLATFORM=OS_OPENBSD
COMMON_FLAGS="$MEMCMP_FLAG -D_REENTRANT -DOS_OPENBSD"
PLATFORM_LDFLAGS="-pthread"
PORT_FILE=port/port_posix.cc
;;
DragonFly)
PLATFORM=OS_DRAGONFLYBSD
COMMON_FLAGS="$MEMCMP_FLAG -D_REENTRANT -DOS_DRAGONFLYBSD"
PLATFORM_LIBS="-lpthread"
PORT_FILE=port/port_posix.cc
;;
OS_ANDROID_CROSSCOMPILE)
PLATFORM=OS_ANDROID
COMMON_FLAGS="$MEMCMP_FLAG -D_REENTRANT -DOS_ANDROID -DLEVELDB_PLATFORM_POSIX"
PLATFORM_LDFLAGS="" # All pthread features are in the Android C library
PORT_FILE=port/port_posix.cc
CROSS_COMPILE=true
;;
HP-UX)
PLATFORM=OS_HPUX
COMMON_FLAGS="$MEMCMP_FLAG -D_REENTRANT -DOS_HPUX"
PLATFORM_LDFLAGS="-pthread"
PORT_FILE=port/port_posix.cc
# man ld: +h internal_name
PLATFORM_SHARED_LDFLAGS="-shared -Wl,+h -Wl,"
;;
IOS)
PLATFORM=IOS
COMMON_FLAGS="$MEMCMP_FLAG -DOS_MACOSX"
[ -z "$INSTALL_PATH" ] && INSTALL_PATH=`pwd`
PORT_FILE=port/port_posix.cc
PLATFORM_SHARED_EXT=
PLATFORM_SHARED_LDFLAGS=
PLATFORM_SHARED_CFLAGS=
PLATFORM_SHARED_VERSIONED=
;;
OS_WINDOWS_CROSSCOMPILE | NATIVE_WINDOWS)
PLATFORM=OS_WINDOWS
COMMON_FLAGS="-fno-builtin-memcmp -D_REENTRANT -DOS_WINDOWS -DLEVELDB_PLATFORM_WINDOWS -DWINVER=0x0500 -D__USE_MINGW_ANSI_STDIO=1"
PLATFORM_SOURCES="util/env_win.cc"
PLATFORM_LIBS="-lshlwapi"
PORT_FILE=port/port_win.cc
CROSS_COMPILE=true
;;
*)
echo "Unknown platform!" >&2
exit 1
esac
# We want to make a list of all cc files within util, db, table, and helpers
# except for the test and benchmark files. By default, find will output a list
# of all files matching either rule, so we need to append -print to make the
# prune take effect.
DIRS="$PREFIX/db $PREFIX/util $PREFIX/table"
set -f # temporarily disable globbing so that our patterns aren't expanded
PRUNE_TEST="-name *test*.cc -prune"
PRUNE_BENCH="-name *_bench.cc -prune"
PRUNE_TOOL="-name leveldb_main.cc -prune"
PORTABLE_FILES=`find $DIRS $PRUNE_TEST -o $PRUNE_BENCH -o $PRUNE_TOOL -o -name '*.cc' -print | sort | sed "s,^$PREFIX/,," | tr "\n" " "`
set +f # re-enable globbing
# The sources consist of the portable files, plus the platform-specific port
# file.
echo "SOURCES=$PORTABLE_FILES $PORT_FILE" >> $OUTPUT
echo "MEMENV_SOURCES=helpers/memenv/memenv.cc" >> $OUTPUT
if [ "$CROSS_COMPILE" = "true" ]; then
# Cross-compiling; do not try any compilation tests.
true
else
CXXOUTPUT="${TMPDIR}/leveldb_build_detect_platform-cxx.$$"
# If -std=c++0x works, use <atomic> as fallback for when memory barriers
# are not available.
$CXX $CXXFLAGS -std=c++0x -x c++ - -o $CXXOUTPUT 2>/dev/null <<EOF
#include <atomic>
int main() {}
EOF
if [ "$?" = 0 ]; then
COMMON_FLAGS="$COMMON_FLAGS -DLEVELDB_PLATFORM_POSIX -DLEVELDB_ATOMIC_PRESENT"
PLATFORM_CXXFLAGS="-std=c++0x"
else
COMMON_FLAGS="$COMMON_FLAGS -DLEVELDB_PLATFORM_POSIX"
fi
# Test whether tcmalloc is available
$CXX $CXXFLAGS -x c++ - -o $CXXOUTPUT -ltcmalloc 2>/dev/null <<EOF
int main() {}
EOF
if [ "$?" = 0 ]; then
PLATFORM_LIBS="$PLATFORM_LIBS -ltcmalloc"
fi
rm -f $CXXOUTPUT 2>/dev/null
fi
PLATFORM_CCFLAGS="$PLATFORM_CCFLAGS $COMMON_FLAGS"
PLATFORM_CXXFLAGS="$PLATFORM_CXXFLAGS $COMMON_FLAGS"
echo "CC=$CC" >> $OUTPUT
echo "CXX=$CXX" >> $OUTPUT
echo "PLATFORM=$PLATFORM" >> $OUTPUT
echo "PLATFORM_LDFLAGS=$PLATFORM_LDFLAGS" >> $OUTPUT
echo "PLATFORM_LIBS=$PLATFORM_LIBS" >> $OUTPUT
echo "PLATFORM_CCFLAGS=$PLATFORM_CCFLAGS" >> $OUTPUT
echo "PLATFORM_CXXFLAGS=$PLATFORM_CXXFLAGS" >> $OUTPUT
echo "PLATFORM_SHARED_CFLAGS=$PLATFORM_SHARED_CFLAGS" >> $OUTPUT
echo "PLATFORM_SHARED_EXT=$PLATFORM_SHARED_EXT" >> $OUTPUT
echo "PLATFORM_SHARED_LDFLAGS=$PLATFORM_SHARED_LDFLAGS" >> $OUTPUT
echo "PLATFORM_SHARED_VERSIONED=$PLATFORM_SHARED_VERSIONED" >> $OUTPUT
|
{
"pile_set_name": "Github"
}
|
/*
* Copyright 2018
* Ubiquitous Knowledge Processing (UKP) Lab and FG Language Technology
* Technische Universität Darmstadt
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package de.tudarmstadt.ukp.clarin.webanno.webapp.remoteapi.config;
import org.springframework.boot.autoconfigure.condition.ConditionalOnExpression;
import org.springframework.context.annotation.Bean;
import org.springframework.context.annotation.Configuration;
import de.tudarmstadt.ukp.clarin.webanno.webapp.remoteapi.LegacyRemoteApiController;
import de.tudarmstadt.ukp.clarin.webanno.webapp.remoteapi.aero.AeroRemoteApiController;
@Configuration
public class RemoteApiConfig
{
public static final String REMOTE_API_ENABLED_CONDITION =
"${remote-api.enabled:false} || ${webanno.remote-api.enable:false}";
@ConditionalOnExpression(REMOTE_API_ENABLED_CONDITION)
@Bean
public AeroRemoteApiController aeroRemoteApiController()
{
return new AeroRemoteApiController();
}
@ConditionalOnExpression(REMOTE_API_ENABLED_CONDITION)
@Bean
public LegacyRemoteApiController legacyRemoteApiController()
{
return new LegacyRemoteApiController();
}
}
|
{
"pile_set_name": "Github"
}
|
Book of Brilliance
At Thorp Academy we love praise! Students receive praise in many ways from applause moments in the classroom, extra applause when they have consistently done something well to year group praise in assembly. We want to consistently have positive conversations with our students because we believe in developing positive relationships with our students.
In order to boost our praise culture even more, we have now introduced the Book of Brilliance. When a student does something 'outstanding' their name will be placed into the Book of Brilliance and a postcard sent home celebrating their success. At the end of each STEPS cycle, we will collect in all of the Brilliance nominations and pick at random a student to receive a special prize.
All students from Year 7 through to Year 13 can be nominated for the Book of Brilliance.
|
{
"pile_set_name": "Pile-CC"
}
|
Unwelcome travelers: Pesticides in the Arctic
Endosulfan. Chlorpyrifos. Chlorothalonil. Not words one would associate with the crisp, cold air and water of the Arctic region. But new research shows that these pesticides, among others, are traveling to the Arctic from as far as South East Asia, India and the United States.
That harmful pesticides travel on wind and water currents to cold northern regions of the world has been known for a while now. But in this latest study, researchers managed to measure the compounds in air and water all the way along their path across the globe, from East Asia to the Arctic.
On a four week expedition from the East China Sea northward to the Chukchi Sea in the high Arctic, researchers tracked the pesticides chlorothalonil, chlorpyrifos, dacthal, dicofol, endosulfan and trifluralin. The data collected will help researchers better understand whether the pesticides travel more readily by air or by water, and how they degrade along the way.
Harsh impacts of contamination
We already know that the chemicals that reach the Arctic region are wreaking havoc on the health of both humans and the fragile environment.
For example, endosulfan is one of the few persistent pesticides whose levels have been found to be increasing in marine biota of the Canadian Arctic. Endosulfan appears to accumulate more in the bodies of humans, animals and the environment in Arctic ecosystems than in warmer climates. This pesticide has severe health impacts for humans, with exposure linked to developmental defects and reproductive harm. In 2011, endosulfan was finally slated for a global phase out through the Stockholm Convention, the international treaty on persistent organic pollutants.
Chlorpyrifos, another pesticide studied by the research team, is one of the highest volume agricultural pesticides used in the U.S. Studies have found that prenatal exposure to chlorpyrifos can have negative impacts on neurodevelopment, including perceptual reasoning, working memory and poorer intellectual development in children. Chlorpyrifos was banned for home use in the U.S. in 2001, but is still used on farms, exposing not only rural residents to health harms, but also communities thousands of miles away in the Arctic.
Arctic communities speak out
With organizations such as the Alaska Community Action on Toxics, communities in the Arctic have long campaigned against pollution of their environment and bodies by such pesticides used in far away places. As Shawna Larson, a long time Indigenous environmental health activist from the region, explains:
These toxic chemicals trespass our bodies and enter our breast milk – our children and infants are getting them. We are seeing impacts of these through things like respiratory health and breast cancer increases.
The Indigenous communities of the Arctic call upon all of us to stop polluting their environment, their bodies and those of their children with these pesticides. By doing so, we will not only protect ourselves and our families, but also families in the Arctic who are asking us to take a stand.
is PAN's Campaign Coordinator. Her work focuses on pesticide impacts on maternal and children’s health as well as international pesticide campaigns. She works closely with network members from other PAN regional centers around the world. Follow @ChandraMedha
1
Satyabroto wrote:
There are established protocols to determine the long range transport of pesticides. These have not been used in the studies you cite. The author of modeling from Zurich has given me written confirmation of the fallacies of his work. The POP Secretary has written to me, asking that these gaps be informed to all POP members. The European pesticide mafia sponsored lie about Endosulfan in sea water can be exposed instantly-just add Endosulfan to sea water: it will dissipate immediately! I am afraid that the pesticide industry laughs up its collective sleeve at the gullibility of well-meaning but ignorant activists.
I admit that pesticide safety is generally ignored in the third world. Please think carefully whether such abuse is limited to Endosulfan alone. Endosulfan bans have opened the floodgates for even more toxic pesticides such as proprietary neonicotinoids, patented by European companies.
I earnestly ask you to shift from vilification of Endosulfan to supporting the safe and judicious use of all pesticides.
Thank you for your courtesy in allowing me to use your esteemed forum to express my views.
2
Satyabroto wrote:
Pesticides such as Endosulfan break down instantly in an alkaline environment. This is a standard measure of emergency containment. It can be demonstrated simply, and is irrefutable. The canard of Endosulfan traveling long distances in sea water is patently ridiculous. Drift and volatility can and should be managed by the use of appropriate application equipment and in specified ambient conditions. Finally, allegations of inter-continental pesticide drift are based on models rather than approved empirical evidence. Please consider these issues in order to distinguish between the important cause of safe and judicious pesticide use versus silly propaganda.
Regarding the use of appropriate protective equipment, you must be aware that real world conditions of use, especially in countries of the Global South are very different than idealized methods of use. Thousands of tragic endosulfan related poisonings have occurred in countries across Africa, Latin America and Asia. PAN and our partners around the world are thrilled that endosulfan has finally been targeted by the global community for a well deserved phased out.
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American Association (20th century) Rookie of the Year Award
The American Association Rookie of the Year Award was an annual award given to the best rookie player in Minor League Baseball's American Association. In 1946, Jerry Witte of the Toledo Mud Hens won the first American Association Rookie of the Year Award. In 1997, Magglio Ordóñez of the Nashville Sounds won the final American Association Rookie of the Year Award.
First basemen and shortstops, with 6 winners each, won the most among infielders, followed by second baseman and third basemen (5). Four catchers also won the award. Eighteen outfielders won the Rookie of the Year Award, the most of any position. Two pitchers won the Rookie of the Year Award.
Seven players each from the Denver Bears/Zephyrs and Indianapolis Indians have been selected for the Rookie of the Year Award, more than any other teams in the league, followed by the Milwaukee Brewers, Omaha Royals, Tulsa Oilers, and Wichita Braves/Aeros (3); the Iowa Cubs, Kansas City Blues, Louisville Redbirds, Nashville Sounds, Oklahoma City 89ers, Springfield Redbirds, and St. Paul Saints (2); and the Buffalo Bisons, Louisville Colonels, Minneapolis Millers, Omaha Cardinals, Omaha Dodgers, and Toledo Mud Hens (1).
Eight players from the St. Louis Cardinals Major League Baseball (MLB) organization won the Rookie of the Year Award, more than any other, followed by the Chicago White Sox and Cincinnati Reds organizations (5); the Boston/Milwaukee Braves organization (4); the Brooklyn/Los Angeles Dodgers, Cleveland Indians, Kansas City Royals, Montreal Expos, and New York Yankees organizations (3); the Chicago Cubs, St. Louis Browns/Baltimore Orioles, and Texas Rangers organizations (2); and the Boston Red Sox, Milwaukee Brewers, and Pittsburgh Pirates organizations (1).
Key
Winners
References
Sepcific
General
Category:American Association (20th century)
Category:Minor league baseball awards
Category:Rookie player awards
Category:Awards established in 1946
Category:1946 establishments in the United States
Category:1997 disestablishments in the United States
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{
"pile_set_name": "Wikipedia (en)"
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Q:
Print login page url in node.tpl.php
It seems nevertheless rather simple, but I do not find the solution.
How to print in node.tpl.php the url of the login page?
The url has to serve for a link:
<a href="<?php print ... ?>"><span>Login</span></a>
A:
Use this if you just want the URL:
<?php print url('user/login'); ?>
If you want to print a link:
<?php print l(t('Login'), 'user/login'); ?>
And in your case it would be:
<?php print l('<span>' . t('Login') . '</span>', 'user/login', array('html' => TRUE)); ?>
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{
"pile_set_name": "StackExchange"
}
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Q:
How do you prove that the following 2 hypothesis classes' VC-dimensions are equal?
Given a hypothesis class $H=\{h:X\to\{0,1\}\}$.
Let $c\in H$ be the correct predictor.
Denote $H^c = \{c\Delta h:h\in H\}$, where $c\Delta h=(h\backslash c)\cup (c\backslash h)$.
Please prove that VCdim($H^c$) = VCdim($H$)
A:
If some $A = (a_1,\dots,a_d\}\subset X$ is shattered by $H$, then, for any vector $b$ = $\{0,1\}^d$,$\exists$ $h \in H s.t. (h(a_1),\dots,h(a_d)) = b$.
It suffices to prove that for any vector
$(h(a_1),\dots,h(a_d)) = b$, $\exists$ $h' \in H s.t. (c\Delta h'(a_1),\dots,c\Delta h'(a_d)) = (h(a_1),\dots,h(a_d))$.
Proof of my claim:
$\forall x_i \in A$, if $c(a_i) = 0$,let $h'(a_i) = h(a_i)$, then $c\Delta h' (a_i) = h(a_i)$.
If $c(a_i) = 1$, let $h'(a_i) = -h(a_i)$, then $c\Delta h'(a_i) = h(a_i)$.
Then $(c\Delta h'(a_1),\dots,c\Delta h'(a_d)) = (h(a_1),\dots,h(a_d))$.
For the same reason, the inverse is also true.
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{
"pile_set_name": "StackExchange"
}
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Magnificent Megan Words
Megan Tan, the former host of 8TV Quickie is now going places with the new travel show, G Travel which is being aired on the new Astro channel 737 GOASEAN. Watching her speak in such a bubbly manner, one would find it hard to believe that she was a very shy kid when growing up.
In fact, Megan’s parents were quite worried at one point as she was so quiet and would only speak when spoken to. So, how did she come out of her shell? “My dad sent me to an English tuition class which encouraged poetry and drama. And then, I became involved in storytelling and debate. I even hosted the TV2 show Golden Kids Club when I was 10 years old. Slowly, bit by bit my personality sort of came out as I grew up.”
Winning the audition
When Megan won the 8TV Quickie audition for a co-host in 2010, life took a 180° turn for her. She was in her final year of studies doing psychology and communication at SEGi College. “That was their first ever open audition. Coincidentally, my dad contributed a lot to that win, my career and who I am today because he was the one who heard about the audition on the radio and told me to try it out.”
So, she went for the audition, queued up with hundreds of people, waited in line for her turn and did her best. “When I got the call and was told that I was among the top six contestants, I was beyond ecstatic and really happy! After that, we went through a series of assignments and then, I got the job. And I won the competition alongside Naqib [Naqib Nadhir Shamsuri].”
And that pretty much started Megan’s career although in the beginning, she thought of it as a hobby. She was still studying and had plans of taking up Masters of Psychology because she was always interested in child psychology and media as well.
Career options
Megan loves hosting various TV shows. “TV hosting was my first love. I always call it a blessing – I guess I was at the right place at the right time. I never thought I would be doing this.” She also discovered her true self along the way and grew from being a college student into a working adult.
Interestingly, Megan wanted to be a doctor during her high school days. However, watching a documentary on a caesarean surgery changed her mind! So, she explored other options and decided to take up psychology. “I have always been fascinated with people’s behaviour and why they act in a certain way. I have been told I’m quite an understanding person and I have a huge amount of patience with people and I am able to empathize a lot. I have an older sister who comes to me for advice.”
Megan believes she can definitely apply her knowledge of psychology in the future regardless of what her career will be. She also thinks it will be great to help children with disabilities and special needs. Being a positive person, Megan chose to surround herself with people who are more positive.
In 2011, Megan was selected to play the lead role in Sakura, a Malaysian telemovie on TV3. “I was very fortunate to be selected because the director was looking for a non-Malay and she took a chance with me which I am very thankful for. The character was half-Japanese and half-Malaysian so I guess she needed someone who looked the part to play the role.”
Megan learnt a lot from that experience because prior to that she never knew what acting was like. “It was very challenging for me because it was my first ever acting gig.” Her role involved a lot of crying and intense scenes and was emotionally challenging.
However, Megan says it was a good experience. “I’m always up for a challenge so that made me love acting as well. As a TV host, I get to be myself but with acting I get to explore different sides of who I am and just to be someone else for a change.”
Megan also plays a supporting role in another Malay movie called Antara Satu, which features Remy Ishak and Bront Palarae as lead actors. Although showbiz is not something that Megan planned for, she counts the 8TV Quickie audition a blessing and everything has worked out for her since then.
Finding a balance
Megan confesses to be quite the planner when it comes to time management. She used to make her own timetable to divide time for rest, reading a book, homework, playtime, etc. “I think it just came naturally to me, an inborn character perhaps. I never really struggled with time management.”
Hence, she is able to find a balance when working. She handles events back to back during busy periods and when more relaxed, spends time with her family. “You need to prioritize at the end of the day and see what is more worthy of your time and then, do that.”
Megan loves to unwind at the end of the day by watching TV. She also loves the beach and island holidays. In contrast, she also loves to visit cities. “Every year I try to take off for 2 weeks. Last year, I went to Gold Coast and Brisbane in Australia. It’s like a refresh button.”
To stay healthy while on the move, Megan has some basic habits – drinking a lot of water, exercising with the help of YouTube videos and sleeping for at least 6 to 8 hours a day. Although she indulges her sweet tooth with the occasional cake, chocolate and ice cream, she follows a healthy diet on a daily basis starting with cereal or a granola bar to kickstart her day. To stay youthful, she uses the basic beauty regimen – cleanse, tone and moisturize followed by applying sunblock.
Moving forward
Megan takes every new show and new project that she engages in as a new learning curve for her. She still feels like she has more to learn after being in showbiz for more than 5 years now. “I would say that this year, for instance, when I saw my name on the nomination list in the Anugerah Bintang Popular that was a wow moment for me. I’m just going to keep doing what I do and hopefully stay relevant and I’ll be able to do this for the rest of my life.”
Besides hosting TV shows and emceeing, Megan is in the midst of launching her lifestyle site that covers everything that she loves and believes in. “I hope to inspire people through this site by just spreading some positivity and the goodness in life.”
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Scoring a “Home” Run in Life
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Viewers of 2012’s American Idol could not have imagined the misery Phillip Phillips was going through while he belted out song after song.
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Enhanced expression of potassium-chloride cotransporter KCC2 in human temporal lobe epilepsy.
Synaptic reorganization in the epileptic hippocampus involves altered excitatory and inhibitory transmission besides the rearrangement of dendritic spines, resulting in altered excitability, ion homeostasis, and cell swelling. The potassium-chloride cotransporter-2 (KCC2) is the main chloride extruder in neurons and hence will play a prominent role in determining the polarity of GABAA receptor-mediated chloride currents. In addition, KCC2 also interacts with the actin cytoskeleton which is critical for dendritic spine morphogenesis, and for the maintenance of glutamatergic synapses and cell volume. Using immunocytochemistry, we examined the cellular and subcellular levels of KCC2 in surgically removed hippocampi of temporal lobe epilepsy (TLE) patients and compared them to control human tissue. We also studied the distribution of KCC2 in a pilocarpine mouse model of epilepsy. An overall increase in KCC2-expression was found in epilepsy and confirmed by Western blots. The cellular and subcellular distributions in control mouse and human samples were largely similar; moreover, changes affecting KCC2-expression were also alike in chronic epileptic human and mouse hippocampi. At the subcellular level, we determined the neuronal elements exhibiting enhanced KCC2 expression. In epileptic tissue, staining became more intense in the immunopositive elements detected in control tissue, and profiles with subthreshold expression of KCC2 in control samples became labelled. Positive interneuron somata and dendrites were more numerous in epileptic hippocampi, despite severe interneuron loss. Whether the elevation of KCC2-expression is ultimately a pro- or anticonvulsive change, or both-behaving differently during ictal and interictal states in a context-dependent manner-remains to be established.
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{
"pile_set_name": "PubMed Abstracts"
}
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2015–16 Kazakhstan Hockey Championship
The 2015–16 Kazakhstan Hockey Championship was the 24rd season since the founding of the Kazakhstan Hockey Championship.
Teams
Regular season
Standings
|}
GP = Games Played, W = Wins, OTW = Overtime win, SOW = Shootout win, OTL = Overtime loss, SOL = Shootout loss, L = Loss
Color code:
Play-off
Quarterfinals
Arlan Kokshetau vs. HC Astana
Beibarys Atyrau vs. Gornyak Rudny
Kulager Petropavl vs. HC Temirtau
Nomad Astana vs. Yertis Pavlodar
Semi-finals
Arlan Kokshetau vs. Yertis Pavlodar
Beibarys Atyrau vs. Kulager Petropavl
Final
Arlan Kokshetau vs. Beibarys Atyrau
References
External links
Kazakhstan Ice Hockey Federation
English language forum for the Kazakhstan Hockey Championship
Category:Kazakhstan Hockey Championship seasons
Kazakhstan Hockey Championship
1
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{
"pile_set_name": "Wikipedia (en)"
}
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<div class="layout-absolute">
<div class="control-scrollbar" data-control="scrollbar">
<div class="control-assetlist" data-control="assetlist" id="<?= $this->getId('asset-list') ?>">
<?= $this->makePartial('items', ['items'=>$data]) ?>
</div>
</div>
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{
"pile_set_name": "Github"
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Navigation
Tag Archives | cheer
Following the World Cup and use Firefox? I have a site that will serve two of your proverbial itches at the same time. Firefox Cup is the new website put out by Mozilla (in association with FIFA) to help you rally behind your favorite soccer team.
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Regulation of interferon-gamma-activated STAT1 by the ubiquitin-proteasome pathway.
STAT proteins (signal transducers and activators of transcription) are latent cytoplasmic transcription factors that are phosphorylated by Janus kinases in response to cytokines. Phosphorylated STAT proteins translocate to the nucleus, where they transiently turn on specific sets of cytokine-inducible genes. The mechanism that controls the amounts of activated STAT proteins is not understood. STAT1 proteins activated by interferon-gamma treatment in HeLa cells were shown to be stabilized by a proteasome inhibitor and ubiquitinated in vivo. Thus, the amount of activated STAT1 may be negatively regulated by the ubiquitin-proteasome pathway.
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{
"pile_set_name": "PubMed Abstracts"
}
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Development of a Tumor-Responsive Nanopolyplex Targeting Pancreatic Cancer Cells and Stroma.
Desmoplasia plays a pivotal role in promoting pancreatic cancer progression and is associated with poor clinical outcome. Targeting the desmoplastic tumor microenvironment in combination with chemotherapy is therefore a promising strategy for pancreatic cancer therapy. Here, we report a novel biodegradable copolymer to codeliver LY2109761 (a TGF-β receptor I/II inhibitor) and CPI-613 (a novel chemotherapy agent) to desmoplastic stroma and tumor cells, respectively, in the tumor microenvironment. Hydrophobic CPI-613 is conjugated to the hydrophilic copolymer via a newly designed MMP-2-responsive linker to form a trigger-responsive nanopolyplex. LY2109761 is hydrophobic and encapsulated into the hydrophobic core of the nanopolyplex. The resulting nanopolyplex is modified with a plectin-1-targeting peptide to enhance the accumulation of the nanopolyplex in pancreatic tumors. The nanopolyplex aims to normalize the stroma by blocking the interaction between tumor cells and pancreatic stellate cells to inhibit the activation of pancreatic stellate cells and subsequently reduce the dense extracellular matrix. Normalized stroma increases the penetration of the nanopolyplex into the tumor. The nanopolyplex shows enhanced accumulation in xenograft pancreatic tumors in a biodistribution study. Moreover, the targeted nanopolyplex markedly inhibits tumor growth in an orthotopic pancreatic cancer mouse model by dual-targeting tumor cells and stroma. Overall, the multifunctional nanopolyplex is a promising platform for pancreatic cancer therapy.
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"pile_set_name": "PubMed Abstracts"
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e first derivative of d**2/2 - 3*d - 2. Let s(x) = -x + 8. Let o be s(-12). Suppose 5*a = -2*t - 2*t + o, 8 = 2*a - 4*t. What is q(a)?
1
Let b(i) be the first derivative of 7*i**2/2 - 2*i - 274. What is b(-5)?
-37
Let z(j) = 5*j + 27. Let l be z(-6). Let s(y) = y. Let i be s(l). Let n(w) = w**2 + 7*w + 13. Let x be n(i). Let f(g) = 6*g**3 - g**2 + g. Give f(x).
6
Let g(p) be the third derivative of -p**6/60 + p**5/5 - 5*p**4/12 + p**3/6 + 41*p**2. Let i be g(5). Let m(d) = 5*d + 1. Give m(i).
6
Let o(v) = v**3 - 11*v**2 - 14*v + 16. Let a = 398 - 386. What is o(a)?
-8
Let r = 63 + -56. Let c(h) = 7 - 4*h**2 - 5*h**2 + 6*h + r*h**2. What is c(5)?
-13
Let s(r) = -r**2 - 3*r. Let k(m) be the first derivative of -2/3*m**3 + 2*m - m**2 + 2. Let l be k(-2). What is s(l)?
2
Suppose 4 - 3 = -q. Let j(a) = a**2 + 107*a**3 - 51*a**3 + a**2 - a**2 - 50*a**3. Give j(q).
-5
Let t(f) = 16*f**2 + 16*f + 1. Let i(y) = -18*y**2 - 19*y - 1. Let b(g) = 5*i(g) + 6*t(g). Calculate b(-1).
6
Let f(o) = 17 - 24 + 5*o + 6. Let i(h) = h**3 - h**2 - 2*h - 1. Suppose 5*g = 4*l + 29, 5*l = -9*g + 4*g + 20. Let w be i(l). Give f(w).
-6
Let n(u) = -u**2 - 14*u - 20. Suppose -135*i = -141*i - 48. Determine n(i).
28
Let t(s) = -24*s + 11. Let r(v) = 27*v - 12. Let j(l) = 6*r(l) + 7*t(l). Determine j(2).
-7
Let f(n) be the second derivative of -11*n**3/6 - 7*n**2/2 + 76*n + 4. Determine f(3).
-40
Suppose 3*x - 23 = -f - 3, 2*x = -4*f + 30. Let g(b) = -1 + b**2 - 4 + 1 - 4*b. Give g(f).
1
Let v(m) = -4*m + 1. Let x = -141 + 135. Determine v(x).
25
Let v(y) be the second derivative of y**3/2 + y**2/2 - 2*y. Let c(b) = -33*b**2 + 2*b + 1. Let t be c(-1). Let l = -35 - t. Calculate v(l).
-2
Suppose 30 = 29*j - 39*j. Let w(p) = -p**3 - 4*p**2 - 3*p - 2. What is w(j)?
-2
Let q(v) = -16*v**2 + 2*v - 9. Let x(i) = -21*i**2 + i - 8. Let r(k) = 4*q(k) - 3*x(k). What is r(5)?
-12
Let k be (-33)/(-55) - (-12)/5. Let o(y) = -10*y - k + 20*y - 6*y + 0*y. Determine o(2).
5
Let t(h) = -h - 4. Let j(b) = 6*b - 5. Let u be j(-6). Let q = u + 57. Suppose 2*g + 0*g + q = 0. What is t(g)?
4
Let q(y) = 8 - 2 - 6 + 6*y. Let t(j) = -j**3 - 10*j**2 - j - 9. Let u = -59 - -49. Let k be t(u). Calculate q(k).
6
Let w(b) be the second derivative of -1/6*b**3 + 0 - b - 9/2*b**2. Let g be w(-5). Let m(q) = q**2 + 5*q + 4. Determine m(g).
0
Let l(r) = -r - 380 + 369 + 3*r. Let p(m) = -m + 6. Let j = -4 + -1. Let v(q) = j*p(q) - 3*l(q). Give v(7).
-4
Let o(c) be the first derivative of 4*c**2 + 1 - 1/4*c**4 + 5/3*c**3 - 4*c. Suppose 3*i = -2*m + 19 - 7, 0 = 2*m + 2*i - 12. Give o(m).
8
Let v be -21*8/(168/(-9)). Let x(n) = -n**2 + 10*n - 12. What is x(v)?
-3
Let h(w) = -w + 7. Let x be (5 - 13/3)*(11 - -1). Calculate h(x).
-1
Let n(k) be the first derivative of -3*k**2 - 13*k + 22. Give n(-3).
5
Let y(h) = 3*h + 5. Suppose 4*m = -8, -4*m = -3*v - 2*v - 522. Let i = 101 + v. What is y(i)?
-10
Let q(h) = 3 + 5*h + 80*h**2 - 79*h**2 + 3*h. What is q(-8)?
3
Let f(g) = -g**2 + 4*g**3 - 7*g**3 - 10*g**2 - 9 + 2*g**3 + 11*g. What is f(-12)?
3
Let z(r) = 14 + 4*r - 17 + 4 + r. Let d(c) = c**2 + 6*c - 9. Let o be d(-7). Calculate z(o).
-9
Let h(o) = -2*o + 9. Suppose 0 = 3*p - 6*a + 4*a - 14, 0 = -2*p - 2*a + 16. Calculate h(p).
-3
Let v(u) be the second derivative of -u**5/20 - u**4/3 + u**3 - 7*u**2/2 - 4*u + 34. Calculate v(-5).
-12
Let a(l) = 0*l - 2*l - 7*l. Let i be a(2). Let n = 13 + i. Let m(p) = -p**2 - 7*p - 2. Give m(n).
8
Let j = 1431 - 1448. Let w(z) = -z**3 - 15*z**2 + 33*z - 23. Determine w(j).
-6
Suppose 3*i = 14*i - 33. Let r(b) = -2*b**3 + 3*b**2 - 2*b. Determine r(i).
-33
Let d(r) = 2*r + 5. Let f(p) = -5*p - 47. Let c be f(-9). Let n(s) = 5*s - 4*s + 2*s. Let j be n(c). Determine d(j).
-7
Let q(g) = -g**2 + 6*g - 1. Let d(a) = -a**2 + a + 4. Let j be d(2). Suppose 0 = z + j*y, 0*z + 4*z = 4*y + 36. Calculate q(z).
-1
Let a be 0/((-2*3)/(-2)). Suppose 3*i + 0*i - 21 = a. Let z(m) = i*m + 5*m + 2 - 9 - m**2 - 4*m. Calculate z(6).
5
Let b(a) be the third derivative of -a**4/24 - 5*a**3/3 + a**2. Let i(h) = 3*h - 5. Let q be i(7). Let y = -22 + q. Calculate b(y).
-4
Let v(z) be the second derivative of 0 + 1/2*z**4 + z + 1/20*z**5 - 7/6*z**3 + 5/2*z**2. Let g = 0 + -7. Give v(g).
5
Suppose o + 7*m - 11*m - 17 = 0, -4*o + 5*m + 24 = 0. Let x(n) = 10*n**2 + 1. Calculate x(o).
11
Let d(f) = -2*f**2 - 12 + 11 - 4*f + f**2. Let r(g) = g**2 + g - 3. Let o be r(0). Give d(o).
2
Let h(p) = -3*p - 4*p + 7*p - 20 - p. Let y be h(-14). Let z(d) be the first derivative of d**2/2 + d + 1. Give z(y).
-5
Let h(i) = -24*i - 8 + 23*i - 1. Give h(-9).
0
Let m(v) be the third derivative of v**4/3 + v**3/6 + v**2. Suppose 0 = -8*c - 8 - 0. Let k be c*(-1 - 2)/(-3). What is m(k)?
-7
Let d be (((-35)/2)/(-7))/(12/(-24)). Let b(x) = -7*x**2 - 10*x - 1. Let i(m) = 4*m**2 + 5*m. Let l(h) = -3*b(h) - 5*i(h). What is l(d)?
3
Let p = -1 - -5. Suppose p*t = t. Let y(q) = 7 + 67*q - 20*q + 4*q**2 - 3*q**2 - 25*q - 21*q. Determine y(t).
7
Suppose 2*g = 3*k - 41, -65 + 13 = -4*k + 4*g. Let x be 2/(-5) + 6/k. Let f(c) be the third derivative of -c**5/60 + c**4/24 - c**3/2 + 9*c**2. What is f(x)?
-3
Let d = -291 + 291. Let q(n) = -2*n**2 - n + 9. Give q(d).
9
Let d = 1 - -4. Let o(y) = -8*y - d - 6*y + 11*y + y**2 - y. Determine o(5).
0
Let w(p) = -p - 3. Let q be 0 + 2 + -8 + 14/7. Determine w(q).
1
Let p(x) = 7*x**2 + 5. Let r be p(-2). Suppose 2*c = -3*u + r, 3*u = u + c + 22. Let a(z) = z**2 - 10*z - 11. Give a(u).
0
Let o be 75/(-200)*-2*(-2)/(-12). Let i(x) be the third derivative of o*x**4 + 0 + 1/2*x**3 + 5*x**2 - 1/60*x**5 + 0*x. Give i(4).
-1
Let z(v) = v**3 + 11*v**2 - 13*v - 11. Let b be z(-12). Let m be ((0/4 - b) + 0)*-1. Let h(u) = -2*u + u**3 + 4*u**2 + 2*u**2 - 7*u**2 + 1. Give h(m).
-1
Let v(r) = 4117*r**3 - 2 - 4116*r**3 + 2*r - 4*r**2 + 1 + 0. Let d be (5/(-2))/(1/2). Let w = -2 - d. What is v(w)?
-4
Let y(f) = 4*f + 2*f**2 - 3*f - 3*f**2 + 5. Let o(s) = -5*s**3 + s**2 - 2*s - 3. Let d be o(-1). Give y(d).
-15
Let w(c) = -c**2 - 8*c - 7. Let q(a) = -a + 13. Let k be q(-7). Let l = k - 28. What is w(l)?
-7
Let d(f) be the third derivative of -f**5/30 + f**4/4 + 7*f**3/6 + 3*f**2 + 4. What is d(5)?
-13
Let j = -15 - -19. Let i(z) = 0*z + 1 + 4*z + 6*z - 8. Let s(d) = -5*d + 4. Let q(r) = 2*i(r) + 5*s(r). Determine q(j).
-14
Let x(v) be the first derivative of -1/3*v**3 + 11/2*v**2 + 25 + 19*v. Calculate x(13).
-7
Let i(g) = 5 + 3*g + 2*g**2 - 3*g**2 - 5. Let z be i(3). Let x(h) = z*h + 2*h - 33*h**2 - 1 + 32*h**2. Give x(3).
-4
Let t(c) be the second derivative of c**5/20 - c**4/3 - 5*c**3/6 - c**2 + 4*c. Suppose -4*j + 2*j - 16 = 0. Let d be (-46)/j - (-3)/(-4). Determine t(d).
-2
Let s(f) = 3 + 147*f**2 - 146*f**2 + 3*f - 5. Calculate s(1).
2
Let s be (-8)/10*20/(-8). Let g(i) = -4*i**s + 0*i**2 + 2*i + 2*i**3 + i**2 - i**3. Suppose 0 = -3*y + 10 - 4. What is g(y)?
0
Let z(y) = -7*y**2 - 49*y - y**3 + 86*y + 42 - 45*y - 48. Let o be (4 + -1)/((-2)/4). What is z(o)?
6
Let k(c) = 4*c + 1. Let s(u) = -2*u**2 + 3*u + 26. Let o be s(-3). Give k(o).
-3
Let n(t) be the second derivative of -t**4/12 + t**3/2 - t**2/2 - 151*t. Give n(4).
-5
Suppose 7*p - 4*p = -15, -2*l - 2*p - 10 = 0. Suppose l = h - 0*h - 4. Let n(a) = h*a - a + 1 - a. Determine n(1).
3
Suppose 6*o + 9 = 9*o. Let x(v) = 1 - 1 + 10*v**2 - 3*v - 9*v**2 - 1. Determine x(o).
-1
Let g(r) = r**2 - 5*r + 1. Let a be (-3)/(-3) - -2 - 1. Suppose 0 = a*m - q + 5*q - 18, m + 5*q - 12 = 0. Let c(d) = d - 3. Let h be c(m). Calculate g(h).
-3
Let l(y) = -2491 + 2*y + 1248 - 6*y + 1243. Calculate l(-10).
40
Let s be 1155/11 + (-1 - 1). Let l = -71 + s. Suppose 2*p + 10 = q, 4*p + l = 4*q + q. Let i(h) = h**2 + 3*h + 1. Give i(p).
1
Suppose 3*u - x = -2*u + 32, 0 = -x - 2. Let o be u/(-4 - -3 - 1). Let h be o/((-2)/(16/(-4))). Let d(m) = m**2 + 8*m + 5. Determine d(h).
-7
Let h be 44/(-11) + -2 + 15 + 1. Let q(d) = h*d + 56 - 56 + d**2. Calculate q(-8).
-16
Let m(b) = -b**3 + 9*b**2 + 10*b + 3. Let y = 165 - 155. Give m(y).
3
Suppose -3*d - 1 = 4*n - 31, -5*n = -15. Let p(r) = 3*r + 2. What is p(d)?
20
Let r be (-14)/(-2)*(-6 - -2 - -5). Let o(u) = -2*u**2 - 11 - 6 - r*u + 12. Let h(y) = y + 2. Let z be h(-6). Give o(z).
-9
Suppose 0 = -3*i - 5*y + 37, 2*i + 2*y - 13
|
{
"pile_set_name": "DM Mathematics"
}
|
Q:
Two groups of checkboxes, if first one is checked second can not be
I have two "groups" of checkboxes (although the first group only contains one checkbox), but if user checks the checkbox from the first group I want to restrict the ability of checking the checkboxes from second group...
<div>
<h3>First group</h3>
<label>
<input type="checkbox" value="1" name="group1" />If checked, checks all the checkboxes in 2nd group</label>
<label>
</div>
<div>
<h3>Second Group</h3>
<label>
<input type="checkbox" class="radio" value="1" name="group2" />1</label>
<label>
<input type="checkbox" class="radio" value="1" name="group2" />1</label>
</div>
A:
I've used a simple jQuery script to solve it.
initially it didn't exactly do what I wanted it to do, but I've managed to work around it with php as I had to make sure that if someone checked the checkbox from the second group that it didn't go to the database.
$('#checkbox1').click(function() {
if( $(this).is(':checked')) {
$("#checkbox2").hide();
} else {
$("#checksbox2").show();
}
});
As for php I simply used a ternary operator to make sure that if checkbox with id checkbox1 is checked then I want to ignore the rest of the checkboxes...
$smnrs = !empty($_POST['all']) ? explode(';', $_POST['all']) : $_POST['seminars'];
in this case $_POST['all'] refers to the first checkbox that if clicked it hides the div holding the other checkboxes.
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{
"pile_set_name": "StackExchange"
}
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Just last week, there was considerable speculation that Microchip would buy Atmel. The deal wasn’t done, and there was precedent that this deal wouldn’t happen – earlier this year, Dialog made an approach at Atmel. Now, though, the deal is done: Microchip will acquire Atmel for $3.56 Billion.
There are three main companies out there making microcontrollers that are neither ancient 8051 clones or ARM devices: TI’s MSP430 series, Microchip and Atmel. Microchip has the very, very popular PIC series microcontrollers, which can be found in everything. Atmel’s portfolio includes the AVR line of microcontrollers, which are also found in everything. From phones to computers to toasters, there’s a very high probablitiy you’re going to find something produced by either Atmel or Microchip somewhere within 15 feet of your person right now.
For the hobbyist electronic enthusiast, this has led to the closest thing we have to a holy war. Atmel chips were a little easier (and cheaper) to program, but were a little more expensive. Microchip’s chips have a very long history and proportionally more proper engineers who are advocates. PIC isn’t Arduino, though, a community that has built a large and widely used code base around the AVR family.
Microchip’s acquisition of Atmel follows several mergers and acquisitions in recent months: NXP and Freescale, Intel and Altera, Avago and Broadcom, and On Semiconductor and Fairchild. The semiconductor industry has cash and wants to spend it. What this means for the Atmel product line is left to be seen. The most popular micros probably won’t be discontinued, but if you’re using unpopular Atmel micros such as the ATtiny10 you might want to grab a reel or two before they’re EOL’d.
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{
"pile_set_name": "OpenWebText2"
}
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Elena Moskaleva
Elena Moskaleva (born 12 November 1957 in Krasnoarmeysk, Moscow Oblast) is a Russian visual artist specialising in optical illusions.
Biography
Elena Moskaleva has studied art from early childhood: first in an art school in her hometown, and later in Moscow Academic College of Fine Art as a pupil of Matilda Bulgakova. After graduating in 1978 Elena began her work as a painter.
Elena is a member of the Moscow Artist Union from 1998 and International Federation of Artists (IFA) UNESCO.
She is a regular participant of major exhibitions in Moscow and her paintings were featured on exhibitions worldwide, most notably in Davos in the 1990.
Work
Elena Moskaleva is one of the rare Russian artists working in the genre of optical illusion. Her paintings have been featured in a number of notable albums dedicated to optical illusions in fine art, along with such artists as Octavio Ocampo (Mexico), Michael Cheval (USA), Oleg Shuplyak (Ukraine) Rafal Olbinski (Poland), Liu Bolin (China), István Orosz (Hungary).
Most optical illusions are weaved into classical fine art genres such as landscapes. Critics have noted that these double images are well-hidden: "She loves producing lovely artworks that come in pastel colors. Let’s see if your eyes are sharp enough to spot the hidden portraits in this painting." The paintings are also cleverly detailed: "Elena is the kind of artist who can play well with details. This is definitely not just a simple landscape painting." Gabriel Todica notes that Elena Moskaleva draws inspiration from nature and constructs "a surreal, warm and idyllic imagery".
Elena Moskaleva's works are featured in several museums as well as in private collections of Brian Eno, Amjad Ali Khan, Eduard Sagalaev, Ted Hartley and Dina Merrill.
Some paintings gallery
Literature
Exhibition "Country Native" Publisher: M .: "Soviet Artist", 1978. 208 pp.
"Youth of the country". Exhibition of the Moscow Union of Artists. "Manezh", Moscow. 1982
"Women-artists of Moscow: The Way in Art". Editor: M. Esmont. Publishing house: Moscow "Decorative art" 2005.
Kalinin Anatoly. "The Vision of Mystery." Mysterious paintings in the past and present. (Encyclopaedia of optical illusions) Moscow, "Kuchkovo Field", 2011
"Optische Illusionen". Brad Honeycutt, Terry Stickels, Foreword by Scott Kim. Bassermann, Germany 2012.
"Infinitely unequal world." Moscow. “Science and Religion” Magazine No.3 2015. (The cover of the magazine, a gallery of paintings and an article about the artist).
The Art of Deception: Illusions to Challenge the Eye and the Mind. by Brad Honeycutt Publisher: “Imagine” (USA) 2014. .
Koten kara saishinsaku made hyakukyuitten (Japanese) by Rei Kitagawa. Publisher: Osaka: Sogensha, 2015.
Gabriel Todica & Gina-Maria Todica, "Duoscopic vision painters". "Lidana" Publisher, (Romanian Edition), Suceava. Romania, 2015.
Gabriel Todica & Gina-Maria Todica, "Duoscopic vision painters", English on-line edition (URL: http://en.calameo.com/read/001926384559dfb5a8b04) Romania, 2017.
Gabriel Todica & Gina-Maria Todica, "Duoscopic art. The universal interferences". By Gabriel Todica. Suceava. "Lidana" Publisher. Romania, 2017.
References
External links
"Autumn. Double Portrait." on YouTube
Elena Moskaleva on Mighty Optical Illusions
"Deviant Art - Elena Moskaleva"
Category:1957 births
Category:Living people
Category:21st-century Russian painters
Category:Fantastic art
Category:Fantastic realism
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{
"pile_set_name": "Wikipedia (en)"
}
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---
abstract: |
In this paper, we design and analyze a Hybrid High-Order discretization method for the steady motion of non-Newtonian, incompressible fluids in the Stokes approximation of small velocities. The proposed method has several appealing features including the support of general meshes and high-order, unconditional inf-sup stability, and orders of convergence that match those obtained for Leray–Lions scalar problems. A complete well-posedness and convergence analysis of the method is carried out under new, general assumptions on the strain rate-shear stress law, which encompass several common examples such as the power-law and Carreau–Yasuda models. Numerical examples complete the exposition.\
**Keywords:** Hybrid High-Order methods, non-Newtonian fluids, power-law, Carreau–Yasuda law, discrete Korn inequality
author:
- 'Michele Botti[^1]'
- 'Daniel Castanon Quiroz [^2]'
- 'Daniele A. Di Pietro [^3]'
- 'André Harnist [^4]'
bibliography:
- 'pstokes.bib'
title: 'A Hybrid High-Order method for creeping flows of non-Newtonian fluids'
---
Introduction {#sec:introduction}
============
In this paper, we design and analyze a Hybrid High-Order (HHO) discretization method for the steady motion of a non-Newtonian, incompressible fluid in the Stokes approximation of small velocities. Notable applications include ice sheet dynamics [@Isaac.Stadler.ea:15], mantle convection [@Schubert.Turcotte.ea:01], chemical engineering [@Ko.Pustejovska.ea:18], and biological fluids rheology [@Lai.Kuei.ea:78; @Galdi.Rannacher.ea:18]. We focus on fluids with shear-rate-dependent viscosity, whose behavior is characterized by a nonlinear strain rate-shear stress function. Physical interpretations and discussions of non-Newtonian fluid models can be found, e.g., in [@Bird.Armstrong.ea:87; @Malek.Rajagopal.ea:95]. Typical examples that are frequently used in the applications include the power-law and Carreau–Yasuda model.
The earliest investigations of fluids with shear-dependent viscosities date back to the pioneering work of Ladyzhenskaya [@Ladyzhenskaya:69]. For a detailed mathematical study of the well-posedness and regularity of the continuous problem, see also [@Malek.Rajagopal:05; @Ruzicka.Diening:07; @Diening.Ettwein:08; @Beirao-da-Veiga:09; @Berselli.Ruzicka:20] and references therein. Early results on the numerical analysis of non-Newtonian fluid flow problems were given in [@Sandri:93; @Barrett.Liu:94; @Glowinski.Rappaz:03]. Later, these results were improved in [@Belenki.Berselli.ea:12] and [@Hirn:13] by proving error estimates that are optimal for fluids with shear thinning behavior (described by a power law exponent ${r}\le 2$). In [@Belenki.Berselli.ea:12], the authors considered a conforming inf-sup stable finite element discretization, while in [@Hirn:13] a low-order scheme with local projection stabilization was proposed. In both works, the use of Orlicz functions is instrumental to unify the treatment of the shear thinning and shear thickening cases (also called pseudoplastic and dilatant, respectively; cf. Example \[ex:Carreau–Yasuda\]). More recently, a finite element method based on a four-field formulation of the nonlinear Stokes equations has been analyzed in [@Sandri:14]. Other notable contributions on the numerical approximation of generalized Stokes problems include [@Diening.Kreuzer.ea:13; @Isaac.Stadler.ea:15; @Kreuzer.Suli:16; @Ko.Suli:18].
The main issues to be accounted for in the numerical solution of non-Newtonian fluid flow problems are the presence of local features emerging from the nonlinear strain rate-shear stress relation, the incompressibility condition leading to indefinite systems, the roughly varying model coefficients, and, possibly, complex geometries requiring unstructured and highly-adapted meshes. The HHO method provides several advantages to deal with the complex nature of the problem, such as the support of general polygonal or polyhedral meshes, the possibility to select the approximation order, and unconditional inf-sup stability. Moreover, HHO schemes can be efficiently implemented thanks to the possibility of statically condensing a large subset of the unknowns for linearized versions of the problem encountered, e.g., when solving the nonlinear system by the Newton method. Hybrid High-Order methods have been successfully applied to the simulation of incompressible flows of Newtonian fluids governed by the Stokes [@Aghili.Boyaval.ea:15] and Navier–Stokes equations [@Di-Pietro.Krell:18; @Botti.Di-Pietro.ea:19*1], possibly driven by large irrotational volumetric forces [@Di-Pietro.Ern.ea:16; @Castanon-Quiroz.Di-Pietro:20]. Works related to the problem of creeping flows of non-Newtonian fluids are [@Botti.Di-Pietro.ea:17] and [@Di-Pietro.Droniou:17; @Di-Pietro.Droniou:17*1], respectively dealing with nonlinear elasticity and Leray–Lions problems. Going from nonlinear coercive elliptic equations to the nonlinear Stokes system involves additional difficulties arising from the pressure and the divergence constraint. Finally, we mention, in passing, that HHO methods are members of a wider family of polytopal methods that also includes, e.g., Virtual Element methods; cf., e.g., [@Beirao-da-Veiga.Lovadina.ea:17; @Beirao-da-Veiga.Lovadina.ea:18] for their application to Newtonian incompressible flows.
The HHO discretization presented in this paper is inspired by the previously mentioned works. It hinges on discontinuous polynomial unknowns on the mesh and on its skeleton, from which discrete differential operators are reconstructed. The reconstruction operators are then used to define a consistency term inspired by the weak formulation of the creeping flow problem and a cleverly designed stabilization term penalizing boundary residuals. We carry out a complete analysis of the proposed method. In particular, under general assumptions on the strain rate-shear stress function, we derive error estimates for the velocity and pressure approximations. The energy-norm error estimate for the velocity given in Theorem \[thm:error.estimate\] is optimal in the sense that it yields the same convergence orders established in [@Di-Pietro.Droniou:17*1 Theorem 7] for the scalar Leray–Lions elliptic problem. A key tool in our analysis is provided by Lemma \[lem:discrete.korn.inequality\], in which we prove a generalization of the discrete Korn inequality of [@Botti.Di-Pietro.ea:19 Lemma 1] to the non-Hilbertian case. The other main contributions are a novel formulation of the requirements on the strain rate-shear stress function allowing a unified treatment of pseudoplastic and dilatant fluids and the identification of a set of general assumptions on the nonlinear stabilization function ensuring the desired consistency properties along with the well-posedness of the discrete problem.
The rest of the paper is organized as follows. In Section \[sec:continuous.setting\] we introduce the strong and weak formulations of the nonlinear Stokes problem and present the assumptions on the strain rate-shear stress function. The construction of the HHO discretization is given in Section \[sec:discrete.setting\] by defining the discrete counterparts of the viscous and coupling terms. Section \[sec:discrete.setting\] also contains the proof of the discrete Korn inequality and the discussion on the nonlinear stabilization function. Section \[sec:well-posedness\] establishes the well-posedness of the discrete problem by proving the Hölder continuity and the strong-monotonicity of the viscous term, as well as the inf-sup stability of the pressure-velocity coupling. In Section \[sec:error.estimate\], we show the consistency of the discrete viscous function and coupling bilinear form. These results are then used to prove the error estimate. In Section \[sec:num.res\], we investigate the performance of the method by performing a convergence test with analytical solution on various families of refined meshes. Finally, in Appendix \[sec:properties.stress\] we provide a sufficient condition for the strain rate-shear stress law to fulfil the assumptions presented in Section \[sec:continuous.setting\].
Continuous setting {#sec:continuous.setting}
==================
Let $\Omega \subset {\mathbb{R}}^d$, $d\in\{2,3\}$, denote a bounded, connected, polyhedral open set with Lipschitz boundary $\partial\Omega$. We consider a possibly non-Newtonian fluid occupying $\Omega$ and subjected to a volumetric force field $\b f : \Omega \to {\mathbb{R}}^d$. Its flow is governed by the generalized Stokes problem, which consists in finding the velocity field $\b u : \Omega \to {\mathbb{R}}^d$ and the pressure field $p : \Omega \to {\mathbb{R}}$ such that
\[eq:stokes.continuous\] $$\begin{aligned}
{2}
-{\b\nabla{\cdot}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b u) + {\b\nabla}p &= \b f &\qquad& \mbox{ in } \Omega, \label{eq:stokes.continuous:momentum} \\
{\b\nabla{\cdot}}\b u &= 0 &\qquad& \mbox{ in } \Omega, \label{eq:stokes.continuous:mass} \\
\b u &= \b 0 &\qquad& \mbox{ on } \partial \Omega, \label{eq:stokes.continuous:bc} \\
\int_\Omega p(\b x){\,\mathrm{d}}\b x &= 0, \label{eq:stokes.continuous:closure}
\end{aligned}$$
where ${\b\nabla{\cdot}}$ denotes the divergence operator applied to vector fields, ${\b{\nabla}_{\mathrm{s}}}$ is the symmetric part of the gradient operator ${\b\nabla}$ applied to vector fields, and, denoting by ${{\mathbb{R}}^{d \times d}_{\mathrm{s}}}$ the set of square, symmetric, real-valued $d\times d$ matrices, ${\b\sigma}: \Omega \times {{\mathbb{R}}^{d \times d}_{\mathrm{s}}} \to {{\mathbb{R}}^{d \times d}_{\mathrm{s}}}$ is the strain rate-shear stress law. In what follows, we formulate assumptions on ${\b\sigma}$ that encompass common models for non-Newtonian fluids and state a weak formulation for problem that will be used as a starting point for its discretization.
Strain rate-shear stress law {#sec:strain.rate.shear.stress.law}
----------------------------
We define the Frobenius inner product such that, for all $\b\tau= (\tau_{ij})_{1 \le i,j \le d}$ and $\b\eta= (\eta_{ij})_{1 \le i,j \le d}$ in ${{\mathbb{R}}^{d \times d}}$, $\b\tau : \b\eta \coloneqq \sum_{i,j=1}^d \tau_{ij}\eta_{ij}$, and we denote by $|\b\tau|_{d \times d}\coloneqq \sqrt{\b\tau : \b\tau}$ the corresponding norm.
\[ass:stress\] Let a real number ${r}\in (1,+\infty)$ be fixed, denote by ${r}' \coloneqq \frac{{r}}{{r}-1} \in (1,+\infty)$ the conjugate exponent of ${r}$, and define the singular exponent of ${r}$ by $$\label{eq:sing}
{r^{\circ}}\coloneq \min({r},2) \in (1,2].$$ The strain rate-shear stress law satisfies
\[eq:ass:sigma\] $$\begin{gathered}
{\b\sigma}(\b x,\b 0) = \b 0 \text{ for almost every } \b x \in \Omega,\label{eq:ass-stress:0}
\\
{\b\sigma}: \Omega \times {{\mathbb{R}}^{d \times d}_{\mathrm{s}}} \to {{\mathbb{R}}^{d \times d}_{\mathrm{s}}} \text{ is measurable}.\label{eq:ass-stress:power-framed}
\end{gathered}$$ Moreover, there exist real numbers $\sigma_{\mathrm{de}} \in [0,+\infty)$ and $\sigma_{\mathrm{hc}},\sigma_{\mathrm{sm}} \in (0,+\infty)$ such that, for all $\b\tau,\b\eta \in {{\mathbb{R}}^{d \times d}_{\mathrm{s}}}$ and almost every $\b x \in \Omega$, we have the Hölder continuity property \[eq:power-framed:s.holder.continuity.strong.monotonicity\] $$\begin{aligned}
\left|
{\b\sigma}(\b x,\b\tau)-{\b\sigma}(\b x,\b\eta)
\right|_{d\times d} &\le \sigma_{\mathrm{hc}} \left(\sigma_{\mathrm{de}}^{r}+|\b\tau|_{d\times d}^{r}+|\b\eta|_{d\times d}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}| \b\tau-\b\eta |_{d\times d}^{{r^{\circ}}-1},\label{eq:power-framed:s.holder.continuity}
\end{aligned}$$ and the strong monotonicity property $$\begin{aligned}
\left({\b\sigma}(\b x,\b\tau)-{\b\sigma}(\b x,\b\eta)\right):(\b\tau-\b\eta) \left(\sigma_{\mathrm{de}}^{r}+|\b\tau|_{d\times d}^{r}+|\b\eta|_{d\times d}^{r}\right)^\frac{2-{r^{\circ}}}{{r}} \ge \sigma_{\mathrm{sm}}|\b\tau-\b\eta|_{d\times d}^{{r}+2-{r^{\circ}}}.\label{eq:power-framed:s.strong.monotonicity}
\end{aligned}$$
Some remarks are in order.
Assumption can be relaxed by taking ${\b\sigma}(\cdot,\b 0) \in L^{{r}'}(\Omega,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}})$. This modification requires only minor changes in the analysis, not detailed for the sake of conciseness.
Inequalities – can be proved starting from the following assumptions, which correspond to the conditions characterizing an ${r}$-power-framed function: For all $\b\tau,\b\eta \in {{\mathbb{R}}^{d \times d}_{\mathrm{s}}}$ with $\b\tau \neq \b\eta$ and almost every $\b x \in \Omega$, $$\begin{aligned}
|{\b\sigma}(\b x,\b\tau)-{\b\sigma}(\b x,\b\eta)|_{d \times d} &\le \sigma_{\mathrm{hc}} \left(\sigma_{\mathrm{de}}^{r}+|\b\tau|_{d \times d}^{r}+|\b\eta|_{d \times d}^{r}\right)^\frac{{r}-2}{{r}}| \b\tau-\b\eta |_{d \times d},
\\
\left({\b\sigma}(\b x,\b\tau)-{\b\sigma}(\b x,\b\eta)\right):\left(\b\tau-\b\eta\right) &\ge \sigma_{\mathrm{sm}}\left(\sigma_{\mathrm{de}}^{r}+|\b\tau|_{d \times d}^{r}+|\b\eta|_{d \times d}^{r}\right)^\frac{{r}-2}{{r}}|\b\tau-\b\eta|_{d \times d}^{2}.
\end{aligned}$$ These relations are reminiscent of the ones used in [@Di-Pietro.Droniou:17*1] in the context of scalar Leray–Lions problems. The advantage of assumptions -, expressed in terms of the singular index ${r^{\circ}}$, is that they enable a unified treatment of the cases ${r}< 2$ and ${r}\ge 2$ in the proofs of Lemma \[lem:ah:holder.continuity.strong.monotonicity\], Theorem \[thm:well-posedness\], Lemma \[lem:consistency:ah\], and Theorem \[thm:error.estimate\] below.
Inequalities and give $$\label{eq:power-framed:constants.bound}
\sigma_{\mathrm{sm}} \leq \sigma_{\mathrm{hc}}.$$ Indeed, let $\b\tau \in {{\mathbb{R}}^{d \times d}_{\mathrm{s}}}$ be such that $|\b\tau|_{d\times d} > 0$. Using the strong monotonicity (with $\b \eta = \b 0$), the Cauchy–Schwarz inequality, and the Hölder continuity (again with $\b \eta = \b 0$), we infer that $$\begin{aligned}
\sigma_{\mathrm{sm}}\left(\sigma_{\mathrm{de}}^{r}+|\b\tau|_{d\times d}^{r}\right)^\frac{{r^{\circ}}-2}{{r}}|\b\tau|_{d\times d}^{{r}+2-{r^{\circ}}} &\leq {\b\sigma}(\cdot,\b\tau):\b\tau\leq |{\b\sigma}(\cdot,\b\tau)|_{d\times d}|\b\tau|_{d\times d}\leq \sigma_{\mathrm{hc}}\left(\sigma_{\mathrm{de}}^{r}+|\b\tau|_{d\times d}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}| \b\tau|_{d\times d}^{{r^{\circ}}}
\end{aligned}$$ almost everywhere in $\Omega$. Hence, $\frac{\sigma_{\mathrm{sm}}}{\sigma_{\mathrm{hc}}} \le \left(\frac{\sigma_{\mathrm{de}}^{r}+|\b\tau|_{d\times d}^{r}}{| \b\tau|_{d\times d}^{r}}\right)^\frac{|{r}-2|}{{r}}$. Letting $|\b\tau|_{d\times d} \to +\infty$ gives .
\[ex:Carreau–Yasuda\] $(\mu,\delta,a,{r})$-Carreau–Yasuda fluids, introduced in [@Yasuda.Armstrong.Cohen:81] and later generalized in [@Hirn:13 Eq. (1.2)], are fluids for which it holds, for almost every $\b x\in\Omega$ and all $\b\tau \in {{\mathbb{R}}^{d \times d}_{\mathrm{s}}}$, $$\label{eq:Carreau--Yasuda}
{\b\sigma}(\b x,\b\tau) = \mu(\b x)\left(\delta^{a(\b x)}+|\b\tau|_{d \times d}^{a(\b x)}\right)^\frac{{r}-2}{a(\b x)}\b\tau,$$ where $\mu : \Omega \to [\mu_-,\mu_+]$ is a measurable function with $\mu_-,\mu_+ \in (0,+\infty)$ corresponding to the local flow consistency index, $\delta \in [0,+\infty)$ is the degeneracy parameter, $a : \Omega \to [a_-,a_+]$ is a measurable function with $a_-,a_+ \in (0,+\infty)$ expressing the local transition flow behavior index, and ${r}\in (1,+\infty)$ is the flow behavior index. The Carreau–Yasuda law is a generalization of the Carreau law (corresponding to $a_- = a_+ = 2$) that takes into account the different local levels of flow behavior in the fluid. The degenerate case $\delta=0$ corresponds to the power-law model. Non-Newtonian fluids described by constitutive laws with a $(\mu,\delta,a,{r})$-structure exhibit a different behavior according to the value of ${r}$. If ${r}> 2$, then the fluid shows shear thickening behavior and is called *dilatant*. Examples of dilatant fluids are wet sand and oobleck. The case ${r}< 2$, on the other hand, corresponds to *pseudoplastic* fluids having shear thinning behavior, such as blood. Finally, if ${r}= 2$, then the fluid is Newtonian and becomes the classical (linear) Stokes problem. We show in Appendix \[sec:properties.stress\] that the strain rate-shear stress law is an ${r}$-power-framed function with $\sigma_{\mathrm{de}} = \delta$, $$\sigma_{\mathrm{hc}} = \begin{cases}
\frac{\mu_+}{{r}-1}2^{\left[-\left(\frac{1}{a_+}-\frac{1}{{r}}\right)^\ominus-1\right]({r}-2)+\frac{1}{r}} & \text{if } {r}< 2,
\\
\mu_+({r}-1)2^{\left(\frac{1}{a_-}-\frac{1}{{r}}\right)^\oplus({r}-2)} & \text{if } {r}\ge 2,
\end{cases}
\quad\text{and}\quad
\sigma_{\mathrm{sm}} = \begin{cases}
\mu_-({r}-1)2^{\left(\frac{1}{a_-}-\frac{1}{{r}}\right)^\oplus({r}-2)} & \text{if } {r}\le 2,
\\
\frac{\mu_-}{{r}-1}2^{\left[-\left(\frac{1}{a_+}-\frac{1}{{r}}\right)^\ominus-1\right]({r}-2)-1} & \text{if } {r}> 2,
\end{cases}$$ where $\xi^\oplus\coloneq\max(0,\xi)$ and $\xi^\ominus\coloneq-\min(0,\xi)$ denote, respectively, the positive and negative parts of a real number $\xi$. As a consequence, it matches Assumption \[ass:stress\].
Weak formulation {#sec:weak.formulation}
----------------
From this point on, we omit both the integration variable and the measure from integrals, as they can be in all cases inferred from the context. We define the following velocity and pressure spaces embedding, respectively, the homogeneous boundary condition for the velocity and the zero-average constraint for the pressure: $$\b U \coloneqq \left\{\b v \in W^{1,{r}}(\Omega,{\mathbb{R}}^d)\ : \ \b v{\ \!\!_{|_{\partial\Omega}}} = \b 0 \right\},
\qquad
P \coloneqq L^{{r}'}_0(\Omega,{\mathbb{R}}) \coloneqq \left\{q \in L^{{r}'}(\Omega,{\mathbb{R}})\ : \ \textstyle\int_\Omega q = 0 \right\}.$$ Assuming $\b f \in L^{{r}'}(\Omega,{\mathbb{R}}^d)$, the weak formulation of problem reads: Find $(\b u,p) \in \b U \times P$ such that
\[eq:stokes.weak\] $$\begin{aligned}
{2}
a(\b u,\b v)+b(\b v,p) &= \displaystyle\int_\Omega \b f \cdot \b v &\qquad \forall \b v \in \b U,\label{eq:stokes.weak:momentum} \\
-b(\b u,q) &= 0 &\qquad \forall q \in P, \label{eq:stokes.weak:mass}
\end{aligned}$$
where the function $a : \b U \times \b U \to {\mathbb{R}}$ and the bilinear form $b : \b U \times L^{{r}'}(\Omega,{\mathbb{R}}) \to {\mathbb{R}}$ are defined such that, for all $\b v,\b w \in \b U$ and all $q \in L^{{r}'}(\Omega,{\mathbb{R}})$, $$\label{eq:a.b}
a(\b w,\b v) \coloneqq \displaystyle\int_\Omega {\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w) : {\b{\nabla}_{\mathrm{s}}}\b v,\qquad
b(\b v,q) \coloneqq -\displaystyle\int_\Omega ({\b\nabla{\cdot}}\b v) q.$$
The test space in can be extended to $L^{{r}'}(\Omega,{\mathbb{R}})$ since, for all $\b v \in \b U$, the divergence theorem and the fact that $\b v{\ \!\!_{|_{\partial\Omega}}} = \b 0$ yield $b(\b v,1) = -\int_\Omega {\b\nabla{\cdot}}\b v = - \int_{\partial\Omega} \b v \cdot \b n_{\partial \Omega} = 0$, with $\b n_{\partial \Omega}$ denoting the unit vector normal to $\partial\Omega$ and pointing out of $\Omega$.
\[rem:a-priori\] It can be checked that, under Assumption \[ass:stress\], the continuous problem admits a unique solution $(\b u,p) \in \b U \times P$; see, e.g., [@Hirn:13 Section 2.4], where slightly stronger assumptions are considered. For future use, we also note the following a priori bound on the velocity: $$\label{eq:continuous.solution:bounds:uh}
|\b u|_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)} \lesssim \left(\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\right)^\frac{1}{{r}-1}+\left(\sigma_{\mathrm{de}}^{2-{r^{\circ}}}\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\right)^\frac{1}{{r}+1-{r^{\circ}}}.$$ To prove , use the strong-monotonicity of ${\b\sigma}$, sum written for $\b v=\b u$ to written for $q=p$, and use the Hölder and Korn inequalities to write $$\begin{aligned}
\sigma_{\mathrm{sm}}\left(
\sigma_{\mathrm{de}}^{r}+ \|{\b{\nabla}_{\mathrm{s}}}\b u\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}\right)^\frac{{r^{\circ}}-2}{{r}} \|{\b{\nabla}_{\mathrm{s}}}\b u\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{{r}+2-{r^{\circ}}}
&\lesssim a(\b u,\b u)
= \displaystyle\int_\Omega \b f \cdot \b u
\lesssim \| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\|{\b{\nabla}_{\mathrm{s}}}\b u\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})},
\end{aligned}$$ that is, $$\label{eq:continuous.solution:bounds:uh:1}
\mathcal{N}\coloneqq \left(
\sigma_{\mathrm{de}}^{r}+ \|{\b{\nabla}_{\mathrm{s}}}\b u\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}\right)^\frac{{r^{\circ}}-2}{{r}} \|{\b{\nabla}_{\mathrm{s}}}\b u\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{{r}+1-{r^{\circ}}} \lesssim \sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}.$$ Observing that $\|{\b{\nabla}_{\mathrm{s}}}\b u\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{{r}+1-{r^{\circ}}} \lesssim \max\left(\|{\b{\nabla}_{\mathrm{s}}}\b u\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})},\sigma_{\mathrm{de}}\right)^{2-{r^{\circ}}}\mathcal{N} $, we obtain, enumerating the cases for the maximum and summing the corresponding bounds, $\|{\b{\nabla}_{\mathrm{s}}}\b u\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})} \lesssim \mathcal{N}^\frac{1}{{r}-1}+(\sigma_{\mathrm{de}}^{2-{r^{\circ}}}\mathcal{N})^\frac{1}{{r}+1-{r^{\circ}}} $. Combining this inequality with gives .
Discrete setting {#sec:discrete.setting}
================
In this section, we recall the notion of polyhedral mesh along with the definitions and properties of $L^2$-orthogonal projectors on local and broken polynomial spaces. Then, after introducing the spaces of discrete unknowns for the velocity and the pressure, we prove a discrete Korn inequality, define the discrete counterparts of the function $a$ and of the bilinear form $b$, and formulate the HHO scheme.
Mesh and notation for inequalities up to a multiplicative constant
------------------------------------------------------------------
We define a mesh as a couple $\mathcal M_h\coloneq({\mathcal{T}}_h,{\mathcal{F}}_h)$, where ${\mathcal{T}}_h$ is a finite collection of polyhedral elements $T$ such that $h=\max_{T\in{\mathcal{T}}_h}h_T$ with $h_T$ denoting the diameter of $T$, while ${\mathcal{F}}_h$ is a finite collection of planar faces $F$ with diameter $h_F$. Notice that, here and in what follows, we use the three-dimensional nomenclature also when $d=2$, i.e., we speak of polyhedra and faces rather than polygons and edges. It is assumed henceforth that the mesh $\mathcal M_h$ matches the geometrical requirements detailed in [@Di-Pietro.Droniou:20 Definition 1.7]. In order to have the boundedness property for the interpolator, we additionally assume that the mesh elements are star-shaped with respect to every point of a ball of radius uniformly comparable to the element diameter; see [@Di-Pietro.Droniou:20 Lemma 7.12] for the Hilbertian case. Boundary faces lying on $\partial\Omega$ and internal faces contained in $\Omega$ are collected in the sets ${\mathcal{F}}_h^{\rm b}$ and ${\mathcal{F}}_h^{\rm i}$, respectively. For every mesh element $T\in{\mathcal{T}}_h$, we denote by ${\mathcal{F}}_T$ the subset of ${\mathcal{F}}_h$ containing the faces that lie on the boundary $\partial T$ of $T$. For every face $F \in {\mathcal{F}}_h$, we denote by ${\mathcal{T}}_F$ the subset of ${\mathcal{T}}_h$ containing the one (if $F\in{\mathcal{F}}_h^{\rm b}$) or two (if $F\in{\mathcal{F}}_h^{\rm i}$) elements on whose boundary $F$ lies. For each mesh element $T\in{\mathcal{T}}_h$ and face $F\in{\mathcal{F}}_T$, $\b n_{TF}$ denotes the (constant) unit vector normal to $F$ pointing out of $T$.
Our focus is on the $h$-convergence analysis, so we consider a sequence of refined meshes that is regular in the sense of [@Di-Pietro.Droniou:20 Definition 1.9] with regularity parameter uniformly bounded away from zero. The mesh regularity assumption implies, in particular, that the diameter of a mesh element and those of its faces are comparable uniformly in $h$ and that the number of faces of one element is bounded above by an integer independent of $h$.
To avoid the proliferation of generic constants, we write henceforth $a\lesssim b$ (resp., $a\gtrsim b$) for the inequality $a\le Cb$ (resp., $a\ge Cb$) with real number $C>0$ independent of $h$, of the constants $\sigma_{\mathrm{de}},\sigma_{\mathrm{hc}},\sigma_{\mathrm{sm}}$ in Assumption \[ass:stress\], and, for local inequalities, of the mesh element or face on which the inequality holds. We also write $a\simeq b$ to mean $a\lesssim b$ and $b\lesssim a$. The dependencies of the hidden constants are further specified when needed.
Projectors and broken spaces
----------------------------
Given $X \in {\mathcal{T}}_h \cup {\mathcal{F}}_h$ and $l \in {\mathbb{N}}$, we denote by ${\mathbb{P}}^l(X,{\mathbb{R}})$ the space spanned by the restriction to $X$ of scalar-valued, $d$-variate polynomials of total degree $\le l$. The local $L^2$-orthogonal projector ${\pi_{X}^{l}} : L^{1}(X,{\mathbb{R}}) \to {\mathbb{P}}^l(X,{\mathbb{R}})$ is defined such that, for all $v \in L^{1}(X,{\mathbb{R}})$, $$\label{eq:proj}
\displaystyle\int_X ({\pi_{X}^{l}} v-v) w = 0 \qquad \forall w \in {\mathbb{P}}^{l}(X,{\mathbb{R}}).$$ When applied to vector-valued fields in $L^1(X,{\mathbb{R}}^d)$ (resp., tensor-valued fields in $L^1(X,{{\mathbb{R}}^{d \times d}})$), the $L^2$-orthogonal projector mapping on ${\mathbb{P}}^l(X,{\mathbb{R}}^d)$ (resp., ${\mathbb{P}}^l(X,{{\mathbb{R}}^{d \times d}})$) acts component-wise and is denoted in boldface font. Let $T\in{\mathcal{T}}_h$, $n\in[0,l+1]$ and $m\in[0,n]$. The following $(n,{r},m)$-approximation properties of ${\pi_{T}^{l}}$ hold: For any $v\in W^{n,{r}}(T,{\mathbb{R}})$,
\[eq:proj:app\] $$\label{eq:proj:app:T}
|v-{\pi_{T}^{l}}v|_{W^{m,{r}}(T,{\mathbb{R}})} \lesssim h_T^{n-m}|v|_{W^{n,{r}}(T,{\mathbb{R}})}.$$ The above property will also be used in what follows with ${r}$ replaced by its conjugate exponent ${r}'$. If, additionally, $n\ge 1$, we have the following $(n,{r}')$-trace approximation property: $$\label{eq:proj:app:F}
\|v-{\pi_{T}^{l}}v\|_{L^{{r}'}(\partial T,{\mathbb{R}})}\lesssim h_T^{n-\frac{1}{{r}'}}|v|_{W^{n,{r}'}(T,{\mathbb{R}})}.$$
The hidden constants in are independent of $h$ and $T$, but possibly depend on $d$, the mesh regularity parameter, $l$, $n$, and ${r}$. The approximation properties are proved for integer $n$ and $m$ in [@Di-Pietro.Droniou:17 Appendix A.2] (see also [@Di-Pietro.Droniou:20 Theorem 1.45]), and can be extended to non-integer vales using standard interpolation techniques (see, e.g., [@Lions.Magenes:72 Theorem 5.1]).
At the global level, for a given integer $l\ge 0$, we define the broken polynomial space ${\mathbb{P}}^l({\mathcal{T}}_h,{\mathbb{R}})$ spanned by functions in $L^1(\Omega,{\mathbb{R}})$ whose restriction to each mesh element $T\in{\mathcal{T}}_h$ lies in ${\mathbb{P}}^l(T,{\mathbb{R}})$, and we define the global $L^2$-orthogonal projector ${\pi_{h}^{l}} : L^{1}(\Omega,{\mathbb{R}}) \to {\mathbb{P}}^l({\mathcal{T}}_h,{\mathbb{R}})$ such that, for all $v \in L^{1}(\Omega,{\mathbb{R}})$ and all $T \in {\mathcal{T}}_h$, $$({\pi_{h}^{l}} v){\ \!\!_{|_{T}}} \coloneq {\pi_{T}^{l}} v{\ \!\!_{|_{T}}}.$$ Broken polynomial spaces are subspaces of the broken Sobolev spaces $$W^{n,{r}}({\mathcal{T}}_h,{\mathbb{R}})\coloneq\left\{ v\in L^{r}(\Omega,{\mathbb{R}})\ : \ v{\ \!\!_{|_{T}}}\in W^{n,{r}}(T,{\mathbb{R}})\quad\forall T\in{\mathcal{T}}_h\right\}.$$ We define the broken gradient operator ${\b\nabla_h}: W^{1,1}({\mathcal{T}}_h,{\mathbb{R}}) \rightarrow L^1(\Omega,{\mathbb{R}}^d)$ such that, for all $v \in W^{1,1}({\mathcal{T}}_h,{\mathbb{R}})$ and all $T \in {\mathcal{T}}_h$, $({\b\nabla_h}v){\ \!\!_{|_{T}}} \coloneq {\b\nabla}v{\ \!\!_{|_{T}}}$. We define similarly the broken gradient acting on vector fields along with its symmetric part ${\b{\nabla}_{{\mathrm{s}},h}}$, as well as the broken divergence operator ${\b\nabla_h \cdot}$ acting on tensor fields. The global $L^2$-orthogonal projector ${\b{\pi}_{h}^{l}}$ mapping vector-valued fields in $L^1(\Omega,{\mathbb{R}}^d)$ (resp., tensor-valued fields in $L^1(\Omega,{{\mathbb{R}}^{d \times d}})$) on ${\mathbb{P}}^l({\mathcal{T}}_h,{\mathbb{R}}^d)$ (resp., ${\mathbb{P}}^l({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}})$) is obtained applying ${\pi_{h}^{l}}$ component-wise.
Discrete spaces and norms
-------------------------
Let an integer $k\ge 1$ be fixed. The HHO space of discrete velocity unknowns is $${{{\und{\b{U}}}}_{h}^{k}} \coloneqq \left\{
{\und{\b{v}}}_h \coloneq ((\b v_T)_{T \in {\mathcal{T}}_h},(\b v_F)_{F\in {\mathcal{F}}_h}) \ : \ \b v_T \in {\mathbb{P}}^k(T,{\mathbb{R}}^d)\ \ \forall T \in {\mathcal{T}}_h\ \mbox{ and }\ \b v_F \in {\mathbb{P}}^k(F,{\mathbb{R}}^d)\ \ \forall F \in {\mathcal{F}}_h \right\}.$$ The interpolation operator ${{\und{\b{I}}}_{h}^{k}} : W^{1,1}(\Omega,{\mathbb{R}}^d) \to {{{\und{\b{U}}}}_{h}^{k}} $ maps a function $\b v \in W^{1,1}(\Omega,{\mathbb{R}}^d)$ on the vector of discrete unknowns ${{\und{\b{I}}}_{h}^{k}}\b v$ defined as follows: $${{\und{\b{I}}}_{h}^{k}} \b v \coloneqq (({\b{\pi}_{T}^{k}} \b v{\ \!\!_{|_{T}}})_{T \in {\mathcal{T}}_h},({\b{\pi}_{F}^{k}} \b v{\ \!\!_{|_{F}}})_{F \in {\mathcal{F}}_h}).$$ For all $T \in {\mathcal{T}}_h$, we denote by ${{{\und{\b{U}}}}_{T}^{k}}$ and ${{\und{\b{I}}}_{T}^{k}}$ the restrictions of ${{\und{\b{I}}}_{h}^{k}}$ and ${{{\und{\b{U}}}}_{h}^{k}}$ to $T$, respectively and, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h}^{k}}$, we let ${\und{\b{v}}}_T \coloneqq (\b v_T,(\b v_F)_{F\in {\mathcal{F}}_T}) \in {{{\und{\b{U}}}}_{T}^{k}}$ denote the vector collecting the discrete unknowns attached to $T$ and its faces. Furthermore, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h}^{k}}$, we define the broken polynomial field $\b v_h\in{\mathbb{P}}^k({\mathcal{T}}_h,{\mathbb{R}}^d)$ obtained patching element unknowns, that is, $$(\b v_h){\ \!\!_{|_{T}}} \coloneqq \b v_T\qquad\forall T \in {\mathcal{T}}_h.$$
We define on ${{{\und{\b{U}}}}_{h}^{k}}$ the $W^{1,{r}}(\Omega,{\mathbb{R}}^d)$-like seminorm $\| {\cdot} \|_{{\boldsymbol{\varepsilon}},{r},h}$ such that, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h}^{k}}$,
\[eq:norm.epsilon.r\] $$\begin{gathered}
\label{eq:norm.epsilon.r.h}
\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} \coloneqq \left(\displaystyle\sum_{T \in {\mathcal{T}}_h}\| {\und{\b{v}}}_T \|_{{\boldsymbol{\varepsilon}},{r},T}^{r}\right)^\frac{1}{{r}}
\\\label{eq:norm.epsilon.r.T}
\text{with
$\| {\und{\b{v}}}_T \|_{{\boldsymbol{\varepsilon}},{r},T} \coloneqq \left(\| {\b{\nabla}_{\mathrm{s}}}\b v_T \|^{r}_{L^{r}(T,{{\mathbb{R}}^{d \times d}})} + \displaystyle\sum_{F \in {\mathcal{F}}_T} h_F^{1-{r}} \| \b v_F - \b v_T\|^{r}_{L^{r}(F,{\mathbb{R}}^d)}\right)^\frac{1}{{r}}$
for all $T \in {\mathcal{T}}_h$.
}
\end{gathered}$$
The following boundedness property for ${{\und{\b{I}}}_{T}^{k}}$ can be proved adapting the arguments of [@Di-Pietro.Droniou:20 Proposition 6.24] and requires the star-shaped assumption on the mesh elements: For all $T \in {\mathcal{T}}_h$ and all $\b v \in W^{1,{r}}(T,{\mathbb{R}}^d)$, $$\label{eq:I:boundedness}
\|{{\und{\b{I}}}_{T}^{k}} \b v\|_{{\boldsymbol{\varepsilon}},{r},T} \lesssim | \b v |_{W^{1,{r}}(T,{\mathbb{R}}^d)},$$ where the hidden constant depends only on $d$, the mesh regularity parameter, ${r}$, and $k$.
The discrete velocity and pressure are sought in the following spaces, which embed, respectively, the homogeneous boundary condition for the velocity and the zero-average constraint for the pressure: $${{{\und{\b{U}}}}_{h,0}^{k}} \coloneqq \left\{ {\und{\b{v}}}_h = ((\b v_T)_{T \in {\mathcal{T}}_h},(\b v_F)_{F\in {\mathcal{F}}_h}) \in {{{\und{\b{U}}}}_{h}^{k}} \ : \ \b v_F = \b 0 \quad \forall F \in {{\mathcal{F}}_h^{\mathrm{b}}}\right\},\quad
{P_{h}^{k}} \coloneqq {\mathbb{P}}^k({\mathcal{T}}_h,{\mathbb{R}})\cap P.$$ By the discrete Korn inequality proved in Lemma \[lem:discrete.korn.inequality\] below, $\| {\cdot} \|_{{\boldsymbol{\varepsilon}},{r},h}$ is a norm on ${{{\und{\b{U}}}}_{h,0}^{k}}$ (the proof is obtained reasoning as in [@Di-Pietro.Droniou:20 Corollary 2.16]).
Discrete Korn inequality {#sec:discrete.korn.inequality}
------------------------
We prove in this section a discrete counterpart of the following Korn inequality (see [@Geymonat.Suquet:86 Theorem 1]): For all $\b v \in\b U$. $$\label{eq:Korn}
\|\b v\|_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)} \lesssim \|{\b{\nabla}_{\mathrm{s}}}\b v\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}.$$ We start by recalling a few preliminary results. The first concerns inequalities between sums of powers, and will be often used in what follows without necessarily recalling this fact explicitly each time. Let an integer $n\ge 1$ and a real number $m \in (0,+\infty)$ be given. Then, for all $a_1,\ldots,a_n \in (0,+\infty) $, we have $$\label{eq:sum-power}
n^{-(m-1)^\ominus}\sum_{i=1}^n a_i^m \le \left(\sum_{i=1}^n a_i\right)^m \le n^{(m-1)^\oplus}\sum_{i=1}^n a_i^m.$$ If $m=1$, then holds with the equal sign. If $m < 1$, [@Ursell:59 Eqs. (5) and (3)] with $\alpha = 1$ and $\beta = m$ give $
n^{m-1}\sum_{i=1}^n a_i^m \le \left(\sum_{i=1}^n a_i\right)^m \le \sum_{i=1}^n a_i^m.
$ If, on the other hand, $m > 1$, [@Ursell:59 Eqs. (3) and (5)] with $\alpha = m$ and $\beta = 1$ give $
\sum_{i=1}^n a_i^m \le \left(\sum_{i=1}^n a_i\right)^m \le n^{m-1}\sum_{i=1}^n a_i^m.
$ Gathering the above cases yields .
The second preliminary result concerns the node-averaging interpolator. Let $\mathfrak T_h$ be a matching simplicial submesh of $\mathcal M_h$ in the sense of [@Di-Pietro.Droniou:20 Definition 1.8]. The node-averaging operator ${\b{I}_{{\mathrm{av}},h}^{k}} : {\mathbb{P}}^k({\mathcal{T}}_h,{\mathbb{R}}^d) \to {\mathbb{P}}^k(\mathfrak T_h,{\mathbb{R}}^d) \cap W^{1,{r}}(\Omega,{\mathbb{R}}^d)$ is such that, for all $\b v_h \in {\mathbb{P}}^k({\mathcal{T}}_h,{\mathbb{R}}^d)$ and all Lagrange node $V$ of $\mathfrak T_h$, denoting by $\mathfrak T_V$ the set of simplices sharing $V$, $$({\b{I}_{{\mathrm{av}},h}^{k}}\b v_h)(V) \coloneq
\begin{cases}
\frac{1}{\rm{card}(\mathfrak T_V)}\sum_{\b\tau\in\mathfrak T_V} \b v_h{\ \!\!_{|_{\b\tau}}}(V) & \text{if }\ V \in \Omega,
\\ \b 0 & \text{if }\ V \in \partial\Omega.
\end{cases}$$ For all $F \in {{\mathcal{F}}_h^{\mathrm{i}}}$, denote by $T_1,T_2\in{\mathcal{T}}_h$ the elements sharing $F$, taken in an arbitrary but fixed order. We define the jump operator such that, for any function $\b v\in W^{1,1}({\mathcal{T}}_h,{\mathbb{R}}^d)$, $[\b v]_F \coloneq (\b v{\ \!\!_{|_{T_1}}}){\ \!\!_{|_{F}}}-(\b v{\ \!\!_{|_{T_2}}}){\ \!\!_{|_{F}}}$. This definition is extended to boundary faces $F\in{{\mathcal{F}}_h^{\mathrm{b}}}$ by setting $[\b v]_F \coloneq \b v{\ \!\!_{|_{F}}}$.
For all $\b v_h \in {\mathbb{P}}^k({\mathcal{T}}_h,{\mathbb{R}}^d)$, it holds $$\label{eq:Iav:bound}
|\b v_h-{\b{I}_{{\mathrm{av}},h}^{k}}\b v_h|_{W^{1,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{r}\lesssim \sum_{F\in{\mathcal{F}}_h} h_F^{1-{r}} \|[\b v_h]_F\|^{r}_{L^{r}(F,{\mathbb{R}}^d)}.$$
Combining [@Di-Pietro.Droniou:20 Eq. (4.13)] (which corresponds to for ${r}=2$) with the local Lebesgue embeddings of [@Di-Pietro.Droniou:20 Lemma 1.25] (see also [@Di-Pietro.Droniou:17 Lemma 5.1]) gives, for any $T\in{\mathcal{T}}_h$, $$\label{eq:Iav:bound:0}
\|\b v_h-{\b{I}_{{\mathrm{av}},h}^{k}}\b v_h\|_{L^{r}(T,{\mathbb{R}}^d)}^{r}\lesssim \sum_{F\in{\mathcal{F}}_{\mathcal V,T}}h_F \|[\b v_h]_F\|^{r}_{L^{r}(F,{\mathbb{R}}^d)},$$ where ${\mathcal{F}}_{\mathcal V,T}$ collects the faces whose closure has non-empty intersection with $\overline{T}$. Using the local inverse inequality of [@Di-Pietro.Droniou:20 Lemma 1.28] (see also [@Di-Pietro.Droniou:17 Eq. (A.1)]) we can write $$\begin{aligned}
|\b v_h-{\b{I}_{{\mathrm{av}},h}^{k}}\b v_h|_{W^{1,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{r}&\lesssim \sum_{T\in{\mathcal{T}}_h} h_T^{-{r}}\|\b v_h-{\b{I}_{{\mathrm{av}},h}^{k}}\b v_h\|_{L^{r}(T,{\mathbb{R}}^d)}^{r}\\
&\lesssim \sum_{T\in{\mathcal{T}}_h}\sum_{F\in{\mathcal{F}}_{\mathcal V,T}} h_F^{1-{r}} \|[\b v_h]_F\|^{r}_{L^{r}(F,{\mathbb{R}}^d)}
\\
&\lesssim \sum_{F\in{\mathcal{F}}_h} \sum_{T\in{\mathcal{T}}_{\mathcal V,F}} h_F^{1-{r}} \|[\b v_h]_F\|^{r}_{L^{r}(F,{\mathbb{R}}^d)}
\\
&\le\max_{F\in{\mathcal{F}}_h}\operatorname{card}({\mathcal{T}}_{\mathcal V,F}) \sum_{F\in{\mathcal{F}}_h} h_F^{1-{r}} \|[\b v_h]_F\|^{r}_{L^{r}(F,{\mathbb{R}}^d)},
\end{aligned}$$ where we have used the fact that $h_T^{-{r}} \le h_F^{-{r}}$ along with inequality to pass to the second line, and we have exchanged the sums after setting ${\mathcal{T}}_{\mathcal V,F} \coloneqq \big\{T \in {\mathcal{T}}_h : \overline F \cap \overline T \neq \emptyset\big\}$ for all $F \in {\mathcal{F}}_h$ to pass to the third line. Observing that $\max_{F\in{\mathcal{F}}_h}\operatorname{card}({\mathcal{T}}_{\mathcal V,F}) \lesssim 1$ (since, for any $F\in{\mathcal{F}}_h$, $\operatorname{card}({\mathcal{T}}_{\mathcal V,F})$ is bounded by the left-hand side of [@Di-Pietro.Droniou:20 Eq. (4.23)] written for any $T\in{\mathcal{T}}_h$ to which $F$ belongs), follows.
(Discrete Korn inequality)\[lem:discrete.korn.inequality\] We have, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}$, $$\label{eq:discrete.Korn}
\| \b v_h \|_{L^{r}(\Omega,{\mathbb{R}}^d)}^{r}+|\b v_h|_{W^{1,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{r}\lesssim \| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}.$$
Let ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}$. Using a triangle inequality followed by , we can write $$\begin{aligned}
|\b v_h|_{W^{1,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{r}&\lesssim |{\b{I}_{{\mathrm{av}},h}^{k}} \b v_h|_{W^{1,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{r}+|\b v_h-{\b{I}_{{\mathrm{av}},h}^{k}}\b v_h|_{W^{1,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{r}\\
&\lesssim \|{\b{\nabla}_{\mathrm{s}}}({\b{I}_{{\mathrm{av}},h}^{k}} \b v_h) \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}+|\b v_h-{\b{I}_{{\mathrm{av}},h}^{k}}\b v_h|_{W^{1,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{r}\\
&\lesssim \|{\b{\nabla}_{{\mathrm{s}},h}}\b v_h \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}+|\b v_h-{\b{I}_{{\mathrm{av}},h}^{k}}\b v_h|_{W^{1,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{r}\\
&\lesssim \|{\b{\nabla}_{{\mathrm{s}},h}}\b v_h \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}+\sum_{F\in{\mathcal{F}}_h} h_F^{1-{r}} \|[\b v_h]_F\|^{r}_{L^{r}(F,{\mathbb{R}}^d)},
\end{aligned}$$ where we have used the continuous Korn inequality to pass to the second line, we have inserted $\pm{\b{\nabla}_{{\mathrm{s}},h}}\b v_h$ into the first norm and used a triangle inequality followed by to pass to the third line, and we have invoked the bound to conclude. Observing that, for any $F\in{\mathcal{F}}_h$, $|[\b v_h]_F| \leq \sum_{T\in{\mathcal{T}}_F}|\b v_F-\b v_T|$ by a triangle inequality, and using , we can continue writing $$|\b v_h|_{W^{1,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{r}\lesssim \|{\b{\nabla}_{{\mathrm{s}},h}}\b v_h \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}+\sum_{F\in{\mathcal{F}}_h}\sum_{T\in{\mathcal{T}}_F}h_F^{1-{r}} \| \b v_F - \b v_T\|^{r}_{L^{r}(F,{\mathbb{R}}^d)}
= \|{\und{\b{v}}}_h\|_{{\boldsymbol{\varepsilon}},{r},h}^{r},$$ where we have exchanged the sums over faces and elements and recalled definition to conclude. This proves the bound for the second term in the left-hand side of . Combining this result with the global discrete Sobolev embeddings of [@Di-Pietro.Droniou:17 Proposition 5.4] yields the bound for the first term in .
Viscous term
------------
### Local symmetric gradient reconstruction
For all $T \in {\mathcal{T}}_h$, we define the local symmetric gradient reconstruction ${\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},T}} : {{{\und{\b{U}}}}_{T}^{k}} \to {\mathbb{P}}^{k}(T,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}})$ such that, for all ${\und{\b{v}}}_T \in {{{\und{\b{U}}}}_{T}^{k}}$, $$\label{eq:G}
\displaystyle\int_T {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},T}} {\und{\b{v}}}_T : \b\tau = \int_T {\b{\nabla}_{\mathrm{s}}}\b v_T : \b\tau + \sum_{F \in {\mathcal{F}}_T} \int_F (\b v_F-\b v_T)\cdot (\b\tau \b n_{TF})\qquad \forall \b\tau \in {\mathbb{P}}^{k}(T,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}}).$$ This symmetric gradient reconstruction, originally introduced in [@Botti.Di-Pietro.ea:17 Section 4.2], is designed so that the following relation holds (see, e.g., [@Botti.Di-Pietro.ea:17*1 Proposition 5] or [@Di-Pietro.Droniou:20 Section 7.2.5]): For all $\b v\in W^{1,1}(T,{\mathbb{R}}^d)$, $$\label{eq:G:proj}
{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},T}} ({{\und{\b{I}}}_{T}^{k}} \b v) = {\b{\pi}_{T}^{k}}({\b{\nabla}_{\mathrm{s}}}\b v).$$ The global symmetric gradient reconstruction ${\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} : {{{\und{\b{U}}}}_{h}^{k}} \to {\mathbb{P}}^{k}({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}})$ is obtained patching the local contributions, that is, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h}^{k}}$, $$\label{eq:Gh}
({\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{v}}}_h){\ \!\!_{|_{T}}} \coloneq {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},T}} {\und{\b{v}}}_T \qquad \forall T\in{\mathcal{T}}_h.$$
### Discrete viscous function
The discrete counterpart of the function $a$ defined by is the function ${\mathrm{a}}_h : {{{\und{\b{U}}}}_{h}^{k}} \times {{{\und{\b{U}}}}_{h}^{k}} \to {\mathbb{R}}$ such that, for all ${\und{\b{v}}}_h,{\und{\b{w}}}_h \in {{{\und{\b{U}}}}_{h}^{k}}$, $$\label{eq:ah}
{\mathrm{a}}_h({\und{\b{w}}}_h, {\und{\b{v}}}_h) \coloneqq \displaystyle\int_\Omega {\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{w}}}_h): {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{v}}}_h +\gamma {\mathrm{s}}_h({\und{\b{w}}}_h,{\und{\b{v}}}_h).$$ In the above definition, recalling , $\gamma$ is a stabilization parameter such that $$\label{eq:gamma}
\gamma \in [\sigma_{\mathrm{sm}},\sigma_{\mathrm{hc}}],$$ while the stabilization function ${\mathrm{s}}_h : {{{\und{\b{U}}}}_{h}^{k}} \times {{{\und{\b{U}}}}_{h}^{k}} \to {\mathbb{R}}$ is such that, for all ${\und{\b{v}}}_h,{\und{\b{w}}}_h \in {{{\und{\b{U}}}}_{h}^{k}}$, $$\label{eq:sh}
{\mathrm{s}}_h({\und{\b{w}}}_h,{\und{\b{v}}}_h) \coloneqq \displaystyle\sum_{T \in {\mathcal{T}}_h}{\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{v}}}_T),$$ where the local contributions are assumed to satisfy the following assumption.
\[ass:sT\] For all $T \in {\mathcal{T}}_h$, the local stabilization function ${\mathrm{s}}_T:{{{\und{\b{U}}}}_{T}^{k}}\times{{{\und{\b{U}}}}_{T}^{k}}\to{\mathbb{R}}$ is linear in its second argument and satisfies the following properties, with hidden constants independent of both $h$ and $T$:
\[eq:ass:sT\]
1. \[ass:sT:stability.boundedness\] *Stability and boundedness.* Recalling the definition of the local $\|{\cdot}\|_{{\boldsymbol{\varepsilon}},{r},T}$-seminorm, for all ${\und{\b{v}}}_T\in{{{\und{\b{U}}}}_{T}^{k}}$ it holds: $$\label{eq:sT:stability.boundedness}
\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},T}}{\und{\b{v}}}_T \|_{L^{r}(T,{{\mathbb{R}}^{d \times d}})}^{r}+ {\mathrm{s}}_T({\und{\b{v}}}_T,{\und{\b{v}}}_T)
\simeq \|{\und{\b{v}}}_T\|_{{\boldsymbol{\varepsilon}},{r},T}^{r}.$$
2. *Polynomial consistency.*\[ass:sT:polynomial.consistency\] For all $\b w\in{\mathbb{P}}^{k+1}(T,{\mathbb{R}}^d)$ and all ${\und{\b{v}}}_T\in{{{\und{\b{U}}}}_{T}^{k}}$, $$\label{eq:sT:polynomial.consistency}
{\mathrm{s}}_T({{\und{\b{I}}}_{T}^{k}} \b w,{\und{\b{v}}}_T) = 0.$$
3. *Hölder continuity.*\[ass:sT:holder-continuity\] For all ${\und{\b{u}}}_T, {\und{\b{v}}}_T, {\und{\b{w}}}_T \in {{{\und{\b{U}}}}_{T}^{k}}$, it holds, setting ${\und{\b{e}}}_T\coloneq{\und{\b{u}}}_T - {\und{\b{w}}}_T$, $$\label{eq:sT:holder-continuity}
\hspace{-0.5cm} \left|{\mathrm{s}}_T({\und{\b{u}}}_T,{\und{\b{v}}}_T)-{\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{v}}}_T)\right|
\lesssim
\left({\mathrm{s}}_T({\und{\b{u}}}_T,{\und{\b{u}}}_T)+{\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{w}}}_T)\right)^\frac{{r}-{r^{\circ}}}{{r}}{\mathrm{s}}_T({\und{\b{e}}}_T,{\und{\b{e}}}_T)^\frac{{r^{\circ}}-1}{{r}}{\mathrm{s}}_T({\und{\b{v}}}_T,{\und{\b{v}}}_T)^\frac{1}{{r}}.$$
4. *Strong monotonicity.*\[ass:sT:strong-monotonicity\] For all ${\und{\b{u}}}_T, {\und{\b{w}}}_T \in {{{\und{\b{U}}}}_{T}^{k}}$ , it holds, setting again ${\und{\b{e}}}_T\coloneq{\und{\b{u}}}_T - {\und{\b{w}}}_T$, $$\label{eq:sT:strong-monotonicity}
\left({\mathrm{s}}_T({\und{\b{u}}}_T,{\und{\b{e}}}_T) - {\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{e}}}_T)\right)\left( {\mathrm{s}}_T({\und{\b{u}}}_T,{\und{\b{u}}}_T)+{\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{w}}}_T)\right)^\frac{2-{r^{\circ}}}{{r}} \gtrsim {\mathrm{s}}_T({\und{\b{e}}}_T,{\und{\b{e}}}_T)^\frac{{r}+2-{r^{\circ}}}{{r}}.$$
If ${r}=2$, ${\mathrm{s}}_T$ can be any symmetric bilinear form satisfying [[(S\[ass:sT:stability.boundedness\])]{}]{}–[[(S\[ass:sT:polynomial.consistency\])]{}]{}. Indeed, property [[(S\[ass:sT:holder-continuity\])]{}]{} coincides in this case with the Cauchy–Schwarz inequality, while, by linearity of ${\mathrm{s}}_T$, property [[(S\[ass:sT:strong-monotonicity\])]{}]{} holds with the equal sign.
\[lem:sT:consist\] For any $T\in{\mathcal{T}}_h$ and any ${\mathrm{s}}_T$ satisfying Assumption \[ass:sT\], it holds, for all $\b w \in W^{k+2,{r}}(T,{\mathbb{R}}^d)$ and all ${\und{\b{v}}}_T \in {{{\und{\b{U}}}}_{T}^{k}}$, $$\label{eq:sT:consist}
|{\mathrm{s}}_T({{\und{\b{I}}}_{T}^{k}} \b w,{\und{\b{v}}}_T)| \lesssim h_T^{(k+1)({r^{\circ}}-1)}| \b w |_{W^{1,{r}}(T,{\mathbb{R}}^d)}^{{r}-{r^{\circ}}}|\b w|_{W^{k+2,{r}}(T,{\mathbb{R}}^d)}^{{r^{\circ}}-1}\| {\und{\b{v}}}_T \|_{{\boldsymbol{\varepsilon}},{r},T},$$ where the hidden constant is independent of $h$, $T$, and $\b w$.
The proof adapts the arguments of [@Di-Pietro.Droniou:20 Propositon 2.14]. Using the polynomial consistency property [[(S\[ass:sT:polynomial.consistency\])]{}]{}, we can write $$\begin{aligned}
|{\mathrm{s}}_T({{\und{\b{I}}}_{T}^{k}} \b w,{\und{\b{v}}}_T)|
&= |{\mathrm{s}}_T({{\und{\b{I}}}_{T}^{k}} \b w,{\und{\b{v}}}_T)-{\mathrm{s}}_T({{\und{\b{I}}}_{T}^{k}}({\b{\pi}_{T}^{k+1}} \b w),{\und{\b{v}}}_T)|
\\ &\lesssim {\mathrm{s}}_T({{\und{\b{I}}}_{T}^{k}} \b w,{{\und{\b{I}}}_{T}^{k}} \b w)^\frac{{r}-{r^{\circ}}}{{r}}{\mathrm{s}}_T({{\und{\b{I}}}_{T}^{k}}(\b w-{\b{\pi}_{T}^{k+1}} \b w),{{\und{\b{I}}}_{T}^{k}}(\b w-{\b{\pi}_{T}^{k+1}} \b w))^\frac{{r^{\circ}}-1}{{r}}{\mathrm{s}}_T({\und{\b{v}}}_T,{\und{\b{v}}}_T)^\frac{1}{{r}} \\
&\lesssim \|{{\und{\b{I}}}_{T}^{k}} \b w\|_{{\boldsymbol{\varepsilon}},{r},T}^{{r}-{r^{\circ}}}\|{{\und{\b{I}}}_{T}^{k}}(\b w-{\b{\pi}_{T}^{k+1}} \b w)\|_{{\boldsymbol{\varepsilon}},{r},T}^{{r^{\circ}}-1}\|{\und{\b{v}}}_T\|_{{\boldsymbol{\varepsilon}},{r},T}\\
&\lesssim | \b w |_{W^{1,{r}}(T,{\mathbb{R}}^d)}^{{r}-{r^{\circ}}}|\b w-{\b{\pi}_{T}^{k+1}} \b w|_{W^{1,{r}}(T,{\mathbb{R}}^d)}^{{r^{\circ}}-1}\|{\und{\b{v}}}_T\|_{{\boldsymbol{\varepsilon}},{r},T}\\
&\lesssim h_T^{(k+1)({r^{\circ}}-1)}| \b w |_{W^{1,{r}}(T,{\mathbb{R}}^d)}^{{r}-{r^{\circ}}}|\b w|_{W^{k+2,{r}}(T,{\mathbb{R}}^d)}^{{r^{\circ}}-1}\|{\und{\b{v}}}_T\|_{{\boldsymbol{\varepsilon}},{r},T},
\end{aligned}$$ where we have used the Hölder continuity [[(S\[ass:sT:holder-continuity\])]{}]{} and observed that, by the consistency property [[(S\[ass:sT:polynomial.consistency\])]{}]{}, ${\mathrm{s}}_T({{\und{\b{I}}}_{T}^{k}}({\b{\pi}_{T}^{k+1}} \b w),{{\und{\b{I}}}_{T}^{k}}({\b{\pi}_{T}^{k+1}} \b w))=0$ to pass to the second line, we have used the boundedness property [[(S\[ass:sT:stability.boundedness\])]{}]{} to pass to the third line, the boundedness of ${{\und{\b{I}}}_{T}^{k}}$ to pass to the fourth line, and the $(k+2,{r},1)$-approximation property of ${\b{\pi}_{T}^{k+1}}$ to conclude.
In what follows, we will need generalized versions of the continuous and discrete Hölder inequalities, recalled hereafter for the sake of convenience. Let $X \subset {\mathbb{R}}^d$ be measurable, $n \in {\mathbb{N}}^*$, and let $t,p_1,\ldots,p_n \in (0,+\infty\rbrack$ be such that $\sum_{i=1}^n\frac{1}{p_i} = \frac{1}{t}$. The continuous $(t;p_1,\ldots,p_n)$-Hölder inequality reads: For any $(f_1,\ldots,f_n) \in \bigtimes_{i=1}^n L^{p_i}(X,{\mathbb{R}})$, $$\label{eq:holder}
\left\| \prod_{i=1}^n f_i \right\|_{L^t(X,{\mathbb{R}})} \le\ \prod_{i=1}^n\| f_i \|_{L^{p_i}(X,{\mathbb{R}})}.$$ Let $m \in {\mathbb{N}}^*$. For all $f : \{1,\ldots,m\} \to {\mathbb{R}}$ and all $q \in [1,+\infty)$, setting $\|f\|_q \coloneqq \left(\sum_{i=1}^m |f(i)|^q\right)^\frac{1}{q}$, and $\|f\|_\infty \coloneqq \max_{1 \le i \le m}|f(i)|$, the discrete $(t;p_1,\ldots,p_n)$-Hölder inequality reads: For any $f_1,\ldots,f_n : \{1,\ldots,m\} \to {\mathbb{R}}$, $$\label{eq:discrete.holder}
\left\| \prod_{i=1}^n f_i \right\|_{t} \le\ \prod_{i=1}^n\| f_i \|_{p_i}.$$
Let ${\mathrm{s}}_h$ be given by with, for all $T\in{\mathcal{T}}_h$, ${\mathrm{s}}_T$ satisfying Assumption \[ass:sT\]. Then it holds, for all ${\und{\b{v}}}_h \in{{{\und{\b{U}}}}_{h}^{k}}$,
\[eq:sh:properties\] $$\label{eq:sh:stability.boundedness}
\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}+ {\mathrm{s}}_h({\und{\b{v}}}_h,{\und{\b{v}}}_h)
\simeq \|{\und{\b{v}}}_h\|_{{\boldsymbol{\varepsilon}},{r},h}^{r}.$$ Furthermore, for all ${\und{\b{u}}}_h, {\und{\b{v}}}_h,{\und{\b{w}}}_h\in{{{\und{\b{U}}}}_{h}^{k}}$ it holds, setting ${\und{\b{e}}}_h\coloneq{\und{\b{u}}}_h - {\und{\b{w}}}_h$, $$\begin{gathered}
\label{eq:sh:holder-continuity}
\left|{\mathrm{s}}_h({\und{\b{u}}}_h,{\und{\b{v}}}_h)-{\mathrm{s}}_h({\und{\b{w}}}_h,{\und{\b{v}}}_h)\right|
\lesssim
\left({\mathrm{s}}_h({\und{\b{u}}}_h,{\und{\b{u}}}_h)+{\mathrm{s}}_h({\und{\b{w}}}_h,{\und{\b{w}}}_h)\right)^\frac{{r}-{r^{\circ}}}{{r}}{\mathrm{s}}_h({\und{\b{e}}}_h,{\und{\b{e}}}_h)^\frac{{r^{\circ}}-1}{{r}}{\mathrm{s}}_h({\und{\b{v}}}_h,{\und{\b{v}}}_h)^\frac{1}{{r}},
\\\label{eq:sh:strong-monotonicity}
\left(
{\mathrm{s}}_h({\und{\b{u}}}_h,{\und{\b{e}}}_h) - {\mathrm{s}}_h({\und{\b{w}}}_h,{\und{\b{e}}}_h)
\right)\left(
{\mathrm{s}}_h({\und{\b{u}}}_h,{\und{\b{u}}}_h)+{\mathrm{s}}_h({\und{\b{w}}}_h,{\und{\b{w}}}_h)
\right)^\frac{2-{r^{\circ}}}{{r}} \gtrsim {\mathrm{s}}_h({\und{\b{e}}}_h,{\und{\b{e}}}_h)^\frac{{r}+2-{r^{\circ}}}{{r}} .
\end{gathered}$$
Finally, for any $\b w \in \b U\cap W^{k+2,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)$, it holds $$\label{eq:sh:consist}
\sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}},\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1}{\mathrm{s}}_h({{\und{\b{I}}}_{h}^{k}} \b w,{\und{\b{v}}}_h) \lesssim h^{(k+1)({r^{\circ}}-1)}| \b w |_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)}^{{r}-{r^{\circ}}}|\b w|_{W^{k+2,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{{r^{\circ}}-1}.$$ Above, the hidden constants are independent of $h$ and of the arguments of ${\mathrm{s}}_h$.
For the sake of conciseness, we only sketch the proof and leave the details to the reader. Summing over $T \in {\mathcal{T}}_h$ immediately yields . The Hölder continuity property follows applying to the quantity in the left-hand side triangle inequalities, using , and concluding with a discrete $(1;\frac{{r}}{{r}-{r^{\circ}}},\frac{{r}}{{r^{\circ}}-1},{r})$-Hölder inequality. Moving to , starting from $|{\mathrm{s}}_h({\und{\b{e}}}_h,{\und{\b{e}}}_h)|$, we use and apply a discrete $(1;\frac{{r}+2-{r^{\circ}}}{2-{r^{\circ}}},\frac{{r}+2-{r^{\circ}}}{{r}})$-Hölder inequality to conclude. Finally, to prove we start from ${\mathrm{s}}_h({\und{\b{I}}}_h^k\b w,{\und{\b{v}}}_h)$, expand this quantity according to , use, for all $T \in {\mathcal{T}}_h$, the local consistency property together with $h_T \le h$, invoke the discrete $(1;\frac{{r}}{{r}-{r^{\circ}}},\frac{{r}}{{r^{\circ}}-1},{r})$-Hölder inequality, and pass to the supremum to conclude.
### An example of viscous stabilization function
Taking inspiration from the scalar case (cf., e.g., [@Di-Pietro.Droniou:17 Eq. (4.11c)]), a local stabilization function that matches Assumption \[ass:sT\] can be obtained setting, for all ${\und{\b{v}}}_T,{\und{\b{w}}}_T \in {{{\und{\b{U}}}}_{T}^{k}}$, $$\label{eq:sT}
{\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{v}}}_T) \coloneqq \int_{\partial T} |{\b{\Delta}^{k}_{\partial T}} {\und{\b{w}}}_T|^{{r}-2}{\b{\Delta}^{k}_{\partial T}} {\und{\b{w}}}_T \cdot {\b{\Delta}^{k}_{\partial T}} {\und{\b{v}}}_T,$$ where, denoting by ${\mathbb{P}}^k({\mathcal{F}}_T,{\mathbb{R}}^d)$ the space of vector-valued broken polynomials of total degree $\le k$ on ${\mathcal{F}}_T$, the boundary residual operator ${\b{\Delta}^{k}_{\partial T}} : {{{\und{\b{U}}}}_{T}^{k}} \to {\mathbb{P}}^k({\mathcal{F}}_T,{\mathbb{R}}^d)$ is such that, for all ${\und{\b{v}}}_T \in {{{\und{\b{U}}}}_{T}^{k}}$, $$({\b{\Delta}^{k}_{\partial T}} {\und{\b{v}}}_T){\ \!\!_{|_{F}}} \coloneq
h_F^{-\frac1{{r}'}}\left(
{\b{\pi}_{F}^{k}}({\b{{\mathrm{r}}}^{k+1}_{T}} {\und{\b{v}}}_T-\b v_F)-{\b{\pi}_{T}^{k}}({\b{{\mathrm{r}}}^{k+1}_{T}} {\und{\b{v}}}_T-\b v_T)
\right)
\qquad\forall F\in{\mathcal{F}}_T,$$ with velocity reconstruction ${\b{{\mathrm{r}}}^{k+1}_{T}} : {{{\und{\b{U}}}}_{T}^{k}} \to {\mathbb{P}}^{k+1}(T,{\mathbb{R}}^d)$ such that $$\begin{gathered}
\displaystyle\int_T ({\b{\nabla}_{\mathrm{s}}}{\b{{\mathrm{r}}}^{k+1}_{T}} {\und{\b{v}}}_T - {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},T}} {\und{\b{v}}}_T) : {\b{\nabla}_{\mathrm{s}}}\b w = 0\qquad\forall\b w \in {\mathbb{P}}^{k+1}(T,{\mathbb{R}}^d), \\
\text{
$\displaystyle\int_T {\b{{\mathrm{r}}}^{k+1}_{T}} {\und{\b{v}}}_T = \int_T \b v_T$, and
$\int_T {\b{\nabla}_{\mathrm{ss}}}{\b{{\mathrm{r}}}^{k+1}_{T}} {\und{\b{v}}}_T = \frac{1}{2}\sum_{F \in {\mathcal{F}}_T} \int_F ({\b v_F \otimes \b n_{TF}} - {\b n_{TF} \otimes \b v_F})$.
}\end{gathered}$$ Above, ${\b{\nabla}_{\mathrm{ss}}}$ denotes the skew-symmetric part of the gradient operator ${\b\nabla}$ applied to vector fields and ${ \otimes }$ is the tensor product such that, for all $\b x = (x_i)_{1 \le i \le d}$ and $\b y = (y_i)_{1 \le i \le d}$ in ${\mathbb{R}}^d$, ${\b x \otimes \b y} \coloneq (x_i y_j)_{1 \le i,j \le d} \in {{\mathbb{R}}^{d \times d}}$.
\[lem:sT\] The local stabilization function defined by satisfies Assumption \[ass:sT\].
The proof of [[(S\[ass:sT:stability.boundedness\])]{}]{} for ${r}=2$ is given in [@Botti.Di-Pietro.ea:17 Eq. (25)]. The result can be generalized to ${r}\neq 2$ using the same arguments of [@Di-Pietro.Droniou:17 Lemma 5.2]. Property [[(S\[ass:sT:polynomial.consistency\])]{}]{} is an immediate consequence of the fact that ${\b{\Delta}^{k}_{\partial T}}({{\und{\b{I}}}_{T}^{k}}\b w) = \b 0$ for any $\b w\in{\mathbb{P}}^{k+1}(T,{\mathbb{R}}^d)$, which can be proved reasoning as in [@Di-Pietro.Droniou:20 Proposition 2.6].
Let us prove [[(S\[ass:sT:holder-continuity\])]{}]{}. First, we remark that, since the function $\alpha \mapsto \alpha^{{r}-2}$ verifies the conditions in , we can apply Theorem \[thm:1d.power-framed\] to infer that the function ${\mathbb{R}}^d\ni\b x \mapsto |\b x|^{{r}-2}\b x$ satisfies for all $\b x,\b y \in {\mathbb{R}}^d$,
\[eq:rho.holder.strong\] $$\begin{gathered}
\big|
|\b x|^{{r}-2}\b x-|\b y|^{{r}-2}\b y
\big| \lesssim \big(
|\b x|^{r}+|\b y|^{r}\big)^\frac{{r}-{r^{\circ}}}{{r}}|\b x-\b y|^{{r^{\circ}}-1},\label{eq:rho:s.holder.continuity}
\\
\big(
|\b x|^{{r}-2}\b x-|\b y|^{{r}-2}\b y
\big) \cdot (\b x-\b y) \big(
|\b x|^{r}+|\b y|^{r}\big)^\frac{2-{r^{\circ}}}{{r}} \gtrsim |\b x-\b y|^{{r}+2-{r^{\circ}}}.\label{eq:rho:s.strong.monotonicity}
\end{gathered}$$
Recalling , we can write $$\begin{aligned}
\left|{\mathrm{s}}_T({\und{\b{u}}}_T,{\und{\b{v}}}_T)-{\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{v}}}_T)\right| &\leq \int_{\partial T} \left||{\b{\Delta}^{k}_{\partial T}} {\und{\b{u}}}_T|^{{r}-2}{\b{\Delta}^{k}_{\partial T}} {\und{\b{u}}}_T-|{\b{\Delta}^{k}_{\partial T}} {\und{\b{w}}}_T|^{{r}-2}{\b{\Delta}^{k}_{\partial T}} {\und{\b{w}}}_T\right|| {\b{\Delta}^{k}_{\partial T}} {\und{\b{v}}}_T|\\
&\lesssim \int_{\partial T} \left(|{\b{\Delta}^{k}_{\partial T}} {\und{\b{u}}}_T|^{r}+|{\b{\Delta}^{k}_{\partial T}} {\und{\b{w}}}_T|^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}| {\b{\Delta}^{k}_{\partial T}} {\und{\b{e}}}_T|^{{r^{\circ}}-1}| {\b{\Delta}^{k}_{\partial T}} {\und{\b{v}}}_T|\\
&\le \left({\mathrm{s}}_T({\und{\b{u}}}_T,{\und{\b{u}}}_T)+{\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{w}}}_T)\right)^\frac{{r}-{r^{\circ}}}{{r}}{\mathrm{s}}_T({\und{\b{e}}}_T,{\und{\b{e}}}_T)^\frac{{r^{\circ}}-1}{{r}}{\mathrm{s}}_T({\und{\b{v}}}_T,{\und{\b{v}}}_T)^\frac{1}{{r}},
\end{aligned}$$ where we have used to pass to the second line and the $(1;\frac{{r}}{{r}-{r^{\circ}}},\frac{{r}}{{r^{\circ}}-1},{r})$-Hölder inequality to conclude.
Moving to [[(S\[ass:sT:strong-monotonicity\])]{}]{}, and the $(1;\frac{{r}+2-{r^{\circ}}}{2-{r^{\circ}}},\frac{{r}+2-{r^{\circ}}}{{r}})$-Hölder inequality yield $$\begin{aligned}
&{\mathrm{s}}_T({\und{\b{e}}}_T,{\und{\b{e}}}_T) \\
&\quad = \int_{\partial T} |{\b{\Delta}^{k}_{\partial T}}{\und{\b{u}}}_T-{\b{\Delta}^{k}_{\partial T}}{\und{\b{w}}}_T|^{r}\\
&\quad
\lesssim \int_{\partial T} \left(|{\b{\Delta}^{k}_{\partial T}} {\und{\b{u}}}_T|^{r}+|{\b{\Delta}^{k}_{\partial T}} {\und{\b{w}}}_T|^{r}\right)^\frac{2-{r^{\circ}}}{{r}+2-{r^{\circ}}}\left[
\left(|{\b{\Delta}^{k}_{\partial T}}{\und{\b{u}}}_T|^{{r}-2}{\b{\Delta}^{k}_{\partial T}}{\und{\b{u}}}_T-|{\b{\Delta}^{k}_{\partial T}}{\und{\b{w}}}_T|^{{r}-2}{\b{\Delta}^{k}_{\partial T}}{\und{\b{w}}}_T\right)\cdot {\b{\Delta}^{k}_{\partial T}}{\und{\b{e}}}_T
\right]^\frac{{r}}{{r}+2-{r^{\circ}}}\\
&\quad
\le \left( {\mathrm{s}}_T({\und{\b{u}}}_T,{\und{\b{u}}}_T)+{\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{w}}}_T)\right)^\frac{2-{r^{\circ}}}{{r}+2-{r^{\circ}}}\left({\mathrm{s}}_T({\und{\b{u}}}_T,{\und{\b{e}}}_T)-{\mathrm{s}}_T({\und{\b{w}}}_T,{\und{\b{e}}}_T)\right)^\frac{{r}}{{r}+2-{r^{\circ}}}.\qedhere
\end{aligned}$$
Pressure-velocity coupling
--------------------------
For all $T \in {\mathcal{T}}_h$, we define the local divergence reconstruction ${{\mathrm{D}}^{k}_{T}} : {{{\und{\b{U}}}}_{T}^{k}} \to {\mathbb{P}}^{k}(T,{\mathbb{R}})$ by setting, for all ${\und{\b{v}}}_T \in {{{\und{\b{U}}}}_{T}^{k}}$, ${{\mathrm{D}}^{k}_{T}}{\und{\b{v}}}_T \coloneq {\mathrm{tr}}({\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},T}}{\und{\b{v}}}_T)$. We have the following characterization of ${{\mathrm{D}}^{k}_{T}}$: For all ${\und{\b{v}}}_T \in {{{\und{\b{U}}}}_{T}^{k}}$, $$\label{eq:D}
\int_T {{\mathrm{D}}^{k}_{T}} {\und{\b{v}}}_T~ q = \int_T ({\b\nabla{\cdot}}\b v_T)~q
+ \sum_{F \in {\mathcal{F}}_T} \int_F (\b v_F-\b v_T)\cdot \b n_{TF}~q \qquad \forall q \in {\mathbb{P}}^{k}(T,{\mathbb{R}}),$$ as can be checked writing for $\b\tau = q\mathrm{I}_d$. Taking the trace of , it is inferred that, for all $T\in{\mathcal{T}}_h$ and all $\b v\in W^{1,1}(T,{\mathbb{R}}^d)$, ${{\mathrm{D}}^{k}_{T}} ({{\und{\b{I}}}_{T}^{k}} \b v) = {\pi_{T}^{k}}({\b\nabla{\cdot}}\b v)$. The pressure-velocity coupling is realized by the bilinear form ${\mathrm{b}}_h : {{{\und{\b{U}}}}_{h}^{k}} \times {\mathbb{P}}^k({\mathcal{T}}_h,{\mathbb{R}}) \to {\mathbb{R}}$ such that, for all $({\und{\b{v}}}_h,q_h) \in {{{\und{\b{U}}}}_{h}^{k}} \times {\mathbb{P}}^k({\mathcal{T}}_h,{\mathbb{R}})$, setting $q_T\coloneq (q_h){\ \!\!_{|_{T}}}$ for all $T\in{\mathcal{T}}_h$, $$\label{eq:bh}
{\mathrm{b}}_h({\und{\b{v}}}_h,q_h) \coloneqq -\sum_{T \in {\mathcal{T}}_h}\int_T {{\mathrm{D}}^{k}_{T}} {\und{\b{v}}}_T~ q_T.$$
Discrete problem
----------------
The discrete problem reads: Find $({\und{\b{u}}}_h,p_h) \in {{{\und{\b{U}}}}_{h,0}^{k}} \times {P_{h}^{k}}$ such that
\[eq:stokes.discrete\] $$\begin{aligned}
{2}
\label{eq:stokes.discrete:momentum} {\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{v}}}_h) + {\mathrm{b}}_h({\und{\b{v}}}_h,p_h) &= \displaystyle\int_\Omega \b f \cdot \b v_h &\qquad& \forall {\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}, \\
\label{eq:stokes.discrete:mass} -{\mathrm{b}}_h({\und{\b{u}}}_h,q_h) &= 0 &\qquad& \forall q_h \in {P_{h}^{k}}.
\end{aligned}$$
Before proceding, some remarks are in order.
The space of test functions in can be extended to ${\mathbb{P}}^k({\mathcal{T}}_h,{\mathbb{R}})$ since, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}$, the divergence theorem together with the fact that $\b v_F = \b 0$ for all $F \in {{\mathcal{F}}_h^{\mathrm{b}}}$ and $\sum_{T\in {\mathcal{T}}_F} \int_F \b v_F \cdot \b n_{TF} = 0$ for all $F \in {{\mathcal{F}}_h^{\mathrm{i}}}$, yield $${\mathrm{b}}_h({\und{\b{v}}}_h,1) = -\sum_{T \in {\mathcal{T}}_h} \sum_{F \in {\mathcal{F}}_T} \int_F \b v_F \cdot \b n_{TF} = -\sum_{F \in {{\mathcal{F}}_h^{\mathrm{i}}}}\sum_{T \in {\mathcal{T}}_F} \int_F \b v_F \cdot \b n_{TF} = 0.$$
When solving the system of nonlinear algebraic equations corresponding to by a first-order (e.g., Newton) algorithm, all element-based velocity unknowns and all but one pressure unknown per element can be locally eliminated at each iteration by computing the corresponding Schur complement element-wise. As all the computations are local, this procedure is an embarrassingly parallel task which can fully benefit from multi-thread and multi-processor architectures. This implementation strategy has been described for the linear Stokes problem in [@Di-Pietro.Ern.ea:16 Section 6.2]. After further eliminating the boundary unknowns by strongly enforcing the boundary condition , we end up solving, at each iteration of the nonlinear solver, a linear system of size $d{\mathrm{card}}({{\mathcal{F}}_h^{\mathrm{i}}}){k+d-1\choose d-1} + {\mathrm{card}}({\mathcal{T}}_h)$.
Well-posedness {#sec:well-posedness}
==============
In this section, after studying the stability properties of the viscous function ${\mathrm{a}}_h$ and of the velocity-pressure coupling bilinear form ${\mathrm{b}}_h$, we prove the well-posedness of problem .
Hölder continuity and strong monotonicity of the viscous function
-----------------------------------------------------------------
\[lem:ah:holder.continuity.strong.monotonicity\] For all ${\und{\b{u}}}_h, {\und{\b{v}}}_h, {\und{\b{w}}}_h \in {{{\und{\b{U}}}}_{h}^{k}}$, setting ${\und{\b{e}}}_h\coloneq{\und{\b{u}}}_h - {\und{\b{w}}}_h$, it holds
\[eq:ah:holder.continuity.strong.monotonicity\] $$\begin{gathered}
\label{eq:ah:holder.continuity}
\left|
{\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{v}}}_h)-{\mathrm{a}}_h({\und{\b{w}}}_h,{\und{\b{v}}}_h)
\right| \lesssim \sigma_{\mathrm{hc}}\left( \sigma_{\mathrm{de}}^{r}+ \| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+\| {\und{\b{w}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r^{\circ}}-1}\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h},
\\\label{eq:ah:strong.monotonicity}
\left({\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{e}}}_h)-{\mathrm{a}}_h({\und{\b{w}}}_h,{\und{\b{e}}}_h)\right)\left( \sigma_{\mathrm{de}}^{r}+\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+\| {\und{\b{w}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\right)^\frac{2-{r^{\circ}}}{{r}} \gtrsim \sigma_{\mathrm{sm}}\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r}+2-{r^{\circ}}}.
\end{gathered}$$
\(i) *Hölder continuity.* Denote by $|\Omega|_d$ the measure of $\Omega$. Using a Cauchy–Schwarz inequality followed by the Hölder continuity of ${\b\sigma}$, we can write $$\label{C2:rge2:1}
\begin{aligned}
&\left|\int_\Omega
\big(
{\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{u}}}_h)-{\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{w}}}_h)
\big):{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h\right| \\
&\quad \le \sigma_{\mathrm{hc}} \int_\Omega \left(\sigma_{\mathrm{de}}^{r}+|{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{u}}}_h|_{d\times d}^{r}+|{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{w}}}_h|_{d\times d}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{e}}}_h|_{d\times d}^{{r^{\circ}}-1} |{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h|_{d \times d} \\
&\quad \lesssim \sigma_{\mathrm{hc}}\left(|\Omega|_d\sigma_{\mathrm{de}}^{r}+\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{u}}}_h \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}+\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{w}}}_h \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}} \\
& \qquad \times \| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{e}}}_h \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{{r^{\circ}}-1}\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}\\
&\quad \lesssim \sigma_{\mathrm{hc}}\left(\sigma_{\mathrm{de}}^{r}+ \| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+\| {\und{\b{w}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r^{\circ}}-1}\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h},
\end{aligned}$$ where we have used the $(1;\frac{{r}}{{r}-{r^{\circ}}},\frac{{r}}{{r^{\circ}}-1},{r})$-Hölder inequality in the second bound and the global seminorm equivalence together with the fact that $|\Omega|_d\lesssim 1$ (since $\Omega$ is bounded) to conclude. For the stabilization term, combining the Hölder continuity of ${\mathrm{s}}_h$ and the seminorm equivalence readily gives $$\label{C2:rge2:2}
\left|
{\mathrm{s}}_h({\und{\b{u}}}_h,{\und{\b{v}}}_h)-{\mathrm{s}}_h({\und{\b{w}}}_h,{\und{\b{v}}}_h)
\right|
\lesssim \left(\sigma_{\mathrm{de}}^{r}+ \| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+\| {\und{\b{w}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r^{\circ}}-1}\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h},$$ where we have additionally noticed that $\sigma_{\mathrm{de}}^{r}\ge 0$ to add this term to the quantity inside parentheses. Using the definition of ${\mathrm{a}}_h$, a triangle inequality followed by and , and recalling that $\gamma \le \sigma_{\mathrm{hc}}$ (cf. ), follows.\
(ii) *Strong monotonicity.* Using the strong monotonicity of ${\b\sigma}$ and the $(1;\frac{{r}+2-{r^{\circ}}}{2-{r^{\circ}}},\frac{{r}+2-{r^{\circ}}}{{r}})$-Hölder inequality , we get $$\label{eq:ah:sm:1}
\hspace{-0.2cm}\begin{aligned}
&\sigma_{\mathrm{sm}}^\frac{{r}}{{r}+2-{r^{\circ}}}\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{e}}}_h\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}\\
&\leq \int_\Omega \left(\sigma_{\mathrm{de}}^{r}+|{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{u}}}_h|_{d\times d}^{r}+|{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{w}}}_h|_{d\times d}^{r}\right)^{\frac{2-{r^{\circ}}}{{r}+2-{r^{\circ}}}}\left)
\left({\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{u}}}_h)-{\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{w}}}_h)\right):{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{e}}}_h
\right)^\frac{{r}}{{r}+2-{r^{\circ}}}\\
&\lesssim \left(\sigma_{\mathrm{de}}^{r}+\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{u}}}_h\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}+\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{w}}}_h\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}\right)^\frac{2-{r^{\circ}}}{{r}+2-{r^{\circ}}} \\
&\qquad \times \left(
\int_\Omega \left(
{\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{u}}}_h)-{\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{w}}}_h)
\right):{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{e}}}_h
\right)^\frac{{r}}{{r}+2-{r^{\circ}}}\\
&\lesssim \left(\sigma_{\mathrm{de}}^{r}+\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+\| {\und{\b{w}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\right)^\frac{2-{r^{\circ}}}{{r}+2-{r^{\circ}}} \left(
\int_\Omega \left(
{\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{u}}}_h)-{\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{w}}}_h)
\right):{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{e}}}_h
\right)^\frac{{r}}{{r}+2-{r^{\circ}}},
\end{aligned}$$ where the conclusion follows from the global seminorm equivalence . Additionally, using the strong monotonicity of ${\mathrm{s}}_h$ together with the fact that $\sigma_{\mathrm{sm}} \le \gamma$ (cf. ) and invoking again the seminorm equivalence , we readily obtain $$\label{eq:ah:sm:2}
\sigma_{\mathrm{sm}}^\frac{{r}}{{r}+2-{r^{\circ}}}{\mathrm{s}}_h({\und{\b{e}}}_h,{\und{\b{e}}}_h)
\lesssim \left(\sigma_{\mathrm{de}}^{r}+\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+\| {\und{\b{w}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\right)^\frac{2-{r^{\circ}}}{{r}+2-{r^{\circ}}}\left(
\gamma{\mathrm{s}}_h({\und{\b{u}}}_h,{\und{\b{e}}}_h)-\gamma{\mathrm{s}}_h({\und{\b{w}}}_h,{\und{\b{e}}}_h)
\right)^\frac{{r}}{{r}+2-{r^{\circ}}}.$$ Finally, combining again the norm equivalence with and , and using yields $$\begin{aligned}
\sigma_{\mathrm{sm}}^\frac{{r}}{{r}+2-{r^{\circ}}}\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\lesssim &\left( \sigma_{\mathrm{de}}^{r}+\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+\| {\und{\b{w}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\right)^\frac{2-{r^{\circ}}}{{r}+2-{r^{\circ}}}\left(
{\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{e}}}_h)-{\mathrm{a}}_h({\und{\b{w}}}_h,{\und{\b{e}}}_h)
\right)^\frac{{r}}{{r}+2-{r^{\circ}}}.
\end{aligned}$$ Raising this inequality to the power $\frac{{r}-2-{r^{\circ}}}{{r}}$ yields .
Stability of the pressure-velocity coupling
-------------------------------------------
\[lem:bh:inf-sup\] It holds, for all $q_h \in {P_{h}^{k}}$, $$\label{eq:bh:inf-sup}
\| q_h \|_{L^{{r}'}(\Omega,{\mathbb{R}})} \lesssim \sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}, \| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1} {\mathrm{b}}_h({\und{\b{v}}}_h,q_h),$$ with hidden constant depending only on $d$, $k$, ${r}$, $\Omega$, and the mesh regularity parameter.
The proof follows the classical Fortin argument (cf., e.g., [@Boffi.Brezzi.ea:13 Section 8.4]), adapted here to the non-Hilbertian setting: we first prove that ${{\und{\b{I}}}_{h}^{k}}$ is a Fortin operator, then combine this fact with the continuous inf-sup condition.\
(i) *Fortin operator.* We need to prove that the following properties hold for any $\b v\in W^{1,{r}}(\Omega,{\mathbb{R}}^d)$:
\[eq:fortin\] $$\begin{gathered}
\| {{\und{\b{I}}}_{h}^{k}} \b v\|_{{\boldsymbol{\varepsilon}},{r},h} \lesssim | \b v |_{W^{1,{r}}(\Omega,{\mathbb{R}}^d),}\label{eq:fortin:boundedness}
\\
{\mathrm{b}}_h({{\und{\b{I}}}_{h}^{k}} \b v,q_h) = b(\b v,q_h)\qquad\forall q_h\in{\mathbb{P}}^k({\mathcal{T}}_h,{\mathbb{R}}).\label{eq:fortin:consistency}
\end{gathered}$$
Property is obtained by raising both sides of to the power ${r}$, summing over $T \in {\mathcal{T}}_h$, then taking the $r$th root of the resulting inequality. The proof of is given, e.g., in [@Di-Pietro.Droniou:20 Lemma 8.12].\
(ii) *Inf-sup condition on ${\mathrm{b}}_h$.* Let $q_h \in {P_{h}^{k}}$ and set $c_h \coloneqq \int_\Omega |q_h|^{{r}'-2}q_h$. Using a triangle inequality, the Hölder inequality, and the fact that $|\Omega|_d\lesssim 1$, we get $$\label{eq:inf-sup:qT}
\| |q_h|^{{r}'-2}q_h-c_h \|_{L^{{r}}(\Omega,{\mathbb{R}})}
\le \| q_h\|_{L^{{r}'}(\Omega,{\mathbb{R}})}^{{r}'-1}+|c_h||\Omega|_d^\frac{1}{{r}}
\le \left(1+|\Omega|_d\right)\| q_h\|_{L^{{r}'}(\Omega,{\mathbb{R}})}^{{r}'-1} \lesssim \| q_h\|_{L^{{r}'}(\Omega,{\mathbb{R}})}^{{r}'-1},$$ where we have used the fact that $|c_h|\le\| q_h\|_{L^{{r}'}(\Omega,{\mathbb{R}})}^{{r}'-1} |\Omega|_d^{\frac1{{r}'}}$ along with $\frac1{r}+\frac1{{r}'}=1$ in the second bound and the fact that $|\Omega|_d\lesssim 1$ to conclude. Since $q_h \in L^{{r}'}(\Omega,{\mathbb{R}})$, bound implies that $|q_h|^{{r}'-2}q_h-c_h \in L^{{r}}_0(\Omega,{\mathbb{R}}) \coloneq \left\{ q \in L^{r}(\Omega,{\mathbb{R}}) : \int_\Omega q = 0 \right\}$ by construction. Thus, using the surjectivity of the continuous divergence operator ${\b\nabla{\cdot}}: \b U \to L^{{r}}_0(\Omega,{\mathbb{R}})$, (c.f. [@Duran.Muschietti.ea:10] and also [@Bogovski:79 Theorem 1]), we infer that there exists $\b v_{q_h} \in \b U$ such that $$\label{eq:velocity.lifting}
-{\b\nabla{\cdot}}\b v_{q_h} = |q_h|^{{r}'-2}q_h-c_h \quad {\mathrm{and}} \quad | \b v_{q_h}|_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)} \lesssim \| |q_h|^{{r}'-2}q_h-c_h \|_{L^{r}(\Omega,{\mathbb{R}})}.$$ Denote by $\$$ the supremum in . Using the fact that $q_h$ has zero mean value over $\Omega$, the equality in together with the definition of $b$, and the second Fortin property , we have $$\|q_h \|_{L^{{r}'}(\Omega,{\mathbb{R}})}^{{r}'}
{=} \int_\Omega \big(|q_h|^{{r}'-2}q_h-c_h\big) q_h
= b(\b v_{q_h},q_h)
= {\mathrm{b}}_h({{\und{\b{I}}}_{h}^{k}}\b v_{q_h},q_h)
\le \$ \| {{\und{\b{I}}}_{h}^{k}} \b v_{q_h} \|_{{\boldsymbol{\varepsilon}},{r},h}
\lesssim \$ \| q_h \|_{L^{{r}'}(\Omega,{\mathbb{R}})}^{{r}'-1},$$ where, to conclude, we have used followed by and . Simplifying yields .
Well-posedness {#well-posedness}
--------------
We are now ready to prove the main result of this section.
\[thm:well-posedness\] There exists a unique solution $({\und{\b{u}}}_h,p_h) \in {{{\und{\b{U}}}}_{h,0}^{k}} \times {P_{h}^{k}}$ to the discrete problem . Additionally, the following a priori bounds hold:
\[eq:discrete.solution:bounds\] $$\begin{aligned}
\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} &\lesssim \left(\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\right)^\frac{1}{{r}-1}+\left(\sigma_{\mathrm{de}}^{2-{r^{\circ}}}\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\right)^\frac{1}{{r}+1-{r^{\circ}}}, \label{eq:discrete.solution:bounds:uh}\\
\| p_h \|_{L^{{r}'}(\Omega,{\mathbb{R}})} &\lesssim \sigma_{\mathrm{hc}}\left(\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}+\sigma_{\mathrm{de}}^{|{r}-2|({r^{\circ}}-1)}\left(\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\right)^\frac{{r^{\circ}}-1}{{r}+1-{r^{\circ}}}\right). \label{eq:discrete.solution:bounds:ph}
\end{aligned}$$
\(i) *Existence.* Denote by ${P_{h}^{k,*}}$ the dual space of ${P_{h}^{k}}$ and let $B_h : {{{\und{\b{U}}}}_{h,0}^{k}} \to {P_{h}^{k,*}}$ be such that, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}$, $$\langle B_h{\und{\b{v}}}_h, q_h \rangle \coloneqq -{\mathrm{b}}_h({\und{\b{v}}}_h,q_h) \qquad \forall q_h \in {P_{h}^{k}}.$$ Here and in what follows, $\langle{\cdot},{\cdot}\rangle$ denotes the appropriate duality pairing as inferred from its arguments. Define the following subspace of ${{{\und{\b{U}}}}_{h,0}^{k}}$ spanned by vectors of discrete unknowns with zero discrete divergence: $$\label{eq:Whk}
{\und{\b{W}}}_h^k \coloneq \operatorname{Ker}(B_h) = \left\{
{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}} : {\mathrm{b}}_h({\und{\b{v}}}_h,q_h) = 0 \quad \forall q_h \in {P_{h}^{k}}
\right\},$$ and consider the following problem: Find ${\und{\b{u}}}_h\in{\und{\b{W}}}_h^k$ such that $$\label{eq:existence:auxiliary}
{\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{v}}}_h) = \int_\Omega \b f\cdot \b v_h\qquad\forall {\und{\b{v}}}_h\in{\und{\b{W}}}_h^k.$$ Existence of a solution to this problem for a fixed $h$ can be proved adapting the arguments of [@Di-Pietro.Droniou:17 Theorem 4.5]. Specifically, equip ${\und{\b{W}}}_h^k$ with an inner product $(\cdot,\cdot)_{\b W,h}$ (which need not be further specified), denote by $\|{\cdot}\|_{\b W,h}$ the induced norm, and let $\b\Phi_h:{\und{\b{W}}}_h^k\to {\und{\b{W}}}_h^k$ be such that, for all ${\und{\b{w}}}_h\in{\und{\b{W}}}_h^k$, $(\b\Phi_h({\und{\b{w}}}_h),{\und{\b{v}}}_h)_{\b W,h} = {\mathrm{a}}_h({\und{\b{w}}}_h,{\und{\b{v}}}_h)$ for all ${\und{\b{v}}}_h\in{\und{\b{W}}}_h^k$. The strong monotonicity of ${\mathrm{a}}_h$ yields, for any ${\und{\b{v}}}_h\in{\und{\b{W}}}_h^k$ such that $\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} \ge \sigma_{\mathrm{de}}$, $$(\b\Phi_h({\und{\b{v}}}_h),{\und{\b{v}}}_h)_{\b W,h}\ge \sigma_{\mathrm{sm}} (\sigma_{\mathrm{de}}^{r}+ \| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r})^\frac{{r^{\circ}}-2}{{r}} \| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r}+2-{r^{\circ}}} \gtrsim \sigma_{\mathrm{sm}}\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\ge C^{r}\sigma_{\mathrm{sm}}\| {\und{\b{v}}}_h\|_{\b W,h}^{r},$$ where $C$ denotes the constant (possibly depending on $h$) in the equivalence of the norms $\|{\cdot}\|_{{\boldsymbol{\varepsilon}},{r},h}$ and $\|{\cdot}\|_{\b W,h}$ (which holds since ${\und{\b{W}}}_h^k$ is finite-dimensional). This shows that $\b\Phi_h$ is coercive hence, by [@Deimling:85 Theorem 3.3], surjective. Let now ${\und{\b{w}}}_h\in{\und{\b{W}}}_h^k$ be such that $({\und{\b{w}}}_h,{\und{\b{v}}}_h)_{\b W,h}=\int_\Omega \b f\cdot \b v_h$ for all ${\und{\b{v}}}_h\in{\und{\b{W}}}_h^k$. By the surjectivity of $\b\Phi_h$, there exists ${\und{\b{u}}}_h\in {\und{\b{W}}}_h^k$ such that $\b\Phi_h({\und{\b{u}}}_h)={\und{\b{w}}}_h$ which, by definition of ${\und{\b{w}}}_h$ and $\b\Phi_h$, is a solution to the discrete problem .
The proof of existence now continues as in the linear case; see, e.g., [@Boffi.Brezzi.ea:13 Theorem 4.2.1]. Denote by ${{{\und{\b{U}}}}_{h,0}^{k,*}}$ the dual space of ${{{\und{\b{U}}}}_{h,0}^{k}}$ and consider the linear mapping $\ell_h\in{{{\und{\b{U}}}}_{h,0}^{k,*}}$ such that, for all ${\und{\b{v}}}_h\in{{{\und{\b{U}}}}_{h,0}^{k}}$, $$\langle\ell_h,{\und{\b{v}}}_h\rangle\coloneq \int_\Omega \b f\cdot \b v_h - {\mathrm{a}}_h({\und{\b{u}}}_h, {\und{\b{v}}}_h).$$ Thanks to , $\ell_h$ vanishes identically for every ${\und{\b{v}}}_h\in{\und{\b{W}}}_h^k$, that is to say, $\ell_h$ lies in the polar space of ${\und{\b{W}}}_h^k$ which, denoting by $B_h^*:{P_{h}^{k}}\to{{{\und{\b{U}}}}_{h,0}^{k,*}}$ the adjoint operator of $B_h$, coincides in our case with $\operatorname{Im}(B_h^*)$ (see, e.g., [@Boffi.Brezzi.ea:13 Theorem 4.14]). Hence, $\ell_h\in\operatorname{Im}(B_h^*)$, and there exists therefore a $p_h\in {P_{h}^{k}}$ such that $B_h^* p_h = \ell_h$. This means that, for all ${\und{\b{v}}}_h\in{{{\und{\b{U}}}}_{h,0}^{k}}$, $${\mathrm{b}}_h({\und{\b{v}}}_h,p_h)
= \langle B_h^* p_h,{\und{\b{v}}}_h\rangle
= \langle\ell_h,{\und{\b{v}}}_h\rangle
= \int_\Omega \b f\cdot \b v_h - {\mathrm{a}}_h({\und{\b{u}}}_h, {\und{\b{v}}}_h),$$ i.e., the $({\und{\b{u}}}_h,p_h)$ satisfies the discrete momentum equation . On the other hand, since ${\und{\b{u}}}_h\in{\und{\b{W}}}_h^k$, we also have, by the definition of ${\und{\b{W}}}_h^k$, $ {\mathrm{b}}_h({\und{\b{u}}}_h,q_h) = 0$ for all $q_h\in {P_{h}^{k}}$, which shows that the discrete mass equation is also verified. In conclusion, $({\und{\b{u}}}_h,p_h)\in{{{\und{\b{U}}}}_{h,0}^{k}}\times {P_{h}^{k}}$ solves .\
(ii) *Uniqueness.* We start by proving uniqueness for the velocity. Let $({\und{\b{u}}}_h,p_h),({\und{\b{u}}}'_h,p'_h) \in {{{\und{\b{U}}}}_{h,0}^{k}} \times {P_{h}^{k}}$ be two solutions of . Making ${\und{\b{v}}}_h = {\und{\b{u}}}_h - {\und{\b{u}}}'_h$ in written first for $({\und{\b{u}}}_h, p_h)$ then for $({\und{\b{u}}}'_h, p'_h)$, then taking the difference and observing that ${\mathrm{b}}_h({\und{\b{u}}}_h-{\und{\b{u}}}'_h,p_h)={\mathrm{b}}_h({\und{\b{u}}}_h - {\und{\b{u}}}'_h,p'_h)=0$ by , we infer that $${\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{u}}}_h - {\und{\b{u}}}'_h)-{\mathrm{a}}_h({\und{\b{u}}}'_h,{\und{\b{u}}}_h - {\und{\b{u}}}'_h) = 0.$$ Thus, the strong monotonicity of ${\mathrm{a}}_h$ yields $\| {\und{\b{u}}}_h - {\und{\b{u}}}'_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 0$, which implies ${\und{\b{u}}}_h = {\und{\b{u}}}'_h$ since $\|{\cdot}\|_{{\boldsymbol{\varepsilon}},{r},h}$ is a norm on ${{{\und{\b{U}}}}_{h,0}^{k}}$. Moreover, using the inf-sup stability of ${\mathrm{b}}_h$ and written first for ${\und{\b{u}}}_h$ then for ${\und{\b{u}}}_h'$, we get $$\begin{aligned}
\| p_h-p'_h \|_{L^{{r}'}(\Omega,{\mathbb{R}})}
&\lesssim \sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}},\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1} {\mathrm{b}}_h({\und{\b{v}}}_h,p_h-p'_h)
\\
&= \sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}},\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1} \left({\mathrm{a}}_h({\und{\b{u}}}'_h,{\und{\b{v}}}_h)-{\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{v}}}_h)\right) = 0,
\end{aligned}$$ hence $p_h=p'_h$.\
(iii) *A priori estimates.* Using the strong monotonicity of ${\mathrm{a}}_h$ (with ${\und{\b{w}}}_h = {\und{\b{0}}}$), equation together with , and the Hölder inequality together with the discrete Korn inequality , we obtain $$\label{eq:well-posedness:0}
\begin{aligned}
\sigma_{\mathrm{sm}}\big(
\sigma_{\mathrm{de}}^{r}+ \| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\big)^\frac{{r^{\circ}}-2}{{r}} \| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r}+2-{r^{\circ}}}
&\lesssim {\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{u}}}_h)
= \displaystyle\int_\Omega \b f \cdot \b u_h
\lesssim \| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}.
\end{aligned}$$ We then conclude as in the continuous case to infer (see Remark \[rem:a-priori\]). To prove the bound on the pressure, we use the inf-sup stability of ${\mathrm{b}}_h$ to write $$\begin{aligned}
\| p_h \|_{L^{{r}'}(\Omega,{\mathbb{R}})}
&\lesssim \sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}, \| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1} {\mathrm{b}}_h({\und{\b{v}}}_h,p_h)
\\
&= \sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}, \| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}
= 1} \left(\displaystyle\int_\Omega \b f \cdot \b v_h - {\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{v}}}_h) \right) \\
&\lesssim \| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)} +\sigma_{\mathrm{hc}}(\sigma_{\mathrm{de}}^{r}+\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r})^\frac{{r}-{r^{\circ}}}{{r}}\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r^{\circ}}-1} \\
&\lesssim \sigma_{\mathrm{hc}}\left(\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}+\sigma_{\mathrm{de}}^{|{r}-2|({r^{\circ}}-1)}\left(\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\right)^\frac{{r^{\circ}}-1}{{r}+1-{r^{\circ}}}\right),
\end{aligned}$$ where we have used the discrete momentum equation to pass to the second line, the Hölder and discrete Korn inequalities together with the Hölder continuity of ${\mathrm{a}}_h$ to pass to the third line, and the a priori bound on the velocity together with $\frac{\sigma_{\mathrm{hc}}}{\sigma_{\mathrm{sm}}}\ge 1$ (see ) to conclude.
Error estimate {#sec:error.estimate}
==============
In this section, after studying the consistency of the viscous and pressure-velocity coupling terms, we prove an energy error estimate.
Consistency of the viscous function {#sec:consistency:viscous.function}
-----------------------------------
\[lem:consistency:ah\] Let $\b w \in \b U \cap W^{k+2,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)$ be such that ${\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w) \in W^{1,{r}'}(\Omega,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}}) \cap W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}})$. Define the viscous consistency error linear form $\mathcal E_{{\mathrm{a}},h}(\b w;\cdot) : {{{\und{\b{U}}}}_{h}^{k}} \to {\mathbb{R}}$ such that, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h}^{k}}$, $$\label{eq:Eah}
\mathcal E_{{\mathrm{a}},h}(\b w;{\und{\b{v}}}_h) \coloneqq \int_\Omega ({\b\nabla{\cdot}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)) \cdot \b v_h + {\mathrm{a}}_h({{\und{\b{I}}}_{h}^{k}} \b w,{\und{\b{v}}}_h).$$ Then, under Assumptions \[ass:stress\] and \[ass:sT\], we have $$\begin{gathered}
\label{eq:consistency:ah}
\sup_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}},\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1} \mathcal E_{{\mathrm{a}},h}(\b w;{\und{\b{v}}}_h)
\lesssim
h^{(k+1)({r^{\circ}}-1)}\bigg[
\sigma_{\mathrm{hc}}\left(\sigma_{\mathrm{de}}^{r}+ |\b w|_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}|\b w|_{W^{k+2,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{{r^{\circ}}-1}
\\
+|{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)|_{W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}})}
\bigg].
\end{gathered}$$
Let ${\und{\b{\hat w}}}_h \coloneqq {{\und{\b{I}}}_{h}^{k}} \b w$ and ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}$. Expanding ${\mathrm{a}}_h$ according to its definition in the expression of $\mathcal E_{{\mathrm{a}},h}$, inserting $\pm\left(
\int_\Omega{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w): {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h
+ \int_\Omega{\b{\pi}_{h}^{k}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w) : {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h
\right)$, and rearranging, we obtain $$\begin{gathered}
\label{eq:consistency:ah:EJ}
\mathcal E_{{\mathrm{a}},h}(\b w;{\und{\b{v}}}_h)
=\!\!
\underbrace{ \int_\Omega ({\b\nabla{\cdot}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)) \cdot \b v_h
{+} \int_\Omega {\b{\pi}_{h}^{k}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)\! :\! {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h
}_{\mathcal T_1}
+\! \underbrace{ \int_\Omega\! \left( {\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w) - {\b{\pi}_{h}^{k}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)\right)\! :\! {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h
}_{\mathcal T_2}
\\
{+} \underbrace{ \int_\Omega\!\left( {\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{\hat w}}}_h) - {\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)\right)\!:\! {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h
}_{\mathcal T_3}
+ \underbrace{\vphantom{\int_\Omega}\gamma {\mathrm{s}}_h({\und{\b{\hat w}}}_h,{\und{\b{v}}}_h)}_{\mathcal T_4}.
\end{gathered}$$ We proceed to estimate the terms in the right-hand side. For the first term, we start by noticing that $$\label{eq:consistency:ah:null}
\sum_{T \in {\mathcal{T}}_h}\sum_{F \in {\mathcal{F}}_T} \int_F \b v_F \cdot\left({\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)\b n_{TF}\right) = 0$$ as a consequence of the continuity of the normal trace of ${\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)$ together with the single-valuedness of $\b v_F$ across each interface $F\in{{\mathcal{F}}_h^{\mathrm{i}}}$ and of the fact that $\b v_F=\b 0$ for every boundary face $F\in{{\mathcal{F}}_h^{\mathrm{b}}}$. Using an element by element integration by parts on the first term of $\mathcal T_1$ along with the definitions of ${\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}$ and of ${\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},T}}$, we can write $$\begin{aligned}
\mathcal T_1
&= \cancel{\int_\Omega \left({\b{\pi}_{h}^{k}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)- {\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)\right) : {\b{\nabla}_{{\mathrm{s}},h}}\b v_h} \\
&\qquad + \sum_{T \in {\mathcal{T}}_h}\sum_{F \in {\mathcal{F}}_T} \left(\int_F (\b v_F-\b v_T)\cdot({\b{\pi}_{T}^{k}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w))\b n_{TF}+\int_F\b v_T\cdot\left({\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)\b n_{TF}\right) \right) \\
&= \sum_{T \in {\mathcal{T}}_h}\sum_{F \in {\mathcal{F}}_T} \int_F (\b v_F-\b v_T)\cdot\left({\b{\pi}_{T}^{k}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)-{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)\right)\b n_{TF},
\end{aligned}$$ where we have used the definition of ${\b{\pi}_{h}^{k}}$ together with the fact that ${\b{\nabla}_{{\mathrm{s}},h}}\b v_h \in {\mathbb{P}}^{k-1}({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}}) \subset {\mathbb{P}}^{k}({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}})$ to cancel the term in the first line, and we have inserted and rearranged to conclude. Therefore, applying the Hölder inequality together with the bound $h_F \le h_T$, we infer $$\label{eq:consistency:ah:T1}
\begin{aligned}
\left|\mathcal T_1\right|
&\le \left(\displaystyle\sum_{T \in {\mathcal{T}}_h}h_T \|{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)- {\b{\pi}_{T}^{k}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w) \|_{L^{{r}'}(\partial T,{{\mathbb{R}}^{d \times d}})}^{{r}'} \right)^\frac{1}{{r}'}\left(\sum_{T \in {\mathcal{T}}_h}\sum_{F \in {\mathcal{F}}_T}h_F^{1-{r}}\| \b v_F-\b v_T\|_{L^{r}(F,{\mathbb{R}}^d)}^{r}\right)^\frac{1}{{r}}
\\
&\lesssim h^{(k+1)({r^{\circ}}-1)} |{\b\sigma}(\cdot, {\b{\nabla}_{\mathrm{s}}}\b w)|_{W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}})}\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h},
\end{aligned}$$ where the conclusion follows using the $((k+1)({r^{\circ}}-1),{r}')$-trace approximation properties of ${\b{\pi}_{T}^{k}}$ along with $h_T \le h$ for the first factor and the definition of the $\|{\cdot}\|_{{\boldsymbol{\varepsilon}},{r},h}$-norm for the second.
For the second term, we use the Hölder inequality and the seminorm equivalence to write $$\label{eq:consistency:ah:T2}
\begin{aligned}
\left|\mathcal T_2\right|
&= \| {\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w)-{\b{\pi}_{h}^{k}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w) \|_{L^{{r}'}(\Omega,{{\mathbb{R}}^{d \times d}})}
\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}{\und{\b{v}}}_h\|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}
\\
&\lesssim h^{(k+1)({r^{\circ}}-1)}|{\b\sigma}(\cdot, {\b{\nabla}_{\mathrm{s}}}\b w)|_{W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}})} \| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h},
\end{aligned}$$ where the conclusion follows from the $((k+1)({r^{\circ}}-1),{r}',0)$-approximation properties of ${\b{\pi}_{T}^{k}}$ along with $h_T\le h$ for the first factor and the global norm equivalence for the second.
For the third term, using the Hölder inequality and again , we get $$\label{eq:consistency:ah:T3:0}
\left|\mathcal T_3\right|
\le \|{\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{\hat w}}}_h)- {\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w) \|_{L^{{r}'}(\Omega,{{\mathbb{R}}^{d \times d}})}\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}.$$ We estimate the first factor as follows: $$\begin{aligned}
&\|{\b\sigma}(\cdot,{\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{\hat w}}}_h)- {\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b w) \|_{L^{{r}'}(\Omega,{{\mathbb{R}}^{d \times d}})}
\\
&\quad
\le \sigma_{\mathrm{hc}} \left\| \left(\sigma_{\mathrm{de}}^{r}+| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{\hat w}}}_h |_{d \times d}^{r}+ | {\b{\nabla}_{\mathrm{s}}}\b w |_{d \times d}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{\hat w}}}_h - {\b{\nabla}_{\mathrm{s}}}\b w |_{d \times d}^{{r^{\circ}}-1}\right\|_{L^{{r}'}(\Omega,{\mathbb{R}})} \\
&\quad
\lesssim \sigma_{\mathrm{hc}} \left(\sigma_{\mathrm{de}}^{r}+\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{\hat w}}}_h \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}+\| {\b{\nabla}_{\mathrm{s}}}\b w \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}\| {\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}} {\und{\b{\hat w}}}_h - {\b{\nabla}_{\mathrm{s}}}\b w \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{{r^{\circ}}-1} \\
&\quad
\lesssim \sigma_{\mathrm{hc}}\left(\sigma_{\mathrm{de}}^{r}+\|{\und{\b{\hat w}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+ |\b w|_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}\| {\b{\pi}_{h}^{k}}({\b{\nabla}_{\mathrm{s}}}\b w) - {\b{\nabla}_{\mathrm{s}}}\b w \|_{L^{r}(\Omega,{{\mathbb{R}}^{d \times d}})}^{{r^{\circ}}-1} \\
&\quad
\lesssim h^{(k+1)({r^{\circ}}-1)}\sigma_{\mathrm{hc}}\left(\sigma_{\mathrm{de}}^{r}+|\b w|_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}|\b w|_{W^{k+2,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{{r^{\circ}}-1},
\end{aligned}$$ where we have used the Hölder continuity of ${\b\sigma}$ in the first bound, the $({r}';\frac{{r}}{{r}-{r^{\circ}}},\frac{{r}}{{r^{\circ}}-1})$-Hölder inequality in the second, the boundedness of $\Omega$ along with and the commutation property of ${\b{{\mathrm{G}}}^{k}_{{\mathrm{s}},h}}$ in the third, and we have concluded invoking the $(k+1,{r},0)$-approximation property of ${\b{\pi}_{T}^{k}}$. Plugging this estimate into , we get $$\label{eq:consistency:ah:T3}
\left|\mathcal T_3\right|
\lesssim h^{(k+1)({r^{\circ}}-1)}\sigma_{\mathrm{hc}}\left(\sigma_{\mathrm{de}}^{r}+|\b w|_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}|\b w|_{W^{k+2,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{{r^{\circ}}-1}
\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}.$$
Finally, using the fact that $\gamma \le \sigma_{\mathrm{hc}}$ together with the consistency of ${\mathrm{s}}_h$ and the norm equivalence , we obtain for the fourth term $$\label{eq:consistency:ah:T4}
\left|\mathcal T_4\right|
\lesssim h^{(k+1)({r^{\circ}}-1)}\sigma_{\mathrm{hc}}|\b w|_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)}^{{r}-{r^{\circ}}}|\b w|_{W^{k+2,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{{r^{\circ}}-1}
\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}.$$
Plug the bounds , , , and into and pass to the supremum to conclude.
Consistency of the pressure-velocity coupling bilinear form
-----------------------------------------------------------
Let $q \in W^{1,{r}'}(\Omega,{\mathbb{R}}) \cap W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{\mathbb{R}})$. Let $\mathcal E_{{\mathrm{b}},h}(q;\cdot) : {{{\und{\b{U}}}}_{h}^{k}} \to {\mathbb{R}}$ be the pressure consistency error linear form such that, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h}^{k}}$, $$\label{eq:Ebh}
\mathcal E_{{\mathrm{b}},h}(q;{\und{\b{v}}}_h) \coloneqq \int_\Omega {\b\nabla}q \cdot \b v_h - {\mathrm{b}}_h({\und{\b{v}}}_h,{\pi_{h}^{k}} q).$$ Then, we have that $$\label{eq:consistency:bh}
\sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}},\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1} \mathcal E_{{\mathrm{b}},h}(q;{\und{\b{v}}}_h) \lesssim h^{(k+1)({r^{\circ}}-1)} |q|_{W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{\mathbb{R}})}.$$
Let ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}$. Integrating by parts element by element, we can reformulate the first term in the right-hand side of as follows: $$\label{eq:consistency:bh:1}
\displaystyle\int_\Omega {\b\nabla}q\cdot \b v_h = - \sum_{T \in {\mathcal{T}}_h} \left( \int_T q({\b\nabla{\cdot}}\b v_T) +\sum_{F \in {\mathcal{F}}_T} \int_F q(\b v_F - \b v_T)\cdot \b n_{TF} \right),$$ where the introduction of $\b v_F$ in the boundary term is justified by the fact that the jumps of $q$ vanish across interfaces by the assumed regularity and that $\b v_F=\b 0$ on every boundary face $F \in {{\mathcal{F}}_h^{\mathrm{b}}}$. On the other hand, expanding, for each $T \in {\mathcal{T}}_h$, ${{\mathrm{D}}^{k}_{T}}$ according to its definition , we get $$\label{eq:consistency:bh:2}
-{\mathrm{b}}_h({\und{\b{v}}}_h, {\pi_{h}^{k}} q) = \sum_{T \in {\mathcal{T}}_h} \left( \int_T {\pi_{T}^{k}} q~({\b\nabla{\cdot}}\b v_T) +\sum_{F \in {\mathcal{F}}_T} \int_F {\pi_{T}^{k}} q~(\b v_F - \b v_T)\cdot \b n_{TF} \right).$$ Summing and and observing that the first terms in parentheses cancel out by the definition of ${\pi_{T}^{k}}$ since ${\b\nabla{\cdot}}\b v_T \in {\mathbb{P}}^{k-1}(T,{\mathbb{R}}) \subset {\mathbb{P}}^k(T,{\mathbb{R}})$ for all $T \in{\mathcal{T}}_h$, we can write $$\begin{aligned}
\mathcal E_{{\mathrm{b}},h}(q;{\und{\b{v}}}_h) &= \sum_{T \in {\mathcal{T}}_h} \left( \cancel{\int_T ({\pi_{T}^{k}} q-q) ({\b\nabla{\cdot}}\b v_T)} +\sum_{F \in {\mathcal{F}}_T} \int_F ({\pi_{T}^{k}} q-q) (\b v_F - \b v_T)\cdot \b n_{TF} \right) \\
&\le \left(\sum_{T \in {\mathcal{T}}_h} h_T\| {\pi_{T}^{k}} q-q \|_{L^{{r}'}(\partial T,{\mathbb{R}})}^{{r}'} \right)^\frac{1}{{r}'} \left(\sum_{T \in {\mathcal{T}}_h}\sum_{F \in {\mathcal{F}}_T} h_F^{1-{r}}\| \b v_F-\b v_T \|_{L^{{r}}(F,{\mathbb{R}}^d)}^{{r}} \right)^\frac{1}{{r}} \\
&\lesssim h^{(k+1)({r^{\circ}}-1)} |q|_{W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{\mathbb{R}})} \| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h},
\end{aligned}$$ where we have used the Hölder inequality along with $h_F\ge h_T$ whenever $F \in {\mathcal{F}}_T$ in the second line and the $((k+1)({r^{\circ}}-1),{r}')$-trace approximation property of ${\pi_{T}^{k}}$ together with the bound $h_F \le h$ and the definition of the $\|{\cdot}\|_{{\boldsymbol{\varepsilon}},{r},h}$-norm to conclude. Passing to the supremum yields .
Error estimate {#error-estimate}
--------------
\[thm:error.estimate\] Let $(\b u,p) \in \b U \times P$ and $({\und{\b{u}}}_h,p_h) \in {{{\und{\b{U}}}}_{h,0}^{k}} \times {P_{h}^{k}}$ solve and , respectively. Assume the additional regularity $\b u \in W^{k+2,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)$, ${\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b u) \in W^{1,{r}'}(\Omega,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}}) \cap W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}})$, and $p \in W^{1,{r}'}(\Omega,{\mathbb{R}}) \cap W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{\mathbb{R}})$. Then, under Assumptions \[ass:stress\] and \[ass:sT\],
\[eq:error.estimate\] $$\begin{aligned}
\label{eq:error.estimate:velocity}
\| {\und{\b{u}}}_h - {{\und{\b{I}}}_{h}^{k}} \b u \|_{{\boldsymbol{\varepsilon}},{r},h}
&\lesssim
h^\frac{(k+1)({r^{\circ}}-1)}{{r}+1-{r^{\circ}}}
\left(\sigma_{\mathrm{sm}}^{-1}\mathcal N_{\b f}^{2-{r^{\circ}}}\mathcal N_{{\b\sigma},\b u,p}\right)^\frac{1}{{r}+1-{r^{\circ}}},
\\
\label{eq:error.estimate:pressure}
\| p_h - {\pi_{h}^{k}} p \|_{L^{{r}'}(\Omega,{\mathbb{R}})}
&\lesssim
h^{(k+1)({r^{\circ}}-1)}\mathcal N_{{\b\sigma},\b u,p}
+
h^{\frac{(k+1)({r^{\circ}}-1)^2}{{r}+1-{r^{\circ}}}} \sigma_{\mathrm{hc}}\mathcal N_{\b f}^{|{r}-2|({r^{\circ}}-1)}
\left(\sigma_{\mathrm{sm}}^{-1}\mathcal N_{{\b\sigma},\b u,p}\right)^\frac{{r^{\circ}}-1}{{r}+1-{r^{\circ}}},
\end{aligned}$$
where we have set, for the sake of brevity, $$\begin{aligned}
\mathcal N_{{\b\sigma},\b u,p}
&\coloneq
\sigma_{\mathrm{hc}}\left(\sigma_{\mathrm{de}}^{r}+|\b u|_{W^{1,{r}}(\Omega,{\mathbb{R}}^d)}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}|\b u|_{W^{k+2,{r}}({\mathcal{T}}_h,{\mathbb{R}}^d)}^{{r^{\circ}}-1}
\\
&\quad
+ |{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b u)|_{W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{{\mathbb{R}}^{d \times d}})}
+ |p|_{W^{(k+1)({r^{\circ}}-1),{r}'}({\mathcal{T}}_h,{\mathbb{R}})},
\\
\mathcal N_{\b f} &\coloneqq \sigma_{\mathrm{de}}+\left(\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\right)^\frac{1}{{r}-1}+\left(\sigma_{\mathrm{de}}^{2-{r^{\circ}}}\sigma_{\mathrm{sm}}^{-1}\| \b f \|_{L^{{r}'}(\Omega,{\mathbb{R}}^d)}\right)^\frac{1}{{r}+1-{r^{\circ}}}.
\end{aligned}$$
\[rem:ocv\] From , neglecting higher-order terms, we infer asymptotic convergence rates of $\mathcal O_{\mathrm{vel}}^k \coloneqq \frac{(k+1)({r^{\circ}}-1)}{{r}+1-{r^{\circ}}}$ for the velocity and $\mathcal O_{\mathrm{pre}}^k \coloneqq \frac{(k+1)({r^{\circ}}-1)^2}{{r}+1-{r^{\circ}}}$ for the pressure, that is, $$\label{eq:asymptotic.order}
\mathcal O_{\mathrm{vel}}^k
= \begin{cases}
(k+1)(r-1) & \text{if $r<2$}, \\
\tfrac{k+1}{r-1} & \text{if $r\ge 2$,}
\end{cases}\quad \text{and} \quad
\mathcal O_{\mathrm{pre}}^k
= \begin{cases}
(k+1)(r-1)^2 & \text{if $r<2$}, \\
\tfrac{k+1}{r-1} & \text{if $r\ge 2$.}
\end{cases}$$ Notice that, owing to the presence of higher-order terms in the right-hand sides of , higher convergence rates may be observed before attaining the asymptotic ones; see Section \[sec:num.res\].
Let $({\und{\b{e}}}_h, \epsilon_h) \coloneqq ({\und{\b{u}}}_h - {\und{\b{\hat u}}}_h,p_h - \hat p_h) \in {{{\und{\b{U}}}}_{h,0}^{k}} \times {P_{h}^{k}}$ where ${\und{\b{\hat u}}}_h \coloneqq{{\und{\b{I}}}_{h}^{k}} \b u \in {{{\und{\b{U}}}}_{h,0}^{k}}$ and $\hat p_h \coloneqq {\pi_{h}^{k}} p \in {P_{h}^{k}}$.\
**Step 1.** *Consistency error.* Let $\mathcal E_h : {{{\und{\b{U}}}}_{h,0}^{k}} \to {\mathbb{R}}$ be the consistency error linear form such that, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}$, $$\label{eq:Eh}
\mathcal E_h({\und{\b{v}}}_h) \coloneqq \int_\Omega \b f \cdot \b v_h - {\mathrm{a}}_h({\und{\b{\hat u}}}_h,{\und{\b{v}}}_h)-{\mathrm{b}}_h({\und{\b{v}}}_h,{\hat p}_h).$$ Using in the above expression the fact that $\b f = -{\b\nabla{\cdot}}{\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b u)+{\b\nabla}p$ almost everywhere in $\Omega$ to write $\mathcal E_h({\und{\b{v}}}_h)=\mathcal E_{{\mathrm{a}},h}(\b u;{\und{\b{v}}}_h) + \mathcal E_{{\mathrm{b}},h}(p;{\und{\b{v}}}_h)$, and invoking the consistency properties of ${\mathrm{a}}_h$ and of ${\mathrm{b}}_h$, we obtain $$\label{eq:error.estimate:step1:eh0}
\$\coloneq
\sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}},\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1}\mathcal E_h({\und{\b{v}}}_h)
\lesssim
h^{(k+1)({r^{\circ}}-1)} \mathcal N_{{\b\sigma},\b u,p}.$$\
**Step 2.** *Error estimate for the velocity.* Using the strong monotonicity of ${\mathrm{a}}_h$, we get $$\label{eq:error.estimate:step2:eh0}
\begin{aligned}
\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r}+2-{r^{\circ}}}
&\lesssim \sigma_{\mathrm{sm}}^{-1}\left(
\sigma_{\mathrm{de}}^{r}+\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+\|{\und{\b{\hat u}}}_h\|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\right)^\frac{2-{r^{\circ}}}{{r}}\left(
{\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{e}}}_h)-{\mathrm{a}}_h({\und{\b{\hat u}}}_h,{\und{\b{e}}}_h)
\right) \\
&\lesssim \sigma_{\mathrm{sm}}^{-1}\mathcal N_{\b f}^{2-{r^{\circ}}}\left(
{\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{e}}}_h)-{\mathrm{a}}_h({\und{\b{\hat u}}}_h,{\und{\b{e}}}_h)
\right),
\end{aligned}$$ where we have used the a priori bound on the discrete solution along with the boundedness of the global interpolator and the a priori bound on the continuous solution to conclude. Using then the discrete mass equation along with (written for $\b v=\b u$) and the continuous mass equation to write ${\mathrm{b}}_h({{\und{\b{I}}}_{h}^{k}} \b u,q_h) = b(\b u,q_h) = 0$, we get ${\mathrm{b}}_h({\und{\b{e}}}_h,q_h) = 0$ for all $q_h \in P^k_h$. Hence, combining this result with and the discrete momentum equation (with ${\und{\b{v}}}_h = {\und{\b{e}}}_h$), we obtain $$\label{eq:error.estimate:step1:eh1}
{\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{e}}}_h)-{\mathrm{a}}_h({\und{\b{\hat u}}}_h,{\und{\b{e}}}_h)
= \int_\Omega \b f \cdot \b e_h - {\mathrm{a}}_h({\und{\b{\hat u}}}_h,{\und{\b{e}}}_h)-\cancel{{\mathrm{b}}_h({\und{\b{e}}}_h,p_h)}
= \mathcal E_h({\und{\b{e}}}_h).$$ Plugging into , we get $$\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r}+2-{r^{\circ}}}
\le \sigma_{\mathrm{sm}}^{-1}\mathcal N_{\b f}^{2-{r^{\circ}}}\$\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}.$$ Simplifying, using , and taking the $({r}+1-{r^{\circ}})$th root of the resulting inequality yields .\
**Step 3.** *Error estimate for the pressure.* Using the Hölder continuity of ${\mathrm{a}}_h$, we have, for all ${\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}}$, $$\label{eq:error.estimate:step3:ah}
\begin{aligned}
\left|{\mathrm{a}}_h({\und{\b{\hat u}}}_h,{\und{\b{v}}}_h)-{\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{v}}}_h)\right|
&\lesssim \sigma_{\mathrm{hc}}\left( \sigma_{\mathrm{de}}^{r}+ \| {\und{\b{\hat u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}+\| {\und{\b{u}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{r}\right)^\frac{{r}-{r^{\circ}}}{{r}}\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r^{\circ}}-1}\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} \\
&\lesssim \sigma_{\mathrm{hc}}\mathcal N_{\b f}^{{r}-{r^{\circ}}}\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r^{\circ}}-1}\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h},
\end{aligned}$$ where the first factor is estimated as in . Thus, using the inf-sup condition , we can write $$\label{eq:error.estimate:step3:epsilonh}
\begin{aligned}
\| \epsilon_h \|_{L^{{r}'}(\Omega,{\mathbb{R}})} &\lesssim \sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}},\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1} {\mathrm{b}}_h({\und{\b{v}}}_h,\epsilon_h) \\
&= \sup\limits_{{\und{\b{v}}}_h \in {{{\und{\b{U}}}}_{h,0}^{k}},\| {\und{\b{v}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h} = 1} \left(\mathcal E_h({\und{\b{v}}}_h)+{\mathrm{a}}_h({\und{\b{\hat u}}}_h,{\und{\b{v}}}_h)-{\mathrm{a}}_h({\und{\b{u}}}_h,{\und{\b{v}}}_h)\right)\\
&\lesssim \$+\sigma_{\mathrm{hc}}\mathcal N_{\b f}^{{r}-{r^{\circ}}}\| {\und{\b{e}}}_h \|_{{\boldsymbol{\varepsilon}},{r},h}^{{r^{\circ}}-1} \\
&\lesssim h^{(k+1)({r^{\circ}}-1)}\mathcal N_{{\b\sigma},\b u,p}
+h^{(k+1)({r^{\circ}}-1)^2}\sigma_{\mathrm{hc}}\mathcal N_{\b f}^{|{r}-2|({r^{\circ}}-1)}
\left(\sigma_{\mathrm{sm}}^{-1}\mathcal N_{{\b\sigma},\b u,p}\right)^\frac{{r^{\circ}}-1}{{r}+1-{r^{\circ}}},
\end{aligned}$$ where we have used the definition of the consistency error together with equation to pass to the second line, to pass to the third line (recall that $\$$ denotes here the supremum in the left-hand side of ), and the bounds and (proved in Step 2) to conclude.
Numerical examples {#sec:num.res}
==================
We consider a manufactured solution to problem in order to assess the convergence of the method, which was implemented within the SpaFEDTe library (cf. <https://spafedte.github.io>). Specifically, we take $\Omega=(0,1)^{2}$ and consider the $(1,0,1,{r})$-Carreau–Yasuda law (corresponding to the power-law model) with Sobolev exponent ${r}\in\{1.5, 1.75, 2, 2.25, 2.5, 2.75\}$. The exact velocity $\b u$ and pressure $p$ are given by, respectively, $$\b u(x,y) = \left(\sin\left(\tfrac{\pi}{2}x\right)\cos\left(\tfrac{\pi}{2}y\right),-\cos\left(\tfrac{\pi}{2}x\right)\sin\left(\tfrac{\pi}{2}y\right)\right),\quad
p(x,y) = \sin\left(\tfrac{\pi}{2} x\right)\sin\left(\tfrac{\pi}{2} y\right)-\tfrac{4}{\pi^2}.$$ The volumetric load $\b f$ and the Dirichlet boundary conditions are inferred from the exact solution. This solution matches the assumptions required in Theorem \[thm:error.estimate\] for $k = 1$, except the case $r = 1.5$ for which ${\b\sigma}(\cdot,{\b{\nabla}_{\mathrm{s}}}\b u) \notin W^{1,{r}'}(\Omega,{{\mathbb{R}}^{d \times d}_{\mathrm{s}}})$. We consider the HHO scheme for $k=1$ on three mesh families, namely Cartesian orthogonal, distorted triangular, and distorted Cartesian; see Figure \[fig:meshes\]. Overall, the results are in agreement with the theoretical predictions, and in some cases the expected asymptotic orders of convergence are exceeded. Specifically, for ${r}\neq 2$, the convergence rates computed on the last refinement surpass in some cases the theoretical ones. As noticed in Remark \[rem:ocv\], this suggests that the asymptotic order is still not attained. A similar phenomenon has been observed on certain meshes for the $p$-Laplace problem; see [@Di-Pietro.Droniou:17*1 Section 3.5.2] and [@Di-Pietro.Droniou.ea:18 Section 3.7].
![Coarsest Cartesian, distorted triangular, and distorted Cartesian mesh used in the numerical tests of Section \[sec:num.res\].\[fig:meshes\]](square.pdf "fig:") ![Coarsest Cartesian, distorted triangular, and distorted Cartesian mesh used in the numerical tests of Section \[sec:num.res\].\[fig:meshes\]](disttri.pdf "fig:") ![Coarsest Cartesian, distorted triangular, and distorted Cartesian mesh used in the numerical tests of Section \[sec:num.res\].\[fig:meshes\]](distsquare.pdf "fig:")
![Numerical results for the test case of Section \[sec:num.res\]. The slopes indicate the expected order of convergence expected from Theorem \[thm:error.estimate\], i.e. $\mathcal O_{\mathrm{vel}}^1 = 2(r-1)$ and $\mathcal O_{\mathrm{pre}}^1 = 2(r-1)^2$ for ${r}\in \{1.5,1.75,2\}$. \[tab:num.res.1\]](conv1.pdf)
![Numerical results for the test case of Section \[sec:num.res\]. The slopes indicate the expected order of convergence expected from Theorem \[thm:error.estimate\], i.e. $\mathcal O_{\mathrm{vel}}^1 = \mathcal O_{\mathrm{pre}}^1 = \frac{2}{r-1}$ for ${r}\in \{2.25,2.5,2.75\}$. \[tab:num.res.2\]](conv2.pdf)
Power-framed functions {#sec:properties.stress}
======================
In the following theorem, we introduce the notion of power-framed function and discuss sufficient conditions for this property to hold.
\[thm:1d.power-framed\] Let $U$ be a measurable subset of ${\mathbb{R}}^n$ with $n\ge1$, $(W,(\cdot,\cdot)_W)$ an inner product space, and $\b \sigma : U \times W \to W$. Assume that there exists a Carathéodory function $\varsigma : U \times \lbrack0,+\infty) \to {\mathbb{R}}$ such that, for all $\b\tau \in W$ and almost every $\b x \in U$,
\[eq:1d.power-framed:stress\] $${\b\sigma}(\b x,\b\tau) = \varsigma(\b x,\|\b\tau\|_W)\b\tau,$$ where $\|{\cdot}\|_W$ is the norm induced by $(\cdot,\cdot)_W$. Additionally assume that, for almost every $\b x \in U$, $\varsigma(\b x,\cdot)$ is differentiable on $(0,+\infty)$ and there exist $\varsigma_{\mathrm{de}} \in \lbrack0,+\infty)$ and $\varsigma_{\mathrm{sm}},\varsigma_{\mathrm{hc}} \in (0,+\infty)$ independent of $\b x$ such that, for all $\alpha \in (0,+\infty)$, $$\begin{aligned}
\varsigma_{\mathrm{sm}} (\varsigma_{\mathrm{de}}^{r}+\alpha^{r})^\frac{{r}-2}{{r}} \leq \frac{\partial(\alpha\varsigma(\b x,\alpha))}{\partial \alpha} \leq \varsigma_{\mathrm{hc}}(\varsigma_{\mathrm{de}}^{r}+\alpha^{r})^\frac{{r}-2}{{r}}. \label{eq:1d.power-framed:eta}
\end{aligned}$$
Then, ${\b\sigma}$ is an *${r}$-power-framed function*, i.e., for all $(\b\tau,\b\eta) \in W^2$ with $\b\tau \neq \b\eta$ and almost every $\b x \in U$, the function ${\b\sigma}$ verifies the Hölder continuity property
\[eq:od:power-framed:holder.continuity.strong.monotonicity\] $$\|{\b\sigma}(\b x,\b\tau)-{\b\sigma}(\b x,\b\eta)\|_W \le \sigma_{\mathrm{hc}} \left(\sigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r}\right)^\frac{{r}-2}{{r}}\| \b\tau-\b\eta \|_W,\label{eq:od:power-framed:holder.continuity}$$ and the strong monotonicity property $$\left({\b\sigma}(\b x,\b\tau)-{\b\sigma}(\b x,\b\eta),\b\tau-\b\eta\right)_W \ge \sigma_{\mathrm{sm}}\left(\sigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r}\right)^\frac{{r}-2}{{r}}\|\b\tau-\b\eta\|_W^{2},\label{eq:od:power-framed:strong.monotonicity}$$
with $\sigma_{\mathrm{de}} \coloneqq \varsigma_{\mathrm{de}}$, $\sigma_{\mathrm{hc}} \coloneqq 2^{2-{r^{\circ}}+{r}^{-1}\left\lceil\hspace{0.02cm}2-{r^{\circ}}\right\rceil}({r^{\circ}}-1)^{-1} \varsigma_{\mathrm{hc}}$, and $\sigma_{\mathrm{sm}} \coloneqq 2^{{r^{\circ}}-{r}-\left\lceil{r}^{-1}({r}-{r^{\circ}})\right\rceil}({r}+1-{r^{\circ}})^{-1} \varsigma_{\mathrm{sm}}$, where ${r^{\circ}}$ is given by and $\lceil{\cdot}\rceil$ is the ceiling function.
The boldface notation for the elements of $W$ is reminescent of the fact that Theorem \[thm:1d.power-framed\] is used with $W = {{\mathbb{R}}^{d \times d}_{\mathrm{s}}}$ in Corollary \[cor:Carreau–Yasuda\] to characterize the Carreau-Yasuda law as an ${r}$-power-framed function and in Lemma \[lem:sT\] with $W = {\mathbb{R}}^d$ to study the local stabilization function ${\mathrm{s}}_T$.
Let $\b x \in U$ be such that holds, and $\b\tau,\b\eta \in W$. By symmetry of inequalities and the fact that ${\b\sigma}$ is continuous, we can assume, without loss of generality, that $\|\b\tau\|_W > \|\b\eta\|_W > 0$.\
(i) *Strong monotonicity.* Let $\beta \in (0,+\infty)$ and let $g : \lbrack\beta,+\infty) \to {\mathbb{R}}$ be such that, for all $\alpha \in \lbrack\beta,+\infty)$, $$g(\alpha) \coloneqq \alpha\varsigma(\b x,\alpha)-\beta\varsigma(\b x,\beta)-C_{\mathrm{sm}}(\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r})^\frac{{r}-2}{{r}}(\alpha-\beta),
\;\text{ with }\ C_{\mathrm{sm}} \coloneqq \tfrac{2^{{r^{\circ}}-{r}}}{{r}+1-{r^{\circ}}}\varsigma_{\mathrm{sm}}.$$ Differentiating $g$ and using the first inequality in , we obtain, for all $\alpha \in \lbrack\beta,+\infty)$, $$\begin{aligned}
\frac{\partial}{\partial \alpha}g(\alpha)
&\geq \varsigma_{\mathrm{sm}}(\varsigma_{\mathrm{de}}^{r}+\alpha^{r})^\frac{{r}-2}{{r}}-C_{\mathrm{sm}}\left(({r}-2)(\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r})^{-\frac{2}{{r}}}(\alpha-\beta)\alpha^{{r}-1}+(\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r})^\frac{{r}-2}{{r}}\right) \\
&\geq \varsigma_{\mathrm{sm}}(\varsigma_{\mathrm{de}}^{r}+\alpha^{r})^\frac{{r}-2}{{r}}-({r}+1-{r^{\circ}})C_{\mathrm{sm}} (\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r})^\frac{{r}-2}{{r}} \\
&\geq \varsigma_{\mathrm{sm}}2^{{r^{\circ}}-{r}}(\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r})^\frac{{r}-2}{{r}}-({r}+1-{r^{\circ}})C_{\mathrm{sm}} (\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r})^\frac{{r}-2}{{r}} = 0,
\end{aligned}$$ where, to pass to the second line, we have removed negative contributions if ${r}< 2$ and used the fact that $(\alpha-\beta)\alpha^{{r}-1} \le \varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r}$ if ${r}\ge 2$, to pass to the third line we have used the fact that $t \mapsto t^{{r}-2}$ is non-increasing if ${r}< 2$, and the fact that $\beta \le \alpha$ otherwise, while the conclusion follows from the definition of $C_{\mathrm{sm}}$. This shows that $g$ is non-decreasing. Hence, for all $\alpha\in\lbrack\beta,+\infty)$, $g(\alpha)\geq g(\beta)=0$, i.e. $$\label{eq:1d.power-framed:bound:1}
\alpha\varsigma(\b x,\alpha)-\beta\varsigma(\b x,\beta) \geq C_{\mathrm{sm}}(\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r})^\frac{{r}-2}{{r}}(\alpha-\beta).$$ Moreover, for all $\alpha,\beta \in (0,+\infty)$, using (with $\beta = 0$) along with the fact that $t \mapsto t^{{r}-2}$ is decreasing if ${r}< 2$ and inequality if ${r}\ge 2$, we infer that $$\label{eq:1d.power-framed:bound:2}
\begin{aligned}
\varsigma(\b x,\alpha)+\varsigma(\b x,\beta) &\ge C_{\mathrm{sm}}\left((\varsigma_{\mathrm{de}}^{r}+\alpha^{r})^\frac{{r}-2}{{r}}+(\varsigma_{\mathrm{de}}^{r}+\beta^{r})^\frac{{r}-2}{{r}}\right) \ge C_{\mathrm{sm}}2^{1-\left\lceil\frac{{r}-{r^{\circ}}}{{r}}\right\rceil}(\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r})^\frac{{r}-2}{{r}}.
\end{aligned}$$ We conclude that ${\b\sigma}$ verifies by using and with $\alpha = \|\b\tau\|_W$ and $\beta = \|\b\eta\|_W$ as follows: $$\begin{aligned}
&({\b\sigma}(\b x,\b\tau)-{\b\sigma}(\b x,\b\eta),\b\tau-\b\eta)_W
\\
&\quad= (\b\tau\varsigma(\b x,\|\b\tau\|_W)-\b\eta\varsigma(\b x,\|\b\eta\|_W),\b\tau-\b\eta)_W \\
&\quad = \|\b\tau\|_W^2\varsigma(\b x,\|\b\tau\|_W)+\|\b\eta\|_W^2\varsigma(\b x,\|\b\eta\|_W)
-(\b\tau,\b\eta)_W \left[\varsigma(\b x,\|\b\tau\|_W) + \varsigma(\b x,\|\b\eta\|_W)\right] \\
&\quad = \left[
\|\b\tau\|_W\varsigma(\b x,\|\b\tau\|_W)-\|\b\eta\|_W\varsigma(\b x,\|\b\eta\|_W)
\right](\|\b\tau\|_W-\|\b\eta\|_W)
\\
&\qquad
+ \left[
\varsigma(\b x,\|\b\tau\|_W)+\varsigma(\b x,\|\b\eta\|_W)
\right](\|\b\tau\|_W\|\b\eta\|_W-(\b\tau,\b\eta)_W)
\\
&\quad\geq C_{\mathrm{sm}}2^{-\left\lceil\frac{{r}-{r^{\circ}}}{{r}}\right\rceil}\left(
\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r}\right)^\frac{{r}-2}{{r}}\left[
(\|\b\tau\|_W-\|\b\eta\|_W)^2+2(\|\b\tau\|_W\|\b\eta\|_W-(\b\tau,\b\eta)_W)
\right] \\
&\quad= C_{\mathrm{sm}}2^{-\left\lceil\frac{{r}-{r^{\circ}}}{{r}}\right\rceil}\left(
\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r}\right)^\frac{{r}-2}{{r}}\|\b\tau-\b\eta\|_W^2.
\end{aligned}$$\
(ii) *Hölder continuity.* Now, setting $C_{\mathrm{hc}} \coloneqq \frac{\varsigma_{\mathrm{hc}}}{{r^{\circ}}-1}$ and reasoning in a similar way as for the proof of to leverage the second inequality in , we have, for all $\alpha \in \lbrack\beta,+\infty)$, $$\label{eq:1d.power-framed:bound:3}
\alpha\varsigma(\b x,\alpha)-\beta\varsigma(\b x,\beta) \le C_{\mathrm{hc}}\left(
\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r}\right)^\frac{{r}-2}{{r}}(\alpha-\beta).$$ First, let ${r}\ge 2$. Using (with $\beta=0$) and the fact that $t \mapsto t^{{r}-2}$ is non-decreasing, we have, for all $\alpha,\beta \in (0,+\infty)$, $$\label{eq:1d.power-framed:bound:4}
\varsigma(\b x,\alpha)\varsigma(\b x,\beta)
\le C_{\mathrm{hc}}^2\left(
\varsigma_{\mathrm{de}}^{r}+\alpha^{r}\right)^\frac{{r}-2}{{r}}\left(
\varsigma_{\mathrm{de}}^{r}+\beta^{r}\right)^\frac{{r}-2}{{r}} \le \left[
C_{\mathrm{hc}}\left(\varsigma_{\mathrm{de}}^{r}+\alpha^{r}+\beta^{r}\right)^\frac{{r}-2}{{r}}
\right]^2.$$ Thus, using inequalities and with $\alpha = \|\b\tau\|_W$ and $\beta = \|\b\eta\|_W$, we infer $$\label{eq:1d.power-framed:bound:5}
\begin{aligned}
&\|{\b\sigma}(\b x,\b\tau)-{\b\sigma}(\b x,\b\eta)\|_W^2
\\
&\quad = \left(
\b\tau\varsigma(\b x,\|\b\tau\|_W)-\b\eta\varsigma(\b x,\|\b\eta\|_W),
\b\tau\varsigma(\b x,\|\b\tau\|_W)-\b\eta\varsigma(\b x,\|\b\eta\|_W)
\right)_W
\\
&\quad = \left[\|\b\tau\|_W\varsigma(\b x,\|\b\tau\|_W)-\|\b\eta\|_W\varsigma(\b x,\|\b\eta\|_W)\right]^2
\\
&\quad \qquad + 2\varsigma(\b x,\|\b\tau\|_W)\varsigma(\b x,\|\b\eta\|_W)\left[
\|\b\tau\|_W\|\b\eta\|_W-(\b\tau,\b\eta)_W
\right]
\\
&\quad \le \left[
C_{\mathrm{hc}}\left(\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r}\right)^\frac{{r}-2}{{r}}
\right]^2\left[
(\|\b\tau\|_W-\|\b\eta\|_W)^2+2(\|\b\tau\|_W\|\b\eta\|_W-(\b\tau,\b\eta)_W)
\right] \\
&\quad = \left[
C_{\mathrm{hc}}\left(\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r}\right)^\frac{{r}-2}{{r}}\|\b\tau-\b\eta\|_W
\right]^2,
\end{aligned}$$ hence ${\b\sigma}$ verifies for ${r}\ge 2$. Assume now ${r}< 2$. Using a triangle inequality followed by and the left inequality in , it is inferred that $$\begin{aligned}
\|{\b\sigma}(\b x,\b\tau)-{\b\sigma}(\b x,\b\eta)\|_W
&\leq \varsigma(\b x,\|\b\tau\|_W)\|\b\tau\|_W+\varsigma(\b x,\|\b\eta\|_W)\|\b\eta\|_W
\\
& \leq C_{\mathrm{hc}}\left((\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r})^\frac{{r}-1}{{r}}+(\varsigma_{\mathrm{de}}^{r}+\|\b\eta\|_W^{r})^\frac{{r}-1}{{r}}\right)
\\
&\leq 2^\frac{1}{{r}}C_{\mathrm{hc}}(2\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r})^\frac{{r}-1}{{r}}
\\
& = 2^\frac{1}{{r}} C_{\mathrm{hc}}(2\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r})^\frac{{r}-2}{{r}}
(2\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r})^\frac1{r},
\\
& \leq 2^\frac{1}{{r}} C_{\mathrm{hc}}(\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r})^\frac{{r}-2}{{r}}
(2\varsigma_{\mathrm{de}}+\|\b\tau\|_W+\|\b\eta\|_W),
\end{aligned}$$ where the last line follows from the fact that $t \mapsto t^{{r}-2}$ is decreasing and again . If $2\varsigma_{\mathrm{de}}+\|\b\tau\|_W+\|\b\eta\|_W\le 2^{2-r}\|\b\tau-\b\eta\|_W$, from the previous bound we directly get the conclusion, i.e. with $\sigma_{\mathrm{hc}}=2^{2-r+\frac{1}{r}}C_{\mathrm{hc}}$. Otherwise, using and a triangle inequality yields $$\label{eq:est_else}
\begin{aligned}
(\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r})^\frac{1}{{r}}(\varsigma_{\mathrm{de}}^{r}+\|\b\eta\|_W^{r})^\frac{1}{{r}}
&\ge 2^{-\frac{2}{r'}}(\varsigma_{\mathrm{de}}+\|\b\tau\|_W)(\varsigma_{\mathrm{de}}+\|\b\eta\|_W) \\
&= 2^{-2(\frac{1}{r'}+1)}\left[
\left(2\varsigma_{\mathrm{de}}+\|\b\tau\|_W+\|\b\eta\|_W\right)^2-\left(\|\b\tau\|_W-\|\b\eta\|_W\right)^2
\right]
\\
&\ge 2^{-2(\frac{1}{r'}+1)}\left[
\left(2\varsigma_{\mathrm{de}}+\|\b\tau\|_W+\|\b\eta\|_W\right)^2-\|\b\tau-\b\eta\|_W^2
\right]
\\
&\ge 2^{-2(\frac{1}{r'}+1)}(1-4^{r-2})\left(2\varsigma_{\mathrm{de}}+\|\b\tau\|_W+\|\b\eta\|_W\right)^2\\
&\ge 2^{\frac{2}{(r-2)r}-2}\left(\varsigma_{\mathrm{de}}^{r}+\|\b\tau\|_W^{r}+\|\b\eta\|_W^{r}\right)^\frac{2}{{r}},
\end{aligned}$$ where we concluded with together with the fact that $2^{-2(\frac{1}{r'}+1)}\left(1-4^{r-2}\right) \ge 2^{\frac{2}{(r-2)r}-2}$. Finally, raising both sides of to the power ${r}-2$, we get a relation analogous to . Hence, proceeding as in , we infer .
\[cor:Carreau–Yasuda\] The strain rate-shear stress law of the $(\mu,\delta,a,{r})$-Carreau–Yasuda fluid defined in Example \[ex:Carreau–Yasuda\] is an ${r}$-power-framed function.
Let $\b x \in \Omega$ and $g : (0,+\infty) \to {\mathbb{R}}$ be such that, for all $\alpha\in(0,+\infty)$, $$g(\alpha)
\coloneqq \frac{\partial}{\partial \alpha}\left[
\alpha\mu(\b x)\left(\delta^{a(\b x)}+\alpha^{a(\b x)}
\right)^\frac{{r}-2}{a(\b x)}
\right]
= \mu(\b x)\left(
\delta^{a(\b x)}+\alpha^{a(\b x)}
\right)^{\frac{{r}-2}{a(\b x)}-1}\left(
\delta^{a(\b x)}+({r}-1)\alpha^{a(\b x)}
\right).$$ We have for all $\alpha \in (0,+\infty)$, $$\mu_- ({r^{\circ}}-1) \left(
\delta^{a(\b x)}+\alpha^{a(\b x)}
\right)^{\frac{{r}-2}{a(\b x)}} \le g(\alpha)
\leq \mu_+ ({r}+1-{r^{\circ}})\left(
\delta^{a(\b x)}+\alpha^{a(\b x)}
\right)^{\frac{{r}-2}{a(\b x)}},$$ and we conclude using together with Theorem \[thm:1d.power-framed\].
[^1]: [<michele.botti@polimi.it>]{}
[^2]: [<danielcq.mathematics@gmail.com>]{}
[^3]: [<daniele.di-pietro@umontpellier.fr>]{}
[^4]: [<andre.harnist@umontpellier.fr>]{}, corresponding author
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"pile_set_name": "ArXiv"
}
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Meta
fruit
#Patience
Patience isn’t something most of us are born with. It surely doesn’t come automatically the moment we take a breath-it’s developed. It’s a process. It takes time.
Children are not automatically patient. As mom looking back, I can’t even count the number of times I told my children “just be patient” or “in a minute!” When you stop to analyze that statement it’s actually quite funny. A little child? Be patient? Most adults struggle with being patient, yet we expect our children to ‘be patient.’
Most people, including children, truly don’t understand what this word means. “Patience.” Yet we expect it from everybody. But are WE being patient?
Children learn patience when it’s demonstrated. They live what they see demonstrated. It is learned over time but so are other characteristics.
I know as a mom, there were times when I demonstrated patience with my children, yes; but there were MUCH more times when I didn’t. I wish I could change that now. I can’t. I was still ‘fruit’ in the process of being developed at the time I was raising my children…
Webster defines it this way:
Patience:
“the capacity to accept or tolerate delay, trouble, or suffering without getting angry or upset. The ability to wait, or to continue doing something despite difficulties, or to suffer without complaining or becoming annoyed.”
The word “patience” historically comes from the Latin, patientia, meaning suffering, which also gives us the word patient, referring to someone who is suffering from being sick or injured.
“Patience” is one of the fruits of the spirit. (Galatians 5:22) Fruit takes time to ripen. So does patience.
The Strong Concordance for the original Greek word translated to our English language for patience is:
#8318 pa’-shens (hupomone, makrothumia):
“Patience” implies suffering, enduring or waiting, as a determination of the will and not simply under necessity. As such it is an essential Christian virtue to the exercise of which there are many exhortations.
We need to “wait patiently” for God, to endure uncomplainingly the various forms of sufferings, wrongs and evils that we meet with, and to bear patiently injustices which we cannot remedy and provocations we cannot remove.
PATIENCE: The quality of forbearance and self-control which shows itself particularly in a willingness to wait upon God and his will. Believers are called upon to be patient in their expectations of God’s actions, and in their relationships with one another.
Patience is often hard to gain and to hard to maintain, but, in Romans 15:5, God is called “the God of patience” as being able to grant that grace to those who look to Him and depend on Him for it.
It is in reliance on God and acceptance of His will, with trust in His goodness, wisdom and faithfulness, that we are enabled to be patient, endure, and to hope stedfastly.
“Patience” is a form of #Love
In 1 Corinthians 13:4, “LOVE is patient.”
Ahhhhhh.
This is key.
“God is love.” (1 John 4:8)
We are to walk in love. (Ephesians 5:2)
When we are patient with one another,
we are demonstrating Gods love. When we are patient with ourselves, we are receiving Gods love.
While we strive to be patient all the time, to be loving all the time, we fail.
Progress takes time. We’re all human.
Praise God that HE never fails! He is ALWAYS patient with us, ALWAYS loving towards us.
Join me today to commit to exercise our patience with one another.
#FaithActs!
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{
"pile_set_name": "Pile-CC"
}
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Suprema Corte dos EUA autoriza que veto de Trump a militares transgêneros entre em vigor
Juízes não analisaram o mérito do caso. Medida tinha sido a bloqueada pela Justiça, que a considerou discriminatória.
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{
"pile_set_name": "OpenWebText2"
}
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Stress in dentistry.
Dentists believe their profession is stressful. Research has indicated this belief is generally based upon patient behaviors and economic pressures. A discussion of stress and adaptation is presented. Since stress can lead to both physical and emotional problems, recognition of stress by the practitioner is discussed. While physical symptoms are easily recognized, emotional behaviors are often overlooked. The practitioner should become aware of these behaviors in the self as well as others. Methods to help reduce and control stress are given.
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{
"pile_set_name": "PubMed Abstracts"
}
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Q:
Summation over a sympy Array
I want to sum over a sympy Array (called arr) using the two indices i and j. Summing over arr[i] results in an integer as In [4] below shows. However, summing over arr[j] does not give a number as result (see In [5] below). Why is that?
In [1]: from sympy import *
In [2]: i, j = symbols("i j", integer=True)
In [3]: arr = Array([1, 2])
In [4]: summation(
...: arr[i],
...: (j, 0, i), (i, 0, len(arr)-1)
...: )
Out[4]: 5
In [5]: summation(
...: arr[j],
...: (j, 0, i), (i, 0, len(arr)-1)
...: )
Out[5]: Sum([1, 2][j], (j, 0, i), (i, 0, 1))
A:
SymPy will evaluate summation if either
Both the summand and the limits for summation are explicit; or
It can find a symbolic expression for the sum, based on the formula for the summand.
Nested summation is performed from left to right. In the first version,
summation(arr[i], (j, 0, i))
falls under item 2: since the summand does not depend on the index j, the sum evaluates to symbolically to (i + 1)*arr[i]. Then the outer sum becomes
summation((i + 1)*arr[i], (i, 0, len(arr)-1))
and this falls under item 1: both the summand and the limits are explicit.
But in the second version,
summation(arr[j], (j, 0, i))
fits neither 1 nor 2. The summand depends on j, we don't have any formula for it (it's just some numbers [1, 2]), and the upper limit of summation is symbolic. There is nothing for SymPy to do with such a sum, so it remains undone. Subsequently, the outer sum is not going anywhere since the inner was not done.
Workaround
In the second case, replacing the outer sum with Python sum makes the inner one explicit, so it gets evaluated.
>>> sum([summation(arr[j], (j, 0, i)) for i in range(len(arr))])
4
Of course, this does not really use symbolic capabilities of SymPy: the inner sum could be Python's sum as well.
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"Content-Transfer-Encoding: 8bit\n"
"Language: be\n"
"Plural-Forms: nplurals=4; plural=(n%10==1 && n%100!=11 ? 0 : n%10>=2 && n%10<=4 && (n%100<12 || n%100>14) ? 1 : n%10==0 || (n%10>=5 && n%10<=9) || (n%100>=11 && n%100<=14)? 2 : 3);\n"
"X-Generator: grunt-wp-i18n 0.4.9\n"
"X-Poedit-Basepath: ../\n"
"X-Poedit-Bookmarks: \n"
"X-Poedit-Country: United States\n"
"X-Poedit-KeywordsList: __;_e;_x:1,2c;_ex:1,2c;_n:1,2;_nx:1,2,4c;_n_noop:1,2;_nx_noop:1,2,3c;esc_attr__;esc_html__;esc_attr_e;esc_html_e;esc_attr_x:1,2c;esc_html_x:1,2c;\n"
"X-Poedit-SearchPath-0: .\n"
"X-Poedit-SourceCharset: UTF-8\n"
"X-Textdomain-Support: yes\n"
#: example-functions.php:117 tests/test-cmb-field.php:255
msgid "Test Metabox"
msgstr ""
#: example-functions.php:130 example-functions.php:436
msgid "Test Text"
msgstr ""
#: example-functions.php:131 example-functions.php:144
#: example-functions.php:157 example-functions.php:165
#: example-functions.php:173 example-functions.php:182
#: example-functions.php:190 example-functions.php:205
#: example-functions.php:213 example-functions.php:221
#: example-functions.php:238 example-functions.php:247
#: example-functions.php:260 example-functions.php:267
#: example-functions.php:274 example-functions.php:288
#: example-functions.php:301 example-functions.php:314
#: example-functions.php:326 example-functions.php:335
#: example-functions.php:343 example-functions.php:352
#: example-functions.php:359 example-functions.php:373
#: example-functions.php:437 example-functions.php:528
#: example-functions.php:536 example-functions.php:543
#: example-functions.php:550 example-functions.php:557
#: example-functions.php:564 example-functions.php:571
#: example-functions.php:598 example-functions.php:606
#: example-functions.php:613 example-functions.php:650
#: tests/test-cmb-field.php:267
msgid "field description (optional)"
msgstr ""
#: example-functions.php:143
msgid "Test Text Small"
msgstr ""
#: example-functions.php:156
msgid "Test Text Medium"
msgstr ""
#: example-functions.php:164
msgid "Custom Rendered Field"
msgstr ""
#: example-functions.php:172
msgid "Website URL"
msgstr ""
#: example-functions.php:181
msgid "Test Text Email"
msgstr ""
#: example-functions.php:189
msgid "Test Time"
msgstr ""
#: example-functions.php:197 example-functions.php:198
msgid "Time zone"
msgstr ""
#: example-functions.php:204
msgid "Test Date Picker"
msgstr ""
#: example-functions.php:212
msgid "Test Date Picker (UNIX timestamp)"
msgstr ""
#: example-functions.php:220
msgid "Test Date/Time Picker Combo (UNIX timestamp)"
msgstr ""
#: example-functions.php:237
msgid "Test Money"
msgstr ""
#: example-functions.php:246
msgid "Test Color Picker"
msgstr ""
#: example-functions.php:259
msgid "Test Text Area"
msgstr ""
#: example-functions.php:266
msgid "Test Text Area Small"
msgstr ""
#: example-functions.php:273
msgid "Test Text Area for Code"
msgstr ""
#: example-functions.php:280
msgid "Test Title Weeeee"
msgstr ""
#: example-functions.php:281
msgid "This is a title description"
msgstr ""
#: example-functions.php:287
msgid "Test Select"
msgstr ""
#: example-functions.php:293 example-functions.php:306
#: example-functions.php:318
msgid "Option One"
msgstr ""
#: example-functions.php:294 example-functions.php:307
#: example-functions.php:319
msgid "Option Two"
msgstr ""
#: example-functions.php:295 example-functions.php:308
#: example-functions.php:320
msgid "Option Three"
msgstr ""
#: example-functions.php:300
msgid "Test Radio inline"
msgstr ""
#: example-functions.php:313
msgid "Test Radio"
msgstr ""
#: example-functions.php:325
msgid "Test Taxonomy Radio"
msgstr ""
#: example-functions.php:334
msgid "Test Taxonomy Select"
msgstr ""
#: example-functions.php:342
msgid "Test Taxonomy Multi Checkbox"
msgstr ""
#: example-functions.php:351
msgid "Test Checkbox"
msgstr ""
#: example-functions.php:358 tests/test-cmb-field.php:266
msgid "Test Multi Checkbox"
msgstr ""
#: example-functions.php:364 tests/test-cmb-field.php:272
msgid "Check One"
msgstr ""
#: example-functions.php:365 tests/test-cmb-field.php:273
msgid "Check Two"
msgstr ""
#: example-functions.php:366 tests/test-cmb-field.php:274
msgid "Check Three"
msgstr ""
#: example-functions.php:372
msgid "Test wysiwyg"
msgstr ""
#: example-functions.php:380
msgid "Test Image"
msgstr ""
#: example-functions.php:381
msgid "Upload an image or enter a URL."
msgstr ""
#: example-functions.php:387
msgid "Multiple Files"
msgstr ""
#: example-functions.php:388
msgid "Upload or add multiple images/attachments."
msgstr ""
#: example-functions.php:395
msgid "oEmbed"
msgstr ""
#: example-functions.php:396
msgid ""
"Enter a youtube, twitter, or instagram URL. Supports services listed at <a "
"href=\"http://codex.wordpress.org/Embeds\">http://codex.wordpress.org/Embeds</a>."
msgstr ""
#: example-functions.php:427
msgid "About Page Metabox"
msgstr ""
#: example-functions.php:456
msgid "Repeating Field Group"
msgstr ""
#: example-functions.php:464
msgid "Generates reusable form entries"
msgstr ""
#: example-functions.php:466
msgid "Entry {#}"
msgstr ""
#: example-functions.php:467
msgid "Add Another Entry"
msgstr ""
#: example-functions.php:468
msgid "Remove Entry"
msgstr ""
#: example-functions.php:481
msgid "Entry Title"
msgstr ""
#: example-functions.php:488
msgid "Description"
msgstr "Апісанне"
#: example-functions.php:489
msgid "Write a short description for this entry"
msgstr ""
#: example-functions.php:495
msgid "Entry Image"
msgstr ""
#: example-functions.php:501
msgid "Image Caption"
msgstr ""
#: example-functions.php:520
msgid "User Profile Metabox"
msgstr ""
#: example-functions.php:527 example-functions.php:597
msgid "Extra Info"
msgstr ""
#: example-functions.php:535
msgid "Avatar"
msgstr ""
#: example-functions.php:542
msgid "Facebook URL"
msgstr ""
#: example-functions.php:549
msgid "Twitter URL"
msgstr ""
#: example-functions.php:556
msgid "Google+ URL"
msgstr ""
#: example-functions.php:563
msgid "Linkedin URL"
msgstr ""
#: example-functions.php:570
msgid "User Field"
msgstr ""
#: example-functions.php:590
msgid "Category Metabox"
msgstr ""
#: example-functions.php:605
msgid "Term Image"
msgstr ""
#: example-functions.php:612
msgid "Arbitrary Term Field"
msgstr ""
#: example-functions.php:634
msgid "Theme Options Metabox"
msgstr ""
#: example-functions.php:649
msgid "Site Background Color"
msgstr ""
#: includes/CMB2.php:129
msgid "Metabox configuration is required to have an ID parameter"
msgstr ""
#: includes/CMB2.php:418
msgid "Click to toggle"
msgstr ""
#: includes/CMB2_Ajax.php:71
msgid "Please Try Again"
msgstr ""
#: includes/CMB2_Ajax.php:173 tests/cmb-tests-base.php:59
msgid "Remove Embed"
msgstr ""
#: includes/CMB2_Ajax.php:177 tests/cmb-tests-base.php:64
msgid "No oEmbed Results Found for %s. View more info at"
msgstr ""
#: includes/CMB2_Field.php:1186
msgid "Add Group"
msgstr ""
#: includes/CMB2_Field.php:1187
msgid "Remove Group"
msgstr ""
#: includes/CMB2_Field.php:1209 includes/CMB2_Field.php:1213
#: tests/test-cmb-field.php:229
msgid "None"
msgstr "Няма"
#: includes/CMB2_Field.php:1269
msgid "Sorry, this field does not have a cmb_id specified."
msgstr ""
#: includes/CMB2_Field_Display.php:408 includes/CMB2_JS.php:139
#: includes/types/CMB2_Type_File_Base.php:75 tests/test-cmb-types-base.php:143
#: tests/test-cmb-types.php:701
msgid "File:"
msgstr ""
#: includes/CMB2_JS.php:86 includes/CMB2_JS.php:119
msgid "Clear"
msgstr "Ачысціць"
#: includes/CMB2_JS.php:87
msgid "Default"
msgstr "Па змаўчанні"
#: includes/CMB2_JS.php:88
msgid "Select Color"
msgstr "Абраць колер"
#: includes/CMB2_JS.php:89
msgid "Current Color"
msgstr "Бягучы колер"
#: includes/CMB2_JS.php:110
msgid "Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday"
msgstr ""
#: includes/CMB2_JS.php:111
msgid "Su, Mo, Tu, We, Th, Fr, Sa"
msgstr ""
#: includes/CMB2_JS.php:112
msgid "Sun, Mon, Tue, Wed, Thu, Fri, Sat"
msgstr ""
#: includes/CMB2_JS.php:113
msgid ""
"January, February, March, April, May, June, July, August, September, "
"October, November, December"
msgstr ""
#: includes/CMB2_JS.php:114
msgid "Jan, Feb, Mar, Apr, May, Jun, Jul, Aug, Sep, Oct, Nov, Dec"
msgstr ""
#: includes/CMB2_JS.php:115
msgid "Next"
msgstr "Наступнае"
#: includes/CMB2_JS.php:116
msgid "Prev"
msgstr "Папярэдняе"
#: includes/CMB2_JS.php:117
msgid "Today"
msgstr ""
#: includes/CMB2_JS.php:118 includes/CMB2_JS.php:128
msgid "Done"
msgstr "Гатова"
#: includes/CMB2_JS.php:122
msgid "Choose Time"
msgstr ""
#: includes/CMB2_JS.php:123
msgid "Time"
msgstr ""
#: includes/CMB2_JS.php:124
msgid "Hour"
msgstr ""
#: includes/CMB2_JS.php:125
msgid "Minute"
msgstr ""
#: includes/CMB2_JS.php:126
msgid "Second"
msgstr ""
#: includes/CMB2_JS.php:127
msgid "Now"
msgstr ""
#: includes/CMB2_JS.php:135
msgid "Use this file"
msgstr ""
#: includes/CMB2_JS.php:136
msgid "Use these files"
msgstr ""
#: includes/CMB2_JS.php:137 includes/types/CMB2_Type_File_Base.php:61
msgid "Remove Image"
msgstr ""
#: includes/CMB2_JS.php:138 includes/CMB2_Types.php:257
#: includes/types/CMB2_Type_File_Base.php:80 tests/test-cmb-types-base.php:143
#: tests/test-cmb-types.php:47 tests/test-cmb-types.php:55
#: tests/test-cmb-types.php:701
msgid "Remove"
msgstr "Выдаліць"
#: includes/CMB2_JS.php:140 includes/types/CMB2_Type_File_Base.php:78
#: tests/test-cmb-types-base.php:143 tests/test-cmb-types.php:701
msgid "Download"
msgstr ""
#: includes/CMB2_JS.php:141
msgid "Select / Deselect All"
msgstr ""
#: includes/CMB2_Types.php:194
msgid "Add Row"
msgstr ""
#: includes/CMB2_hookup.php:145
msgid ""
"Term Metadata is a WordPress > 4.4 feature. Please upgrade your WordPress "
"install."
msgstr ""
#: includes/CMB2_hookup.php:149
msgid "Term metaboxes configuration requires a 'taxonomies' parameter"
msgstr ""
#: includes/helper-functions.php:93
msgid "No oEmbed Results Found for %s. View more info at %s"
msgstr ""
#: includes/helper-functions.php:279
msgid "Save"
msgstr "Захаваць"
#: includes/types/CMB2_Type_File.php:36 tests/test-cmb-types.php:683
#: tests/test-cmb-types.php:701
msgid "Add or Upload File"
msgstr ""
#: includes/types/CMB2_Type_File_List.php:36 tests/test-cmb-types.php:639
#: tests/test-cmb-types.php:663
msgid "Add or Upload Files"
msgstr ""
#: includes/types/CMB2_Type_Taxonomy_Multicheck.php:27
#: includes/types/CMB2_Type_Taxonomy_Radio.php:25
msgid "No terms"
msgstr ""
#. Plugin Name of the plugin/theme
msgid "CMB2"
msgstr ""
#. Plugin URI of the plugin/theme
msgid "https://github.com/CMB2/CMB2"
msgstr ""
#. Description of the plugin/theme
msgid ""
"CMB2 will create metaboxes and forms with custom fields that will blow your "
"mind."
msgstr ""
#. Author of the plugin/theme
msgid "WebDevStudios"
msgstr ""
#. Author URI of the plugin/theme
msgid "http://webdevstudios.com"
msgstr ""
#: includes/CMB2_JS.php:109
msgctxt "Valid formatDate string for jquery-ui datepicker"
msgid "mm/dd/yy"
msgstr ""
#: includes/CMB2_JS.php:129
msgctxt ""
"Valid formatting string, as per "
"http://trentrichardson.com/examples/timepicker/"
msgid "hh:mm TT"
msgstr ""
|
{
"pile_set_name": "Github"
}
|
Poland has hit back after the European Parliament voted in support of launching sanctions against it.
The 438 to 152 resolution in favour of initiating Article 7 proceedings against the Central European country — which could see its EU voting rights suspended, among other penalties — was preceded by a fierce debate, the Associated Press reports.
Guy Verhofstadt, a former Prime Minister of Belgium, a European Parliament group leader, and a Brexit negotiations representative — logged as a “reliable ally” by the Open Society organisation run by billionaire open borders campaigner George Soros — accused the Polish government of having “lost its senses”.
Verhofstadt later took to social media to disparage the Slavic country at greater length, saying it had “degraded itself” to the level of Hungary, another conservative EU member-state which is frequently subject to the Belgian’s vituperative attacks.
Poland could still be a leader in Europe, but has degraded itself to the gang of Orbàn and its illiberal societies. Kaczynski has copied Orbàn by politicizing the constitutional court, curtailing the civil society, muzzling the free media #EPlenary — Guy Verhofstadt (@guyverhofstadt) November 15, 2017
In theory, the European establishment’s major issue with Poland is its attempts to increase the accountability of the judiciary, which they claim undermine the rule of law.
The Poles insist they are only trying to strengthen the system of checks and balances, as, at present, a judicial bench which harbours holdovers from the Communist era and answers only to itself can block the executive and the legislature, but cannot be checked by the executive or the legislature itself.
There is a lot of #fakenews concerning the reform of the judiciary in Poland. Help us to fight lies and disinformation. ➡️Retweet please! pic.twitter.com/xkeINAag7u — Prawo i Sprawiedliwość (@pisorgpl) July 22, 2017
How Poland chooses to organise its judiciary internally is thought by many to be a mere pretext for EU intervention, however, with the Central European country being unpopular for its friendly relationship with U.S. President Donald Trump’s administration and its status as a key bastion of opposition to efforts to redistribute illegal immigrants throughout the EU by a system of compulsory migrant quotas.
Indeed, Ryszard Legutko, who heads Poland’s ruling Law and Justice Party (PiS) delegation of MEPs, has accused EU elites — and in particular Germany’s Manfred Weber, who heads the dominant European People’s Party (EPP) bloc in the European Parliament — of harbouring a “colonial” attitude towards the EU’s eastern member-states.
With respect to Weber’s early and enthusiastic denunciation of Poland’s judicial reforms, Legutko pointed out that “Mr. Weber does not know the Polish language, did not know the contents of these laws, did not know any expert opinions, [and] is not interested in the subject at all” — but still felt able to weigh immediately after their publication.
The EU Parliament's Brexit negotiations rep just branded Trump white supremacist and Poland and Hungary “alt-right” https://t.co/L2ITTWKsWj — Jack Montgomery ن (@JackBMontgomery) September 13, 2017
“This is not a dialogue, it is not an invitation to talk, it is an ultimatum,” said Legutko, highlighting the EU’s apparent hypocrisy in turning a blind eye to the excesses of the Spanish government in Catalonia while launching an “anti-Polish crusade” against his country.
“This is what Shakespeare called ‘the insolence of office’ — the insolence of bureaucracy; the impudence of power.
“You think you can say anything. You think you can do anything.
“Your actions will not harm Poland, we have dealt with bigger problems — they will harm the European Union,” he warned.
“All the anti-EU diatribes made in this parliament have done less harm to the image of the Union than you have.
“To destroy the image of the EU, you have done more than Nigel Farage and Marine Le Pen together.”
Follow Jack Montgomery on Twitter: @JackBMontgomery
|
{
"pile_set_name": "OpenWebText2"
}
|
/*
* DO NOT ALTER OR REMOVE COPYRIGHT NOTICES OR THIS HEADER.
*
* Copyright (c) 2009 Sun Microsystems Inc. All Rights Reserved
*
* The contents of this file are subject to the terms
* of the Common Development and Distribution License
* (the License). You may not use this file except in
* compliance with the License.
*
* You can obtain a copy of the License at
* https://opensso.dev.java.net/public/CDDLv1.0.html or
* opensso/legal/CDDLv1.0.txt
* See the License for the specific language governing
* permission and limitations under the License.
*
* When distributing Covered Code, include this CDDL
* Header Notice in each file and include the License file
* at opensso/legal/CDDLv1.0.txt.
* If applicable, add the following below the CDDL Header,
* with the fields enclosed by brackets [] replaced by
* your own identifying information:
* "Portions Copyrighted [year] [name of copyright owner]"
*
* $Id: SsoServerTopologyImpl.java,v 1.2 2009/10/21 00:03:15 bigfatrat Exp $
*
* Portions Copyrighted 2011-2015 ForgeRock AS.
*/
package com.sun.identity.monitoring;
import com.sun.identity.shared.debug.Debug;
import com.sun.management.snmp.agent.SnmpMib;
import javax.management.MBeanServer;
import javax.management.ObjectName;
import java.net.MalformedURLException;
import java.net.URL;
import java.util.Map;
/**
* This class extends the "SsoServerTopology" class.
*/
public class SsoServerTopologyImpl extends SsoServerTopology {
private static Debug debug = null;
/**
* Constructor
*/
public SsoServerTopologyImpl (SnmpMib myMib) {
super(myMib);
init(myMib, null);
}
public SsoServerTopologyImpl (SnmpMib myMib, MBeanServer server) {
super(myMib, server);
init(myMib, server);
}
private void init (SnmpMib myMib, MBeanServer server) {
if (debug == null) {
debug = Debug.getInstance("amMonitoring");
}
String classModule = "SsoServerTopologyImpl.init:";
/*
* server topology has the
* servers table (all servers known to this server)
* SsoServerServerTable
* sites table (sites and servers)
* SsoServerSiteMapTable
* site map table (site-to-server mapping)
* SsoServerSitesTable
*
* this init should get instances of
* SsoServerServerEntryImpl
* SsoServerSitesEntryImpl
* SsoServerSiteMapEntryImpl
* and add them to their corresponding tables.
*/
Map<String, String> ntbl = Agent.getNamingTable();
Map<String, String> sidtbl = Agent.getSiteIdTable();
for (Map.Entry<String, String> entry : sidtbl.entrySet()) {
String svrId = entry.getKey();
String svrURL = ntbl.get(svrId);
String siteId = sidtbl.get(svrId);
URL url = null;
String proto = null;
String host = null;
int port = 0;
try {
url = new URL(svrURL);
proto = url.getProtocol();
host = url.getHost();
port = url.getPort();
} catch (MalformedURLException mue) {
debug.error(classModule + "invalid URL: " +
svrURL + "; " + mue.getMessage());
}
Integer iport = Integer.valueOf(1);
Integer iid = Integer.valueOf(0);
try {
iport = Integer.valueOf(port);
iid = Integer.valueOf(svrId);
} catch (NumberFormatException nfe) {
debug.error(classModule + "invalid port (" +
port + ") or server id (" + svrId + "): " +
nfe.getMessage(), nfe);
}
SsoServerServerEntryImpl ssrv =
new SsoServerServerEntryImpl(myMib);
ssrv.ServerPort = iport;
ssrv.ServerHostName = host;
ssrv.ServerProtocol = proto;
ssrv.ServerId = iid;
/* need a way to know what the real status is */
ssrv.ServerStatus = Integer.valueOf(1);
final ObjectName svrName =
ssrv.createSsoServerServerEntryObjectName(server);
try {
SsoServerServerTable.addEntry(ssrv, svrName);
if ((server != null) && (svrName != null)) {
server.registerMBean(ssrv, svrName);
}
} catch (Exception ex) {
debug.error(classModule + svrURL, ex);
}
/*
* fill the SsoServerSitesTable.
* entries have siteid, site name, and site state
* sidKeys has the serverIDs; the values are the site they
* belong to.
*
* unfortunately, SiteConfiguration.getSites(SSOToken) needs
* an SSOToken, which can be gotten after the server is more
* closer to being operational than when the Agent is started,
* so that part will have to be updated at a later time.
*
* where the key == value in sidKeys is the one that is the site
*/
if (debug.messageEnabled()) {
debug.message(classModule + "svrId = " + svrId
+ ", siteId = " + siteId);
}
try {
Integer.valueOf(siteId);
} catch (NumberFormatException nfe) {
debug.error(classModule + "invalid siteid ("
+ siteId + "): " + nfe.getMessage(), nfe);
}
}
}
}
|
{
"pile_set_name": "Github"
}
|
Machita incident
The Machita incident occurred in southern Arizona between October 1940 and May 1941 when an elderly O'odham chief and medicine man, Pia Machita (), resisted arrest by the Bureau of Indian Affairs for inciting his people to dodge the draft. It has since been called the "most dramatic of Indian resistance" to the United States during the World War II-era.
Background
Pia Machita (, meaning He Has no Metate), was born around 1860 and was eighty to eighty-four years old when the trouble began. He lived with his small band of about thirty people in the northwestern area of the Hickiwan District, at an isolated village called Stoa Pitk. Machita identified as a Mexican citizen. He openly said that he did not recognize the Gadsden Purchase of 1853, by which the United States took "control" of O'odham land, and therefore he did not recognize the authority of the Indian Bureau or of the O'odham tribal government.
The Tohono O'odham tribe of southern Arizona was one of the last to begin assimilation. In the 1930s, they conducted non-violent resistance to the Indian Bureau's construction of wells on the Papago Reservation, and were concerned about the loss of land. Leaders such as Machita feared that using the wells would make their people dependent on them; they preferred the traditional methods of collecting and storing rain and spring water. In a 1934 meeting to discuss the Indian Reorganization Act with T.B. Hall, the superintendent of the Sells Indian agency, Machita said that "his people owed allegiance to Mexico." After the interview, Machita stopped cooperating with the Indian Bureau in regards to land conservation, the inoculation of cattle, and the taking of the 1940 census.
Following the signing of the Selective Training and Service Act in 1940 by President Franklin D. Roosevelt, Indian agents tried to draft Indian men into the armed forces. Machita considered enrollment in the draft to be another means for the United States government to take away his people's freedom, so he encouraged the young men to refuse to register. According to author Brad Melton, the majority of Machita's band was illiterate and therefore ineligible for the draft, but the chief was unaware of this in his resistance. By 1942, however, nearly 99 percent of eligible Native American men in Arizona had registered for the draft, and they enlisted at a high rate.
Incident
On October 13, 1940, Indian agents arrived at Stoa Pitk to enlist 30 men for the draft, but the natives refused to comply. In response, the tribal chief of police and a force of United States Marshals under the command of Ben McKinney launched a raid against Stoa Pitk to arrest Machita. The raid began at 2:00 AM on October 16, 1940. Entering with guns drawn and tear gas grenades at the ready, the raiders captured Machita without a shot fired. However, while they were on their way out, the O'odham villagers confronted the raiders and released their chief, severely beating one of the marshals in the process. When the scuffle was over, the police retreated to Tucson and Machita fled into the desert with 25 followers.
The Bureau of Indian Affairs tried to move quickly to suppress the "draft rebels," because they feared that the resistance to the draft would spread to other reservations. But, for the next seven months the old chief remained on the run, evading both the police and the military. Machita and his band could have easily crossed the border into Sonora, Mexico, but all accounts suggest that they were within Arizona the entire time. O'odham oral tradition says that aircraft from the United States Army bombed their villages; however, the "bombs" were sacks of flour dropped to mark the villages, which blended in so well with the surrounding desert. Machita and his band were finally apprehended without incident at Stoa Pitk on May 21, 1941. Machita was sentenced to serve eighteen months at the Terminal Island Federal Prison, but a tribal chairman named Peter Blaine managed to persuade Machita's judge to let him go early.
The following appeared in a 1941 newspaper editorial:
See also
Native Americans and World War II
References
Category:1940 in Arizona
Category:1941 in Arizona
Category:Conflicts in 1940
Category:Conflicts in 1941
Category:History of Pima County, Arizona
Category:Military history of the United States during World War II
Category:Tohono O'odham
Category:Combat incidents
Category:Native American history of Arizona
|
{
"pile_set_name": "Wikipedia (en)"
}
|
`Cavendish-HEP-2000/11`\
`CERN-TH/2000-354`\
`MC-TH-00/11`\
`hep-ph/0011047`\
\
[J.R. Forshaw$^{1}$, D.A. Ross${^2}$ and A. Sabio Vera${^3}$]{}\
\
[*[${^1}$Department of Physics and Astronomy, University of Manchester, Oxford Road, Manchester M13 9PL, U.K.\
${^2}$ Division Théorique, CERN, CH1211-Geneva 23, Switzerland [^1]\
$^{3}$ Cavendish Laboratory, University of Cambridge, Madingley Road, Cambridge, CB3 0HE, U.K. ]{}*]{}\
[We describe a formalism for solving the BFKL equation with a coupling that runs for momenta above a certain infrared cutoff. By suitably choosing matching conditions proper account is taken of the fact that the BFKL diffusion implies that the solution in the infrared (fixed coupling) regime depends upon the solution in the ultraviolet (running coupling) regime and vice versa. Expanding the BFKL kernel to a given order in the ratio of the transverse momenta allows arbitrary accuracy to be achieved.]{}
Diffractive processes are described, at least within the framework of perturbative QCD, by the BFKL equation [@bfkl]. This equation sums the leading and next-to-leading $\ln s$ [@BFKL2] terms for the amplitude involving the exchange in the $t-$channel with the quantum numbers of the vacuum.
In the case of fixed coupling, the energy dependence of these diffractive processes is determined by the emergence of a branch cut in the Mellin transform plane ($\omega-$plane), with a branch point at $\omega > 0$. Lipatov [@lipatov86] has demonstrated that accounting for the running of the strong coupling together with some (non-perturbative) information about the infrared behaviour of QCD leads to a separation of the $\omega-$plane singularity structure into a series of isolated poles. More recently, Thorne [@thorne] has shown that if one uses the solution to the BFKL equation with running coupling, the factor in the amplitude which is totally calculable in perturbative QCD has an essential singularity at $\omega=0$, such that there is no power-like energy dependence. This is in accord with the recent work of Ciafaloni, Colferai and Salam, who have shown that the leading $\omega$-plane singularity is of non-perturbative origin [@ccs].
The BFKL equation is a diffusion equation and so there will always be some contribution from the infrared region. One way of treating this region is to assume that the strong coupling ceases to run below a certain scale. In this case, we expect that for sufficiently low values of the transverse momenta of the exchanged gluons, the $s-$behaviour will be dominated by the fixed coupling solution, whereas for large enough transverse momenta the solution of [@thorne] will dominate. We should like to understand the smooth extrapolation between these two extremes.
In this letter we describe a formalism for solving the BFKL equation with strong coupling running above some infrared scale, in which we can see how the transition from the fixed coupling to the running coupling solution arises.
[**Formalism for Solving the BFKL Equation with Running Coupling**]{}
To begin with we consider only the leading order BFKL kernel and describe later how the formalism may be extended in order to include the substantial part of the higher order corrections.
Since the BFKL equation is a diffusion equation there is always diffusion into the infrared regime, where renormalization group improved perturbation theory breaks down and one needs supplementary information about the behaviour of QCD beyond perturbation theory. For our purposes we simulate this infrared behaviour by assuming that the coupling freezes below a critical value of $t \equiv \ln(k^2/\Lambda_{QCD}^2),
\ t=t_0$. We also make the assumption that $\alpha_s(t_0)$ is sufficiently small that perturbative results in the infrared regime maintain some level of credibility.
The full BFKL equation is solved in terms of a complete set of eigenfunctions $f_\omega(t)$ of the kernel with eigenvalue $\omega$. For any $\omega$ there will be some diffusion into the infrared regime. We therefore write $f_\omega(t)$ as f\_(t) = f\_\^<(t) (t\_0-t) + f\_\^>(t) (t-t\_0) and the kernel as $$\begin{aligned}
K(t,t^\prime) &=& \left[ \frac{1}{b \, t_0} {\cal K}^<(t,t^\prime)
\, \theta(t_0-t') + \frac{1}{b \, t }{\cal K}^<(t,t^\prime)
\, \theta(t'-t_0) \right] \, \theta(t-t^\prime) \ + \nonumber \\ & & \
\left[ \frac{1}{b \, t_0} {\cal K}^>(t,t^\prime)
\, \theta(t_0-t') + \frac{1}{b \, t^\prime }{\cal K}^>(t,t^\prime)
\, \theta(t'-t_0) \right] \, \theta(t^\prime-t) \end{aligned}$$ where $b=\beta_0 /12$, $\beta_0=11-2n_f/3$, being the first coefficient of the $\beta-$function for the running of the QCD coupling. We define $ {\cal K}^<(t,t^\prime)$ and $ {\cal K}^>(t,t^\prime)$ as the limits of sums, i.e. $${\cal K}^<(t,t^\prime) \ = \ \lim_{N \to \infty} {\cal K}^<_N(t,t^\prime)$$ $${\cal K}^>(t,t^\prime) \ = \ \lim_{N \to \infty} {\cal K}^>_N(t,t^\prime)$$ where \^<\_N(t,t\^) = \_[r=0]{}\^N { e\^[(r+1/2)(t\^-t)]{}- (t-t\^) } \^>\_N(t,t\^) = \_[r=0]{}\^N { e\^[(r+1/2)(t-t\^)]{}- (t-t\^) }. The functions $e^{\gamma \, t}$ are eigenfunctions of these kernels with eigenvalues $\chi_N^<(\gamma)$ and $\chi_N^>(\gamma)$ respectively, i.e. $$\begin{aligned}
\int_{-\infty}^{t} {\cal K}^<_N(t,t^\prime) e^{\gamma t^\prime} dt^\prime
&=& \chi_N^<(\gamma) e^{\gamma t} \nonumber \\
\int_{t}^{\infty} {\cal K}^>_N(t,t^\prime) e^{\gamma t^\prime} dt^\prime
&=& \chi_N^>(\gamma) e^{\gamma t}\end{aligned}$$ where \_N\^<() = \_[r=0]{}\^N { - } \_N\^>() = \_[r=0]{}\^N { - }. Note that $\chi_{\infty}^<(\gamma) = \gamma_E - \psi(1/2+\gamma)$ and $\chi_{\infty}^>(\gamma) = \gamma_E - \psi(1/2-\gamma)$, and we have the leading order BFKL kernel.
In this paper we truncate the kernel after $N$ terms. Note that the case $N=0$ reduces to the collinear model of [@ccs]. For this truncated kernel the spectrum of eigenvalues is -\_[r=0]{}\^N b t\_0 \_[r=0]{}\^N . \[range\] The infrared part of the eigenfunction $ f_\omega^<(t)$ obeys the integral equation $$\begin{aligned}
b \, t_0 \, \omega \, f_\omega^<(t) & = & \int_{-\infty}^t
{\cal K}^<_N(t,t^\prime) f_\omega^<(t^\prime) \, dt^\prime
\ + \ \int_t^{t_0}
{\cal K}^>_N(t,t^\prime) f_\omega^<(t^\prime) \, dt^\prime \nonumber \\ & &
+ \ \int_{t_0}^\infty {\cal K}^>_N(t,t^\prime)
\frac{t_0}{t^\prime} f_\omega^>(t^\prime)dt^\prime
\label{bfkl<} \end{aligned}$$ whereas the ultraviolet part of the solution $f_\omega^>(t)$, obeys the integral equation $$\begin{aligned}
b \, t \omega \, f_\omega^>(t) & = & \int_{t_0}^t
{\cal K}^<_N(t,t^\prime) f_\omega^>(t^\prime) \, dt^\prime
\ + \ \int_t^{\infty}
{\cal K}^>_N(t,t^\prime) \frac{t}{t^\prime} f_\omega^>(t^\prime) \, dt^\prime \nonumber \\ & &
+ \ \int^{t_0}_{-\infty} {\cal K}^<_N(t,t^\prime) f_\omega^<(t^\prime) \,
dt^\prime.
\label{bfkl>} \end{aligned}$$ We note that these equations are both inhomogeneous, reflecting the fact that even for $t < t_0$, where the coupling is fixed, the BFKL equation involves diffusion into the running coupling regime and vice versa.
We can convert these two equations into homogeneous integro-differential equations by operating on both sides of eq.(\[bfkl<\]) with the operator $${\cal O}^N_<(t) \ = \ \frac{d}{dt} \left( \frac{d}{dt}-1 \right)
\cdots \left(\frac{d}{dt}-N \right) e^{-t/2}$$ and operating on both sides of eq.(\[bfkl>\]) with the operator $${\cal O}^N_>(t) \ = \ \frac{d}{dt} \left( \frac{d}{dt}+1 \right)
\cdots \left(\frac{d}{dt}+N \right) e^{t/2}.$$ These equations are $(N+1)^{th}$ order in derivatives and so each one of these has solutions which contain $N+1$ arbitrary constants of integration. However, these constants are fixed by the requirement that the original integral equations (\[bfkl<\],\[bfkl>\]) must be obeyed, together with the requirements the eigenfunctions should be normalizable, which means that $f_\omega^<(t)$ must be square integrable as $t \to -\infty$ and $f_\omega^>(t)$ must be square integrable as $t \to \infty$.
The general solution to the integro-differential equation for $f_\omega^<(t)$ is f\_\^<(t) = \_[j=1]{}\^[N+2]{} a\_j e\^[\^0\_j t]{}, \[mistress\] where $\gamma^0_j$ are the solutions to b t\_0 = \_N\^<() + \_N\^>() \_N() \[fixed\] with $\Re e (\gamma) \geq 0$ to ensure square integrability as $t \to -\infty$. In the allowed range of eigenvalues, eq.(\[range\]), there will be $N+2$ such solutions. For example, in the case $N=0$ the solutions are \^0\_j = i \[n0\] where $$\lambda_0= \frac{1}{b \, \omega \, t_0 + 2}.$$ For the allowed range, $\lambda_0 \, > \, 1/4$, and so these values are purely imaginary. In the case $N=1$ we have \^0\_j = \[n1\] where $$\lambda_1= \frac{1}{b \, \omega \, t_0 + 3}.$$ For the allowed range, $\lambda_1 \, > \, 3/16$ and we see that two of the solutions are purely imaginary, $\pm i \nu_1$, and two purely real $\pm \beta_1$. Thus the general solution is f\_\^<(t) = a\_1 e\^[i\_1 t]{} + a\_2 e\^[-i\_1 t]{} + a\_3 e\^[\_1t]{}. \[soln<1\]
For the integro-differential equation for $f_\omega^>(t)$, it is convenient to work in terms of the Laplace transform $\tilde{f}_\omega(\gamma)$ defined by = d \_() e\^[t]{}, \[laplace\] in which the integral over $\gamma$ is performed over some suitable contour, described below. The function $\tilde{f}_\omega(\gamma)$ obeys the differential equation b \^\_() + \_N() \^\_()+ \_N\^[> ]{} \_() = 0, where the prime indicates differentiation with respect to $\gamma$. This equation can be solved in WKB approximation yielding the result \_() = { - \^( \_N(\^) +) d\^}, \[soln>\] where $$V(\gamma,\omega) \ = \ \chi_N^2(\gamma)-4 \, \omega \, b \,
\chi_N^{> \, \prime}(\gamma).$$ Note that if we set the term $\chi_N^{> \, \prime}(\gamma)$ to zero we recover the expression obtained in [@thorne] for the case of deep-inelastic scattering in which the transverse momenta are ordered and the coupling is chosen to run always with $t$.
The solution (\[soln>\]) is a valid approximation except near the points where $V(\gamma)$ vanishes. We could improve the solution by expanding $V(\gamma)$ to linear order around the zeroes and matching the solutions either side to an Airy function. However, the singularities in $\tilde{f}_\omega$ at these zeroes are integrable so that such an improvement would have negligible effect on the inverse Laplace transform.
For $t<t_c$ the solution is oscillatory. The value of this critical value $t_c$ can be estimated by approximating the integral of eq.(\[laplace\]) by the saddle point at $$2 \, \omega \, b \, t \ = \ \chi_N(\gamma)+\sqrt{V(\gamma,\omega)}.$$ $t_c$ is the minimum value of $t$ for which this has a solution for purely real $\gamma$. Again, if we were to neglect $\chi_N^{> \, \prime}(\gamma)$, this would occur at $\gamma=0$ and we have approximately $$t_c \ = \ \frac{1}{b \,\omega} \chi_N(0).$$
This oscillatory part is “matched” to the fixed-coupling solution by requiring consistency with the original integral equations (\[bfkl<\], \[bfkl>\]). To see how this is possible, we need to examine in more detail the possible contours of integration for eq.(\[laplace\]).
[**The $\gamma$-contour**]{}
From the positions of the simple poles in $\chi_N^<(\gamma)$ and $\chi_N^>(\gamma)$, we note that $\tilde{f}_\omega(\gamma)$ has branch points on the real axis at $\gamma=r+1/2$ and $\gamma=-1/2-r$ for $r=0, \cdots N$. The branch cuts can be “combed” in the direction of the positive or negative real axis in such a way as to leave a portion of the real axis between $n-1/2$ and $n+1/2$ for which $\tilde{f}_\omega(\gamma)$ is analytic. $n$ runs from $-N$ to $N$.
For each such “combing” a contour, ${\cal C}_n$ can be chosen that crosses the real axis between $n-1/2$ and $n+1/2$. Since $t>0$ we require that the ends of the contour turn over so that at the ends of the contour $\Re e \, \gamma \to -\infty$, thus ensuring that the inverse Laplace transform integral exists. The integral over each such contour is a valid solution to the integro-differential equation for $f^>_\omega(t)$ and since this equation is linear, the most general solution which is square integrable as $t \to \infty$ is the sum of the integrals over these contours with $-N \, \le \, n \, \le 0$, with arbitrary coefficients $b_n$, i.e. \_[n=-N]{}\^0 b\_n \_[[C]{}\_n]{} d \_() e\^[t]{}, \[master\] with $\tilde{f}_\omega(\gamma)$ given by eq.(\[soln>\]).[^2] As an example we consider the $N=1$ case. The four “combings” are shown in Fig. \[fig1\] together with the four contours, ${\cal C}_n$.
(420,450) (170,420)[(20,20)[$\gamma$]{}]{} (0,450)[(1,0)[200]{}]{} (20,450)(20,0)[9]{}[(0,-1)[5]{}]{} (0,250)[(1,0)[200]{}]{} (20,250)(20,0)[9]{}[(0,1)[5]{}]{} (0,350)[(1,0)[200]{}]{} (0,450)[(0,-1)[200]{}]{} (0,440)(0,-20)[10]{}[(1,0)[5]{}]{} (100,450)[(0,-1)[200]{}]{} (200,440)(0,-20)[10]{}[(-1,0)[5]{}]{} (200,450)[(0,-1)[200]{}]{} (80,253)(0,10)[20]{}[(0,1)[5]{}]{} (60,270)[${\cal C}_{-1}$]{} (0,348)
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(90,348)
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(110,347)
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(130,346)
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(15,240)[-4]{}(35,240)[-3]{}(55,240)[-2]{}(75,240)[-1]{} (97,240)[0]{} (117,240)[1]{}(137,240)[2]{}(157,240)[3]{}(177,240)[4]{}
(390,420)[(20,20)[$\gamma$]{}]{} (220,450)[(1,0)[200]{}]{} (240,450)(20,0)[9]{}[(0,-1)[5]{}]{} (220,250)[(1,0)[200]{}]{} (240,250)(20,0)[9]{}[(0,1)[5]{}]{} (220,350)[(1,0)[200]{}]{} (220,450)[(0,-1)[200]{}]{} (220,440)(0,-20)[10]{}[(1,0)[5]{}]{} (320,450)[(0,-1)[200]{}]{} (420,440)(0,-20)[10]{}[(-1,0)[5]{}]{} (420,450)[(0,-1)[200]{}]{} (317,253)(0,10)[20]{}[(0,1)[5]{}]{} (323,270)[${\cal C}_{0}$]{} (220,347)
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(290,348)
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(330,348)
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(350,347)
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(235,240)[-4]{}(255,240)[-3]{}(275,240)[-2]{}(295,240)[-1]{} (337,240)[1]{}(357,240)[2]{}(377,240)[3]{}(397,240)[4]{} (317,240)[0]{}
(170,190)[(20,20)[$\gamma$]{}]{} (0,220)[(1,0)[200]{}]{} (20,220)(20,0)[9]{}[(0,-1)[5]{}]{} (0,20)[(1,0)[200]{}]{} (20,20)(20,0)[9]{}[(0,1)[5]{}]{} (0,120)[(1,0)[200]{}]{} (0,220)[(0,-1)[200]{}]{} (0,440)(0,-20)[10]{}[(1,0)[5]{}]{} (100,220)[(0,-1)[200]{}]{} (200,440)(0,-20)[10]{}[(-1,0)[5]{}]{} (200,220)[(0,-1)[200]{}]{} (120,23)(0,10)[20]{}[(0,1)[5]{}]{} (107,40)[${\cal C}_{1}$]{} (70,117)
------------------------------------------------------------------------
(90,118)
------------------------------------------------------------------------
(0,116)
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(130,116)
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(15,10)[-4]{}(35,10)[-3]{}(55,10)[-2]{}(75,10)[-1]{} (97,10)[0]{} (117,10)[1]{}(137,10)[2]{}(157,10)[3]{}(177,10)[4]{}
(390,190)[(20,20)[$\gamma$]{}]{} (220,220)[(1,0)[200]{}]{} (240,220)(20,0)[9]{}[(0,-1)[5]{}]{} (220,20)[(1,0)[200]{}]{} (240,20)(20,0)[9]{}[(0,1)[5]{}]{} (220,120)[(1,0)[200]{}]{} (220,220)[(0,-1)[200]{}]{} (220,440)(0,-20)[10]{}[(1,0)[5]{}]{} (320,220)[(0,-1)[200]{}]{} (420,440)(0,-20)[10]{}[(-1,0)[5]{}]{} (420,220)[(0,-1)[200]{}]{} (360,23)(0,10)[20]{}[(0,1)[5]{}]{} (344,40)[${\cal C}_{2}$]{} (220,116)
------------------------------------------------------------------------
(220,115)
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(330,118)
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(310,117)
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(235,10)[-4]{}(255,10)[-3]{}(275,10)[-2]{}(295,10)[-1]{} (337,10)[1]{}(357,10)[2]{}(377,10)[3]{}(397,10)[4]{} (317,10)[0]{}
Only ${\cal C}_{-1}$ and ${\cal C}_0$ give a square integrable solution, so the general solution is f\^>\_(t) = t { b\_[-1]{} \_[-]{}\^d e\^[-t]{} \_(i-1) e\^[it]{} + b\_0 \_[-]{}\^d \_(i) e\^[it]{} }\[soln>1\].
Returning now to the original equations (\[bfkl<\]) and (\[bfkl>\]), we see that these are obeyed by the solutions (\[master\]) and (\[mistress\]) provided \_[j=1]{}\^[N+2]{} a\_j -t\_0 \_[n=-N]{}\^0 b\_n \_[[C]{}\_n]{} d = 0 (r=0 N), \[match1\] \_[j=1]{}\^[N+2]{} a\_j + \_[n=-N]{}\^0 b\_n \_[[C]{}\_n]{} d = 0 (r=0 N). \[match2\] Thus we obtain $2N+2$ relations between the $N+2$ coefficients $a_j$ and the $N+1$ coefficients $b_k$ (the overall normalization of these coefficients is determined by the normalization condition of the eigenfunctions). This then determines uniquely the required eigenfunctions.
Equations (\[bfkl<\], \[bfkl>\]) guarantee the continuity of the eigenfunctions at $t=t_0$, i.e. $f^<_\omega(t_0)=f^>_\omega(t_0)$, but the derivative is not continuous. This results from the fact that we have taken an expression for the coupling as a function of $t$, whose derivative is not continuous at $t=t_0$.
We can now see how the inverse Mellin transform, $f(s,t)$ of the solution $f_\omega(t)$ extrapolates smoothly between the power-like behaviour for $t \sim t_0$ and the softer behaviour (with at most logarithmic dependence on $s$) for $t \gg t_0$.
Examining the $\gamma-$ integral for one particular contour, ${\cal C}_n$, and for $t > t_0$, we see that this will be dominated by a saddle point $\gamma_s(\omega,t)$, which is the solution to 2 b t = \_N()+. \[saddle\] This is multi-valued and the dominant saddle point will be the one closest to the integration contour. We call this saddle point $\gamma^n_s(\omega,t)$. In other words, $f^>_\omega(t)$ of eq.(\[laplace\]) from the contour ${\cal C}_n$ will contain an $\omega-$dependent prefactor, which may be written (after a suitable integration by parts) $$\exp\left\{ \int^t
\gamma^n_s(\omega,t^\prime) dt^\prime \right\}.$$ The essential singularity at $\omega=0$ is now encoded in $\gamma^n_s(\omega,t)$ which acquires a singularity as $\omega \to 0$, i.e. the R.H.S. of (\[saddle\]) can only tend to zero as $|\gamma| \to \infty$.
Now examining eqs.(\[match1\], \[match2\]), we see that the contour integrals multiplying the coefficients $b_n$ are also dominated by a similar saddle point but with $t$ set to $t_0$. Thus these coefficients appear in eqs.(\[match1\], \[match2\]) with a prefactor $$\exp\left\{ \int^{t_0}
\gamma^n_s(\omega,t^\prime) dt^\prime \right\}.$$ Therefore these coefficients also possess an essential singularity at $\omega=0$. Furthermore $b_n$ will contain factors of the form $\exp(\gamma^j_0(\omega) t_0)$ from the L.H.S. of (\[match1\], \[match2\]).
For $t$ close to $t_0$ each term in the sum of eq.(\[master\]), i.e. the product of $b_n$ and the contribution to $f^>_\omega(t)$ from the integral over the contour ${\cal C}_n$ will have a dominant $\omega-$dependence of the form { \^n\_s(,t\_0)(t-t\_0)+\_0\^j()t\_0 }. \[neweq\] Note that due to the partial cancellation, the coefficient of the term that gives rise to the essential singularity vanishes as $t \to t_0$.
For sufficiently large $s$, the inverse Mellin transform probes small $\omega$, where the term in the exponent proportional to $\gamma^n_s(\omega,t_0)$ will dominate even if $(t-t_0)$ is small and the $s$-behaviour is dominated by the essential singularity in the Laplace transform, $\tilde{f}_\omega(\gamma)$. However, for more moderate values of $s$ we can neglect this term when $t$ is sufficiently close to $t_0$ and the $s-$dependence will be dominated by the fixed coupling power-like behaviour. As $t$ is increased away from $t_0$, the boundary in $s$ where the soft behaviour takes over from the power-like behaviour decreases and we see that as $t \to \infty$ we recover the solution of [@thorne].
This formalism is considerably simplified if we assume that $t_0$ is sufficiently large that $\exp(-t_0) \ll 1$. In this case we only need consider the right-most contour consistent with square-integrability as $t \to \infty$. This is the contour ${\cal C}_0$. In this case, within the approximation of performing the $\gamma-$contour integral and the inverse Mellin transform by the saddle-point method, the $s-$dependence may be written as $s^{\tilde{\omega}(s,t)},$ where $\tilde{\omega}(s,t)$ is the solution to (s) = - { (t-t\_0) \_[t\_0]{}\^t \^0\_s(,t\^) dt\^ + \_0\^m() [Min]{}(t,t\_0) } \[plot\], and $\gamma_0^m(\omega)$ is the solution to eq.(\[fixed\]) with the largest real part. In Fig. \[fig2\] we plot $\tilde{\omega}(s,t)$ against $t$ for a large value of $s \ (\ln s =23)$. For simplicity we have taken the $N=0$ case, although we expect the result to be qualitatively the same for higher values of $N$, and we take $t_0=4$. We see that it is almost constant for $t \, < \, t_0$ and diminishes as one increases $t$ from $t_0$, indicating the smooth transition from hard to soft $s-$dependence as $t$ is increased. The discontinuity of the slope at $t=t_0$ is a reflection of the fact that we have taken a sharp discontinuity in the slope of the running coupling at $t_0$ and would be smoothed out if a smoother transition were taken.
The asymptotic behaviour is only obtained for much larger values of $t$ and in Fig. \[fig3\] we show the $s$ dependence of $\tilde{\omega}(s,t)$ for $t=40$ and notice that it is much closer to zero than the case where $t \sim t_0$ and decreases as $\ln s$ increases, resulting in an $s-$dependence for the amplitude that has no fixed power of $s$.
[**Accounting for Higher Order Corrections**]{}
The higher order BFKL kernel [@BFKL2] does not lend itself readily to an expansion in powers of $e^{t-t^\prime}$. Furthermore, it is known that these corrections are large.
However, it has been pointed out [@salam] that a substantial part of the higher order corrections consist of “collinear corrections” which are required to ensure correct behaviour when the formalism is applied to deep inelastic scattering. It was shown in [@salam] and confirmed in [@us] that once these corrections are accounted for, the remaining higher order corrections are modest. The simplest way of encoding these collinear corrections and summing them is to replace $\gamma$ by $(\gamma-\omega/2)$ in $\chi_N^<(\gamma)$ and by $(\gamma+\omega/2)$ in $\chi_N^>(\gamma)$ [@ags; @salam].
This formalism is readily adapted to the procedure described here. In the expression (\[mistress\]) for $f_\omega^<(t)$ the quantities $\gamma_j^0(\omega)$ are taken to be the solutions to the implicit equation \_N\^<(-/2)+\_N\^>(+/2) = b t\_0, \[gamm1\] and the expression for the Laplace transform of $f_\omega^>(t)$ becomes \_() = {- \^( \_N\^<(\^-/2)+\_N\^>(\^+/2) + ) d\^ }, \[soln2>\]where V(,) = (\_N\^<(-/2) +\_N\^>(+/2))\^2 -4 b \_N\^[> ]{} (+/2). Provided that we restrict our analysis to the case $|\omega|<1$, the singularity structure and consequently the analysis of the contours of integration remains unchanged from the leading order case, although the exact positions of the branch points will have moved.
[**Acknowledgement**]{} ASV wishes to thank the University of Manchester and the CERN Theory Division where this work started and acknowledges the support of PPARC (Posdoctoral Fellowship: PPA/P/S/1999/00446). DAR wishes to thank the CERN Theory Division for its hospitality.
[99]{} V.S. Fadin, E.A. Kuraev and L.N. Lipatov, [*Sov. Phys. JETP*]{} [**44**]{} 443 (1978)\
Y.Y. Balitsky and L.N. Lipatov, [*Sov. J. Nucl. Phys.*]{} [**28**]{} 822 (1978) V.S. Fadin and L.N. Lipatov, [*Phys. Lett.*]{} [**B429**]{} 127 (1998)\
G.Camici and M. Ciafaloni, [*Phys. Lett.*]{} [**B430**]{} 349 (1998) L.N. Lipatov [*Sov. Phys. JETP*]{} [**63**]{} 904 (1986) R.S. Thorne, [*Phys. Rev.*]{} [**D60**]{} 054031 (1999); [*Phys. Lett.*]{} [**B474**]{} 372 (2000) M. Ciafaloni, D. Colferai and G.P. Salam, [*JHEP*]{} [**9910:017**]{} (1999); [*JHEP*]{} [**0007:054**]{} (2000) C.P. Salam [*JHEP*]{} [**9807:019**]{} (1998) J.R. Forshaw, D.A. Ross and A. Sabio Vera, [*Phys. Lett*]{} [**B455**]{} 273 (1999) B. Andersson, G. Gustafson and J. Samuelsson, [*Nucl. Phys.*]{} [**B467**]{} 443 (1996)
[^1]: On Leave of absence from:\
Department of Physics and Astronomy, University of Southampton, Southampton, SO17 1BJ, U.K.
[^2]: We have absorbed the factor of $2\pi i$ in the denominator in eq.(\[laplace\]) into the definition of the coefficients $b_n$.
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{
"pile_set_name": "ArXiv"
}
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Q:
Why windows 10 UWP framework Stream class does not have Close method?
Why windows 10 UWP framework Stream class does not have Close method?
What do I do in order to release the used stream, I have used Dispose method as of now but is there any other way I can release the stream?
And why microsoft have removed Close method from the Stream class?
A:
You are indeed supposed to be using Dispose(), or better yet enclosing your streams in a using block. MSDN says you're not expected to call System.IO.Stream.Close() directly and you should be calling Dispose() instead anyway. So there isn't much of an issue here.
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{
"pile_set_name": "StackExchange"
}
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# Programmer: limodou
# E-mail: limodou@gmail.com
#
# Copyleft 2006 limodou
#
# Distributed under the terms of the GPL (GNU Public License)
#
# NewEdit is free software; you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation; either version 2 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with this program; if not, write to the Free Software
# Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
#
# $Id$
import wx
from modules import Mixin
from modules import common
pagename = tr("Spell Check")
def createSpellCheckWindow(win):
if not win.panel.getPage(pagename):
import SpellCheck
page = SpellCheck.SpellCheck(win.panel.createNotebook('bottom'))
win.panel.addPage('bottom', page, pagename)
return pagename
Mixin.setMixin('mainframe', 'createSpellCheckWindow', createSpellCheckWindow)
def add_mainframe_menu(menulist):
menulist.extend([('IDM_TOOL', #parent menu id
[
(160, 'IDM_TOOL_SPELLCHECK', tr('Spell Check') + '\tF7', wx.ITEM_NORMAL, 'OnToolSpellCheck', tr('Spell check for current document.')),
]),
])
Mixin.setPlugin('mainframe', 'add_menu', add_mainframe_menu)
def OnToolSpellCheck(win, event):
try:
from enchant.checker import SpellChecker
except:
common.showerror(win, tr('You should install PyEnchant module first.\n Or there are something wrong as import the module'))
return
p = win.createSpellCheckWindow()
win.panel.showPage(p)
Mixin.setMixin('mainframe', 'OnToolSpellCheck', OnToolSpellCheck)
def pref_init(pref):
pref.default_spellcheck_dict = ''
Mixin.setPlugin('preference', 'init', pref_init)
|
{
"pile_set_name": "Github"
}
|
Anchoring the project is the conversion of the long-dormant, 12-acre thermal transfer plant site on the west bank into public green space. It would feature an outdoor amphitheater for the symphony and other events. Before work begins, groundbreaking is set this fall for a 4.5-acre riverfront lawn and landing area on the east side to connect to the newly opened Cumberland Park.
It’s been amazing to see the transformation of downtown Nashville the last 15-20 years. The last three mayors of Nashville have had foresight and resolve to create a truly great downtown. As someone who lives in Hendersonville and doesn’t pay Davidson county taxes, I feel somewhat inappropriate to celebrate something I don’t contribute to. However, all the attractions downtown has taken my dollars into Nashville for the great city experiences.
|
{
"pile_set_name": "Pile-CC"
}
|
// Drawing mixins
// generic drawing of more complex things
@function draw_widget_edge($c:$borders_edge) {
// outer highlight "used" on most widgets
@return 0 1px $c;
}
// provide font size in rem, with px fallback
@mixin fontsize($size: 24, $base: 16) {
font-size: round($size) + pt;
//font-size: ($size / $base) * 1rem;
}
@mixin draw_shadows($shadow1, $shadow2:none, $shadow3:none, $shadow4:none) {
//
// Helper function to stack up to 4 box-shadows;
//
@if $shadow4!=none { box-shadow: $shadow1, $shadow2, $shadow3, $shadow4; }
@else if $shadow3!=none { box-shadow: $shadow1, $shadow2, $shadow3; }
@else if $shadow2!=none { box-shadow: $shadow1, $shadow2; }
@else { box-shadow: $shadow1; }
}
// entries
@mixin entry($t, $fc:$selected_bg_color, $edge: $borders_edge) {
//
// Entries drawing function
//
// $t: entry type
// $fc: focus color
// $edge: set to none to not draw the bottom edge or specify a color to not use the default one
//
// possible $t values:
// normal, focus, insensitive
//
@if $t==normal {
background-color: $base_color;
border-color: $borders_color;
}
@if $t==focus {
border-color: if($fc==$selected_bg_color,
$selected_borders_color,
darken($fc,35%));
box-shadow: inset 0 0 0 1px $fc;
}
@if $t==hover { }
@if $t==insensitive {
color: $insensitive_fg_color;
border-color: $insensitive_bg_color;
box-shadow: none;
}
}
// buttons
@function draw_border_color ($c) {
//
// colored buttons want the border form the base color
//
@return if($variant == 'light', darken($c, 18%), darken($c, 4%));
}
@function draw_text_shadow_color ($tc:$fg_color, $bg:$bg_color) {
//
// calculate the color of text shadows
//
// $tc is the text color
// $bg is the background color
//
$lbg: lightness($bg)/100%;
@if lightness($tc)<50% { @return rgba(255,255,255,$lbg/($lbg*1.3)); }
@else { @return rgba(0,0,0,1-$lbg*0.8); }
}
@function draw_button_hilight_color($c) {
//
// calculate the right top highlight color for buttons
//
// $c: base color;
//
@if lightness($c)>90% { @return white; }
@else if lightness($c)>80% { @return rgba(255,255,255, 0.7); }
@else if lightness($c)>50% { @return rgba(255,255,255, 0.5); }
@else if lightness($c)>40% { @return rgba(255,255,255, 0.3); }
@else { @return rgba(255,255,255, 0.1); }
}
@mixin draw_button_text_shadow ($tc:$fg_color, $bg:$bg_color) {
//
// helper function for the text emboss effect
//
// $tc is the optional text color, not the shadow color
//
// TODO: this functions needs a way to deal with special cases
//
$shadow: draw_text_shadow_color($tc, $bg);
@if lightness($tc)<50% {
text-shadow: 0 1px $shadow;
icon-shadow: 0 1px $shadow;
}
@else {
text-shadow: 0 -1px $shadow;
icon-shadow: 0 -1px $shadow;
}
}
@mixin button($t, $c:$bg_color, $tc:$fg_color, $edge: $borders_edge, $shadow: $shadow_color) {
//
// Button drawing function
//
// $t: button type,
// $c: base button color for colored* types
// $tc: optional text color for colored* types
// $edge: set to none to not draw the bottom edge or specify a color to not
// use the default one
// $shadow: set to none to not draw the drop shadow or specify a color to not
// use the default one
//
// possible $t values:
// normal, hover, active, insensitive, insensitive-active,
// backdrop, backdrop-active, backdrop-insensitive, backdrop-insensitive-active,
// osd, osd-hover, osd-active, osd-insensitive, osd-backdrop, undecorated
//
$hilight_color: draw_button_hilight_color($c);
$button_edge: if($edge == none, none, draw_widget_edge($edge));
$blank_edge: if($edge == none, none, draw_widget_edge(transparentize($edge,1)));
$button_shadow: if($shadow == none, none, 0 1px 1px 0 $shadow);
// normal button
@if $t==normal {
color: $tc;
background-color: lighten($c, 3%);
border-color: draw_border_color($c);
@include draw_shadows($button_shadow);
// box-shadow: 0 1px 1px 0 rgba(0,0,0,0.1);
text-shadow: 0 1px $text_shadow_color;
icon-shadow: 0 1px $text_shadow_color;
}
// focused button
@if $t==focus {
color: $tc;
text-shadow: 0 1px $text_shadow_color;
icon-shadow: 0 1px $text_shadow_color;
box-shadow: inset 0 0 0 2px transparentize($selected_bg_color, 0.4);
//border-color: $selected_bg_color;
}
// hover button
@else if $t==hover {
color: $tc;
background-color: lighten($c, if($variant == 'light', 8%, 5%));
border-color: if($variant == 'light', draw_border_color(lighten($c, 7%)), draw_border_color($c));
@include draw_shadows($button_shadow);
text-shadow: 0 1px $text_shadow_color;
icon-shadow: 0 1px $text_shadow_color;
}
// active button
@else if $t==active {
color: $tc;
background-color: darken($c,3%);
border-color: draw_border_color(if($variant == 'light', $c, darken($c,7%)));
text-shadow: none;
icon-shadow: none;
box-shadow: none;
}
// insensitive button
@else if $t==insensitive {
color: $insensitive_fg_color;
border-color: $insensitive_borders_color;
background-color: $insensitive_bg_color;
box-shadow: none;
text-shadow: none;
icon-shadow: none;
}
// reset
@else if $t==undecorated {
border-color: transparent;
background-color: transparent;
background-image: none;
@include draw_shadows(inset 0 1px rgba(255,255,255,0),$blank_edge);
text-shadow: none;
icon-shadow: none;
}
}
// overview icons
@mixin overview-icon($color) {
.overview-icon {
@extend %icon_tile;
color: $color;
}
&:hover,
&:selected {
.overview-icon {
background-color: transparentize($color, .9);
}
}
&:focus {
.overview-icon {
background-color: transparentize($color, .7);
// border-color: $selected_bg_color;
}
}
&:drop {
.overview-icon {
background-color: transparentize($selected_bg_color, .15);
}
}
&:active,
&:checked {
.overview-icon {
background-color: transparentize(darken($osd_bg_color, 10%), .5);
}
}
}
|
{
"pile_set_name": "Github"
}
|
'The Sea of Trees': Cannes Review
This pre-Cannes Roadside Attractions acquisition officially ends Matthew McConaughey’s exceptional recent run of top-notch performances
Gus Van Sant’s sticky, gooey side — previously on display in the likes of Finding Forrester and especially in the 2011 Restless — oozes out once more in the woefully sentimental and maudlin The Sea of Trees. What happens to the more tough-minded and adventurous sides of the director’s personality on such ventures is a mystery, as they are entirely absent in this theoretically promising tale of two distraught men, an American and a Japanese, who meet while venturing into Japan’s infamous “suicide forest” to kill themselves. This pre-Cannes Roadside Attractions acquisition officially ends Matthew McConaughey’s exceptional recent run of top-notch performances and films, although his name will attract a bit of business in a modest theatrical release.
There are numerous ways that the spectacle of an American man headed to Japan to officially do himself in could be treated. But screenwriter Christopher Sparling (2010’s Buried) has chosen an approach that is sincere to the point of utter banality, a posture further reinforced by an obvious music score, inescapably indulgent acting and the project’s overriding motivation to turn a story of suicidal distress into something generically life-affirming in the most elementary Hollywood manner.
Sporting a scruffy, short beard and glasses, Massachusetts science teacher Arthur Brennan leaves the keys in his car at the airport and takes no luggage on his flight to Japan, where he heads straight to the Aokigahara Forest. Considered a haunted place going back centuries, this lushly wooded, darkly green enclave in the distant foothills of Mount Fuji is festooned with video cameras and signs reminding visitors that “You only have one life. Take good care of it.”
See more Cannes: The Red-Carpet Arrivals (Photos)
Blithely ignoring a “no entry” barrier, Arthur, wearing just a thin trench coat over his street clothes, stumbles upon physical evidence of previous like-minded death-seekers, including skeletons, and begins having flashbacks of nasty exchanges with his vituperative alcoholic wife Joan (Naomi Watts).
But then he encounters a man who looks rather worse off than he does, Takumi Nakamura (Ken Watanabe), a failed businessman who conveniently speaks good English, is bloody from cuts but has, after two days in the forest, somehow not managed to accomplish what he came to do.
After a flash flood nearly does them both in, the men abruptly decide they don’t want to die after all, and Trees becomes a survival tale as the guys, who take turns getting injured worse than the other, struggle to find a way to contact help (cellphone service is shamefully unreliable in the suicide forest), while Arthur wallows in memories of his wife’s battle of cancer.
This cheery scenario isn’t helped by the increasingly maudlin and sorry-for-himself blathering by Arthur, who breaks down repeatedly and truly has nothing other than dully commonplace things to say about Joan and their life together. As the character sinks deeper into wet, self-pitying gushings, McConaughey’s performance conversely becomes less expressive and more ordinary, to the point where you simply don’t care about how he feels and what happens to him.
As for the distinguished Watanabe, he has never been less so, here in a stressed out role that seems defined by deliberate vagueness. Watts hits her prescribed dramatic highs and lows with customary skill, but the characters compose a uniformly dull and not detailed lot with little but platitudes to utter.
Although most of the forest scenes were actually shot not in Japan but at Purgatory Chasm and other woodsy areas in summertime Massachusetts, the film does have an agreeably dark green-dominated look that’s easy on the eyes.
Production company: GN/Waypoint Enterprises
Cast: Matthew McConaughey, Ken Watanabe, Naomi Watts, Katie Aselton, Jordan Gavaris
Director: Gus Van Sant
Screenwriter: Chris Sparling
Producers: Gil Netter, Ken Kao, Kevin Halloran, F. Gary Gray, Brian Dobbins, Allen Fischer, Chris Sparling
Director of photography: Kasper Tuxen
Production designer: Alex DiGerlando
Costume designer: Danny Glicker
Editor: Pietro Scalia
Composer: Mason Bates
Rated PG-13, 110 minutes
|
{
"pile_set_name": "OpenWebText2"
}
|
Q:
Difference between listing a generator and looping
Looking at this answer, it seems that using a list comprehension (or for loop with append) is equivalent to calling list(..) on an iterator. Since generators are iterators too, I'd expect the same for generators. However, if you run
def permute(xs, count, low = 0):
if low + 1 >= count:
yield xs
else:
for p in permute(xs, low + 1):
yield p
for i in range(low + 1, count):
xs[low], xs[i] = xs[i], xs[low]
for p in permute(xs, low + 1):
yield p
xs[low], xs[i] = xs[i], xs[low]
print("Direct iteration")
for x in permute([1, 2], 2):
print(x)
print("Listing")
for x in list(permute([1, 2], 2)):
print(x)
It prints:
Direct iteration
[1, 2]
[2, 1]
Listing
[1, 2]
[1, 2]
Why is this happening?
A:
You're modifying and yielding the same list xs over and over. When the generator is running the list contents are changing. It looks like it's working because although each print(x) prints the same list object, that object has different contents each time.
On the other hand, the second loop runs the generator to completion and collects all of the list references up. Then it prints out the lists—except they're all the same list, so every line is the same!
Change the two print(x) lines to print(x, id(x)) and you'll see what I mean. The ID numbers will all be identical.
Direct iteration
[1, 2] 140685039497928
[2, 1] 140685039497928
Listing
[1, 2] 140685039497736
[1, 2] 140685039497736
A quick fix is to yield copies of the list instead of the original list. The yield p's are fine, but yield xs should become:
yield xs[:]
With that fix, the results are as expected:
Direct iteration
[1, 2] 140449546108424
[2, 1] 140449546108744
Listing
[1, 2] 140449546108424
[2, 1] 140449546108808
Same results from both loops, and the ID numbers are different.
|
{
"pile_set_name": "StackExchange"
}
|
The tangible appeal of college rockers is based on the way their musical personalities reflect the lifestyles of their core listeners. Indie, punk, and noise mavens flying high on the CMJ charts possess a scruffy, unconventional charm, much like that of their fans, stumbling to 10 a.m. class in pajamas.
Singer-songwriters represent the same kind of familiarity, albeit on a more mainstream, soccer-mom-sanctioned scale: John Mayer is the hunky frat boy, perfect for having a secret crush on; Dave Matthews is the aging alum who shows up to party during Homecoming weekend.
What these disparate approaches have in common is accessibility. The lack of buffed-up pop pretensions means that fans are just as likely to be roommates or drinking buddies with any of these bands as they would be members. Acoustic-oriented songwriters also create personal connections, with heartfelt confessions articulating the same feelings and emotions that their listeners experience.
Such is the immediate appeal of Howie Day, a 22-year-old whose sparse 2000 debut album, Australia, had the intimate atmosphere of a heart-to-heart conversation between dorm mates. During a September interview, the laid-back Day -- calling from his hometown, the "huge metropolitan area" of Bangor, Maine, as he says dryly -- doesn't sound very different from any other bored college kid looking for entertainment in suburbia.
"We were going to go play miniature golf yesterday, and it was closed," he laughs. "I was like 'Come on, it's like 75 degrees outside, it's beautiful,' and this place was closed, 'cause there's just nobody here, except in the summertime. You play a big city, and anything you want to do after the show, you can go do it. But here, it's like 'Want to go to the movies? You want to go out to eat?' 'Cause that's about it."
What's not mundane about Day is his meteoric rise to stardom. A guitar whiz who began playing solo in clubs at age 15, he became known for his impassioned vocals and extensive use of samplers, delays, and other gadgets, which added layers of harmony and countermelodies to his skeletal acoustic sound. He cultivated a rabid fan base from relentless touring, especially in the Northeast ("There are so many colleges [there], and we played, like, all of 'em," he laughs); devotees consequently spread the word of his dynamic shows via the internet and extensive trading of live bootlegs. Self-financing the recording of Australia, Day sold a staggering 30,000 copies independently, before Epic signed him and re-released it in 2002.
While addressing the same themes of romantic love, longing, and regret, Stop All the World Now, his second full-length, is a giant step forward. Day recorded Now in London, working with producer/Killing Joke member Youth and ex-Verve bassist Simon Jones, among others.
Their influence gives Now a distinctly British chime. Rich piano drives "Trouble in Here," while shimmering bits of keyboards and percussion dot "Sunday Morning." "Come Lay Down" ends in squalls of tortured riffs, vocals, and electronic effects reminiscent of Radiohead's "Paranoid Android," while Day's anguished, ragged howls Bono-fy the U2 upsweep of "You and a Promise." "Collide" and "I'll Take You On" even feature needling strings with the grandiose scope of the Verve's "The Drugs Don't Work."
"The first record was somewhat of a shoestring budget, completely do-it-yourself," Day explains. "This one, we obviously had the major label behind it and the opportunity to bring in the orchestra and all that posh stuff. Youth had done [the Verve's] Urban Hymns, and I was a fan of that record -- it had that vibe where there was orchestra all over it. I thought, 'Wow, that would be cool, to go for something like that, a big-sounding record.' And some of the songs really seemed like they would take to it, so it was just another thing we did."
To those used to Day's stripped-back sound, Now is definitely a shock. The third night of his current tour, which also features him backed by a full band for the first time, demonstrated the mixed reactions toward his new direction. Playing to 2,000 people at Boston's sold-out Avalon Ballroom, he was greeted by camera flashes to rival a paparazzi blitzkrieg and screams like "I just sold my psychology book to see Howie Day!" There was also enthusiastic applause for new songs such as Now's soaring lead single, "Perfect Time of Day."
But Day drew the most cheers for a midset solo interlude, during which he played older tracks "Ghost" and "Sorry So Sorry" with his usual array of guitar gizmos. Whether the response came thanks to fans' familiarity with the tracks or simply because they prefer Howie solo remains to be seen. But Day anticipated the crowd's response to the fleshed-out sound.
"Fans have a thing that they do, where any change is bad," he laughs. "But ultimately, that's just their initial reaction. Fans stick by the artists that seem to reinvent themselves and are constantly changing. That's how you last as an artist and keep yourself and everybody else interested. If you do the same thing over and over -- you just kind of spin out, the wheels spin."
But Day's more lush sound and crowded stage setup haven't changed him. His unassuming plaid shirt and shock of electric-charged spiky hair make him as approachable and low-key now as he was before he had beaucoup label bucks supporting him. And as the lavish-but-grounded-in-reality Now proves, Day is still like a comforting, platonic best guy friend -- always there to lend sage advice and an understanding ear, with boundless and genuine empathy.
"Recording the record in England might make it sound English, but the songwriting is still very much me," Day explains. "[It comes] from the place where I live and who I really am, and my friends and family around me. It was good to be in that place while I was writing.
"When someone comes up to me after a show and says, 'Oh, you know, I cried,' it's like 'Really? Wow, that's really cool.' So that's the ultimate goal, I guess, to go out and move people and put out a record that can take them back to that show, that they can listen to over and over again."
|
{
"pile_set_name": "Pile-CC"
}
|
Founded in 2016 in London, Ethical Hour Ltd limited offers investors from around the world favorable conditions to earn in the Forex market and on the London Stock Exchange. The company?s business is managed by a team of professional trade analysts, lawyers, multi-currency and stock market traders. The Ethical Hour Ltd limited is an incredibly ambitious and purposeful company. While being a relatively new player in the trading world, the company has registered remarkable growth over the past few months. Basically this is due to the tremendous support of our customers, partners and staffers. In addition, continual improvement of trading conditions, start-demand financial instruments, taking care of every client - all this has ensured the rapid development of the company.
Our online investment platform encompasses all aspects of user interaction with company. You will need just few easy steps to invest. We offer you the favorable and highly profitable investment plans and hope you will select an option to suit your demands. You can earn a huge sum of money without any efforts, the more you deposit, the more you earn. With Ethical Hour Ltd you won?t need to track any financial news, check your open positions and close them with huge losses.
|
{
"pile_set_name": "Pile-CC"
}
|
Tensions are rising between Iran and the U.S., and President Trump isn’t showing any signs of backing down to the oppressive regime. During his recent State of the Union, President Trump referred to Iran as a “radical regime” who does “bad things.”
“My administration has acted decisively to confront the world’s leading state sponsor of terror: the radical regime in Iran,” Trump said Tuesday evening, delivering his address in the U.S. House of Representatives. “They do bad, bad things. To ensure this corrupt dictatorship never acquires nuclear weapons, I withdrew the United States from the disastrous Iran nuclear deal,” he said, referring to the 2015 sanctions-relief-for-nuclear-rollback agreement negotiated under President Barack Obama. “And last fall, we put in place the toughest sanctions ever imposed by us on a country. “We will not avert our eyes from a regime that chants death to America and threatens genocide against the Jewish people,” he continued, to applause, mostly from the Republican side. “We must never ignore the vile poison of anti-Semitism, or those who spread its venomous creed.”
Yesterday, CBS News reported from Tehran where hundred of thousands of Iranians were celebrating the 40th anniversary of the Islamic Revolution.
Speaking in the capital Tehran, President Hassan Rouhani told a huge crowd Iran didn’t need to ask the world’s permission to develop missiles, and it would continue to build up its military power despite U.S. sanctions.
Some of the people in the crowd were old enough to have actually participated in the revolution, but for the younger ones, the Islamic Republic that followed is the only country they’ve ever known. That means all they’ve ever known is a relationship with the U.S. that ranges from hostile, to downright toxic.
Now, according to the Free Beacon – Iran is being accused of committing cyber attacks on the U.S. and of recruiting a U.S. Air Force member to steal classified information from the U.S. government, including the identities of U.S. agents.
The Trump administration has announced a new package of sanctions on Iranian entities tied to the cyber backing of U.S. individuals, a move that comes on the heels of American authorities indicting a U.S. Air Force officer who allegedly tried to pass classified information to Tehran after defecting to the country.
The Department of Justice has announced early Wednesday that it had indicted Monica Elfriede Witt, also known as Fatemah Zahra, a former active duty U.S. Air Force Intelligence Specialist and Special Agent, for attempting to pass classified American information to Iran.
The disclosure of this information leak was timed to coincide with an announcement by the Treasury Department that it is sanctioning a handful of Iranian entities for their role in cyber hacks on Americans.
The sanctions hit an Iranian-based entity tied to the country’s Revolutionary Guards Corps, or IRGC. This includes “efforts to recruit and collect intelligence from foreign attendees [of various conferences], including U.S. persons, and four associated individuals,” according to the Treasury Department.
Should Trump appoint a new Supreme Court Justice before the election?
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“Treasury is taking action against malicious Iranian cyber actors and covert operations that have targeted Americans at home and overseas as part of our ongoing efforts to counter the Iranian regime’s cyber attacks,” Treasury Secretary Steven Mnuchin said in a statement. “Treasury is sanctioning New Horizon Organization for its support to the IRGC-QF. ”
|
{
"pile_set_name": "OpenWebText2"
}
|
Peacock — who was born without part of his brain and suffers from multiple mental health issues — filed a misdemeanor assault charge in November with the help of a magistrate. Prosecutors later reviewed a video of the incident and decided to drop the misdemeanor and pursue felonies.
|
{
"pile_set_name": "OpenWebText2"
}
|
South Ferry, Brooklyn
South Ferry was a ferry landing on the Brooklyn side of the East River, at the foot of Atlantic Avenue below the Brooklyn Heights neighborhood. It is now Piers 5 and 6 in Brooklyn Bridge Park.
History
The name "South Ferry" does not derive from serving the southern tip of Manhattan and what was then known as "South Brooklyn", it was the name of one of the ferries between what were then the separate cities of New York and Brooklyn. The "Old Ferry", which later was renamed the "Fulton Ferry", crossed between Manhattan and Brooklyn from streets that in each city would eventually be renamed "Fulton Street". The "New Ferry" crossed further east, between Catherine Street in Manhattan, and Main Street in Brooklyn.
As the City of Brooklyn grew, the area south of Atlantic Avenue (known as "South Brooklyn") began to become built-up, but lacked easy access to the ferry terminals in the northern parts of the city of Brooklyn. Thus, the South Ferry Company established the South Ferry on May 16, 1836 to connect Lower Manhattan to the foot of Atlantic Avenue in Brooklyn and the month-old Brooklyn and Jamaica Railroad – later the Atlantic Avenue Railroad's streetcar line, and later still part of the Long Island Rail Road, now called the Atlantic Branch – through the Cobble Hill Tunnel. "South Ferry" is still the name of the area of lower Manhattan where the ferry's landing was, and was also the name of the Brooklyn landing and ferry house, although the name is no longer in use.
The Fulton Ferry Company, which then operated only the Fulton Ferry, merged with the South Ferry Company in 1839 to form the New York and Brooklyn Union Ferry Company.
In the 20th and early 21st centuries, the site served cargo as Brooklyn Piers 5 and 6, which are now part of Brooklyn Bridge Park.
See also
Battery Maritime Building
South Ferry (Manhattan)
List of ferries across the East River
References
Category:Transportation in Brooklyn
Category:Piers in New York City
|
{
"pile_set_name": "Wikipedia (en)"
}
|
Empty Canvas
December 2, 2006
One of my friend ask me last night on Y!M..
“Ram..if you have to imagine your girlfriend..what would be she like?”
“Well, have you ever try to imagine a beautiful painting, but all you can see is an empty canvas?”
“Huh? you mean?”
“I can't even imagine.”
I signed out.
Well, i don't know whether there's too many girl whom i liked, or actually there is none. Weird, isn't it?
I have gone through so many difficult times, but my friends always cheer me up.
So i smiled.
A smile that hurt.
A canvas that still empty.
Waiting for me,
and her.
|
{
"pile_set_name": "Pile-CC"
}
|
Breast milk provides optimal nutrition for infants, and it gives them immune protection that no formula company has been able to replicate. How many other secrets does it contain? Many mothers claim that it is also an effective treatment for eye infections, or conjunctivitis. The anecdotal evidence for this practice is overwhelming, but is there any scientific evidence that it actually works?
What is conjunctivitis?
Conjunctivitis is an infection and/or swelling of the membrane that lines the eyelids. Symptoms include redness, swelling, and goopiness of the eyes. The most common cause of conjunctivitis is a viral infection, also known as pink eye. Pink eye is highly contagious and often passed around daycares and schools.
Viral conjunctivitis usually goes away without treatment within a week. Bacterial conjunctivitis is less common and is often treated with antibiotic eye drops [1]. Allergies or irritation (from something like shampoo, for example) can also cause conjunctivitis in children [2].
Babies can also have a blocked tear duct, which causes excessive tearing, sometimes with thick, goopy tears. A blocked tear duct can affect a baby off and on for the first year of life – beyond that, the child should see an eye doctor for treatment [2].
What is the research on breast milk and eye infections?
There are three studies that might have some relevance to this question, but all of them focus on eye infections or blocked tear ducts in newborns. To my knowledge, there are no studies of breast milk as a treatment for conjunctivitis in older babies or children.
Note that colostrum was used in the studies described below. Colostrum is the first milk produced for several days after the baby’s birth, before the mature milk comes in. Colostrum is much higher in antibodies than mature milk.
Study #1: Conducted in India, 51 newborns were given drops of colostrum in their eyes for 3 days, while 72 control newborns received no eye treatments [3]. About 35% of the control infants and 6% of the colostrum infants developed visible eye infections during the experiment. At first glance, these results make colostrum look like a champion infection-preventer! Unfortunately, this is an example of a study that had so many design problems that the data just aren’t that useful. During the 4 years prior to the study, the hospital had just a 5% rate of conjunctivitis. Why then did the control group have a 35% rate of infection? This isn’t clear. The colostrum babies roomed in the South Wing of the hospital, and many of them were delivered by C-section. The control babies were housed in the North Wing and were all vaginal births. It would have been better to randomize the colostrum and control babies with some in each wing so that they had equal pathogen exposure. What if the North Wing (control) had a huge outbreak during the two months of this study? On the bright side, this study found no safety issues with using colostrum in newborns’ eyes.
Study #2: This was an in vitro study (conducted in petri dishes) of eye infections in 22 Nigerian newborns [4]. The infected babies’ eyes were swabbed, and the bacteria on the swabs were incubated with several different antibiotics, colostrum, and mature milk. The major bacteria types found in this study were Staph aureus and coliforms, and the graphs below show how sensitive they were to 3 of the most effective antibiotics, colostrum, and mature milk.
For example, the growth of Staph aureus was 100% inhibited by the antibiotic gentamicin, 50% inhibited by colostrum, and not inhibited at all by mature milk. What does this study tell us? It tells us that the effectiveness of breast milk against eye infections depends on the type of infection and that colostrum is more effective than mature milk. Remember that this study only looked at two types of bacteria among the many that might cause eye infections, and it didn’t look at viral infections at all. Plus, we always have to be careful about interpreting an in vitro study, because bacteria might grow differently on a petri dish vs. on the eye.
Study #3: A small study conducted in Spain retrospectively compared antibiotic drops and breast milk as treatments for blocked tear ducts in newborns [5]. The blocked tear ducts cleared up faster with breast milk than with antibiotics, and breast milk appeared to be completely safe.
Conclusion: Will breast milk cure my child’s eye infection? What about her blocked tear duct?
There isn’t enough research on the subject to know for sure. The studies described above show that using breast milk in a baby’s eye is likely safe and may be effective against bacterial infections and blocked tear ducts. Colostrum appears to be more effective than mature milk, probably because it has higher concentrations of antibodies (especially IgA). Whether or not mature milk will cure an older baby or child’s viral pink eye has not been studied at all.
One important caveat: If your newborn has an eye infection, you should call your child’s pediatrician right away. If left untreated, neonatal conjunctivitis can cause lasting damage to your child’s eyes, including blindness. Don’t risk waiting several days to see if breast milk clears things up in these cases.
(As always, I am not a medical doctor, and the information presented here is not medical advice. Please seek the help of a medical professional if you need medical advice.)
Have you tried breast milk as a treatment for eye infections? Did it seem to help?
REFERENCES
1. PubMed Health. Conjunctivitis. A.D.A.M. Medical Encyclopedia 2010 [cited 2011 November 6].
2. Fields, D. and A. Brown. Baby 411: Clear Answers and Smart Advice for Your Baby’s First Year. 3rd ed. Boulder, CO: Windsor Peak Press. 2008.
3. Singh, M., P.S. Sugathan, and R.A. Bhujwala. Human colostrum for prophylaxis against sticky eyes and conjunctivitis in the newborn. J Trop Pediatr. 28(1): p. 35-7. 1982.
4. Ibhanesebhor, S.E. and E.S. Otobo. In vitro activity of human milk against the causative organisms of ophthalmia neonatorum in Benin City, Nigeria. J Trop Pediatr. 42(6): p. 327-9. 1996.
5. Verd, S. Switch from antibiotic eye drops to instillation of mother’s milk drops as a treatment of infant epiphora. J Trop Pediatr. 53(1): p. 68-9. 2007.
|
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"pile_set_name": "OpenWebText2"
}
|
Bill O’Reilly in 2015 on the set of “The O'Reilly Factor” in New York. (Brendan McDermid/Reuters)
Fox News and its star host Bill O’Reilly appear to have developed a strategy in response to allegations of serial sexual harassment and the mass defections of advertisers from O’Reilly’s program: Say as little as possible.
The voluble TV personality has said nothing on the air about the controversy since it broke over the weekend. Fox News has all but ignored any reporting about it in its broadcasts and on its website; its one acknowledgment was a 25-second summary on its “Media Buzz” program on Sunday. It has not mentioned the advertiser reaction.
Fox’s parent company, meanwhile, has confined its comments to a brief statement issued Saturday saying, in part, that it “takes matters of workplace behavior very seriously.”
Dozens of advertisers have suspended their sponsorship of O’Reilly’s top-rated program, “The O’Reilly Factor,” since the story broke that O’Reilly and Fox have settled five claims that he harassed women at Fox, paying out $13 million since 2002. A sixth woman, who has not sought payment, said she, too, was pressured for sex by O’Reilly and was punished at Fox when she refused.
Fox News’s only statement on the matter was one issued Tuesday from its top ad executive, Paul Rittenberg, who said ads withdrawn from “The O’Reilly Factor” would be moved to other Fox programs.
(Erin Patrick O'Connor/The Washington Post)
The network declined again Thursday to respond to questions. Fox’s parent, 21st Century Fox, did not respond at all when asked for comment.
The takeaway from Fox’s non-response isn’t clear. On one hand, the lack of supportive statements for O’Reilly could reflect official disapproval, while Fox has shown no outward signs that it has disciplined O’Reilly or that it intends to punish its biggest star.
Conversely, the blanket of silence could represent the best of a series of bad options. By not responding publicly, O’Reilly, Fox and 21st Century may be hoping that the attention surrounding the issue will eventually subside.
So far, O’Reilly’s audience has not only stuck with him — it has grown. “The O’Reilly Factor” attracted 3.8 million viewers Tuesday night, according to Nielsen, a 20 percent increase over the program’s ratings a week before and 19 percent more than on the same date last year.
O’Reilly’s silence in this instance stands in stark contrast to the last time he was the story. After Mother Jones magazine published a piece in 2015 questioning O’Reilly’s claims about reporting on the Falkland Islands war in the early 1980s, O’Reilly mounted an aggressive campaign to rebut the article’s premise.
In various interviews with reporters, he called the story “slander” and labeled its principal author, David Corn, “a liar” and “a guttersnipe” who should be put in “the kill zone.” O’Reilly also warned a New York Times reporter, Emily Steel, that if the Times’ coverage of the topic was inaccurate or inappropriate, he would be “coming after you with everything I have. You can take it as a threat.” (Steel was an author of the Times story, published Saturday, about O’Reilly’s harassment settlements.)
O’Reilly’s attack on Corn and other journalists in 2015 did not quell the controversy, however. News organizations soon dug up other instances in which O’Reilly had exaggerated his exploits as a reporter.
For Fox, the current controversy is complicated by its connection to a larger scandal about the network — the sexual-harassment allegations that led to the ouster of its chairman, Roger Ailes, last year.
Given that context, O’Reilly and Fox may have no choice but to keep mum now lest they remind people of the earlier scandal, Corn said.
“O’Reilly lives to fight,” he said. “But in this instance, who’s he going to attack? The women? Anything he can say would only elongate the newsiness of this scandal. His only play is to hope this passes. It must make him very, very sad that there’s no one for him to insult here.”
(O’Reilly addressed the issue Saturday in a brief statement portraying himself as a target of opportunistic people.)
Crisis management experts, however, say silence is rarely a good idea in the midst of controversy.
Michael Fineman, who heads a crisis-counseling company, advises clients in such situations to put out all the facts at once, take responsibility for the controversy, express concern for those affected and make assurances of reform.
In this case, that may mean Fox should remove O’Reilly from the air, temporarily or permanently, said Steven Fink, the author of “Crisis Communications: The Definitive Guide to Managing the Message.” Fink said NBC News sent a strong and reassuring signal to viewers and nervous advertisers in 2015 by suspending anchor Brian Williams for six months after finding that he exaggerated various stories.
“As long as O’Reilly’s on the air, I don’t think this story will die,” Fink said. “In an era of social media, there are enough people who will not let this go by quietly.”
But Eric Dezenhall, a Washington-based communications counselor, said Fox and O’Reilly have very few choices. “Crisis management is the art of navigating abominable options,” said Dezenhall, who has appeared on O’Reilly’s show. “The question is not whether silence is the best option. It is a question of it being the least awful option given a variety of variables we just don’t know about as outsiders.”
|
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"pile_set_name": "OpenWebText2"
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|
Little Pea
Little Pea by Amy Krouse Rosenthal is a funny, simple and sweet book to read during mealtime. This book is about a young pea who wants to grow up to be big and strong. What he needs to grow up to be big and strong is candy, which is Little Pea’s least favorite food! His favorite food is spinach, which he eats up in no time for dessert. Many kids can relate to how Little Pea feels about having to eat all of his meal before devouring dessert. This book is silly, cute and fun for all ages. Learning concepts include colors, descriptive concepts, prepositions, days of the week and sequencing. Great for picky eaters!
|
{
"pile_set_name": "Pile-CC"
}
|
Q:
Manipulating CSV Data with Javascript
I have two .csv files and i need to make one table for both files in simple html page.
First file (devices.csv) has id,name,units where units the number of ports that device can connect.
Second file (connections.csv) has reference id for the first file and unit_number that is connected in each device.
Now the final result should read the text files and display the information in a way that will allow the user to check how many units are within each devices and which units are connected or free.
devices.csv
id,name,units
1,CAB-01,20
2,CAB-02,10
3,DP-01,4
4,DP-02,12
5,CAB-01,0
6,DP-01,24
connections.csv
device_id,unit_number
1,1
1,3,
1,17
1,18
1,19
7,1
1,20
2,10
3,1
3,2
1,5
4,12
4,1
1,6
2,1
1,7
3,4
1,8
1,9
4,11
4,1
4,3
1,10
2,2
2,3
2,4
3,3
1,12
1,14
4,4
1,15
1,16
2,6
2,8
5,1
my js file :
function handleFiles(files) {
// Check for the various File API support.
var data = new Object;
if (window.FileReader) {
var j = 0, k = files.length;
for (var i = 0; i < k; i++) {
//j++;
getAsText(files[i]);
};
}
// FileReader are supported.
//}
else {
alert('FileReader are not supported in this browser.');
}}
function getAsText(fileToRead) {
var reader = new FileReader();
reader.onload = loadHandler;
reader.onerror = errorHandler;
reader.readAsText(fileToRead);
}
function loadHandler(event) {
var csv = event.target.result;
processData(csv);
}
function processData(csv) {
var allTextLines = csv.split(/\r\n|\n/);
var lines = [];
while (allTextLines.length) {
lines.push(allTextLines.shift().split(','));
}
console.log(lines);
drawOutput(lines);
}
function errorHandler(evt) {
if(evt.target.error.name == "NotReadableError") {
alert("Canno't read file !");
}
}
function drawOutput(lines){
var table = document.createElement("table");
for (var i = 0; i < lines.length; i++) {
var row = table.insertRow(-1);
for (var j = 0; j < lines[i].length; j++) {
var firstNameCell = row.insertCell(-1);
firstNameCell.appendChild(document.createTextNode(lines[i][j]));
console.log(firstNameCell);
};
}
document.getElementById("output").appendChild(table);
}
please help
A:
Before pushing it all into DOM (or HTML) you should convert the data from the two sources into one. Say, each device should be represented as: "name", "units", "unit_numbers"
Let's try & implement it:
var data_devices = ["1,CAB-01,20", "2,CAB-02,10", "3,DP-01,4", "4,DP-02,12", "5,CAB-01,0", "6,DP-01,24"];
var data_connections = ["1,1", "1,3,", "1,17", "1,18", "1,19", "7,1", "1,20", "2,10", "3,1", "3,2", "1,5", "4,12", "4,1", "1,6", "2,1", "1,7", "3,4", "1,8", "1,9", "4,11", "4,1", "4,3", "1,10", "2,2", "2,3", "2,4", "3,3", "1,12", "1,14", "4,4", "1,15", "1,16", "2,6", "2,8", "5,1"];
var data = {};
data_devices.forEach(function(d) {
d = d.split(",");
data[d[0]] = { "name":d[1], "units":d[2], "unit_numbers":[] };
});
data_connections.forEach(function(d) {
d = d.split(",");
if(data[d[0]]) data[d[0]].unit_numbers.push(d[1]);
});
The data variable is now queryable & looks like this:
{
"1": {
"name": "CAB-01",
"units": "20",
"unit_numbers": [
"1",
"3",
"17",
"18",
"19",
"20",
"5",
"6",
"7",
"8",
"9",
"10",
"12",
"14",
"15",
"16"
]
},
"2": {
"name": "CAB-02",
"units": "10",
"unit_numbers": [
"10",
"1",
"2",
"3",
"4",
"6",
"8"
]
},
"3": {
"name": "DP-01",
"units": "4",
"unit_numbers": [
"1",
"2",
"4",
"3"
]
},
"4": {
"name": "DP-02",
"units": "12",
"unit_numbers": [
"12",
"1",
"11",
"1",
"3",
"4"
]
},
"5": {
"name": "CAB-01",
"units": "0",
"unit_numbers": [
"1"
]
},
"6": {
"name": "DP-01",
"units": "24",
"unit_numbers": []
}
}
|
{
"pile_set_name": "StackExchange"
}
|
1965 World Figure Skating Championships
The 1965 World Figure Skating Championships were held in Colorado Springs, Colorado, USA from March 2 to 7. At the event, sanctioned by the International Skating Union, medals were awarded in men's singles, ladies' singles, pair skating, and ice dance.
Results
Men
Judges:
Edwin Kucharz
William E. Lewis
Zdeněk Fikar
N. Valdes
Eugen Romminger
Ferenc Kertész
Sonia Bianchetti
Yvonne S. McGowan
Sergei Vasiliev
Ladies
Judges:
Martin Felsenreich
Ralph S. McCreath
Emil Skákala
Jeanine Donnier-Blanc
Carla Listing
Pamela Davis
Haruo Konno
Jane Sullivan
Tatiana Tolmacheva
Pairs
Judges:
Walter Malek
Ralph S. McCreath
Erika Schiechtl
Carla Listing
Ercole Cattaneo
Pamela Davis
René Schlageter
H. Janes
Tatiana Tolmacheva
Ice dance
Judges:
Walter Malek
Dorothy Leamen
Emil Skákala
Lysiane Lauret
Ferenc Kertész
Robert S. Hudson
M. Ridgely
Sources
Result list provided by the ISU
Category:World Figure Skating Championships
World Figure Skating Championships
Category:Sports competitions in Colorado Springs, Colorado
Category:International figure skating competitions hosted by the United States
Category:1965 in American sports
World Figure Skating Championships
Category:March 1965 sports events
Category:1960s in Colorado Springs
|
{
"pile_set_name": "Wikipedia (en)"
}
|
Current scenario and future strategies to fight artemisinin resistance.
Despite several setbacks in the fight against malaria such as insecticide and drug resistance as well as low efficacy of available vaccines, considerable success in reducing malaria burden has been achieved in the past decade. Artemisinins (ARTs and their combination therapies, ACTs), the current frontline drugs against uncomplicated malaria, rapidly kill plasmodial parasites and are non-toxic at short exposures. Though the exact mode of action remains unclear, the endoperoxide bridge, indispensable for ART activity, is thought to react with heme released from hemoglobin hydrolysis and generate free radicals that alkylate multiple protein targets, thereby disrupting proteostasis pathways. However, rapid development of ART resistance in recent years with no potential alternatives on the horizon threaten the elimination efforts. The Greater Mekong Subregion in South-East Asia continues to churn out mutants resistant to multiple ACTs and detected in increasingly expanding geographies. Extensive research on ART-resistant strains have identified a potential candidate Kelch13, crucial for mediating ART resistance. Parasites with mutations in the propeller domains of Plasmodium falciparum Kelch13 protein were shown to have enhanced phosphatidylinositol 3-kinase levels that were concomitant with delayed parasite clearance. Current research focused on understanding the mechanism of Kelch13-mediated ART resistance could provide better insights into Plasmodium resistome. This review covers the current proposed mechanisms of ART activity, resistance strategies adopted by the parasite in response to ACTs and possible future approaches to mitigate the spread of resistance from South-East Asia.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Castle Rebirth
When I tried to revisit my childhood and play some castle, I realized, while still a great game, its a little dated. I decided that I am going to be revamping the beloved BYOND classic, to better use some of BYONDs newerish features.
|
{
"pile_set_name": "Pile-CC"
}
|
Loss of natural dentition: multi-level effects among a geriatric population.
To quantify the impact of edentulousness on residual ridge volume, denture stomatitis (DS), as well as oral health behaviours among geriatric denture-wearers. Residual ridge resorption (RRR) is the primary intraoral complication of complete edentulism, but individual variation among geriatric patients has been observed. Data collection relied upon a 10-year retrospective chart review of all complete denture-wearing geriatric patients presenting at the Removable Prosthodontics Clinic, Dental School of Athens, between 1993 and 2002. Analyses relied on descriptive, bivariate, and multivariate methods based on ordinal logistic regression. A total of 873 records of geriatric patients (age mean = 72; median = 70; range = 65-95) comprised our analytical sample. Subjects' mean (SD) time since edentulation was 7.7 (10.2) years. Eleven percent were diagnosed with temporomandibular disorder (TMD). While 28% of patients reported cleaning their dentures at least daily, 6% presented with denture stomatitis (DS). Each added year of edentulism increased the odds of mandibular RRR: OR (95% CI) = 1.05 (1.03, 1.07). Nightly denture wear was the strongest risk factor for DS. Finally, independent of age and sex, each year of being edentulous increased the odds of presenting with TMD: OR (95% CI) = 1.03 (1.01, 1.05). Time since edentulation was strongly associated with mandibular but not maxillary RRR, as well as TMD development.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
Introduction {#s1}
============
It is commonly accepted that in order for a neuronal population to encode the value of a quantity x, it must contain cells tuned to a range of values of x. Thus for example the retina can encode information about the wavelength of light because it contains three different types of cones with different tuning to wavelength, and the primary visual cortex can encode feature orientation because it contains neurons tuned to a range of orientations. This is unproblematic because natural images contain a wide range of light wavelengths and object orientations. However, the same argument applied to stereo vision produces some more challenging conclusions.
The expected vertical disparity in natural viewing depends on position in the retina, with opposite signs in opposite quadrants of the visual field. The range in vertical disparities encountered at a given position depends on a number of assumptions about eye movement and scene statistics, but all attempts to estimate it agree that it is extremely narrowly distributed compared to horizontal disparity [@pcbi.1000754-Liu1], [@pcbi.1000754-Hibbard1], [@pcbi.1000754-Read1]. Thus, if disparity sensors in the brain were to reflect disparity in the natural world, we would expect the distribution of two-dimensional disparity tuning at a given retinotopic location to be highly elongated, virtually one-dimensional, with a wide range of horizontal disparity and a narrow range of vertical disparity, centered on the value expected for that retinotopic location. Yet, vertical disparities which hardly ever occur in normal visual experience can still have demonstrable effects on perception in the lab [@pcbi.1000754-Helmholtz1], [@pcbi.1000754-Ogle1], and there is evidence that stereo matching occurs in all 2D directions, vertical as well as horizontal [@pcbi.1000754-Farell1]. Thus, the brain clearly can extract unusual vertical disparities, on relatively local scales [@pcbi.1000754-SerranoPedraza1], [@pcbi.1000754-Rogers1], [@pcbi.1000754-Kaneko1]. This has led to the conclusion that the brain must contain neurons tuned to a range of vertical disparities, including highly unusual ones, on the assumption that otherwise, these disparities could not be perceived [@pcbi.1000754-Durand1], [@pcbi.1000754-Durand2], [@pcbi.1000754-Gonzalez1].
Motivated by this, a number of physiological studies have examined two-dimensional disparity tuning in cortical neurons in monkey primary visual cortex (V1). Near the fovea, most disparity-tuned neurons are tuned to vertical disparities which are not significantly different from zero, given the confidence interval on the measurement [@pcbi.1000754-Cumming1]. In the visual periphery, neurons tuned to non-zero vertical disparities have been reported [@pcbi.1000754-Durand1], [@pcbi.1000754-Durand2], [@pcbi.1000754-Gonzalez1]. Unfortunately, these studies only reported disparity in head-centric coordinates, which can differ substantially from retino-centric disparity [@pcbi.1000754-Read2]. For example, it is perfectly possible for a neuron tuned to a substantial head-centric vertical disparity, say 0.3°, to be tuned to a vertical disparity of 0° on the retina [@pcbi.1000754-Read1]. Thus, the published data do not enable us to draw any conclusions about 2D disparity tuning on the retina. Furthermore, these studies did not report the retinal location of individual neurons, making it impossible to assess whether a range of vertical disparity tuning is found at a single retinotopic location.
Given this lack of data from physiology, theoretical considerations become important. A clear understanding of how, in principle, neurons could represent two-dimensional disparity is essential for guiding future physiology experiments. We recently argued [@pcbi.1000754-Read3] that a population of model binocular neurons like that shown in [Figure 1](#pcbi-1000754-g001){ref-type="fig"}, tuned to a range of horizontal disparities and orientations but all tuned to zero vertical disparity on the retina, nevertheless encodes information about the vertical disparity of the stimulus. This original model only extracted the magnitude, not the sign, of the local vertical disparity, and we later demonstrated that this was inconsistent with human psychophysics [@pcbi.1000754-SerranoPedraza2]. However, this model did not make optimal use of the information available in the population. In the present paper, I show that this population of disparity sensors does contain information about both the magnitude and the sign of the vertical disparity at that point in the retina, even if all neurons in the population are tuned to the same vertical disparity. With an appropriate decoding technique, information about the two-dimensional disparity can be deduced from activity in this one-dimensional population. This result is of interest in its own right as a theoretical demonstration that it is possible to extract the value of a quantity from a neuronal population, all of whose members respond optimally to the same value of that quantity. From the point of view of understanding stereo vision, it means that two-dimensional disparity may be represented far more efficiently than previously appreciated.
![A neuronal population which explicitly encodes horizontal, but not vertical, disparity.\
The shaded region represents the space of two-dimensional disparity on the retina [@pcbi.1000754-Read2]. The purple disks represent the preferred 2D disparity of an idealized population of disparity sensors. Although these sensors form a one-dimensional population, all tuned to zero vertical disparity, they can nevertheless encode two-dimensional stimulus disparity, e.g. the stimulus disparity represented by the green dot, which has both a horizontal and a vertical component. (Cf [figure 1](#pcbi-1000754-g001){ref-type="fig"} of Serrano-Pedraza & Read [@pcbi.1000754-SerranoPedraza2].)](pcbi.1000754.g001){#pcbi-1000754-g001}
Methods {#s2}
=======
Overview {#s2a}
--------
The essential insight guiding this paper is relatively trivial. According to the stereo energy model of disparity-selective neurons [@pcbi.1000754-Ohzawa1], [@pcbi.1000754-Ohzawa2], cells with obliquely-oriented receptive fields will also have obliquely-oriented disparity tuning surfaces, like the one illustrated in [Figure 2A](#pcbi-1000754-g002){ref-type="fig"}. This cell\'s optimal disparity is marked with a red circle. It has zero vertical component, i.e. the cell responds best to zero vertical disparity. [Figure 2B](#pcbi-1000754-g002){ref-type="fig"} shows two cross-sections through this surface, corresponding to vertical disparity tuning curves for two different horizontal disparities, as indicated by the vertical lines in [Figure 2A](#pcbi-1000754-g002){ref-type="fig"}. At the optimal horizontal disparity (red curve), the cell responds best to zero vertical disparity. But at horizontal disparities away from the optimum (e.g. purple curve), the cell\'s response is reduced, but is now tuned to a non-zero vertical disparity. Thus, while the cell in [Figure 2](#pcbi-1000754-g002){ref-type="fig"} is "tuned to zero vertical disparity" in that its optimum 2D disparity has zero vertical component, when it is probed at horizontal disparities on either side of the optimum, it responds best to vertical disparities on either side of zero. This suggests that, given cells tuned to a range of orientations and horizontal disparities, one could potentially extract the stimulus orientation, horizontal disparity *and* vertical disparity. Of course, it may not be quite that simple. In order to use the cells\' tuning to vertical disparity away from the optimal horizontal disparity, one has to know what the horizontal disparity is. Extracting this may be hard in the presence of vertical disparity, since then none of the cells in the population is tuned to the correct stimulus disparity. Also, because the tuning to vertical disparity occurs only at sub-optimal horizontal disparities, the neuron\'s activity is weaker, so more subject to noise. Thus, this intuitive idea has to be rigorously tested by simulation. This is what is achieved in this paper.
{#pcbi-1000754-g002}
The simulations consist of two neuronal populations: one encoding population, which takes left and right retinal images and performs the initial encoding of binocular disparity, and one decoding population, which estimates the disparity of the stimulus. The encoding population is like that in [Figure 1](#pcbi-1000754-g001){ref-type="fig"}: it consists of a set of neurons tuned to a range of horizontal disparities, orientations and spatial frequencies, but all tuned to the same vertical disparity. For simplicity, I shall set this vertical disparity to be zero, which is appropriate for the parafoveal region.
The encoding neurons are based on the stereo energy model [@pcbi.1000754-Ohzawa1], normalized so as to report the effective local binocular correlation [@pcbi.1000754-Read3], [@pcbi.1000754-Banks1], [@pcbi.1000754-Filippini1]. The activity of this population is then decoded by a separate, higher-level population, using a template-matching approach like that of Tsai & Victor [@pcbi.1000754-Tsai1]. The synaptic weights from the encoding to the decoding population store the mean response of the population to stimuli with a range of different two-dimensional disparities. To estimate the two-dimensional disparity of a test image, I simply calculate the correlation between the population response to the test image, and the stored average population response for each known 2D disparity. The stimulus disparity is taken to be that giving the highest correlation, i.e. the best match to the mean response.
Disparity encoding {#s2b}
------------------
### Receptive fields {#s2b1}
The monocular receptive fields were Gabor functions varying in their preferred orientation θ, spatial frequency f, receptive field size σ, receptive field phase φ, and position on the retina ([Figure 3](#pcbi-1000754-g003){ref-type="fig"}). The two receptive fields of a given binocular neurons always had the same orientation, frequency and size, but could differ in their phase and position, reflecting the properties of real neurons in primary visual cortex [@pcbi.1000754-DeAngelis1], [@pcbi.1000754-Anzai1], [@pcbi.1000754-Prince1], [@pcbi.1000754-Bridge1], [@pcbi.1000754-Read4]. Thus, the model binocular simple cells in general had both position and phase disparity [@pcbi.1000754-DeAngelis1]. All model binocular simple cells were tuned to the same cyclopean position, which was the origin. That is, the mean of the receptive field centers in the left and right eyes was (0,0) for all cells.
{ref-type="supplementary-material"}.](pcbi.1000754.g003){#pcbi-1000754-g003}
The aim of this study is to demonstrate that vertical disparity can be implicitly encoded by a population of neurons that are all tuned to a single vertical disparity. Here, I choose this single vertical disparity tuning to be zero, reflecting the vertical disparity expected at the fovea, (0,0). At other retinotopic locations, a different value would be appropriate, reflecting the expected vertical disparity at that location [@pcbi.1000754-Read2]. The particular value chosen is not important to the demonstration, only the fact that it is the same for all neurons in the population. Including phase disparity in the model makes this slightly more complicated, since for neurons tuned to non-vertical orientations, phase disparity adds both a horizontal and a vertical component to the preferred disparity. To deal with this, each neuron is given a position disparity chosen to cancel out the component introduced by the phase disparity. Thus, even in considering a single neuron, there are several different meanings of disparity to distinguish. In this paper, Δ*x* ~enc~ will indicate the preferred horizontal disparity of an encoding neuron, i.e. the horizontal disparity which elicits its maximum firing rate (the preferred vertical disparity of all encoding neurons is Δ*y* ~enc~ = 0). Δφ indicates the phase disparity of an encoding neuron. Finally (Δ*x* ~pos~,Δ*y* ~pos~) indicates the two-dimensional position disparity, chosen to beFor sufficiently narrow-band cells, this ensures that the neuron is tuned to the desired horizontal disparity of Δ*x* ~enc~, and to zero vertical disparity.
The left and right eye receptive fields of the binocular simple cell tuned to orientation θ, frequency f, receptive field size σ, phase φ and horizontal disparity Δx are thenwhere x′ and y′ are retinal coordinates offset to the centre of the receptive field, and rotated to line up with the cell\'s preferred orientation: taking the + signs for *x*′~L~, *y*′~L~, and the − minus signs for *x*′~R~, *y*′~R~, and where the position disparity (Δ*x* ~pos~,Δ*y* ~pos~) is as specified in Equation 1.
The population included a range of values for preferred orientation θ, spatial frequency *f*, receptive field size σ, phase φ, phase disparity Δφ and horizontal disparity Δ*x* ~enc~ , as follows:
1. Orientation θ: 6 values, −60°, −30°, 0°, 30°, 60° and 90°. 90° is horizontal, 0° is vertical.
2. Phase φ: 2 values, 0 or π/2 (this is all that is needed to achieve a phase-invariant complex cell)
3. Horizontal position disparity Δ*x* ~enc~: 21 values, −10 to 10 pixels in steps of 1 pixel.
4. Spatial frequency: 5 values, 0.200, 0.112, 0.0707, 0.0420, 0.0250 cycles per pixel, corresponding to spatial periods λ of 5.00, 8.41, 14.14, 23.81, 40.00 pixels. Receptive field size σ was set equal to 0.35λ.
5. Phase disparity Δφ: 5 values, 0, ±π/4 and ±π/2.
Thus, there were 6×2×21×5×5 = 6300 binocular simple cells. These values were chosen to maximize physiological plausibility while giving reasonable simulation run-times. The different parameters have different effects on the model\'s performance. Self-evidently, sensitivity to a range of horizontal disparities is essential. The model\'s ability to extract the sign of vertical disparity depends on neurons tuned to oblique orientations ([Figure 2](#pcbi-1000754-g002){ref-type="fig"}). A range of spatial frequencies is not required for the model to extract vertical disparity in principle, but does improve the range of vertical disparity magnitudes over which the model performs well. For small vertical disparities, neurons tuned to high spatial frequencies are most sensitive to the disparity. For large vertical disparities, it is neurons tuned to low spatial frequencies which are most informative, since only these have receptive fields large enough to detect the disparity. A range of phase and phase disparity is not necessary for the model to work in principle, but helps to improve the model\'s accuracy [@pcbi.1000754-Read5].
### Stereo energy model {#s2b2}
The output from each receptive field was taken to be the inner product of each eye\'s image I(x,y) with the corresponding receptive field:and similarly for *v* ~R~. *I*(*x*,*y*) represents the contrast of the image at the point (*x*,*y*) relative to the mean luminance: positive values represent bright pixels, and negative values dark ones. In the standard energy model [@pcbi.1000754-Ohzawa1], [@pcbi.1000754-Ohzawa2], [@pcbi.1000754-Qian1], [@pcbi.1000754-Qian2], the response of binocular simple cells would beIt will be convenient to split this into monocular and binocular terms: Energy-model complex cells, which are invariant to stimulus phase, are built by summing the response of binocular simple cells tuned to different phases:As noted in the previous section, my population of simple cells includes only two values of phase, 90° apart. This produces the same results as summing over large number of simple cells with randomly-scattered phase, and is thus a widely-used short-cut in simulating complex-cell responses [@pcbi.1000754-Qian1], [@pcbi.1000754-Adelson1], [@pcbi.1000754-Fleet1].
The stereo energy, E, represents something close to the cross-correlation function between the filtered, windowed images. The problem with using this to extract stimulus disparity is that it reflects not only the degree of similarity between the shifted left- and right-eye images, but also their monocular contrast energy. Thus an energy-model unit may respond strongly either because it is genuinely tuned to the stimulus disparity, or because both its monocular receptive fields happen to contain features which drive them well -- whether or not those features match between the eyes. This makes it difficult to extract stimulus disparity from the stereo energy computed in Equation 3.
### Effective binocular correlation {#s2b3}
To overcome this, I based my template-matching on the response of normalized correlation detectors [@pcbi.1000754-Read3], [@pcbi.1000754-Banks1], [@pcbi.1000754-Filippini1]. These are based on the stereo energy model, but are normalized so that their response ranges between +1 (when the left and right images are identical), and −1 (when the left image is an inverted version of the right). This is achieved by dividing the binocular terms of the energy-model complex cell by the monocular terms:Physiologically, this could be computed by combining the outputs of energy-model neurons with phase-disparities π apart. If two neurons are identical except that their phase-disparities are π apart, then if the first neuron computes E = (M+B), the second will compute (M−B). M and B are then available from the sum and difference of this pair of neurons. Thus the simulations implicitly use the full range of phase disparity, even though only phase disparity in the range \[−π/2,+π/2\] is explicitly simulated.
The quantity *C* computes the correlation coefficient between filtered, local regions of the left and right eye\'s images [@pcbi.1000754-Read5]. It can be thought of as the effective binocular correlation experienced by that cell, and takes values in the range \[−1,1\]. To avoid any later confusion, note that this correlation is quite distinct from the Pearson product-moment correlation coefficient used below to assess how well population activity elicited by a test stimulus matches a template.
I view the population of binocular correlation detectors, *C*(*θ*, *f*,Δφ,Δ*x* ~enc~), as performing the initial encoding of disparity within my model. Recall that there are 6 different orientations, 5 different frequencies, 5 different phase disparities and 21 different horizontal disparities, so the population *C*(*θ*, *f*,Δφ,Δ*x* ~enc~) consists of 3150 different correlation-detectors.
Normalizing the stereo energy *E* so as to obtain the effective binocular correlation *C* removes the confounding effect of monocular contrast, making it much easier to extract the stimulus disparity from peaks in the population activity. *C* has the useful property that it is exactly equal to 1 when the stimulus disparity matches the cell\'s preferred disparity. This is true for *any* pair of stereo images, irrespective of spectral content etc, provided only that the left eye\'s image is related to the right eye\'s image by exactly the same offset relating left and right receptive fields. Under these circumstances, *v* ~L~(*θ, f,φ,Δφ,Δx* ~enc~) = *v* ~R~(*θ, f,φ,Δφ,Δx* ~enc~) for all *θ, f,φ,Δφ,Δx* ~enc~; 2*v* ~L~ *v* ~R~ is then the same as *v* ~L~ ^2^+*v* ~R~ ^2^, and it follows immediately that *C* = 1.
### Noise {#s2b4}
As [Figure 2](#pcbi-1000754-g002){ref-type="fig"} makes clear, these neurons become effectively tuned to non-zero vertical disparities only when stimulated at their non-optimal horizontal disparity. Thus, in this model, vertical disparity is encoded only by neurons firing at below their optimal rate. Given this, it becomes important to be sure that this signal would not be lost in noise in a real neuronal population. To incorporate realistic neuronal noise, I convert the correlation *C*, which can take values \[−1,1\], into an observed spike count, which is necessarily positive or zero. First, I define the mean spike count, *R* ~m~, as *R* ~m~ = *U*(1+*C*), where *U* is the mean number of spikes elicited by a binocularly uncorrelated stimulus. R~m~ is in the range \[0,2*U*\], where 2*U* is the mean number of spikes a perfectly binocularly correlated stimulus elicits from neurons tuned to its disparity. I model neuronal noise as a Poisson process [@pcbi.1000754-Dean1], [@pcbi.1000754-Bair1]. Thus, the actual number of spikes elicited by the stimulus on any given presentation is *R*, where *R* is a random variable drawn from a Poisson distribution with mean *R* ~m~.
The effective level of neuronal noise then depends on the value chosen for *U*. This will depend on the neurons\' maximal firing rate and the length of time assumed to be available for the judgment. If we assume that the firing rate for the optimal disparity is 100Hz [@pcbi.1000754-Prince2] and that the neuronal response is averaged over a 160ms window (since humans can discriminate temporal changes in disparity up to ∼6Hz, [@pcbi.1000754-Norcia1]), this suggests that the most active neurons might fire 16 spikes in the time available for a disparity judgment, yielding an estimate of around 8 spikes for *U*. Since the variance of Poisson noise is equal to its mean, larger values of *U* produce lower noise, and smaller values would mean greater neuronal noise. In fact, as I discuss below, the model is extremely resilient to neuronal noise. To demonstrate this, the results presented here use *U* = 1. This means that the average neuron fires only 1 spike in the time available for a perceptual judgment, resulting in a very large amount of neuronal noise (coefficient of variance 70% for even optimally-tuned neurons).
Variation in the stimuli also contributes an additional effective source of noise. In this model, a stereo stimulus where left and right images are related simply by a shift will always produce an effective binocular correlation of *C* = 1 in neurons tuned to the disparity of the stimulus. However, neurons which are not tuned to the stimulus will produce a correlation which is on average less than 1, but whose precise value depends on the particular properties of the image, e.g. where the regions of high and low contrast happen to fall in relation to the receptive fields. When it comes to estimating the disparity of a single image, this stimulus-driven variation in response has the same deleterious effect as neuronal noise. If the stimulus disparity has a vertical component, it will stimulate none of the neurons optimally, meaning that *C* will be less than 1 (thus variable) for all neurons, and the neurons will be firing at a lower rate (thus subject to more Poisson noise). Thus, both sources of noise are larger for stimuli with vertical disparity.
Disparity decoding {#s2c}
------------------
### Storing templates {#s2c1}
The first step was to generate many examples of the population\'s response to stimuli of known disparity. These "template" stimuli were uniform-disparity random noise patterns. Each pixel in the left eye\'s image, *I* ~L~, was given a random value drawn from a Gaussian with zero mean and unit standard deviation. The right eye\'s image, *I* ~R~, was offset horizontally and/or vertically from the first eye\'s image, and new random pixels were generated to fill the gap ([Figure 4](#pcbi-1000754-g004){ref-type="fig"}).
{ref-type="supplementary-material"}.](pcbi.1000754.g004){#pcbi-1000754-g004}
I produced random noise images with different horizontal and vertical disparities Δ*x* ~stim~ and Δ*y* ~stim~. Δ*x* ~stim~ and Δ*y* ~stim~ both ranged from −10 to 10 pixel in steps of 1 pixel, making a total of 441 different two-dimensional stimulus disparities. At each of these 441 stimulus disparities, I generated 500 random image-pairs, each generated with a different random seed *j*, making a total of 220,500 test stereograms.
For each image-pair (Δ*x* ~stim~,Δ*y* ~stim~, *j*), I calculated the effective binocular correlation as described in Equation 4. I converted this to a mean spike count, and averaged this over 500 different random images, to obtain *W* is the mean number of spikes produced by sensors tuned to orientation θ, frequency *f*, phase disparity Δφ and horizontal disparity tuning Δ*x* ~enc~, when averaged over many different presentations of many different noise images with the same 2D stimulus disparity (Δ*x* ~stim~,Δ*y* ~stim~). The averaging over different presentations of the same image removes the neuronal noise, while the averaging over different images removes stimulus-dependent noise. I envisage this as representing the information stored in the system as a result of visual experience.
### Template matching {#s2c2}
The disparity of an unknown test stimulus can then be estimated by comparing the response of the population to that particular test image with the stored, average response elicited by stimuli with known two-dimensional disparity. The stimulus is taken to have the 2D disparity whose stored activity profile best matches the current activity [@pcbi.1000754-Tsai1].
Let *R* ~test~(*θ*, *f*, Δ*φ*, Δ*x~enc~*) be the number of spikes fired by the encoding population to the particular test image under consideration. Remember that this neuronal population includes cells tuned to 6 different orientations θ, 5 different frequencies *f*, 5 different phase disparities and 21 different horizontal disparities Δ*x* ~enc~, so *R* ~test~(*θ*, *f*, Δ*φ*, Δ*x* ~enc~) is a set of 3150 individual spike-counts. To estimate the disparity of the test stimulus, I compare the population\'s response to the test image, *R* ~test~(θ, *f*, Δ*φ*, Δ*x~enc~*), with the stored mean spike-counts, W, for each of the 441 template stimulus disparities. That is, for each possible two-dimensional disparity (Δ*x* ~dec~, Δ*y* ~dec~) (subscript "dec" for decoding), I calculate the Pearson correlation coefficient, *r*(Δ*x* ~dec~, Δ*y* ~dec~), between the set of 3150 spike-counts obtained for this particular test image, *R* ~test~(θ, *f*, Δφ, Δ*x~enc~*), and the set of 3150 values stored in *W*(*θ*, *f*, Δ*φ*,Δ*x* ~enc~;Δ*x* ~dec~, Δ*y* ~dec~):where Corr(a,b) represents the usual Pearson product-moment correlation coefficient between a and b:where the sum Σ, averages \<\> and standard deviations std are all taken over *θ*, *f*, Δ*φ*, Δ*x* ~enc~, while holding Δ*x* ~dec~ and Δ*y* ~dec~ constant.
I shall always use the word Pearson when referring to this correlation, in order to avoid possible confusion with the effective binocular correlation computed by the encoding neurons, Equation 4. In the figures, I shall use a "jet" colormap (running from blue-green-red) to represent spike-counts based on effective binocular correlation, and a "hot" colormap (black-red-yellow-white) to represent Pearson correlation.
To model the lack of sensitivity to disparity in anti-correlated stereograms [@pcbi.1000754-Cogan1], [@pcbi.1000754-Read6], [@pcbi.1000754-Tanabe1], [@pcbi.1000754-Janssen1], [@pcbi.1000754-Cumming2], I finally set any negative correlations to zero, computingwhere ⌊⌋ indicates halfwave rectification: ⌊*x*⌋ = *x* for *x*\>0, and zero otherwise.
The two-dimensional disparity of the test stimulus is then taken to be the values (Δ*x* ~dec~, Δ*y* ~dec~) which maximizes the halfwave-rectified Pearson correlation *P*(Δ*x* ~dec~,Δ*y* ~dec~).
Matlab code (The Mathworks, Natick, MA; [www.mathworks.com](http://www.mathworks.com)) to run the simulations and generate most of the figures is available as Supplementary Material (although due to the size of the neuronal populations, running all the simulations presented in this paper takes weeks). Details of which functions to use are given in each figure legend. Other functions called by this code are grouped together in the file [Protocol S11](#pcbi.1000754.s011){ref-type="supplementary-material"}.
Results {#s3}
=======
All members of the neuronal population are tuned to zero vertical disparity {#s3a}
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First, it is important to establish that -- despite their wide range in phase disparity, position disparity and orientation -- all the units in our encoding population genuinely are tuned to zero vertical disparity. To this end, [Figure 5](#pcbi-1000754-g005){ref-type="fig"} shows two-dimensional disparity tuning surfaces for 15 example members of the model population of 3150 neurons. Disparity tuning surfaces like this have been measured for real neurons by Cumming [@pcbi.1000754-Cumming1], Durand et al, [@pcbi.1000754-Durand1], [@pcbi.1000754-Durand2] and Gonzalez et al [@pcbi.1000754-Gonzalez1]. Each panel in [Figure 5](#pcbi-1000754-g005){ref-type="fig"} shows the disparity tuning surface for a different model neuron in the encoding population. The pseudocolor represents the mean number of spikes fired by that neuron to stimuli with a given disparity, averaged over many different random noise images. All the neurons shown have the same spatial frequency, f = 0.071cyc/pix, and preferred horizontal disparity, Δ*x* ~enc~ = 6pix. The three rows show neurons tuned to different orientations: vertical, oblique and horizontal, as specified to the left of each row. The five columns show neurons with different phase-disparities Δ*φ*, as labelled at the top of each column. The phase disparity controls the symmetry of the disparity tuning surface: odd-symmetric for Δ*φ* = ±*π*/2, even-symmetric for Δ*φ* = 0, intermediate for Δ*φ* = ±*π*/4. As described in the [Methods](#s2){ref-type="sec"}, phase disparity shifts the preferred disparity in a direction orthogonal to the neuron\'s orientation. Model neurons in the encoding population were given just the right amount of position disparity (Equation 1) to cancel this out and place their peak sensitivity in the region expected for normal vision. This 2D position disparity (Δ*x* ~pos~,Δ*y* ~pos~) is indicated above each panel. When there is no phase disparity (Δ*φ* = 0, middle column), the position disparity is simply equal to the desired disparity tuning, here (6,0). Elsewhere, the model neurons have to be given additional amounts of vertical and/or horizontal position disparity in order to bring the preferred 2D disparity back to the desired value. The white cross in each panel marks the stimulus disparity which elicited the highest response from that neuron, averaged over the 500 images. In every case this is very close to (6,0), indicating that the position disparity specified in Equation 1 has had the desired effect. This was true for all 1350 neurons in our population, as well as the 15 examples shown in [Figure 5](#pcbi-1000754-g005){ref-type="fig"}, demonstrating that Equation 1 achieves its aim of making all neurons in the encoding population respond best to zero vertical disparity.
{ref-type="supplementary-material"}, averaging over 500 stimuli, and the figure was generated with [Protocol S4](#pcbi.1000754.s004){ref-type="supplementary-material"}.](pcbi.1000754.g005){#pcbi-1000754-g005}
Vertical disparity is implicitly encoded in the pattern of activity across the population {#s3b}
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We now move to considering how stimulus vertical disparity is encoded within this population. To do this, instead of plotting the mean response of individual neurons to stimuli with different disparities, as was done in [Figure 5](#pcbi-1000754-g005){ref-type="fig"}, we now plot the mean response of many neurons to stimuli with a given disparity. This is what is shown in [Figure 6](#pcbi-1000754-g006){ref-type="fig"}.
{ref-type="fig"}, where the neuron\'s preferred horizontal disparity was fixed in each panel and the horizontal axis was the horizontal disparity of the stimulus). Each panel shows the mean number of spikes which stimuli with this disparity elicit from 126 neurons, tuned to 21 different horizontal disparities Δx~enc~ and 6 orientations θ, plotted on the horizontal and vertical axes respectively. The 5 panels in each row show sets of 126 neurons tuned to 5 different preferred spatial frequencies. Thus together each row shows the mean response of the zero-phase-disparity sub-population, 630 neurons, averaged over 500 random stimuli with the same stimulus disparity. The stimulus horizontal disparity, Δx~stim~, was set equal to −2 pixels throughout (marked with the arrow in each panel); the stimulus vertical disparity, Δy~stim~, was set to a different value in each row, as indicated to the left of each row. The colorscale is the same as in [Figure 5](#pcbi-1000754-g005){ref-type="fig"}, indicated on the right. Matlab code: The mean responses were obtained with [Protocol S3](#pcbi.1000754.s003){ref-type="supplementary-material"}, and the figure was generated with [Protocol S5](#pcbi.1000754.s005){ref-type="supplementary-material"}.](pcbi.1000754.g006){#pcbi-1000754-g006}
Each row of [Figure 6](#pcbi-1000754-g006){ref-type="fig"} shows the average spike count, *W*(*θ*, *f*,Δ*φ*,Δ*x* ~enc~;Δ*x* ~stim~,Δ*y* ~stim~), for all zero-phase-disparity neurons in the population, elicited by one particular stimulus disparity (Δ*x* ~stim~,Δ*y* ~stim~). (The choice to display the 630 neurons with Δφ = 0 is arbitrary; qualitatively similar plots are obtained for the other phase disparities.) The 6 rows show the response of this population to 6 different stimulus vertical disparities Δy~stim~, as indicated to the left of each row. In each case the stimulus horizontal disparity is Δ*x* ~stim~ = −2 pixels, marked with the arrow in each panel. Each panel shows *W*(*θ*, *f*,Δ*φ*,Δ*x* ~enc~;Δ*x* ~stim~,Δ*y* ~stim~) as a function of Δ*x* ~enc~ (horizontal axis) and θ (vertical axis), for the spatial frequency *f* indicated at the top of the column. Thus, the 6 rows of [Figure 6](#pcbi-1000754-g006){ref-type="fig"} correspond to 6 of the 441 stored responses of this population, which will be used in our template-matching algorithm to extract an estimate of stimulus disparity.
The neurons above the arrow in each panel are those tuned to the horizontal disparity of the stimulus under consideration, Δ*x* ~enc~ = Δ*x* ~stim~. As one would expect, the effective correlation is generally high in this region (dark red colors). The stimulus vertical disparity Δ*y* ~stim~ is 4 pixels in row A, 2 pixels in row B, 0 pixels in row C, and so on as indicated to the left of each row. Although the cells in the population are tuned to many different horizontal disparities, Δ*x* ~enc~, they are all tuned to zero vertical disparity. Thus the middle row, [Figure 6C](#pcbi-1000754-g006){ref-type="fig"}, is the only case where any neurons are tuned to the exact two-dimensional disparity of the stimulus. Here, neurons with Δ*x* ~enc~ = Δ*x* ~stim~ = −2 have receptive fields which exactly match the binocular disparity of the stimulus. Their correlation is therefore *C* = 1 for every noise image with this disparity, and so the mean spike-count *W* = (1+*C*) is exactly 2. The mean spike-count falls below 2 to either side of the arrow, as the difference between the horizontal disparity of the stimulus and that preferred by the neurons increases. The rate of decrease depends on the spatial frequency channel, since this controls the size of the receptive fields. For the left-most column, *f* = 0.2 cycles/pixel, the standard deviation of the receptive field envelope, σ, is just 1.25 pixels. For the right-most column, *f* = 0.025 cycles/pixel and σ = 10 pixels, meaning that the effective correlation experienced by these neurons is still high even for neurons tuned to disparities several pixels away from the stimulus. The rate of decrease also depends on the orientation. In our model population, the receptive field envelopes are isotropic, but the rate of change of the receptive field function is still fastest orthogonal to the cell\'s preferred orientation *θ* (see [Figure 3](#pcbi-1000754-g003){ref-type="fig"}). Thus, for each spatial frequency channel, the rate of change along the horizontal direction is fastest for the vertically-oriented cells (*θ* = 0°), and slowest for the horizontally-oriented ones (*θ* = ±90°). This effect can be seen in [Figure 6C](#pcbi-1000754-g006){ref-type="fig"}: the red region of high correlation extends further to either side of the optimal disparity for the horizontally-oriented cells at the top and bottom of each panel.
The same effect of receptive-field size can be seen as we look at rows other than row C, thus increasing the distance between the neurons\' preferred vertical disparity (0) and that of the stimulus. The peak response anywhere in the population declines as we move along a column away from Δ*y* ~stim~ = 0, as described by Read & Cumming [@pcbi.1000754-Read3]. Again, this decrease is most apparent for the higher-frequency channels, where receptive fields are smaller. For the highest-frequency channel (0.2 cyc/pix), where σ is just 1.25 pixels, a vertical disparity of −8 pixels (row F) is enough to make the portions of the images falling within the left and right-eye receptive fields completely uncorrelated. This means that the average binocular correlation is zero, and so with the spiking model I have adopted, the mean spike count is just 1, everywhere in the panel.
The most interesting, and informative, panels of [Figure 6](#pcbi-1000754-g006){ref-type="fig"} are those where the stimulus has a non-zero, but relatively small, vertical disparity (rows A,B,D,E). Here, the effective binocular correlation C has fallen below 1, but is still above zero. In this case, the red region of high spike-counts takes on a distinctive diagonal slant, whose direction depends on the sign of stimulus vertical disparity. Where stimulus vertical disparity is positive (rows A, B), spike-counts are highest for receptive fields tilted counter-clockwise from vertical (positive *θ*) when horizontal disparity is positive, and for receptive fields tilted clockwise from vertical (negative *θ*) when horizontal disparity is negative. When stimulus vertical disparity is negative (rows D, E, F), the situation is reversed. The reason is exactly the geometry sketched in [Figure 2](#pcbi-1000754-g002){ref-type="fig"}. This slant is the "signature" of vertical disparity, and will enable us to decode vertical disparity from this population.
2D stimulus disparity can be extracted from the response of this population {#s3c}
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[Figure 6](#pcbi-1000754-g006){ref-type="fig"} showed the average response of a neuronal population, averaged across thousands of stimuli with the same disparity. As we have seen, this average response possesses a structure which reflects the vertical disparity of the stimulus. However, this averaging process conceals important features of the response to single images. Most importantly, the response of the neuronal population to single images is affected not only by the disparity, but also by the luminance features of the particular image. These features cancel out to nothing when averaged over many random images, but the brain cannot take advantage of this when estimating the disparity of a single image. The stereo correspondence problem is complicated by these "false matches" due to particular features of the image [@pcbi.1000754-Fleet1]. Normalizing stereo energy so as to calculate the effective binocular correlation *C* is enough to solve the problem in the absence of vertical disparity. Then, as explained in the [Methods](#s2){ref-type="sec"}, the stimulus horizontal disparity can be identified from the horizontal disparity tuning of the cell with *C* = 1 (mean spike count = 2*U*). However, when there is a mismatch between the cell\'s preferred vertical disparity and the vertical disparity of the stimulus, the correlation will not usually reach 1 even for cells tuned to the horizontal disparity of the stimulus, so the false-match problem creeps in again. Secondly, neuronal populations are subject to noise. In principle, this may be reduced by averaging either over a long time period, or over a large pool of neurons with similar tuning and independent noise. Here, I have made the conservative assumption that neither of these options is available, so the neuronal population is subject to very large amounts of trial-to-trial noise, with the coefficient of variation at least 70%.
To bring home just how much variation these two sources of noise contribute, [Figure 7](#pcbi-1000754-g007){ref-type="fig"} shows the spikes elicited in response to a single example test image, with stimulus disparity Δ*x* ~stim~ = −2 and Δ*y* ~stim~ = +2 pixels. For comparison, [Figure 6B](#pcbi-1000754-g006){ref-type="fig"} showed the average response of the same population to stimuli with this disparity, with both neuronal and stimulus-driven noise averaged away. The 5 panels of [Figure 6B](#pcbi-1000754-g006){ref-type="fig"} are thus the "template" which [Figure 7](#pcbi-1000754-g007){ref-type="fig"} is meant to match (though note that because up to 6 spikes were produced by the single presentation in [Figure 7](#pcbi-1000754-g007){ref-type="fig"}, while the mean number of spikes never rises above 2, different colorscales were used in the two plots). At first glance, the task might appear to be impossible, given the very high levels of noise. However, certain features of similarity are indeed detectable between [Figure 7](#pcbi-1000754-g007){ref-type="fig"} and [Figure 6B](#pcbi-1000754-g006){ref-type="fig"}. At the lower spatial frequencies (right-hand panels), where the stimulus vertical disparity is not so large as a fraction of receptive field size, there is a slight tendency for neurons tuned to the horizontal disparity of the stimulus, marked with the arrows, to fire more spikes. Similarly, the slanted structure of the most responsive region is already hinted at. Furthermore, recall that for reasons of space, [Figures 6](#pcbi-1000754-g006){ref-type="fig"} and [7](#pcbi-1000754-g007){ref-type="fig"} show only the 630 neurons with zero phase-disparity; once we include the other phase disparities, there are a further 2520 neurons whose instantaneous response can be matched to the corresponding template. As I show below, despite the major differences between the single-image response shown in [Figure 7](#pcbi-1000754-g007){ref-type="fig"} and its template shown in [Figure 6B](#pcbi-1000754-g006){ref-type="fig"}, the population provides enough information for the correct template to be reliably identified.
{ref-type="fig"}, only neurons with zero phase disparity are shown, Δφ = 0. The different panels each show 126 neurons tuned to different spatial frequencies *f*, while 21 preferred horizontal disparity tunings Δx~enc~ and 6 orientations θ are shown by the horizontal and vertical axes, respectively. In each panel, an arrow marks the neurons tuned to the horizontal disparity of the stimulus. The colorscale is the same in all panels. The average response of the population to all Gaussian-noise stimuli with this disparity was shown in [Figure 6B](#pcbi-1000754-g006){ref-type="fig"} (note different colorscale). This mean response differs from the single-stimulus response shown here because the latter is affected by stimulus-dependent variation, reflecting the properties of this particular image, and Poissonian noise on neuronal spiking. Matlab code: This figure was generated by [Protocol S6](#pcbi.1000754.s006){ref-type="supplementary-material"}.](pcbi.1000754.g007){#pcbi-1000754-g007}
As described in the [Methods](#s2){ref-type="sec"}, I assess the quality of the match between the population response to a single image and the stored average population response by calculating the Pearson correlation coefficient between the two. [Figure 8](#pcbi-1000754-g008){ref-type="fig"} uses pseudocolor to show the Pearson correlation coefficients *r*(Δ*x* ~dec~,Δ*y* ~dec~) for all 441 disparities. The black cross marks the disparity of the stimulus. In this example, the highest Pearson correlation is obtained from the decoder tuned to this disparity, so for this single test image, the stimulus disparity is correctly extracted.
{ref-type="supplementary-material"}.](pcbi.1000754.g008){#pcbi-1000754-g008}
[Figure 9](#pcbi-1000754-g009){ref-type="fig"} quantifies the accuracy with which this algorithm performs across many test images. The plots show frequency histograms for the estimated disparity (red for horizontal disparity, blue for vertical) for 1000 different random test images with a fixed disparity. None of the 1000 test images was in the set of 500 images used to obtain the template responses, although they were all Gaussian noise images like those in [Figure 4](#pcbi-1000754-g004){ref-type="fig"}. Each column in [Figure 9](#pcbi-1000754-g009){ref-type="fig"} shows results for a different test disparity (Δ*x* ~test~,Δ*y* ~test~). The root-mean-squared error between the disparity estimated for each test image and its actual value is given above each panel. The algorithm\'s performance does not depend on the horizontal disparity of the test image (provided, of course, that it falls within the range to which the encoding population is tuned), so the three particular horizontal disparities chosen are immaterial. In contrast, performance does depend strongly on the vertical disparity tested. The three rows of [Figure 9](#pcbi-1000754-g009){ref-type="fig"} show results for increasing vertical disparity magnitudes: A: Δ*y* ~test~ = 0, B: Δ*y* ~test~ = 2, C: Δ*y* ~test~ = −4 pixels.
{ref-type="fig"}. The root-mean-squared error between the estimated disparity and the correct value is indicated at the top of each panel. Matlab code: The disparity estimates were obtained with [Protocol S7](#pcbi.1000754.s007){ref-type="supplementary-material"}, and the figure was generated with [Protocol S8](#pcbi.1000754.s008){ref-type="supplementary-material"}.](pcbi.1000754.g009){#pcbi-1000754-g009}
In [Figure 9A](#pcbi-1000754-g009){ref-type="fig"}, the test images had zero vertical disparity. Thus, the encoding population contains sensors tuned to the exact 2D disparity of the test images. Under these circumstances, unsurprisingly, both horizontal and vertical disparity are reconstructed with great accuracy. In [Figure 9B](#pcbi-1000754-g009){ref-type="fig"}, the test images had a vertical disparity of 2 pixels. An example population response to a single test image with this disparity was shown in [Figure 7](#pcbi-1000754-g007){ref-type="fig"}, while the template response (averaged over many training images with this disparity) was shown in [Figure 6B](#pcbi-1000754-g006){ref-type="fig"}. Here, no sensors in the encoding population are tuned to the 2D disparity of the stimulus. This naturally reduces the accuracy, but the RMS error is still only half a pixel. Critically, both the magnitude and sign of the vertical disparity can still be estimated from the reduction in the peak spike count [@pcbi.1000754-Read3] and the slant in the region of high spike count.
[Figure 9C](#pcbi-1000754-g009){ref-type="fig"} shows results when the test images had a vertical disparity of −8 pixels. This is large compared to the receptive field size of most channels, so the RMS error increases further, but the sign of the vertical disparity is still reliably detected. Horizontal disparity is also extracted, but with a larger error which would correspond to a reduced stereoacuity. This is qualitatively consistent with human performance: human stereo perception becomes worse as vertical disparity increases, and is destroyed by relatively small amounts [@pcbi.1000754-Stevenson1], [@pcbi.1000754-Prazdny1]. Here, almost all the "work" is being done by the low spatial-frequency channels, but these are still enough to extract 2D disparity, without being excessively degraded by the higher-frequency channels for which the stimulus is effectively uncorrelated. Ultimately, of course, as vertical disparity moves beyond the range spanned by the largest receptive fields, performance will fall to chance, again as human performance does.
Response to anti-correlated stereograms {#s3d}
---------------------------------------
Disparity is encoded within this model by the population of binocular correlation detectors *C*(*θ*, *f*,Δ*x*). This population, which is all tuned to zero vertical disparity on the retina, performs the initial encoding of disparity. It was chosen to resemble primary visual cortex, V1. For example, these initial disparity encoders are tuned to a particular spatial frequency and orientation, and they continue to respond to disparity in anti-correlated stimuli. Anti-correlated stereograms are those in which one eye\'s image has been contrast-inverted, so that black pixels are replaced with white. Since I use zero to represent the mean luminance, this corresponds to inverting the sign of one eye\'s image. Thus, the product *v* ~L~ *v* ~R~ changes sign when the stimulus is made anti-correlated. This means that the disparity tuning of binocular correlation-detectors inverts for anti-correlated stimuli. A similar inversion is found in V1 [@pcbi.1000754-Cumming3], [@pcbi.1000754-Ohzawa3], although with a slight reduction in amplitude.
Disparity is extracted from the activity of these V1 correlation-detectors by a higher-level brain area. The properties of this decoding area should ideally match those of human perception. For example, neurons in this region should not respond to disparity in anti-correlated stereograms, since these produce no perception of depth in humans or monkeys [@pcbi.1000754-Cogan1], [@pcbi.1000754-Read6], [@pcbi.1000754-Cumming2], and neurons in higher visual areas such as IT and V4 do not respond to disparity in anti-correlated stimuli [@pcbi.1000754-Tanabe1], [@pcbi.1000754-Janssen1]. In this paper, I have used the Pearson correlation coefficient, *r*, to quantify how well the population response to a test image matches the mean population response to template images. To match the lack of response to disparity in anti-correlated stereograms, I set the response of the decoding population equal to the half-wave-rectified Pearson correlation, replacing negative *r* with 0. This has no effect on correlated stereograms, where the maximum *r* is positive, but it prevents the decoder responding systematically to disparity in anti-correlated stereograms.
[Figure 8](#pcbi-1000754-g008){ref-type="fig"} illustrated the response of the population of disparity decoders (prior to the half-wave rectification) to one example test stimulus, showing that the maximally-responding decoders were those tuned to disparities close to that of the stimulus. [Figure 10](#pcbi-1000754-g010){ref-type="fig"} plots the disparity tuning surface of a single disparity decoder, the one tuned to (Δ*x* ~stim~,Δ*y* ~stim~) = (−6,−3), for both correlated and anti-correlated stereograms. The pseudocolor of each pixel shows the mean \<*P*(Δ*x* ~stim~,Δ*y* ~stim~)\> averaged across 40 different random images with the same disparity (Δ*x* ~test~,Δ*y* ~test~), specified by the pixel\'s position on the axes. [Figure 10A](#pcbi-1000754-g010){ref-type="fig"} shows the disparity tuning surface for normal, correlated stereograms. Unsurprisingly, the response is largest when the two-dimensional disparity of the test stimulus matches the preferred disparity of the decoder, indicated with the cross. Similar disparity tuning surfaces were plotted in [Figure 5](#pcbi-1000754-g005){ref-type="fig"} for the encoding neurons. The disparity tuning surfaces for the decoding neurons differ in two respects. First, they are isotropic rather than elongated, because the decoding neurons receive inputs from cells tuned to all orientations ([Figure 11](#pcbi-1000754-g011){ref-type="fig"}). Second, the peak response is obtained for a non-zero vertical disparity, whereas the encoding neurons were all tuned to zero vertical disparity.
{ref-type="supplementary-material"} and the figure was plotted by [Protocol S10](#pcbi.1000754.s010){ref-type="supplementary-material"}.](pcbi.1000754.g010){#pcbi-1000754-g010}
{#pcbi-1000754-g011}
[Figure 10B](#pcbi-1000754-g010){ref-type="fig"} shows the disparity tuning surface for the same decoder as in [Figure 10A](#pcbi-1000754-g010){ref-type="fig"}, but this time obtained with anti-correlated stereograms. As noted, anti-correlated stimuli elicit no perception of depth, and neurons in brain areas which are believed to have solved the correspondence problem do not discriminate disparity in anti-correlated stereograms. The Pearson correlation coefficient *r* between the response to an anti-correlated stereogram and the stored average responses for correlated stereograms is almost always negative, meaning that half-wave rectification ensures the decoder response *P*(Δ*x* ~stim~,Δ*y* ~stim~) is zero. Accordingly, the disparity tuning surface in [Figure 10B](#pcbi-1000754-g010){ref-type="fig"} is almost completely flat, in agreement with the physiological data for areas IT and V4 [@pcbi.1000754-Tanabe1], [@pcbi.1000754-Janssen1]. Thus, both encoding and decoding neurons in this simulation have properties consistent with those of the corresponding neuronal populations, as far as these are known.
Discussion {#s4}
==========
This paper has implemented a simple physiologically-inspired two-dimensional stereo correspondence algorithm. It consists of two model "brain areas": one which performs the initial encoding of binocular disparity between left and right images, and one which decodes this activity so as to arrive at an estimate of the two-dimensional disparity in the images. The unusual feature of this model is that the encoding neurons are all tuned to the same vertical disparity (zero). Despite this, the decoding neurons are able to successfully recover 2D stimulus disparity. This is possible because vertical disparity causes distinctive patterns of activity across the encoding population. The model uses its stored knowledge about these patterns, in the form of templates of expected activity, to deduce the stimulus disparity.
Neuronal correlates {#s4a}
-------------------
The model has a simple physiological interpretation. The population of disparity encoders, C(θ,f,Δx~enc~), was designed to represent primary visual cortex, V1. Neurons in this area are tuned to different orientations *θ*, spatial frequencies *f* and horizontal disparities Δ*x* ~enc~, and respond to disparity in anti-correlated stereograms. This encoding area projects to a higher brain area which extracts stimulus disparity. Neurons in this decoding area are tuned to both horizontal and vertical disparity, but are not sensitive to orientation or spatial frequency. They do not respond to disparity in anti-correlated stereograms. The perceived disparity corresponds to the preferred disparity of the most active neuron in the decoding area.
The stored templates of the population activity expected for different stimulus disparities, *W*, can be viewed as the synaptic weights in the projection from the early encoding area to the decoding area ([Figure 11](#pcbi-1000754-g011){ref-type="fig"}). That is, *W*(*θ*, *f*,Δ*φ*,Δ*x* ~enc~;Δ*x* ~dec~,Δ*y* ~dec~) describes the strength of the synaptic connection from the encoding neuron tuned to orientation *θ*, frequency *f*, phase disparity Δ*φ* and horizontal disparity Δ*x* ~enc~, onto the decoding neuron tuned to horizontal disparity Δ*x* ~dec~ and vertical disparity Δ*y* ~dec~. The firing rate of the decoding neuron depends on the total activity of its input neurons weighted by the strength of each synapse (the term *Σ R* ~test~ *W* in Equation 6), after undergoing a subtractive and a divisive normalization, and finally a threshold non-linearity (Equation 7). The threshold non-linearity is a universal feature of neuronal circuits, since firing rates cannot go negative. Both subtractive and divisive normalization have been extensively discussed in the literature, and plausible neuronal mechanisms have been proposed to implement them [@pcbi.1000754-Carandini1], [@pcbi.1000754-Carandini2], [@pcbi.1000754-Heeger1], [@pcbi.1000754-Simoncelli1], [@pcbi.1000754-Tolhurst1], [@pcbi.1000754-Ayaz1].
Robustness to noise {#s4b}
-------------------
This model is able to successfully decode two-dimensional disparity, including both the magnitude and sign of vertical disparity, from the activity of the encoding population. This demonstrates that information regarding vertical disparity is implicitly encoded within this population. The accuracy of this information, unsurprisingly, declines as the vertical disparity of the stimulus increases ([Figure 9](#pcbi-1000754-g009){ref-type="fig"}), consistent with psychophysical data. In the model, this decline occurs because information about the stimulus disparity is being carried by neurons which are not optimally tuned to it. Partly, this is because of neuronal noise: the effective signal-to-noise level declines as we move away from the peak of the neuron\'s tuning surface. I modelled neuronal spiking as a Poisson process, and deliberately chose a low spike count so that the Poisson noise would be large. In these simulations, neurons optimally tuned to the stimulus disparity have a coefficient of variation (CV, the ratio of standard deviation to mean) of 70%, while neurons which are tuned so far from the stimulus disparity that it appears effectively uncorrelated to them have a CV of 100%. However, the main reason for the decline in decoding accuracy is not neuronal noise, but fluctuations in the stimulus. For the uniform-disparity stimuli examined here, receptive fields tuned to the 2D stimulus disparity always experience an effective binocular correlation of exactly 1 (CV = 0%), whereas away from the 2D stimulus disparity the effective binocular correlation is, on average, smaller, and also much more variable. This means that as vertical disparity moves away from the value to which the neurons are tuned (here, zero), the stimulus-dependent fluctuations contribute much more variability to the neuronal spiking.
Nevertheless, despite these two potent sources of noise in the model, the simulations reveal that it performs extremely well. This is because the decoding process uses the responses of thousands of encoding neurons. Although every neuron is tuned to different parameters, and so their responses cannot be directly pooled, the decoding process effectively averages out noise when it correlates the responses of thousands of neurons with the stored templates. For this reason, the model is extremely robust to neuronal noise. If the reader runs the code in the Supplementary Material, reducing the Poisson noise by setting `Neurons.MeanSpikeUncorr` to a value greater than its current value of 1, s/he will be able to verify that the results show only a slight improvement in accuracy.
Relationship to previous models of vertical disparity encoding {#s4c}
--------------------------------------------------------------
The model of Read & Cumming [@pcbi.1000754-Read3] was discussed in the [Introduction](#s1){ref-type="sec"}. That model worked by detecting changes in vertical disparity magnitude across the visual field. In contrast, the present model is purely local; all neurons simulated were tuned to the same cyclopean position in the visual field. This model would therefore work even with the induced-effect stimulus of Serrano-Pedraza & Read [@pcbi.1000754-SerranoPedraza2]. Serrano-Pedraza & Read [@pcbi.1000754-SerranoPedraza2] were correct to reject the particular decoding model proposed by Read & Cumming [@pcbi.1000754-Read3], but wrong to conclude that vertical disparity must be explicitly encoded. A more sophisticated decoding of the same encoding population is consistent with their psychophysical results.
Matthews et al. [@pcbi.1000754-Matthews1] also modelled the perceptual effects of vertical disparity using energy-model neurons with different orientation tuning. The present algorithm differs substantially from theirs. Most importantly, their model does not ever estimate stimulus vertical disparity. Their decoding algorithm extracts a one-dimensional estimate of horizontal disparity, assuming that vertical disparity is zero. This means that when vertical disparity actually is present, it causes horizontal disparity to be mis-estimated: a vertical disparity V is misinterpreted as a horizontal disparity of Vcotθ, where θ is the cell\'s preferred orientation relative to horizontal (eq. 6 of Matthews et al.). They postulate that the perceptual effects of vertical disparity are a direct consequence of this confusion between horizontal and vertical disparity components. In contrast, the present model explicitly decodes both horizontal and vertical disparity. Vertical disparity does not cause horizontal disparity to be systematically mis-estimated (although it does increase the random error, [Figure 9](#pcbi-1000754-g009){ref-type="fig"}). Thus, the present model is agnostic on the question of how vertical disparity causes its perceptual effects: the two-dimensional disparity decoded by the present algorithm would have to be fed into one of the many models of that process (e.g. [@pcbi.1000754-Read2], [@pcbi.1000754-Garding1],[@pcbi.1000754-Backus1],[@pcbi.1000754-Gillam1],[@pcbi.1000754-Mayhew1]. Second, in order to explain how the "mistaken" disparity *V*cot*θ* produces a perceptual effect when averaged over neurons tuned to all possible orientations *θ*, Matthews et al. [@pcbi.1000754-Matthews1] invoke a radial bias for *θ* [@pcbi.1000754-Leventhal1], [@pcbi.1000754-Vidyasagar1], [@pcbi.1000754-Bauer1]. The present algorithm does not depend on any such anisotropy. In the simulations presented here, *θ* was assumed to be isotropic; any anisotropy would not affect the performance of the algorithm. This means that the present model is almost the opposite of that in Matthews et al. Their neuronal population explicitly encodes both horizontal and vertical disparity, but their decoding algorithm deliberately extracts only horizontal disparity. My population explicitly encodes only horizontal disparity, but my decoding algorithm extracts both horizontal and vertical disparity.
Consistency with known physiology {#s4d}
---------------------------------
As sketched in [Figure 2](#pcbi-1000754-g002){ref-type="fig"}, the present algorithm depends critically on the obliquely-oriented disparity-tuning surfaces predicted by the stereo energy model. It is therefore important to know whether real neurons display such oriented disparity-tuning surfaces. In monkey V1, Cumming [@pcbi.1000754-Cumming1] examined two-dimensional disparity-tuning surfaces for random-dot patterns, and compared their orientation to the cell\'s orientation tuning for grating stimuli. He found many cells with the obliquely-oriented disparity tuning used here. However, most cells had disparity-tuning surfaces elongated along the horizontal axis, independent of the cell\'s orientation tuning for gratings. Cumming argued that this represented a specialization for horizontal disparity not predicted by the energy model. This non-energy-model population can be modeled by combining several energy-model units with different horizontal disparity tuning [@pcbi.1000754-Read1]. The oblique disparity tuning predicted by the energy model is also found in cat visual cortex [@pcbi.1000754-Sasaki1], and in peripheral monkey V1 [@pcbi.1000754-Durand2]. Thus, the existing physiological evidence suggests that neurons with the obliquely-oriented disparity-tuning surfaces used by this model do exist, and may form the inputs for a second stage of disparity encoding consisting of neurons with horizontally-oriented disparity-tuning surfaces.
Neurons in V1 contain both position and phase disparity [@pcbi.1000754-DeAngelis1], [@pcbi.1000754-Anzai1], [@pcbi.1000754-Prince1], [@pcbi.1000754-Anzai2]. The model presented here works equally well whether position disparity alone, or both position and phase disparity, are included. In this paper, I specified a relationship between position disparity, phase disparity, frequency and orientation (Equation 1) which ensured that all neurons in the population were tuned to zero vertical disparity. (If this relationship did not hold, the model would contain neurons tuned to a range of vertical disparities, so its success would be trivial.) No physiological study has yet quantified both phase disparity and vertical disparity tuning, yet the results of [@pcbi.1000754-Cumming1] imply that something like Equation 1 may hold in reality, at least in the central 10° or so of the visual field.
In the visual periphery, very little is currently known about the distribution of 2D retinal disparity, despite the fact that this is where the range of naturally-occurring vertical disparities is largest [@pcbi.1000754-Read2], [@pcbi.1000754-Rogers2]. The existing physiological studies have reported their results only in head-centric Helmholtz coordinates, and have not examined tuning as a function of position on the retina. The encoding population described here, where all neurons at a given retinotopic location are tuned to the same vertical disparity on the retina ([Figure 1](#pcbi-1000754-g001){ref-type="fig"}), is consistent with the very limited existing physiological data available [@pcbi.1000754-Read3]. Only future physiological studies can resolve the issue. These should obtain a full 2D disparity tuning surface for every neuron; as [Figure 2](#pcbi-1000754-g002){ref-type="fig"} shows, 1D cross-sections can give misleading results. They should be clear about the definition of vertical disparity they are using, reporting data in retinal, as well as head-centric, coordinates. Finally, they need to examine disparity tuning as a function of position on the retina (not just eccentricity), in order to test whether the mean and variation in preferred vertical disparity varies across the retina as predicted from natural image statistics [@pcbi.1000754-Read2]. These studies should be carried out in both early visual cortex and in higher areas such as IT believed to underlie perception. The present model predicts that the range of preferred vertical disparities will be larger in the higher cortical areas.
Significance {#s4e}
------------
This paper demonstrates a highly efficient strategy for representing 2D stimulus disparity. 2D disparity is represented explicitly only at the decoding level, with the initial encoding being one-dimensional. Because the disparity decoding area does not represent other stimulus properties such as orientation, spatial frequency and phase, this results in a huge reduction in the number of neurons required.
Irrespective of whether the model here is ultimately validated physiologically, it nevertheless provides a vivid demonstration that populations of disparity-tuned neurons contain a much richer array of information than previously appreciated. It places a caveat on the common wisdom that in order to encode a quantity *X*, a neuronal population needs to be tuned to a range of values of *X*. In this example, horizontal and vertical disparity are completely independent quantities in the external world, but they are bound together with orientation at the initial encoding stage in the brain. Subsequently, vertical disparity can be extracted from neurons via their tuning to horizontal disparity and orientation alone. Under these very special circumstances, the common wisdom ceases to hold.
Supporting Information {#s5}
======================
######
Matlab code for running the simulations presented in this paper (Fig_ExampleRFs.m)
(1.00 KB TXT)
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Click here for additional data file.
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Matlab code for generating [Fig 4](#pcbi-1000754-g004){ref-type="fig"} (Fig_ExampleImages.m)
(1.00 KB TXT)
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Click here for additional data file.
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Matlab code ([www.mathworks.com](http://www.mathworks.com)) for running the simulations presented in this paper (gets templates). GetTemplates.m
(1.00 KB TXT)
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Click here for additional data file.
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Matlab file, for generating [Fig 5](#pcbi-1000754-g005){ref-type="fig"} (Fig_DispTunSurfEncoders.m)
(3.00 KB TXT)
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Click here for additional data file.
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Matlab code ([www.mathworks.com](http://www.mathworks.com)) for running the simulations presented in this paper (Fig_MeanResponses.m)
(2.00 KB TXT)
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Click here for additional data file.
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Matlab code ([www.mathworks.com](http://www.mathworks.com)) for running the simulations presented in this paper (Fig_FitDisparity.m)
(3.00 KB TXT)
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Click here for additional data file.
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Matlab code ([www.mathworks.com](http://www.mathworks.com)) for running the simulations presented in this paper (FitDisparity.m)
(2.00 KB TXT)
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Click here for additional data file.
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Matlab code ([www.mathworks.com](http://www.mathworks.com)) for running the simulations presented in this paper (Fig_FreqHists.m)
(3.00 KB TXT)
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Click here for additional data file.
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Matlab code for generating [Fig 10](#pcbi-1000754-g010){ref-type="fig"} (DispTunSurfDecoders.m)
(2.00 KB TXT)
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Click here for additional data file.
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Matlab code for generating [Fig 10](#pcbi-1000754-g010){ref-type="fig"} (Fig_DispTunSurfDecoders.m)
(1.00 KB TXT)
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Click here for additional data file.
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Zip archive containing 7 files with Matlab functions necessary to run the simulations and generate the figures in the paper (Protocol_S11.zip)
(0.14 MB ZIP)
######
Click here for additional data file.
Thanks to Bruce Cumming for helpful discussions, and to Ignacio Serrano-Pedraza for helpful comments on the manuscript.
The author has declared that no competing interests exist.
This research was supported by Royal Society University Research Fellowship UF041260 ([www.royalsociety.org](http://www.royalsociety.org)) and Medical Research Council New Investigator Award 80154 ([www.mrc.ac.uk](http://www.mrc.ac.uk)). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
[^1]: Conceived and designed the experiments: JCAR. Performed the experiments: JCAR. Analyzed the data: JCAR. Wrote the paper: JCAR.
|
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|
RECOMMENDED FOR FULL-TEXT PUBLICATION
Pursuant to Sixth Circuit I.O.P. 32.1(b)
File Name: 17a0206p.06
UNITED STATES COURT OF APPEALS
FOR THE SIXTH CIRCUIT
NANCY ROELL, as executrix of the estate of Gary L. ┐
Roell, Sr., │
Plaintiff-Appellant, │
│
> No. 16-4045
v. │
│
│
HAMILTON COUNTY, OHIO/HAMILTON COUNTY BOARD │
OF COUNTY COMMISSIONERS; JIM NEIL, in his official
│
capacity as the Hamilton County Sheriff; JOSEPH │
HUDDLESTON, MATTHEW ALEXANDER, and WILLY │
DALID, individually and in their official capacities as │
employees of Hamilton County, │
Defendants-Appellees. │
┘
Appeal from the United States District Court
for the Southern District of Ohio at Cincinnati.
No. 1:14-cv-00637—Sandra S. Beckwith, District Judge.
Argued: June 13, 2017
Decided and Filed: September 5, 2017
Before: MOORE, GILMAN, and COOK, Circuit Judges.
_________________
COUNSEL
ARGUED: Alphonse A. Gerhardstein, GERHARDSTEIN & BRANCH, CO LPA, Cincinnati,
Ohio, for Appellant. Pamela Sears, HAMILTON COUNTY PROSECUTOR’S OFFICE,
Cincinnati, Ohio, for Appellees. ON BRIEF: Alphonse A. Gerhardstein, GERHARDSTEIN
& BRANCH, CO LPA, Cincinnati, Ohio, for Appellant. Pamela Sears, Jerome A. Kunkel,
HAMILTON COUNTY PROSECUTOR’S OFFICE, Cincinnati, Ohio, George D. Jonson, Linda
L. Woeber, MONTGOMERY, RENNIE & JONSON, Cincinnati, Ohio, for Appellees.
GILMAN, J., delivered the opinion of the court in which COOK, J., joined. MOORE, J.
(pp. 23–29), delivered a separate dissenting opinion.
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 2
_________________
OPINION
_________________
RONALD LEE GILMAN, Circuit Judge. Gary Roell, who suffered from chronic mental
illness, caused a disturbance at his neighbor’s condominium while experiencing a condition
known as excited delirium. Hamilton County sheriff’s deputies arrived to find Roell half-naked,
muttering unintelligibly, and standing next to a broken window holding a hose and the remnants
of a hanging plant. While attempting to subdue Roell, the deputies physically struggled with him
and unsuccessfully tased him multiple times. Roell stopped breathing during the encounter with
the deputies and was pronounced dead shortly thereafter. His death was documented by the
coroner as natural, resulting from his excited delirium.
Roell’s wife, Nancy Roell, appeals the district court’s grant of summary judgment in
favor of the individual deputies on her claim under 42 U.S.C. § 1983. She also appeals the grant
of summary judgment in favor of Hamilton County on her claims under both § 1983 and the
Americans with Disabilities Act (the ADA). For the following reasons, we AFFIRM the
judgment of the district court.
I. BACKGROUND
A. Factual background
Roell suffered from mental illness, including schizoaffective disorder and paranoid
delusions, for many years. Although Roell’s symptoms could be successfully controlled by
medication, he had a history of noncompliance with his drug regimen. When he did not take his
medication, Roell’s mental health deteriorated and his unpredictable behavior rendered him a
danger to both himself and to others.
Roell stopped taking his medication in June 2013 and began exhibiting signs of mental
decompensation by early August. Sometime in the late evening hours of August 12 or the early
morning hours of August 13, Roell entered a state of excited delirium. Nancy Roell was out of
town during this time, participating in a church mission in New Jersey. In the midst of his
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 3
excited delirium, Roell damaged his and Nancy’s condominium by scattering debris, clothes, and
other household items inside and around the building. Roell then went to the condominium of
his neighbor, Rachana Agarwal, and threw a flower pot through her window.
Agarwal was awakened by the noise of shattering glass and went downstairs to find Roell
standing outside of her condominium by the broken window. She attempted to talk to Roell,
who was screaming something about “water.” Roell then pulled the screen from Agarwal’s
window and threw it at her. At that point, Agarwal became scared and ran back inside the
condominium, where she told her son, Soham, to call 911. Soham dialed 911 and handed the
phone to Agarwal, who told the operator that her neighbor was “acting crazy.” Agarwal testified
that, during this time, Roell appeared to be angry, his face red and his eyes bulging, and he kept
muttering unintelligible things about water. Roell was also pacing back and forth in front of
Agarwal’s broken window, periodically peering into her condominium.
Deputies Matthew Alexander, Willy Dalid, and Joseph Huddleston responded to the
dispatch of a “neighbor trouble” call. First to arrive at Agarwal’s condominium were Deputies
Alexander and Huddleston, who were told by Agarwal that Roell was “in the back breaking
things.” They entered the gated patio area and saw Roell standing by Agarwal’s broken window
holding a garden hose with a metal nozzle in one hand and a garden basket in the other. The
garden basket was a hanging plant surrounded by peat moss and held together with plastic wire.
Roell was wearing a t-shirt but was otherwise naked. According to Deputy Alexander, Roell was
screaming “no” and something about water when he and Deputy Huddleston arrived.
Deputy Huddleston proceeded to ask Roell what he was doing. Although Deputy
Huddleston could not recall Roell’s response, he testified that Roell immediately turned and
approached him and Deputy Alexander in an aggressive manner. Roell still had the hose and the
garden basket in his hands. Deputy Alexander similarly recalled that he and Deputy Huddleston
told Roell to “show us your hands” and that Roell, “immediately, within seconds,” charged at
them at a “pretty brisk walk.” Deputy Alexander also said that Roell approached them still
holding the hose and the garden basket.
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 4
Soham Agarwal was watching the events unfold from inside the condominium and heard
Roell screaming about how “he didn’t have water and we had water.” In addition, Soham
observed the deputies telling Roell to calm down, to stop resisting, to come over to them, and to
drop whatever he had in his hands. Soham recalled that Roell repeatedly shouted that he did not
have a weapon. But Soham also testified that, despite Roell’s assertions that he was unarmed,
Roell was facing the deputies swinging the hose “as if he was trying to hit somebody.” Rachana
Agarwal, also watching from the inside of her condominium, confirmed that the deputies told
Roell to calm down and that Roell was swinging the hose nozzle at the deputies. Agarwal
observed the deputies and Roell approach each other, with Roell proceeding at a pace between a
walk and a sprint, still holding the hose.
As Roell approached the deputies, Deputy Huddleston told Roell to stop and to get on the
ground or he would be tased. Deputy Huddleston then unholstered his X2 Taser and arced it as a
warning. Arcing a taser does not deploy the device; it simply creates a sound. Roell flinched
when Deputy Huddleston arced his taser but kept approaching. Deputy Huddleston once more
arced his taser and commanded Roell to get on the ground. Roell again flinched but continued to
approach the deputies. Deputy Huddleston then holstered his taser and reached out to grab one
of Roell’s arms. At the same time, Deputy Alexander grabbed Roell’s other arm.
Roell swung the garden basket at Deputy Huddleston as they met. Deputy Huddleston,
Deputy Alexander, and Roell all fell to the ground outside of the gated patio area during their
struggle. Roell was wet and slippery, either from sweat or water, and managed to break free
from the deputies’ grasp. As Roell tried to enter back through the patio gate, Deputy Huddleston
tased him. Deputy Huddleston testified that taser appeared to have some effect because Roell
buckled over a little bit. Roell nonetheless continued into the patio and closed the gate. The
deputies followed him through the gate while Deputy Huddleston’s taser was still on its five-
second deployment cycle. By that time, Deputy Dalid had arrived at the scene. All three
deputies tried to restrain Roell’s arms, but were unsuccessful because he was combative and
thrashing around on the ground. Deputy Alexander testified that he was punched in the face by
Roell at some point during the struggle.
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 5
While Deputies Alexander and Dalid attempted to hold Roell’s arms, Deputy Huddleston
tried to deploy his taser in drive-stun mode to the back of Roell’s leg. This court has previously
explained the use of a taser in drive-stun mode as follows:
In drive-stun mode, ‘the operator removes the dart cartridge and pushes two
electrode contacts located on the front of the taser directly against the victim. In
this mode, the taser delivers an electric shock . . . [,] but does not cause an
override of the victim’s central nervous system as it does in dart-mode.’
Cockrell v. City of Cincinnati, 468 F. App’x 491, 492 (6th Cir. 2012) (quoting Mattos v.
Agarano, 661 F.3d 433, 443 (9th Cir. 2011) (en banc)). In deploying his taser in drive-stun
mode, Deputy Huddleston hoped to complete the cycle necessary to achieve Roell’s
neuromuscular incapacitation, believing that one of the barbs from his previous attempt to tase
Roell had not connected. The taser failed to incapacitate Roell, however, and he continued to
struggle with the deputies on the ground. Deputy Huddleston again holstered his taser and tried
to control Roell’s legs, while Deputies Alexander and Dalid attempted to control Roell’s arms.
Roell managed to escape the grasp of all three deputies and stood up in a face-to-face
position with Deputy Alexander, whose back was against a tree. Deputy Huddleston once more
tased Roell using the device’s dart-mode, this time deploying two barbs into his back. Although
the taser still did not take effect, the deputies were able to get Roell on the ground and handcuff
him. Because of Roell’s continued resistance, the deputies had to restrain Roell’s hands in front
of his body by using two sets of handcuffs.
Roell appeared “somewhat under control” once he was handcuffed, but he continued to
thrash his legs and kicked Deputy Huddleston in the groin. Deputy Huddleston then sent Deputy
Alexander to get leg shackles from the one of the patrol cars so that Roell’s feet could also be
restrained. Once the deputies shackled Roell’s legs, they positioned him on his left side. Deputy
Dalid was trying to control Roell’s upper body by holding on to his right shoulder. Both Deputy
Huddleston and Deputy Dalid testified that, once restrained, Roell went limp and began to snore.
Roell would wake up, thrash around, and then go limp and lapse back into snoring. Deputy
Dalid observed Roell doing this twice before he noticed that Roell had no pulse and had stopped
breathing. By that time, Corporal (now Sergeant) Mikal Steers arrived on the scene and began
administering CPR to Roell until the life squad arrived. Although Corporal Steers detected a
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 6
faint pulse on several occasions, he was unable to revive Roell. The emergency medical
technicians were also unable to revive Roell, and he was pronounced dead at the hospital
emergency room.
Dr. Jennifer Schott, the deputy coroner, determined that the cause of Roell’s death was
“excited delirium due to schizoaffective disorder” and that the manner of his death was natural.
Included with the Death Record was a report drafted by Dr. Schott, stating that Roell had a
history of “physical altercation with police officers” and that the “use of a conducted energy
device against decedent” had occurred. Also noted were Roell’s various abrasions and
contusions, injuries from the taser barbs, and four broken ribs. The report, however, did not find
that any of these injuries contributed to Roell’s death. In her affidavit, Dr. Schott stated that she
performed a microscopic examination of Roell’s barb wounds and found no evidence that the
conducted energy device used on Roell caused any electrical burns. Nor did Dr. Schott find any
evidence that Roell had been asphyxiated, which is consistent with the absence of any evidence
that the deputies applied compressive force in attempting to restrain Roell.
B. Procedural background
In August 2014, Nancy Roell, as the executrix of Roell’s estate, filed suit in the United
States District Court for the Southern District of Ohio against both Hamilton County and the
Hamilton County Board of County Commissioners (collectively, Hamilton County), as well as
against Sheriff Jim Neil and Deputies Alexander, Dalid, and Huddleston. She first asserted
claims pursuant to 42 U.S.C § 1983, alleging that (1) Deputies Alexander, Dalid, and Huddleston
violated Roell’s Fourth Amendment right to be free from excessive force, and (2) Hamilton
County and Sheriff Neil are subject to municipal liability for the deputies’ alleged use
of excessive force. Nancy Roell also brought intentional-discrimination and failure-to-
accommodate claims against all of the defendants under Title II of the ADA. Finally, she
asserted a state-law claim for the wrongful death of Roell against all of the defendants and a
state-law claim for assault and battery against Deputies Alexander, Dalid, and Huddleston.
In February 2016, the defendants filed a “Motion to Dismiss and Motion for Summary
Judgment” pursuant to Rule 56(c) of the Federal Rules of Civil Procedure, which the district
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 7
court granted in part and denied the remainder as moot. First, the court held that Deputies
Alexander, Dalid, and Huddleston were entitled to qualified immunity on Nancy Roell’s § 1983
claim, with the result that Sheriff Neil and Hamilton County were also not liable under § 1983.
Roell v. Hamilton Cty. Bd. of Cty. Comm’rs, No. 1:14-CV-637, 2016 WL 4363112, at *14 (S.D.
Ohio Aug. 16, 2016). The court next ruled that Nancy Roell had failed to establish a viable
claim under the ADA because she did not produce any evidence that the defendants intentionally
discriminated against Roell because of his disability. Id. Finally, the court held that Nancy
Roell had abandoned her state-law claims against Hamilton County and Sheriff Neil. The court
then declined to exercise supplemental jurisdiction over the remaining state-law claims asserted
against the individual deputies and therefore denied as moot the defendants’ motion to dismiss
and/or for summary judgment as to those claims. Id.
In rendering its decision, however, the district court did not specify whether it resolved
the defendants’ motion using the summary-judgment standard or the motion-to-dismiss standard.
Id. But the content of the defendants’ motion, the extensive discovery period, and the court’s
consideration of materials outside of the pleadings indicate that the case was decided on
summary-judgment grounds. In any event, Nancy Roell appeals only the district court’s grants
of summary judgment in favor of (1) Deputies Alexander, Dalid, and Huddleston on her § 1983
claim, and (2) Hamilton County on her § 1983 and her ADA claims.
II. ANALYSIS
A. Standard of review
We review de novo a district court’s grant of summary judgment. Watson v. Cartee,
817 F.3d 299, 302 (6th Cir. 2016). Summary judgment is appropriate when no genuine dispute
of material fact exists and the moving party is entitled to judgment as a matter of law. Fed. R.
Civ. P. 56(a). A genuine dispute of material fact exists “if the evidence is such that a reasonable
jury could return a verdict for the nonmoving party.” Anderson v. Liberty Lobby, Inc., 477 U.S.
242, 248 (1986). The moving party bears the burden to “demonstrate the absence of a genuine
[dispute] of material fact.” Celotex Corp. v. Catrett, 477 U.S. 317, 323 (1986). Finally, “[i]n
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 8
making this assessment, we must view all evidence in the light most favorable to the nonmoving
party.” Tennial v. United Parcel Serv., Inc., 840 F.3d 292, 301 (6th Cir. 2016).
B. Nancy Roell’s § 1983 claim against Deputies Alexander, Dalid, and Huddleston
Nancy Roell claims that Deputies Alexander, Dalid, and Huddleston violated Roell’s
Fourth Amendment rights when they used excessive force to subdue him. The deputies pled the
affirmative defense of qualified immunity, which “protects government officials ‘from liability
for civil damages insofar as their conduct does not violate clearly established statutory or
constitutional rights of which a reasonable person would have known.’” Pearson v. Callahan,
555 U.S. 223, 231 (2009) (quoting Harlow v. Fitzgerald, 457 U.S. 800, 818 (1982)). Nancy
Roell bears the “ultimate burden of proof” to show that the deputies are not entitled to qualified
immunity. See Sheets v. Mullins, 287 F.3d 581, 586 (6th Cir. 2002).
“We ask two questions in evaluating whether a law-enforcement officer is entitled to
qualified immunity on an excessive-force claim: ‘(1) whether the officer violated the plaintiff’s
constitutional rights under the Fourth Amendment; and (2) whether that constitutional right was
clearly established at the time of the incident.’” Estate of Hill v. Miracle, 853 F.3d 306, 312 (6th
Cir. 2017) (quoting Kent v. Oakland County, 810 F.3d 384, 390 (6th Cir. 2016)). These
questions can be answered in any order. Pearson, 555 U.S. at 236. In holding that the deputies
were entitled to qualified immunity, the district court answered both questions in the negative.
The court concluded that the deputies did not violate Roell’s Fourth Amendment rights and that,
even if they did, no caselaw clearly established that the degree of force used by the deputies
violated such rights. We will address each of these conclusions in turn.
1. The deputies likely did not violate Roell’s Fourth Amendment rights.
The Fourth Amendment “guarantees citizens the right ‘to be secure in their
persons . . . against unreasonable . . . seizures’ of the person.” Graham v. Connor, 490 U.S. 386,
394 (1989). In determining whether an officer has used excessive force in violation of the
Fourth Amendment, “we employ an objective-reasonableness test, asking ‘whether the officers’
actions are objectively reasonable in light of the facts and circumstances confronting them,
without regard to their underlying intent or motivation.’” Hill, 853 F.3d at 312 (quoting
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 9
Graham, 490 U.S. at 397). This test “requires a careful balancing of ‘the nature and quality of
the intrusion on the individual’s Fourth Amendment interests’ against the countervailing
governmental interests at stake.” Graham, 490 U.S. at 396 (quoting Tennessee v. Garner,
471 U.S. 1, 7 (1985)).
The Supreme Court has articulated three factors for us to consider in determining the
objective reasonableness of a particular use of force. These factors are (1) “the severity of the
crime at issue,” (2) “whether the suspect poses an immediate threat to the safety of the officers or
others,” and (3) “whether he is actively resisting arrest or attempting to evade arrest by flight.”
Graham, 490 U.S. at 396. In evaluating these factors, we must keep in mind that “[t]he
‘reasonableness’ of a particular use of force must be judged from the perspective of a reasonable
officer on the scene, rather than with the 20/20 vision of hindsight.” Id. Finally, although the
Graham factors are instructive, they “are not an exhaustive list, as the ultimate inquiry is
‘whether the totality of the circumstances justifies a particular sort of seizure.’” Livermore ex
rel. Rohm v. Lubelan, 476 F.3d 397, 404 (6th Cir. 2007) (quoting St. John v. Hickey, 411 F.3d
762, 771 (6th Cir. 2005)).
The first Graham factor—“the severity of the crime at issue”—supports a finding that
some degree of force was justified in order to restrain and arrest Roell. Deputies Alexander,
Dalid, and Huddleston responded to a “neighbor trouble” call and were quickly informed by a
frightened Agarwal that Roell was “breaking things” in her backyard. They found Roell half-
naked, muttering unintelligibly, and standing next to a broken window, which they reasonably
inferred was shattered as a result of Roell’s actions. In other words, Roell had committed a
series of property crimes that a reasonable officer could infer might escalate. The fact that Roell
had not yet committed a more serious felony did not preclude the deputies from using force to
restrain him. See Cockrell v. City of Cincinnati, 468 F. App’x 491, 495 (6th Cir. 2012)
(recognizing numerous cases holding that an officer’s use of a taser against a plaintiff who is
“actively resisting arrest by physically struggling with, threatening, or disobeying officers” is not
a violation of the plaintiff’s clearly established Fourth Amendment rights, even if the plaintiff is
suspected of committing only a misdemeanor).
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 10
Application of the second Graham factor—whether Roell posed an immediate threat to
the deputies or to others—also indicates that the deputies’ use of force was warranted. When the
deputies first encountered Roell, he was holding objects that could have been used as weapons
amid a scene of property destruction. See In re Fortney, 832 N.E.2d 1257, 1268–69 (Ohio Ct.
App. 2005) (noting that Ohio law “defines a deadly weapon as ‘any instrument, device, or thing
capable of inflicting death, and designed or specially adaptable for use as a weapon, or
possessed, carried, or used as a weapon” and recognizing that a stick, when used as a club, can
constitute a deadly weapon). The deputies therefore had a reasonable basis to believe that Roell
presented an immediate threat to the Agarwals and to the deputies themselves “in light of the
facts and circumstances confronting” them. See Graham, 490 U.S. at 397.
First, Roell posed a potential threat to the Agarwals, who were still inside the
condominium. Because Roell had already thrown a potted plant through the Agarwal’s
condominium window, the deputies were reasonably concerned that he might break into their
residence and cause further destruction. Roell also posed an immediate threat to the deputies
themselves. Rahana Agarwal, Soham Agarwal, Deputy Alexander, and Deputy Huddleston all
testified that Roell quickly approached the deputies while waving the metal nozzle of a hose in a
threatening manner. Deputy Huddleston testified that the hose and the metal nozzle could have
been used as a weapon to hit or to choke him.
Although Soham Agarwal heard Roell say that he had no weapon and heard the deputies
tell Roell to come over to them, these observations do not create a genuine dispute of material
fact as to whether Roell approached the deputies in a manner that posed an immediate threat to
their safety. Even if Roell asserted that he was unarmed and moved towards the deputies in
response to their commands, the undisputed evidence regarding the aggressive nature of his
approach remains unchanged.
Finally, we turn to the third Graham factor and analyze whether Roell was actively
resisting arrest. Undisputed record evidence shows that Roell resisted the deputies’ attempts to
restrain and handcuff him by kicking, flailing, and wriggling away from their grasp. Nancy
Roell responds that the deputies “foreseeably caused any resistance or escalated the encounter by
failing to use verbal and tactical de-escalation.” But even if we assume that the deputies
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 11
escalated the encounter with Roell—an assertion that we find dubious—law-enforcement
officers cannot be held liable solely because they created the circumstances requiring the
application of force. See Livermore ex rel. Rohm v. Lubelan, 476 F.3d 397, 406 (6th Cir. 2007)
(rejecting the notion that a “Fourth Amendment claim against police officers who used deadly
force may survive summary judgment, even where the particular seizure is reasonable, if the
defendant police officers acted recklessly in creating the circumstances which required the use of
deadly force”). Analysis of the third Graham factor therefore supports our conclusion that the
deputies were justified in using some degree of force in attempting to restrain Roell.
Our analysis of the Graham factors, however, is not the end of the excessive-force
inquiry. We must also assess whether the “totality of the circumstances justified” the “particular
sort of . . . seizure” imposed upon Roell. See Tennessee v. Garner, 471 U.S. 1, 8–9 (1985). The
totality of the circumstances includes “the fact that at the time of the . . . struggle, the defendant
officers had reason to believe that [Roell] was either on drugs or mentally unstable.” See Landis
v. Baker, 297 F. App’x 453, 465 (6th Cir. 2008). Although the officers were unaware that Roell
was experiencing an episode of excited delirium, Deputy Huddleston testified that Roell’s
behavior indicated that he was suffering from some sort of mental illness.
The deputies were therefore required to take into account Roell’s diminished capacity
before using force to restrain him. See Champion v. Outlook Nashville, Inc., 380 F.3d 893, 904
(6th Cir. 2004) (“The diminished capacity of an unarmed detainee must be taken into account
when assessing the amount of force exerted.”). But no caselaw supports Nancy Roell’s assertion
the deputies were prohibited from using any physical force against Roell before first attempting
alternative de-escalation techniques. See Cook v. Bastin, 590 F. App’x 523, 530 (6th Cir. 2014)
(holding that no excessive force was used in handcuffing and physically restraining a man
suffering from excited delirium who posed a threat to the law-enforcement officers and who was
resisting arrest). In sum, we agree with the district court’s observation that “the fact that Roell’s
resistance was probably caused by his excited delirium did not preclude the deputies from using
a reasonable amount of force to bring him under control.” Roell, 2016 WL 4363112, at *8.
Despite Roell’s apparent diminished capacity, he had committed a series of property
crimes, was a threat to the Agarwals and to the deputies, and was actively resisting arrest.
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 12
“[A] reasonable officer on the scene” could have concluded the use of force was necessary based
on the totality of these circumstances. See Graham, 490 U.S. at 396. “[T]he question is not
whether any force was justified” but, instead, whether the deputies “could reasonably use the
degree of force employed against” Roell. See Martin v. City of Broadview Heights, 712 F.3d
951, 958 (6th Cir. 2013) (emphasis in original). The type of force employed by the deputies
against Roell—physically restraining his limbs, wrestling with him, attempting to tase him, and
shackling his arms and legs—was likely not excessive. But we need not definitively answer this
question because, at the time of the alleged violation, no caselaw clearly established that the
degree of force used by the deputies violated Roell’s Fourth Amendment rights.
2. The constitutional right alleged by Roell was not clearly established.
“In order for a right to be clearly established for the purposes of qualified immunity,
‘[t]he contours of the right must be sufficiently clear that a reasonable official would understand
that what he is doing violates that right.’” Estate of Hill v. Miracle, 853 F.3d 306, 316 (6th Cir.
2017) (quoting Anderson v. Creighton, 483 U.S. 635, 640 (1987)). “The relevant, dispositive
inquiry . . . is whether it would be clear to a reasonable officer that his conduct was unlawful in
the situation he confronted.” Saucier v. Katz, 533 U.S. 194, 202 (2001), abrogated on other
grounds by Pearson v. Callahan, 555 U.S. 223, 236 (2009). We must therefore determine
whether a right was clearly established “in light of the specific context of the case, not as a broad
general proposition.” Id. at 201.
Requiring this “particularized” showing “is not to say that an official action is protected
by qualified immunity unless the very action in question has previously been held unlawful, but
it is to say that in the light of pre-existing law the unlawfulness must be apparent.” Anderson,
483 U.S. at 640 (internal citations omitted). The content of this pre-existing law is determined
by looking “first to decisions of the Supreme Court, then to decisions of this court and other
courts within our circuit, and finally to decisions of other circuits.” Champion, 380 F.3d at 902
(quoting Higgason v. Stephens, 288 F.3d 868, 876 (6th Cir. 2002)). “An action’s unlawfulness
may be plain ‘from direct holdings, from specific examples described as prohibited, or from the
general reasoning that a court employs’” in these cases. Martin, 712 F.3d at 961 (quoting
Champion, 380 F.3d at 902).
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 13
With these general principles in mind, we turn to the question at hand: whether Nancy
Roell has demonstrated “the prior articulation of a prohibition against the type of excess force
exerted” against Roell, sufficient to defeat the deputies’ affirmative defense of qualified
immunity. See Champion, 380 F.3d at 902. We must determine, in other words, whether a
reasonable officer would have known that the forcible physical restraint employed in this case
against an individual who appeared mentally impaired, yet posed a potential threat to the officers
and to others, violated that person’s Fourth Amendment rights.
Nancy Roell argues that Martin v. City of Broadview Heights, 712 F.3d 951 (6th Cir.
2013), demonstrates that the deputies violated Roell’s clearly established rights. The decedent in
Martin broke into an apartment while naked and high on LSD. Id. at 954–55. Four police
officers arrived on the scene to find Martin speaking quickly and nonsensically. Id. Martin
calmed down momentarily to ask for help and to be arrested, but then “jogged away” when the
officers tried to handcuff him. Id. The officers caught up with Martin and fell on top of him. In
addition, they delivered “compliance body shots” to Martin’s side, struck him in the face with
two “hammer punches,” kneeled on his calves, struck his face, back, and ribs at least five times,
and held Martin in a face-down position. Id. at 954–55. Two of the officers heard Martin emit a
“gurgling sound” during this struggle and, when they rolled him over, he was unresponsive. Id.
at 955. Although the coroner determined that Martin died from an acute psychotic episode with
excited delirium due to intoxication, a forensic pathologist who conducted Martin’s autopsy
concluded that asphyxia was the likely cause of his death.
The Martin court held that “[a] reasonable officer should have known that subduing an
unarmed, minimally dangerous, and mentally unstable individual with compressive body weight,
head and body strikes, neck or chin restraints, and torso locks would violate that person’s clearly
established right to be free from excessive force.” Id. at 693. In doing so, the court observed
that the officers were obligated to “de-escalate the situation and adjust the application of force
downward” when confronted with an unarmed individual who “exhibited conspicuous signs that
he was mentally unstable.” Id. at 962. We agree with the district court, however, that this
statement must be viewed in the context of the officers’ applied use of force, which was
characterized by the Martin court as “severe.” Id. at 958; see also Roell, 2016 WL 4363112 at
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 14
*9 (“More reasonably, Martin stands for the proposition that officers should try to de-escalate
the situation with a mentally disturbed suspect before resorting immediately to severe force to
subdue him.”).
Unlike the officers in Martin, Deputies Alexander, Dalid, and Huddleston did not
repeatedly beat Roell or apply compressive body pressure to his back. They instead “grappled
with Roell’s arms and legs to try to control him, which they eventually did.” Roell, 2016 WL
4363112 at *9. Deputy Huddleston did attempt to tase Roell, but no electricity was conducted
into his body. And although this court has observed that use of a taser entails a higher level of
force “than simply knocking someone back to the ground,” Wells v. City of Dearborn Heights,
538 F. App’x 631, 639 (6th Cir. 2013), a “growing national judicial consensus” exists that the
use of a taser in dart mode constitutes only an intermediate use of force. Bryan v. MacPherson,
630 F.3d 805, 810 (9th Cir. 2010) (Wardlaw, J., concurring). Martin, moreover, was “unarmed
and minimally dangerous,” whereas Roell was threateningly waving a hose with a metal nozzle
that could be used as a weapon.
Because of these factual differences, Martin did not put the deputies on notice that their
actions violated Roell’s clearly established right to be free from excessive force. Nor do the
other cases cited by Nancy Roell, which hold that police use excessive force when they deploy
gratuitous force or a taser against an individual who is already restrained or is doing nothing to
resist arrest, provide such notice. See, e.g., Eldridge v. City of Warren, 533 F. App’x 529, 535
(6th Cir. 2013) (holding that the police used excessive force when they tased an individual who
was suffering from a hypoglycemic episode and whose “noncompliance was not paired with any
signs of verbal hostility or physical resistance”); Landis v. Baker, 297 F. App’x 453, 461, 464
(6th Cir. 2008) (holding that the police used excessive force against an individual suffering from
a mental health crisis who “was not actively resisting arrest or posing a threat to anyone” when
they struck him ten times with a baton, held him face down into two feet of mud and water and
repeatedly tased him); Champion v. Outlook Nashville, Inc., 380 F.3d 893, 901 (6th Cir. 2004)
(holding that the police used excessive force against a severely autistic man who “stopped
resisting arrest and posed no flight risk” when they “sprayed him with pepper spray even after he
was immobilized by handcuffs and a hobbling device”). But see Rudlaff v. Gillispie, 791 F.3d
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 15
638, 641 (6th Cir. 2015) (collecting cases and concluding that [o]ur cases firmly establish that it
is not excessive force for the police to tase someone (even multiple times) when the person is
actively resisting arrest.” (emphasis in original)).
We believe that this case is instead more analogous to Cook v. Bastin, 590 F. App’x 523
(6th Cir. 2014). In that case, a severely autistic man became agitated, stripped naked, caused
extensive property damage to his room in an adult daycare center, and ripped the shirt of the
daycare center’s Crisis Manager. Id. at 525. The police arrived to find the man, Roland
Campbell, digging his lacerated fingers into an electrical socket. They observed the Crisis
Manager’s torn and bloody shirt, which they interpreted as an indication that physical violence
had occurred. The officers were told that Campbell was out-of-control, suffered from mental
disabilities, and needed to be taken to a mental facility.
Campbell was handcuffed without incident and placed in a sitting position. While the
police waited for the medical transport unit, however, Campbell “began thrashing and kicking,
making grunting sounds as he tried to free himself from the handcuffs,” rolled onto a prone
position, and began scooting on his stomach towards the doorway. Id. at 526. The officers
attempted to gain control of Campbell by restraining his arms and legs, while the Crisis Manager
held his torso. During the struggle, Campbell pulled the men into the hallway, freed one of his
hands from the cuffs, and “pick[ed] himself and everybody up off the ground with the one hand
about three or four inches.” Id. Campbell then collapsed, fell unconscious, and died as a result
of acute cardiorespiratory failure. The Cook court held that the degree of force used by the
officers was reasonable because Campbell had committed significant property destruction and a
physical assault, posed an immediate threat to himself, the officers, and to others, and attempted
to free himself from the officers’ restraint. Id. at 530–31.
Like Campbell, Roell caused significant property damage, was a threat to the officers and
to others, and resisted arrest during an episode of excited delirium. Although Deputies
Alexander, Dalid and Huddleston did not observe any “signs of physical violence,” they did
observe that Roell was holding objects that could be used as weapons. True enough, the
deputies’ wrestled with and attempted to tase Roell, arguably deploying a higher level of force
than the officers in Campbell. But this court has previously held that an officer’s “single use of
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 16
the taser in drive-stun mode” against a mentally unstable plaintiff who was a threat to officer
safety and his own safety, and who was resisting police attempts to transport him to the hospital,
did not constitute excessive force. See Caie v. West Bloomfield Township, 485 F. App’x 92, 94–
96 (6th Cir. 2012). And there is no question that the degree of force employed by Deputies
Alexander, Dalid, and Huddleston was far less than the unconstitutionally severe force used by
the officers in Martin. In sum, the relevant caselaw does not clearly establish that the deputies
violated Roell’s Fourth Amendment rights because their actions fell in the “hazy border between
excessive and acceptable force.” See Brosseau v. Haugen, 543 U.S. 194, 201 (2004) (quoting
Saucier, 533 U.S. at 206).
Finally, Nancy Roell relies on the procedures articulated in the training materials of the
Ohio Peace Officer Training Commission (OPTC) and in proffered expert testimony in an effort
to prove that Roell’s right to be free from excessive force was clearly established. She first
argues that the deputies did not follow the OPTC procedures when they neglected to recognize
that Roell was exhibiting the common symptoms of excited delirium, proceeded to engage Roell
before staging the scene with multiple officers and medical personnel, and failed to use verbal
de-escalation techniques before attempting to physically restrain him. Nancy Roell also points to
the expert testimony of Dr. Michael Lyman, who stated that de-escalation was the “standard
technique” recommended for crime-related encounters with excited-delirium subjects and who
opined that, had the deputies used verbal de-escalation, Roell would have likely been talked into
surrendering without an altercation. Based on this evidence, Nancy Roell argues that the
deputies had a “clearly established duty” to use de-escalation techniques prior to using force
against Roell.
In considering her argument, we must “evaluate the officers’ use of certain tactics ‘in
light of testimony regarding the training that [the officers] received.’” Martin, 712 F.3d at 960
(quoting Griffith v. Coburn, 473 F.3d 650, 657 (6th Cir. 2007)). But we also must judge the
reasonableness of a particular use of force “from the perspective of a reasonable officer on the
scene, rather than with the 20/20 vision of hindsight.” Graham, 490 U.S. at 396. A finding of
qualified immunity is therefore not precluded simply because the deputies acted contrary to their
training. City of San Francisco v. Sheehan, 135 S. Ct. 1765, 1777 (2015) (“Even if an officer
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 17
acts contrary to her training, however, . . . that does not itself negate qualified immunity where it
would otherwise be warranted.”). In addition, although the deputies did not follow every OPTC
protocol, we note that the training materials acknowledge that the use of a taser might be
effective in controlling an individual suffering from excited delirium, that a physical struggle
might ensue, and that force might be appropriate or necessary in order to restrain the individual.
Dr. Lyman’s expert testimony, which essentially opines on the best approach that the
deputies could have taken in ideal circumstances, similarly does not establish that the deputies
violated Roell’s clearly established rights. As an initial matter,“[t]he Fourth Amendment . . .
does not require police officers to take the better approach[,] . . . only that they take a reasonable
approach.” Cook v. Bastin, 590 F. App’x 523, 528 (6th Cir. 2014). And “so long as ‘a
reasonable officer could have believed that his conduct was justified,’ a plaintiff cannot ‘avoi[d]
summary judgment by simply producing an expert’s report that an officer’s conduct leading up
to a deadly confrontation was imprudent, inappropriate, or even reckless.’” Sheehan, 135 S. Ct.
at 1777 (quoting Billington v. Smith, 292 F.3d 1177, 1189 (9th Cir. 2002)).
In sum, Nancy Roell points to no caselaw clearly establishing that the deputies violated
Roell’s Fourth Amendment rights in effectuating his arrest. Even assuming that law-
enforcement officers must “adjust the application of force downward” when confronted with a
conspicuously mentally unstable arrestee, Martin, 712 F.3d at 962, no precedent establishes that
the level of force used by the deputies in this case was excessive or that the deputies were
required to use only verbal de-escalation techniques. The content of the OPTC training material
and Nancy Roell’s proffered expert testimony do not change our conclusion. Deputies
Alexander, Dalid, and Huddleston are therefore entitled to qualified immunity, meaning that the
district court did not err in granting summary judgment to the them on Nancy Roell’s § 1983
claim.
C. Nancy Roell’s § 1983 claim against Hamilton County
Nancy Roell also challenges the district court’s grant of summary judgment in favor of
Hamilton County on her claim for municipal liability under § 1983. She put forth three theories
as to why Hamilton County is subject to municipal liability: (1) Hamilton County’s policy and
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 18
custom for handling mentally-ill individuals was the driving force behind the deputies’ use of
excessive force, (2) Hamilton County failed to adequately train the deputies, and (3) Hamilton
County ratified the deputies’ use of excessive force.
We recognize that “[a] municipality or county cannot be liable under § 1983 absent an
underlying constitutional violation by its officers.” Blackmore v. Kalamazoo County, 390 F.3d
890, 900 (6th Cir. 2004). The district court held that Deputies Alexander, Dalid, and Huddleston
did not violate Roell’s Fourth Amendment rights under the first prong of the qualified-immunity
analysis. It therefore granted summary judgment in favor of Hamilton County based on that
ground and did not address any of Nancy Roell’s theories for municipal liability.
We, on the other hand, have utilized the second prong of the qualified-immunity analysis
to conclude that the deputies are entitled to summary judgment because no caselaw clearly
established that the degree of force used by the deputies violated Roell’s Fourth Amendment
rights. In doing so, we have reached no conclusion with respect to whether Roell’s rights were
actually violated. We must therefore address Nancy Roell’s three theories for Hamilton
County’s liability by assuming, without deciding, that Roell’s Fourth Amendment rights were
violated by the deputies’ excessive use of force.
Hamilton County is subject to liability under § 1983 for its policy on handling mentally
ill individuals only if Nancy Roell can “demonstrate ‘a direct causal link between the policy and
the alleged constitutional violation.’” See Brown v. Chapman, 814 F.3d 447, 463 (6th Cir. 2016)
(quoting Graham ex rel. Estate of Graham v. County of Washtenaw, 358 F.3d 377, 383 (6th Cir.
2004)). But Nancy Roell does not point to any policy that is the “moving force” behind the
deputies’ actions. See id. She instead argues that Hamilton County’s lack of adequate policies
and training caused the deputies’ use of excessive force.
Inadequate training can serve as the basis for municipal liability under § 1983 where it
“amounts to deliberate indifference to the rights of persons with whom the police come into
contact.” City of Canton v. Harris, 489 U.S. 378, 388 (1989). To succeed on this claim, Nancy
Roell “must show ‘(1) that a training program is inadequate to the tasks that the officers must
perform; (2) that the inadequacy is the result of the [County’s] deliberate indifference; and
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 19
(3) that the inadequacy is closely related to or actually caused the plaintiff’s injury.’” Brown,
814 F.3d at 463 (quoting Plinton v. County of Summit, 540 F.3d 459, 464 (6th Cir. 2008)).
Nancy Roell cannot meet the first prong of this test, however, because Hamilton County had a
satisfactory training program in place regarding officer interactions with individuals suffering
from mental illness and excited delirium.
The record shows that the deputies received training on topics that included the use of
force and tasers, crisis intervention techniques, interacting with the special-needs population and
mentally ill suspects, and recognizing the symptoms of excited delirium. Finally, we note that
Nancy Roell’s argument that Hamilton County failed to train its deputies is completely
inconsistent with her § 1983 claim that the deputies’ use of excessive force was evidenced by the
fact that they failed to follow Hamilton County’s procedures regarding officer interactions with
individuals suffering from excited delirium.
This leaves Nancy Roell with her argument that Hamilton County ratified the use of
excessive force by Deputies Alexander, Dalid, and Huddleston when it conducted an inadequate
investigation of the events. Specifically, she asserts that the investigation merely rubber-stamped
the deputies’ unconstitutional conduct, neglected to discover what actually took place, and failed
to review whether the deputies’ actions violated Hamilton County’s policies and procedures.
Once again, however, the record demonstrates otherwise.
The internal investigation included interviews of multiple witnesses, detailed fact-
finding, and incorporates additional investigations by the Criminal Investigations Unit of the
Sheriff’s Office and the Hamilton County Coroner. In addition, Nancy Roell’s own expert, Dr.
Lyman, testified that he could not think of any additional interviews that should have been
conducted during the investigation, could not point to any physical evidence that was not
preserved or test results that were not considered, and could not identify any specific
inadequacies in the collection of testimonial or tangible evidence. We therefore disagree with
Nancy Roell’s argument that “no serious investigation” occurred regarding the deputies’ use of
force. See Marchese v. Lucas, 758 F.2d 181, 188 (6th Cir. 1985). Because Hamilton County is
not subject to municipal liability under any of her theories, the district court did not err in
granting summary judgment to the county on her § 1983 claim.
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 20
D. Nancy Roell’s ADA claim against Hamilton County
Finally, Nancy Roell appeals the district court’s grant of summary judgment in favor of
Hamilton County based on her claim under Title II of the ADA. Title II provides that “no
qualified individual with a disability shall, by reason of such disability, be excluded from
participation in or be denied the benefits of the services, programs, or activities of a public entity,
or be subjected to discrimination by any such entity.” 42 U.S.C. § 12132. Two types of claims
are cognizable under Title II: claims for intentional discrimination and claims for a reasonable
accommodation. Ability Ctr. of Greater Toledo v. City of Sandusky, 385 F.3d 901, 907 (6th Cir.
2004).
The district court dismissed Nancy Roell’s ADA claim because it found no evidence that
the defendants intentionally discriminated against Roell based on his disability. In so holding,
however, the court failed to consider Nancy Roell’s failure-to-accommodate theory. Under this
theory, Nancy Roell asserted that Hamilton County had a duty to accommodate Roell’s disability
by “having its officers take steps to calm the situation, converse with Mr. Roell in a non-
threatening manner, pause to gather information from Rachana Agarwal, refrain from the
application of force, and summon EMS to the scene at the earliest moment possible.”
Neither the Supreme Court nor this circuit has squarely addressed whether Title II of the
ADA applies in the context of an arrest. Nancy Roell urges us, however, to adopt the reasoning
of several of our sister circuits that have found Title II applicable to law-enforcement activities,
including arrests.
A few opinions have indeed indicated that arrestees might be able to bring cognizable
claims under Title II. But, in doing so, they have also noted that the exigent circumstances
inherent in an arrest inform the reasonable-accommodation analysis. See, e.g., Sheehan v. City of
San Francisco, 743 F.3d 1211, 1232 (9th Cir. 2014), rev’d in part, cert. dismissed in part, 135 S.
Ct. 1765 (2015) (holding that “the ADA . . . applies to arrests, though we agree with the Eleventh
and Fourth Circuits that exigent circumstances inform the reasonableness analysis under the
ADA, just as they inform the distinct reasonableness analysis under the Fourth Amendment”);
Bahl v. County of Ramsey, 695 F.3d 778, 784 (8th Cir. 2012) (noting that “[e]ven if the ADA
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 21
applied to [a] traffic stop,” the defendant police officer was not required to accommodate the
plaintiff’s disability “under the exigencies of the traffic stop”). But see Hainze v. Richards,
207 F.3d 795, 801 (5th Cir. 2000) (“Title II does not apply to an officer’s on-the-street responses
to reported disturbances or other similar incidents, whether or not those calls involve subjects
with mental disabilities, prior to the officer’s securing the scene and ensuring that there is no
threat to human life.”).
We need not decide whether Title II applies in the context of arrests because, even if
Nancy Roell’s failure-to-accommodate claim is cognizable, Hamilton County is entitled to
summary judgment based on the facts of this case. This circuit has previously held that “the
‘determination of what constitutes reasonable modification is highly fact-specific, requiring case-
by-case inquiry.’” Anderson v. City of Blue Ash, 798 F.3d 338, 356 (6th Cir. 2015) (quoting
Lentini v. Cal. Ctr. for the Arts, 370 F.3d 837, 844 (9th Cir. 2004)). Deputies Alexander, Dalid,
and Huddleston unquestionably faced exigent circumstances while attempting to restrain and
arrest Roell. As detailed above, they responded to an unsecured scene to find an individual who
had committed, at the very least, a series of property crimes and who posed a continuing threat to
the deputies and to others. In fact, almost immediately after the deputies arrived, Roell swiftly
approached them brandishing a hose with a metal nozzle and a garden basket. The deputies, in
other words, were required to make a series of quick, on-the-spot judgments in a continuously
evolving environment.
Nancy Roell’s proposed accommodations—that the deputies use verbal de-escalation
techniques, gather information from the witnesses, and call EMS services before engaging with
Roell—were therefore “unreasonable . . . in light of the overriding public safety concerns.” See
Tucker v. Tennessee, 539 F.3d 526, 536 (6th Cir. 2008), abrogated on other grounds by
Anderson v. City of Blue Ash, 798 F.3d 338 (6th Cir. 2015); cf. Hainze, 207 F.3d at 802
(recognizing that “[o]nce the area was secure and there was no threat to human safety, the . . .
Sheriff’s deputies would have been under a duty to reasonably accommodate [plaintiff’s]
disability in handling and transporting him to a mental health facility”).
In the context of the exigent circumstances surrounding Roell’s arrest, Nancy Roell
cannot make out a viable ADA claim under her failure-to-accommodate theory. Nor has she
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 22
presented any evidence that Hamilton County intentionally discriminated against Roell based on
his disability. The district court therefore did not err in granting summary judgment in favor of
Hamilton County on Nancy Roell’s ADA claim.
III. CONCLUSION
For all of the reasons set forth above, we AFFIRM the judgment of the district court.
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 23
_________________
DISSENT
_________________
KAREN NELSON MOORE, Circuit Judge, dissenting. Our circuit law clearly states that
when an individual “exhibit[s] conspicuous signs that he [is] mentally unstable” and is
“unarmed,” “Champion require[s] the officers to de-escalate the situation and adjust the
application of force downward.” Martin v. City of Broadview Heights, 712 F.3d 951, 962 (6th
Cir. 2013) (quoting Champion v. Outlook Nashville, Inc., 380 F.3d 893, 904 (6th Cir. 2004)).
There are disputed facts as to whether Roell was unarmed and as to how aggressively Roell was
acting, which determine how much force was appropriate. Although the law governing this case
is clear, the facts surrounding Roell’s death are not. The district court erred by granting
summary judgment on Nancy Roell’s § 1983 claim against Deputies Alexander, Dalid, and
Huddleston. I would reverse summary judgment on this claim, and I respectfully dissent.
I. GOVERNING LAW
Because the law governing this case is clearly established and straightforward, I begin by
setting out the basic legal principles that govern this case. First, I agree with the majority’s
recitation of the familiar summary-judgment standard, although not with its application of the
standard to this case. See Maj. Op. at 7–8. Second, I agree with its summary of the Graham
factors. See Maj. Op. at 8–9 (citing Graham v. Connor, 490 U.S. 386, 396 (1989)).
As for the law at the heart of this matter, I cannot agree with the majority’s
characterization. Sixth Circuit cases clearly establish that officers must “take into account ‘the
diminished capacity of an unarmed detainee . . . when assessing the amount of force exerted.’”
Martin, 712 F.3d 962 (quoting Champion, 380 F.3d at 904). Martin states the rule very simply:
When an individual “exhibit[s] conspicuous signs that he [is] mentally unstable” and is
“unarmed,” “Champion require[s] the officers to de-escalate the situation and adjust the
application of force downward.” Id.; see also Landis v. Baker, 297 F. App’x 453, 465 (6th Cir.
2008) (“A determination of the reasonableness of the defendant officers’ conduct must take into
account the fact that at the time of the fatal struggle, the defendant officers had reason to believe
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 24
that [the arrestee] was either on drugs or mentally unstable and they knew that he was
unarmed.”). If it is apparent to officers that an individual is unarmed and mentally unstable, then
the officers must de-escalate and may not use as much force as would be permissible when
confronted with an individual who was either mentally stable or armed.
While the majority acknowledges that Champion mandates that “[t]he deputies were . . .
required to take into account Roell’s diminished capacity before using force to restrain him,” it
essentially brushes this requirement aside by asserting that “no caselaw supports Nancy Roell’s
assertion the deputies were prohibited from using any physical force against Roell before first
attempting alternative de-escalation techniques.” Maj. Op. at 11. I agree that the deputies were
not necessarily prohibited from using any physical force on Gary Roell, but that point is
irrelevant to this case. The question in this case is whether the officers complied with their
obligation, under Champion and Martin, to adjust their use of force downward. Even if the
officers were permitted to use some physical force, they could have violated Champion and
Martin by failing to adjust the level of force downward.
II. APPLICATION OF THE CLEARLY ESTABLISHED
LAW TO THE FACTS OF THIS CASE
There are several unresolved questions of fact relevant to whether the officers had, and, if
so, whether they complied with, an obligation to adjust the level of force downward. There are
some basic facts that I agree are not in dispute. No one disputes that Roell had long lived with
chronic, severe mental illness, including schizoaffective disorder and delusional disorder, nor
does anyone dispute that when he went off his medication he could become unpredictable,
dangerous, and violent. R. 98 (N. Roell Dep. at 72, 97, 167) (Page ID #4513, 4538, 4608). No
one disputes that at 2:30 a.m. on August 13, the Roells’ neighbor, Rachana Agarwal, woke up to
a loud noise and found Roell standing at Agarwal’s window wearing only a t-shirt, nude from the
waist down. R. 90 (Agarwal Dep. at 10) (Page ID #3765); R. 77 (Huddleston Dep. at 66) (Page
ID #493). Scared, Agarwal called 911 and said that her neighbor was “acting crazy.” R. 90
(Agarwal Dep. at 27) (Page ID #3782). There is no dispute that when the officers arrived on the
scene, they wrestled with Roell and tased him multiple times before eventually subduing him and
handcuffing him with two sets of handcuffs and shackles. R. 77 (Huddleston Dep. at 98–100,
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 25
117–19) (Page ID #525–27, 544–46). There is also no dispute that Roell stopped breathing
while he was shackled, that he never regained consciousness, and that he was pronounced dead
at the hospital. See R. 96-1 (Death Record) (Page ID #4286).
Beyond these basic facts, there are many disputes over important details of the events
leading to Roell’s death. First, there is a fact question as to whether Roell was armed, given that
he was holding a hose and a hanging planter but may not have been using these items as
weapons. Second, there is a fact question as to how aggressively Roell acted when he
approached the officers. Without resolving these factual disputes, it is impossible to know
whether the amount of force was appropriate under the circumstances.
A. We do not know whether Gary Roell was unarmed
There is a fact question as to whether Roell was unarmed under Ohio law. Determining
whether Roell was unarmed is crucial, because if Roell was unarmed, the Champion/Martin rule
would apply and require the officers to adjust the level of force downward. If Roell was armed,
the Champion/Martin rule would not apply.
The majority correctly notes that Ohio law “defines a deadly weapon as ‘any instrument,
device, or thing capable of inflicting death, and designed or specially adaptable for use as a
weapon, or possessed, carried, or used as a weapon.’” Maj. Op. at 10 (quoting In re Fortney,
832 N.E.2d 1257, 1268 (Ohio Ct. App. 2005)). The hose and peat-moss hanging planter are not
instruments “designed or specially adaptable for use as a weapon” but at least the hose, which
had a metal tip, is an instrument that could be “used as a weapon.” In re Fortney, 832 N.E.2d at
1268.
The evidence is not clear as to whether Roell was using the peat-moss planter or hose as
weapons. Soham Agarwal testified that he definitely remembered Roell saying that he did not
have a weapon. Soham Agarwal testified that Roell “kept saying he didn’t have a weapon. I
remember him saying that.” R. 91 (S. Agarwal Dep. at 20) (Page ID #3858). “He kept shouting
-- he just kept shouting, I don’t have a weapon. That’s all I could hear him saying.” Id. at 37–38
(Page ID #3875–76). Rachana Agarwal testified that she thinks she heard Roell tell the officers
that he did not have a weapon. R. 90 (Agarwal Dep. at 75) (Page ID #3830). Huddleston did not
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 26
recall Roell saying that he did not have a weapon. R. 77 (Huddleston Dep. at 68–69) (Page ID
#495–96).
If Roell repeatedly shouted that he did not have a weapon, that indicates that he was not
using the hose and peat-moss planter as weapons. Roell’s incoherent mumbling about water also
indicates that he was holding the hose because he was fixated on the Agarwals’ water, not
because he planned to use the hose as a weapon. R. 90 (Agarwal Dep. at 60) (Page ID #3815).
Of course, neither Roell’s repeatedly shouting that he did not have a weapon, nor his mumbling
about water conclusively prove that he was unarmed. But the innocuous nature of a soft, peat-
moss planter, the fact that Roell was mumbling about water while holding the hose, and witness
testimony that Roell repeatedly shouted that he was unarmed at least create a question of
material fact as to whether Roell was using the planter and hose as weapons.
B. We do not know how aggressively Gary Roell was acting
The majority attempts to justify the level of force the officers used by arguing that the
situation may have been on the brink of escalating and arguing that Roell was acting
aggressively. In fact, it is not clear how aggressively Roell was acting, meaning that it is not
clear how much force might have been appropriate under the circumstances. Moreover, neither
of these arguments takes into account the obligation to adjust the level of force downward when
confronted with an apparently mentally unstable and unarmed individual.
The majority states that there is undisputed evidence of the aggressive nature of the way
Roell approached the officers. Maj. Op. at 10. In fact, the testimony does not make clear how
aggressively Roell was acting when he approached the officers. At least three different
witnesses testified in three different ways about why and how Gary Roell approached the officers
when he arrived at the Agarwals’ house. Huddleston’s testimony largely mirrored the testimony
of the other officers. He testified that Roell, unprompted, “turned around and started coming
toward myself and Deputy Alexander in an aggressive manner.” R. 77 (Huddleston Dep. at 67)
(Page ID #494). Huddleston also testified that he did not tell Roell to walk toward him, but
rather “told [Roell] to drop what he had in his hands and get on the ground.” Id. at 68 (Page ID
#495).
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 27
Agarwal was more equivocal. At one point she testified that “I saw the hose and him,
you know, running with it towards the officers.” R. 90 (Agarwal Dep. at 38) (Page ID #3793).
Later, she testified that she “cannot say that for sure now” whether Roell was running or
walking, id. at 44 (Page ID #3799), and “I don’t want to say running, but I saw him going
towards the officer with that thing [the hose] in his hand,” id. at 50 (Page ID #3805); see also id.
at 56 (Page ID #3811). Agarwal also testified that it was not as if Roell was approaching the
officers and they were standing still, but rather that Roell and the officers “were both moving
towards each other.” Id. at 42 (Page ID #3796).
In starker contrast to Huddleston’s testimony, Agarwal’s son, Soham Agarwal, recalled
that Gary Roell approached the officers because they instructed him to do so. R. 91 (S. Agarwal
Dep. at 20) (Page ID #3858). He said:
Q. So after the police officers arrived, what was the first thing you heard
either Gary or the officers say to each other?
A. I think the first thing I heard was the officers telling him to like cooperate
or to come over there, to stop doing what he was doing when they came
into the backyard.
Q. So they said come over to them? Is that what you heard?
A. Something like that, yes.
Id. at 37–38 (Page ID #3875–76).
In support of its contention that there is undisputed evidence of the aggressive nature of
the way Roell approached the officers, the majority states that Soham Agarwal testified that
“Roell was facing the deputies swinging the hose ‘as if he was trying to hit somebody.’” Maj.
Op. at 4 (quoting R. 91 (S. Agarwal Dep. at 32) (Page ID #3870)). This statement slightly
mischaracterizes Soham Agarwal’s testimony, and, although slight, the difference between
Soham Agarwal’s testimony and the majority’s characterization of Soham Agarwal’s testimony
is important. Soham Agarwal actually testified that Roell had something in his hand, and that
while “it was a little dark still, so it was hard to tell what it was. . . . it seemed like it was the hose
that he had held previously -- and that he was kind of like swinging it around, as if he was trying
to hit somebody.” R. 91 (S. Agarwal Dep. at 32) (Page ID #3870). Obviously, Soham
Agarwal’s testimony does not unequivocally state that Roell was acting in a calm, unaggressive
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 28
manner, but it also does not unequivocally state that Roell was swinging the hose as if he was
trying to hit someone. Instead, Soham Agarwal stated that it was dark enough that it was hard to
tell what was happening, that Roell was holding something that “seemed like it was the hose,”
and that Roell was “kind of like swinging” whatever he was holding “as if he was trying to hit
somebody.” Id. This distinction is important because, along with Rachana Agarwal’s testimony,
it underscores that it was not at all clear to the disinterested witnesses how aggressively (or
unaggressively) Roell was acting. It was Huddleston, rather than Soham or Rachana Agarwal,
who characterized Roell as aggressive.
The majority also states that although Roell committed only property crimes, it was
reasonable for the officers to infer that his crimes might escalate and therefore reasonable for
them to tase him. Maj. Op. at 9. First of all, this point is debatable. The only support the
majority offers is an unpublished case that is distinguishable because it held that tasing the
suspect did not clearly constitute excessive force because the suspect was fleeing. See Cockrell
v. City of Cincinnati, 468 F. App’x 491, 498 (6th Cir. 2012) (“[I]t is not clear whether tasing a
suspect who fled from the scene of a nonviolent misdemeanor constituted excessive force, as of
July 2008.”); see also id. (Cole, C.J., concurring) (“I am persuaded that Cockrell, as of July 3,
2008, did not have a clearly established right not to be tased for fleeing from a non-violent
misdemeanor. I write separately because, given the totality of the circumstances, I believe that
Officer Hall’s use of force was excessive.”). Second, even if tasing an unarmed individual is not
generally a constitutional violation, that does not change the fact that officers have an obligation
to adjust the level of force downward if the individual is apparently mentally unstable and
unarmed. Even if an officer generally is permitted to tase an individual who is suspected of
committing only misdemeanors, that does not mean that that the officers in this case were
permitted to tase Roell, given that he was apparently mentally unstable and may have been
unarmed.
The majority also attempts to analogize this case to Cook v. Bastin, 590 F. App’x 523
(6th Cir. 2014), but in doing so notes that in Cook the officers observed Campbell “digging his
lacerated fingers into an electrical socket” and “observed the Crisis Manager’s torn and bloody
shirt, which they interpreted as an indication that physical violence had occurred.” Maj. Op. at
No. 16-4045 Roell v. Hamilton Cty Bd. of Comm’rs, et al. Page 29
15. This case is dissimilar to Cook because the officers observed no signs that violence had
occurred, only signs that property damage occurred. In addition, as the majority acknowledges,
the officers in Cook used less force than the officers in this case used against Roell. Id.
C. There are disputed facts, making summary judgment inappropriate
Because we do not know whether Gary Roell was unarmed according to Ohio law, we do
not know whether the Champion/Martin rule applies to the officers’ confrontation with Roell.
See Martin, 712 F.3d at 962 (quoting Champion, 380 F.3d at 904) (officers must “take into
account ‘the diminished capacity of an unarmed detainee . . . when assessing the amount of force
exerted’”). Because we do not know how aggressively Roell was acting, we do not know
whether the level of force the officers used was appropriate under the circumstances. As a result,
summary judgment is not an appropriate resolution of this case. A jury should resolve the
disputed, material facts and ultimately determine whether the officers complied with their
obligation to adjust the level of force downward. Therefore, as to the majority’s resolution of
Nancy Roell’s § 1983 claim against Deputies Alexander, Dalid, and Huddleston, I respectfully
dissent.
|
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Ultraviolet radiation-induced ubiquitination and proteasomal degradation of the large subunit of RNA polymerase II. Implications for transcription-coupled DNA repair.
We have shown previously that UV radiation and other DNA-damaging agents induce the ubiquitination of a portion of the RNA polymerase II large subunit (Pol II LS). In the present study UV irradiation of repair-competent fibroblasts induced a transient reduction of the Pol II LS level; new protein synthesis restored Pol II LS to the base-line level within 16-24 h. In repair-deficient xeroderma pigmentosum cells, UV radiation-induced ubiquitination of Pol II LS was followed by a sustained reduction of Pol II LS level. In both normal and xeroderma pigmentosum cells, the ubiquitinated Pol II LS had a hyperphosphorylated COOH-terminal domain (CTD), which is characteristic of elongating Pol II. The portion of Pol II LS whose steady-state level diminished most quickly had a relatively hypophosphorylated CTD. The ubiquitinated residues did not map to the CTD. Importantly, UV-induced reduction of Pol II LS level in repair-competent or -deficient cells was inhibited by the proteasome inhibitors lactacystin or MG132. These data demonstrate that UV-induced ubiquitination of Pol II LS is followed by its degradation in the proteasome. These results suggest, contrary to a current model of transcription-coupled DNA repair, that elongating Pol II complexes which arrest at intragenic DNA lesions may be aborted rather than resuming elongation after repair takes place.
|
{
"pile_set_name": "PubMed Abstracts"
}
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Oberto was Verdi's first staged operas and was heard for the first time at La Scala, Milan in November 1839. As a young and unknown composer, Verdi was subject to the rules governing the opera industry in Italy. Even so, ... more »there are many scenes in this early work that reveal unmistakable signs of the composer's individual style.« less
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{
"pile_set_name": "Pile-CC"
}
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Seals have been used to isolate fluids at various pressures and temperatures. Such seals have existed for use in packing rings, seal rings, piston rings, and gland structures in industrial equipment such as cylinders, pumps and valves and in oil-field equipment such as downhole tools and surface equipment, requiring seals, for example, against high pressure and low pressure liquids and gases, for reciprocating rods, for pistons, for valves and for other applications.
However, such seals may be eroded and/or extruded or destroyed for machinery equipment wherein sealing needs to be established at the most severe sealing environments, which include seal gland design, pressures, fluid medias and temperatures.
Such seals, whether of the dynamic or static type, are usually made, or have portions made, of materials which, to some extent, are resilient or at least deformable. In order to seal effectively, it is not necessary, but could be possible, that the sealing device be placed under some compressive loading between the components of the assembly to be sealed. Because of the compressing load, there is a tendency for portions of deformable seals to be subjected to extrusion forces which will either distort the seal and impair its effectiveness as a seal or, in more severe cases, force portions of the seal into clearances between the components to be sealed.
In an attempt to overcome this extrusion problem, workers in the field have resorted to various techniques. One common practice employed to prevent such extrusion is the use of a back-up ring of knitted mesh as shown in U.S. Pat. No. 4,219,204. Additionally, seals having the seal lip configuration with an insert discussed below are also known in the art and are manufactured by Parker Seal Company, polypac seal.
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Mandatory Ultrasound Bills Everywhere, and the Continued Fight Over Contraception
On this episode of Reality Cast, I’ll be interviewing Tara Culp-Ressler about the surge of transvaginal ultrasound bills in the states. Also, more on the reaction to the contraception mandate clarification and a segment on why it’s important not to victim-blame Rihanna.
Laci Green has a video out chronicling what life was before Roe v. Wade.
roe *
She also recounts how class determined back then how safe an abortion you could get, with privileged women getting quiet abortions from doctors and poor women going to back alley providers.
*******
So last week, I reported on the newly clarified HHS regulations regarding contraception, which laid out how the administration plans to make sure that nearly all women will have their contraception covered by their insurance while carving out exceptions so non-profit religious organizations don’t have to pay for directly if they don’t want to. The non-profits were hiding behind the moral taint of having to “pay” for non-procreative sex, even though the benefits are earned benefits held by the employees, meaning that the groups were not paying for them so much as the employees were. I argued that the Catholic authorities, especially the Conference of Catholic Bishops, would reject this clarification for one simple reason: This was never about religious liberty, moral taint, or money. It was about separating women from their contraception and any policy that addressed their stated concerns about money but allowed women to access contraception through insurance would be rejected.
I was right, according to the new report by NPR. They explained how much religious entities are not being required to pay for contraception.
contraception 1 *
So this must be very, very clear by now: They are not paying for contraception. They weren’t in the first place, but now they’ve got so much distance between their health care dollars and the eventual use of contraception that the claim that they’re going to get some slut taint by women spending their earned health care dollars the employer released to them is even more ridiculous. There is simply no way on God’s green earth that this is about religious liberty, except insofar as employers want to deprive employees of the religious liberty to choose their own contraception. So that leaves only one remaining objection, which is that they believe that if you work for them, they get to have a vote in your private reproductive and sexual decisions.
And now they’re basically admitting that.
contraception 2 *
In other words, they simply believe they get veto power over how employees spend their compensation. If they could find an easy legal way to prevent employees from spending their checks on contraception, they’d clearly try for that, too, but in the meantime, they’re going to force you to pay twice over for your contraception, once when you earned it by working and again because they want to force you not to use your earned benefits on contraception. And yes, I mean twice. Since the insurance you’re paying for with your cash and labor covers contraception, by forcing the insurance companies not to cover you, they are forcing you to pay for a benefit that you will be forced not to receive. Lots of force to force their religious beliefs on you!
The opt-out thing is clearly some political nonsense set up to imply people are required to use contraception if they don’t want. There’s already an opt-out clause. If you don’t want to use contraception, you opt out by simply not getting a prescription for it. Easy.
That this is about giving employers control over employees was also made clear by this.
contraception 3 *
So they’re saying that secular employers should be able to withhold benefits earned by employees because they disapprove of their employees’ sex lives. This has nothing to do with religion, except the word is being tossed around a lot to confuse the issue. This is about a bunch of misogynist employers who think, because you work for them, your sexual and reproductive lives belong to them. If they get their way on this, they will absolutely look for new avenues to meddle with your private life, because this is about power and control, and not religion.
**********
Insert interview
**********
So Rihanna has gotten back together with Chris Brown. I feel almost bad recapping the whole story, since even those of you who have never even heard a song by either of them probably know the story, but in case you haven’t, here goes: Four years ago at a pre-Grammy party, the two, who were dating, got into a fight in the car. During this fight, according to the Los Angeles police report, Brown tried to force Rihanna out of a moving vehicle, but deterred by her seat belt, he shoved her head against a passenger window, punched her in the eye with his left hand, and then kept driving while punching with his right hand. She was sent to the hospital with a swollen, bruised and bleeding face. She broke up with him shortly thereafter, but for the past year or so has teasing out a reconciliation, first calling him a friend, then doing a song with him, then taking pictures of him in her bed and now this.
rihanna 1 *
Showing up and canoodling at the Grammies is an overt act of symbolism of the absolutely creepiest kind, because both of them missed the 2009 Grammies because of the beating. Indeed, one can imagine what a power trip it must be for an abusive man like Brown to get his victim to snuggle with him at a party that he forced her to miss because her injuries at his hands were that bad. That kind of symbolic domination is exactly the kind of thing that abusers love, because it makes them feel like they have total control over their victim. Indeed, this is far from the only public display of Rihanna’s devotion to Brown, a devotion that is publicly being displayed in such a way to draw attention to the beating and how much she supposedly doesn’t seem to hold him accountable for it.
rihanna 2 *
There are two ways to deal with seeing something as upsetting as a woman who has been the victim of such serious abuse completely forgive and try to exonerate the man who beat her. There’s the way I prefer, which is to use this opportunity to educate yourself and others about the realities of domestic violence, and how the abusers manipulate and guilt trip their victims until the victims are suffering from low self-esteem and feel that only the abuser can validate them. Often an abuser will tell his victim that he’s the only one who really understands her and that everyone else just doesn’t understand their love, and she should therefore trust him and treat everyone else like the enemy. The displays of affection that would seem over the top even for a non-abusive couple are part of this whole thing of creating the illusion that it’s an abuser and his victim against the world. For victims, getting away from the emotionally warped world the abuser has created for them is incredibly hard to do, which is why victims usually return a number of times before escaping, and why prosecutors usually have to create cases against abusers knowing the victims will resist attempts to put their abusers in jail.
Or you could just blame the victim and pretend that’s feminism, which is what Lena Dunham did on Alec Baldwin’s show.
rihanna 3 *
This was really disappointing to me, because Dunham’s show “Girls” has shown a remarkably nuanced understanding of how women are socialized to defer to men and how women who judge other women for it often are themselves deferring to some man who is power tripping on them. While none of her characters are being beaten, she often shows them putting up with men stepping all over boundaries and manipulating them, and doing so precisely because women are trained from the cradle to defer to male authority. Abuse victims stay with their abusers for the same reason that the characters on “Girls” stay with men who deliberately play mind games with them or stay with men who, as in one episode, lock them in an inescapable room full of horrible images for hours while calling it “art” or stay with men who are clear that they will treat you like a masturbation toy instead of a partner in bed: Because women are told over and over again in a multitude of ways that if we stand up for ourselves, we’ll be shrewish bitches and no one will ever love us ever again. In fact, abusers often tell victims no one else will ever love them ever again, and because our society is so hateful to women, it’s easy for victims to fall for this line.
Which is why blaming Rihanna is such a bad idea: You are telling her and every abuse victim overhearing it that you agree with the abuser that the victim is bad and unworthy of love. Which, in turn, makes it hard for the victim to leave, because she sees you shaking your head at her and thinks, “Gosh, he’s right that everyone else hates me and he’s the only shot at love I’ll ever have.
It’s worth remembering the man interviewing Dunham was the same guy who left this message for his daughter on her voice mail.
rihanna 4 *
Now, calling a 12-year-old girl a “pig” because she doesn’t want to talk to you—gosh, hard to see why!—isn’t the same thing as beating your girlfriend to a pulp. But it’s still abusive nonsense. I don’t judge Dunham for doing the interview instead of refusing because of some ambiguous duty to be a role model. We all make our compromises. But she should be more forgiving of the fact that the choice to leave an abusive boyfriend is a lot harder than the choice to boycott an interviewer that is known to call his daughter a “pig”, and consider that before she starts throwing stones.
*********
And now for the Wisdom of Wingnuts, oh boy it’s prom time again. And prom planning means, inevitably, people who want to use the prom as a chance to exclude and bully gay kids. In this case, it’s an Indiana high school that has a group trying to plan a separate prom that excludes gay kids. Here’s one teacher, defending it by saying gays have no purpose in life.
prom *
How someone can be a teacher and so cruel to their students is beyond me. I will say it’s funny that people are claiming to do this out of Christian concerns about immorality. Because all the fornicating and drinking that straight students do at prom is apparently super moral, as long as it’s straight people.
Mandatory transvaginal ultrasound is rape, pure & simple. Anything put into a person’s body without their express permission is rape. Men wouldn’t tolerate a mandatory transrectal ultrasound for a prostate check yet women are expected to just relax & accept this violation. Anyone supporting this requirement is a pig (& I’m probably insulting pigs).
Re: tolerating other abusive behavior, I can confirm from experience (w/everything except beatings) that you’ve hit it right on. Abusers are capable of an unbelievable level of manipulation that the victim doesn’t even necessarily realize is taking place. It’s taken me a long time to begin recovering from what I was put through & I know that I still have a ways to go. The best thing anyone can do for the victim is offer them a safe haven as needed until they can tear themselves out of the situation.
nettwench14
Exactly spot on. What’s the difference between an employer paying for your health insurance, or giving you a paycheck, either of which can be used to purchase contraception? This argument never made sense to me at all.
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[The phenotypic heterogeneity of meningococcal strains by their serogroup trait].
It is shown that heterogeneity of meningococci of the outlined serogroups is formed due to appearance of nonagglutinable individuals in subpopulations but heterogeneity of polyagglutinable strains is characterized by incorporation not only of cross-reacting cells, but also microcommunities of each separate group which make a total feature. Serologically inactive strains either may be homogeneous or may form variants with low (to 20%) and high (to 44%) specific weight of agglutinable colonies. Strains in the centres embrace different concentrations of microcommunities which are identical by their serogroup properties to subpopulations of the meningitis pathogen.
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Jorai
Jorai is a suburb of Cooch Behar, West Bengal. (Elevation: 53 m above sea level, Zone: NFR/Northeast Frontier)
Jorai (jo'-ra-i) is of Hebrew origin and has many possible meanings. It could mean "whom Jehovah teaches," or the name of a Gadite chief (dwelling at Gilead in Bashan, in the reign of Jothan king of Judah), or possibly the name of a clan (1 Ch 5:13). However, in this case, the name is derived from a rivulet called Jorai Nodi - a tributary of the River Sankosh .
The small suburb is famous for its marathon football league and Raas-mela (fair based on Radha-Krishna's life). Jorai also features a railway station by the same name (there are three railway stations, Kamakhyaguri KAMG, Jorai JOQ and Srirampur SRPB, which belong to three separate districts, Alipurduar, Coochbehar (both in West Bengal) and Kokrajhar (in Assam), respectively).
Major localities
Jorai Bazaar, Aastami Ghat অষ্টমী ঘাট, Jorai High School (H.S.), Jorai Railway Station, Naothowa নাওথোয়া, Paschim Rampur পশ্চিম রামপুর, Dakshin Rampur দক্ষিন রামপুর, Aashor Para আসরপাড়া, Wilson Road, Uttar Rampur উত্তর রামপুর, Madhya Rampur মধ্যরামপুর, Najirandeutikhata নাজিরান দেউতিখাতা, and Chhat Valka ছাটভল্কা.
Occupations
Most of the people rely on agriculture. Businesses such as timber, fishing, retail clothing, and shops are also common here. Assam-Bengal Commercial/Sales Tax office used to provide a large number of jobs. But post GST regime, Jorai and it's neighbour Barobisha have witnessed massive unemployement due to the unification in taxes and abolishing of State sales Tax gate, which would otherwise serve many people a source of income. Computer learning centers and railways provide other job opportunities. Jorai's connectivity with other parts has been hampered recently, after the North Bengal State Transport Corporation's bus terminus shifted from here to Alipurduar.
Cultural activities
Cultural activities started with the emergence of "Jatra" culture which was initially patronized by the late Sukumar Ghosh সুকুমার ঘোষ, the founder of Jorai Madan-mohan Bari মদনমোহন বাড়ী (the place for community worship and fare). Aashor para drama club (এনাদের "সব পেয়েছির আসর" একসময় বেশ বিখ্যাত ছিল), Pragati Sangha, Danpiter ashor ডানপিটের আসর, Kishore Sangha, North Bengal State Transport employees (এনাদের বিশ্বকর্মা পুজো একসময় বেশ বিখ্যাত ছিল) and Jorai Railways employees geared up the cultural activities further in the 1980s and 1990s.
Sports
The marathon football league held every year witnesses a massive upsurge of spectators around its neighborhood area. However, with the advent of cricket in the 1990s, the football craze has been reduced considerably.
Other Jorai towns and some important facts
There is a town named Jorai in the North West Frontier Province, Pakistan (latitude: 34.87324 and longitude: 72.88318).
There is a town named Jorai in Madhya Pradesh, India (latitude: 25.42779 and longitude: 77.74414).
Boirali maach (বৈরালী মাছ): The rare fishes of Himalyan foothills - Danio rerio, Danio dangila and Barilius Barila are available in Raidak, Jorai and Sankosh river. Boirali fish derives its nutrition from microscopic Dufnia, Cyclop or from green algae Spirogyra or Volvox. These fishes are nowadays facing the crisis of extinction due to water pollution, excess use of pesticides and the frequent vibration caused by dynamite explosions in the hills.(Web page developed by Sudipto Ghosh)
Category:Cities and towns in Cooch Behar district
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Which sidebar images do you want for June? (Pick your 3 Favourites!)
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Adenocarcinoma of the head of the pancreas: determination of surgical unresectability with thin-section pancreatic-phase helical CT.
This study was conducted to evaluate newly introduced criteria for unresectability of pancreatic cancer with thin-section pancreatic-phase helical CT. Twenty-five patients with adenocarcinoma in the head of the pancreas underwent thin-section pancreatic-phase helical CT. The major peripancreatic vessels were categorized on a scale of 1-4, according to the degree of circumferential involvement by tumor. The maximum diameters of the small peripancreatic veins--gastrocolic trunk, anterosuperior pancreaticoduodenal vein, and posterosuperior pancreaticoduodenal vein--were recorded. Findings on CT were compared with the results of surgery in each patient. Sixteen patients had surgically resectable tumors, and nine patients had surgically unresectable tumors. CT and surgical correlation was available for 98 major peripancreatic vessels; 85 were resectable and 13 were unresectable. Of category 1 vessels, 72 (97%) of 74 were resectable at surgery. Of category 2 vessels, 12 (71%) of 17 were resectable. One (50%) of two category 3 vessels and none (0%) of five category 4 vessels were resectable at surgery. CT showed a dilated gastrocolic trunk in two patients; one of these patients had a surgically resectable tumor, but the other patient had a surgically unresectable tumor. In patients with adenocarcinoma in the head of the pancreas, the degree of circumferential vessel involvement by tumor as shown by CT is useful in predicting which patients will have surgically unresectable tumors. A dilated gastrocolic trunk should not be used as an independent sign of surgical unresectability.
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Grass strip corridors in agricultural landscapes enhance nest-site colonization by solitary wasps.
Corridors that connect otherwise isolated habitats have often been proposed as a management strategy to mitigate negative effects of habitat fragmentation. Non-crop corridors may have the potential to enhance the connectivity for arthropod predators in cropland landscapes, especially for species that require multiple habitats, such as cavity-nesting wasps which use wooded habitat for nesting and grassland habitat for foraging. However, the effects of corridors in nonexperimental landscapes have been rarely examined. We studied the species richness and abundance of cavity-nesting wasps and their parasitoids in standardized trap nests located in three habitat types (forest edge, hedge, grass strip) and in three grass-strip types (connected to a forest edge, slightly isolated, highly isolated from a forest edge). Species richness and the abundance of wasps (Hymenoptera: Sphecidae, Eumenidae, Pompilidae) were highest at forest edges, which provide natural nesting sites, and lowest in grass strips, with few natural nesting sites. Wasp abundance in grass strips connected to forest edges was 270% higher than in slightly isolated grass strips and 600% higher than in highly isolated grass strips. The abundance of caterpillar-hunting eumenid wasps was 600% higher in connected grass strips than in slightly and highly isolated grass strips. Species richness of wasps was enhanced by 180% in connected grass strips compared to highly isolated grass strips. Parasitism rates were not directly influenced by habitat or grass-strip type, but increased with increasing parasitoid diversity that was higher at forest edges than in grass strips. We conclude that grass-strip corridors enhance the colonization of nesting sites, presumably by facilitating wasp movements. In agricultural landscapes, where nesting sites are limited and food availability changes frequently, rapid colonization of nests may enhance population viability. Higher wasp abundance in connected nesting sites may be directly linked to higher biocontrol of pest caterpillars within the foraging range around nests. Although grass strips can reduce the negative effects of habitat fragmentation, non-crop habitats such as forest habitats and hedges providing nesting sites are required within the home range of wasps to allow reproduction in agricultural landscapes.
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Friday, September 19, 2014
The last words I heard before the darkness took me and my dreams were shattered.
I was on my way to having it all.Friends, family and a future.Everything I had wished for but never thought possible.
Denham King showed me just how good life could be. A life where love and happiness were within reach.
Almost.
I should have known it would never last.My past is a dark, damp cloud, that has seeped into my skin and left a cold promise.A promise of hurt and pain.A promise of a long, hard fight, where the stakes are high and the risks threaten lives.
When your world gets thrown in all directions, and your dreams for the future are torn from your grasp; how do you go on?
Can I fight the demons that haunt me?Can love save me from fate’s cruel path?
Holding Aces (The Kingdom, #1)
They say that time heals all wounds. But mine are set in so deeply, they’ve taken on a life of their own, lurking in the shadows at every turn and haunting my thoughts.
The girl I once was has been replaced by a stranger. I don’t even know who I am anymore. I run. And I hide. Pretending to be someone I’m not… Until I meet Denham King. My burst of color in an otherwise grey world. And for the first time in my life, I find myself running towards someone instead of running away. But fate can be cruel, and I can’t escape my past. Can I?
Nikki Groom is a hopeless romantic, lover of all things happily ever after and firm believer that love makes the world go around. In her spare time, you will find Nikki laughing with her very treasured family, walking with her beloved dog in the hundred acre wood or curled up in a cosy corner with words and wine. She lives in East Sussex with her husband and two children. Having turned her hand to many things over the years, Nikki is now proud to add ‘author’ to that list. Having always been a dreamer, Nikki’s imagination stretches far and wide, which enables her to get lost in faraway places and imaginary people.
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Pavel Rovinski
Pavel Apolonovič Rovinski (1831 , Russian Empire — 1916 Petrograd, Russian Empire) was Russian historian, Slavist, ethnologist and geographer. Elementary school, built in 1994 in Podgorica, Montenegro is named after him. There is a Society of Montenegrin-Russian Friendship () founded in Podgorica, Montenegro, on November 24, 2007.
Selected works
Obodska štamparija na Rijeci Crnojevića u Crnoj Gori i njen značaj na slovenskom jugu, Odbor za proslavu četiristogodišnjice Obodske štamparije, 1893
Crna Gora u svojoj prošlosti i sadašnjosti( Montenegro in its Past and Present), ,
Zapisi O Srbiji, 1868-1869: Iz Putnikovih Beležaka,
References
External links
Text about Pavle Rovinski and his work about population of Slavic ancestry in Albania, written by Vukale Đerković
Biography of Pavle Rovinski on web site of elementary school in Montenegr, named after him
Category:1831 births
Category:1916 deaths
Category:Russian historians
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映画作家の想田和弘氏がツイッターのハッシュタグを用いて行っている実験が恐ろしいと話題になっています。詳細は以下から。
これまで幾度となく「全く問題ない」「批判は当たらない」などと記者会見で繰り返し批判をかわしてきた菅官房長官。説明責任を果たしていないとの批判もありましたが、当たり前のように発せられるこれらの言葉にいつしか慣れてしまった人も多いのではないでしょうか。
「選挙」「精神」「演劇1・2」などを観察映画という独自の手法で撮影してきた映画作家の想田和弘氏が昨日からツイッター公式アカウント上で始めた実験が、菅官房長官の実際の言葉を用いて延々と自分へのリプライに答えていくというもの。
想田氏はハッシュタグ#菅官房長官語で答える を用いてこの返答を行っていますが、どんな問いかけや誹謗中傷に対しても幾つかのパターンで応答できてしまう上に、それらを無効化してしまうまさしくマジックワードであることが明らかにされていきます。
フォロアーらも最初は微笑ましく見ていたものがそのうち苛立ちを覚え始め、最後には恐怖を感じさせるという事態になっており、通常届いていたクソリプ（編集部注：クソのようなリプライ）も激減してしまったとのことです。
ついにはこれは想田氏の新しい表現活動の一部と言えるのではないかとの意見も。
これがあくまでも現役の官房長官の記者会見での発言のコピペであるという事実から、政権と国民との間の意思の疎通が恐ろしいほどにできていなかったのではないかという感想が多くの人から漏れ聞こえてくるようになります。
さらには#橋下語で攻撃 #安倍語で補足 というハッシュタグも登場、バリエーションは豊かになりましたがコミュニケーション不在は進む一方
ツイッター上では大喜利になりがちなハッシュタグという存在で、あくまで大喜利を装いながらも官房長官らの実際の発言を用いることで炙りだされたものは何だったのか。慣れてしまった記者会見ではなく、別の人の口から同じ言葉が出ることで、見えてくるものもありそうです。
なお、このタグについてはこちらのtogetterに多くのつぶやきがまとめられています。
【追記】
想田氏が自らのFBでこの実験についての解説を行っていましたので追記します。
#菅官房長官語で答える コツは、相手の質問や抗議に対して決して答えないこと。自然にしていると、思わずうっかり答えそうになるんですけど、そこをグッとこらえる。そして木で鼻を括ったような定型句を繰り出す。するとコミュニケーションがそこで遮断され... Posted by 想田 和弘 on 2015年10月1日
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VF-38
Fighter Squadron 38 or VF-38 was an aviation unit of the United States Navy. Originally established on 20 June 1943, it was disestablished on 31 January 1946. It was the only US Navy squadron to be designated as VF-38.
Operational history
VF-38 equipped with the F6F Hellcat supported the New Georgia Campaign deploying to Henderson Field on Guadalcanal in September 1943. While deployed in the Solomon Islands during 1943 VF-38 shot down 7 Japanese aircraft.
See also
History of the United States Navy
List of inactive United States Navy aircraft squadrons
List of United States Navy aircraft squadrons
References
Category:Strike fighter squadrons of the United States Navy
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Optical microscopy has been a commonly used method of investigation in medicine and biology. Numerous biological samples, including live cells, are quite transparent under visible light illumination and behave essentially as phase objects. Techniques such as phase contrast and Nomarski microscopy provide contrast of nearly invisible samples by transforming the phase information into intensity distribution and thus reveal structural details of biological systems. However, the information obtained with these techniques about the phase shift associated with the illuminating field is only qualitative. Retrieving quantitative phase information from transparent objects with high accuracy and low noise allows for measurements in the biological investigation of structure and dynamics. Both interferometric and non-interferometric techniques have been proposed for quantitative phase imaging of biological samples. Also Fourier phase microscopy (FPM) has been developed as an extremely low-noise phase imaging method. Due to the sub-nanometer phase stability over extended periods of time, FPM is suitable for investigating dynamics in biological systems on time scales from seconds to a cell lifetime.
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Metadata-Version: 1.0
Name: discover
Version: 0.4.0
Summary: Test discovery for unittest. Backported from Python 2.7 for Python 2.4+
Home-page: http://pypi.python.org/pypi/discover/
Author: Michael Foord
Author-email: michael@voidspace.org.uk
License: UNKNOWN
Description: This is the test discovery mechanism and ``load_tests`` protocol for unittest
backported from Python 2.7 to work with Python 2.4 or more recent (including
Python 3).
.. note::
Test discovery is just part of what is new in unittest in Python 2.7. All
of the new features have been backported to run on Python 2.4-2.6, including
test discovery. This is the
`unittest2 package <http://pypi.python.org/pypi/unittest2>`_.
discover can be installed with pip or easy_install. After installing switch the
current directory to the top level directory of your project and run::
python -m discover
python discover.py
(If you have setuptools or `distribute <http://pypi.python.org/pypi/distribute>`_
installed you will also have a ``discover`` script available.)
This will discover all tests (with certain restrictions) from the current
directory. The discover module has several options to control its behavior (full
usage options are displayed with ``python -m discover -h``)::
Usage: discover.py [options]
Options:
-v, --verbose Verbose output
-s directory Directory to start discovery ('.' default)
-p pattern Pattern to match test files ('test*.py' default)
-t directory Top level directory of project (default to
start directory)
For test discovery all test modules must be importable from the top
level directory of the project.
For example to use a different pattern for matching test modules run::
python -m discover -p '*test.py'
(For UNIX-like shells like Bash you need to put quotes around the test pattern
or the shell will attempt to expand the pattern instead of passing it through to
discover. On Windows you must *not* put quotes around the pattern as the
Windows shell will pass the quotes to discover as well.)
Test discovery is implemented in ``discover.DiscoveringTestLoader.discover``. As
well as using discover as a command line script you can import
``DiscoveringTestLoader``, which is a subclass of ``unittest.TestLoader``, and
use it in your test framework.
This method finds and returns all test modules from the specified start
directory, recursing into subdirectories to find them. Only test files that
match *pattern* will be loaded. (Using shell style pattern matching.)
All test modules must be importable from the top level of the project. If
the start directory is not the top level directory then the top level
directory must be specified separately.
The ``load_tests`` protocol allows test modules and packages to customize how
they are loaded. This is implemented in
``discover.DiscoveringTestLoader.loadTestsFromModule``. If a test module defines
a ``load_tests`` function then tests are loaded from the module by calling
``load_tests`` with three arguments: `loader`, `standard_tests`, `None`.
If a test package name (directory with `__init__.py`) matches the
pattern then the package will be checked for a ``load_tests``
function. If this exists then it will be called with *loader*, *tests*,
*pattern*.
.. note::
The default pattern for matching tests is ``test*.py``. The '.py' means
that it will match test files and *not* match package names. You can
change this by changing the pattern using a command line option like
``-p 'test*'``.
If ``load_tests`` exists then discovery does *not* recurse into the package,
``load_tests`` is responsible for loading all tests in the package.
The pattern is deliberately not stored as a loader attribute so that
packages can continue discovery themselves. *top_level_dir* is stored so
``load_tests`` does not need to pass this argument in to
``loader.discover()``.
discover.py is maintained in a google code project (where bugs and feature
requests should be posted): http://code.google.com/p/unittest-ext/
The latest development version of discover.py can be found at:
http://code.google.com/p/unittest-ext/source/browse/trunk/discover.py
CHANGELOG
=========
2010/06/11 0.4.0
----------------
* Addition of a setuptools compatible test collector. Set
"test_suite = 'discover.collector'" in setup.py. "setup.py test" will start
test discovery with default parameters from the same directory as the setup.py.
* Allow test discovery using dotted module names instead of a path.
* Addition of a setuptools compatible entrypoint for the discover script.
* A faulty load_tests function will not halt test discovery. A failing test
is created to report the error.
* If test discovery imports a module from the wrong location (usually because
the module is globally installed and the user is expecting to run tests
against a development version in a different location) then discovery halts
with an ImportError and the problem is reported.
* Matching files during test discovery is done in
``DiscoveringTestLoader._match_path``. This method can be overriden in
subclasses to, for example, match on the full file path or use regular
expressions for matching.
* Tests for discovery ported from unittest2. (The tests require unittest2 to
run.)
Feature parity with the ``TestLoader`` in Python 2.7 RC 1.
2010/02/07 0.3.2
----------------
* If ``load_tests`` exists it is passed the standard tests as a ``TestSuite``
rather than a list of tests.
2009/09/13 0.3.1
----------------
* Fixed a problem when a package directory matches the discovery pattern.
2009/08/20 0.3.0
----------------
* Failing to import a file (e.g. due to a syntax error) no longer halts
discovery but is reported as a failure.
* Discovery will not attempt to import test files whose names are not valid Python
identifiers, even if they match the pattern.
Keywords: unittest,testing,tests
Platform: UNKNOWN
Classifier: Development Status :: 4 - Beta
Classifier: Environment :: Console
Classifier: Intended Audience :: Developers
Classifier: License :: OSI Approved :: BSD License
Classifier: Programming Language :: Python
Classifier: Programming Language :: Python :: 2.4
Classifier: Programming Language :: Python :: 2.5
Classifier: Programming Language :: Python :: 2.6
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3
Classifier: Programming Language :: Python :: 3.0
Classifier: Programming Language :: Python :: 3.1
Classifier: Programming Language :: Python :: 3.2
Classifier: Operating System :: OS Independent
Classifier: Topic :: Software Development :: Libraries
Classifier: Topic :: Software Development :: Libraries :: Python Modules
Classifier: Topic :: Software Development :: Testing
|
{
"pile_set_name": "Github"
}
|
[Quality of fundamental movement patterns in chronic low back pain patients: a quasi-experimental cross-sectional study].
Chronic back pain may be associated with alterations of motor control and maladaptive movement. However, instruments that systematically screen fundamental movement patterns are rare. Using a newly developed functional movement analysis, this study aims to examine whether persons with chronic unspecific low back pain display altered quality of fundamental movement patterns and whether asymmetry exists between body sides. 20 patients with chronic back pain (♀ = 8, ♂ = 12; 49.4 ± 11.3 years) and 20 healthy controls (♀ = 12, ♂ = 8; 47.7 ± 10.7 years) completed the functional movement analysis. It consists of 11 items screening movements of daily life. Eight of them were to complete left and right. The overall score and the number of observed asymmetries (in items to complete left and right) constituted the primary outcomes. A preliminary analysis of reliability (four raters, four subjects) with pilot character was conducted using intraclass correlation (ICC). To compare differences in means, independent t-tests were performed. In case of significance, we calculated the effect size (Cohen's d). The reliability analysis showed an ICC (2.1) of 0.82 (95 % CI: 0.72 - 0.90). Patients with chronic low back pain (31.95 ± 5.82) scored significantly lower than healthy subjects (44.01 ± 5.27; p < 0.001, d = 2.17). Additionally, patients averaged 3.8 ± 1.28 asymmetries while pain-free participants only demonstrated 1.4 ± 0.94 (p < 0.001; d = 2.14). Faulty and dysbalanced movement patterns appear to be linked to chronic low back pain. Nonetheless, given an existing relation, it remains unclear whether the detected deficiencies are causes or consequences of pain. Further studies about the reliability of the presented screening tool are needed.
|
{
"pile_set_name": "PubMed Abstracts"
}
|
We have sent you an email with your verification code.This code is to make sure that the email address you have given
us is correct. To complete the registration process, please
enter the code with your information below...
|
{
"pile_set_name": "Pile-CC"
}
|
MR. DAVID GREGORY: This Sunday, is Syria a game changer for President Obama as the security threats mount on his watch?
A new chapter in Syria’s brutal civil war. The administration says the Assad regime appears to have used chemical weapons.
(Videotape)
PRESIDENT BARACK OBAMA: To use potential weapons of mass destruction on civilian populations crosses another line with respect to international norms and international law, and that is going to be a game changer.
(End videotape)
GREGORY: If confirmed, what is the president prepared to do? Are there any good options? How should the lessons of Iraq weigh on the Obama team’s thinking?
With us this morning, ranking member of the Senate Armed Services Committee, Arizona Republican John McCain.
Then, the terror debate after Boston. Should more have been done to track the suspects when red flags were raised? A debate between Republican Congressman Peter King of the Intelligence and Homeland Security Committee’s and Democratic Congressman of Minnesota Keith Ellison.
Also, this morning, perspective on the threats testing the president from former British Prime Minister Tony Blair.
And our roundtable this morning includes Democratic Senator Amy Klobuchar as the group reflects on the Bush Library Dedication this week and reacts to the president’s big Saturday night with Washington journalists.
ANNOUNCER: From NBC News in Washington, the world’s longest running television program, this is MEET THE PRESS with David Gregory.
GREGORY: And good Sunday morning. Washington is a little bleary-eyed this morning after what’s come to be known as nerd prom in our nation’s capital where politicians, celebrities, journalists, all mingle for a night of some bipartisan fun, the president finding way to poke fun at Washington’s disarray.
(Videotape, Last Night)
PRESIDENT BARACK OBAMA: I know Republicans are still sorting out what happened in 2012, but one thing they all agree on is they need to do a better job reaching out to minorities. And-- and look, call me self-centered, but I can think of one minority they could start with. Hello.
(End videotape)
GREGORY: We’re going to have some highlights and reaction from last night, but we want to start with the very serious topic of Syria this morning. The looming threat after this week’s revelation about the possible use of chemical weapons, and for that we turn to Senator John McCain of Arizona who is in Arizona this morning. Senator, welcome.
GREGORY: As you know the White House said this week after this intelligence estimate came out about the use of chemical weapons that the case that Syria actually did that is not airtight. What do you say?
SEN. MCCAIN: Well, it may not be airtight. The Israelis and the British are far more affirmative in their assessment of it. But, David, we should not be-- our actions should not be dictated on-- by whether Bashar Assad used these chemical weapons or not. First of all, sooner or later, he most likely would in order to-- to maintain his hold on power. But what has happened here is the president drew red lines about chemical weapons thereby giving a green light to Bashar Assad to do anything short of that including scud missiles and helicopter gun ships and air strikes and mass executions and atrocities that are on a scale that we have not seen in a long, long time.
GREGORY: So the president says that this is a red line if confirmed, and he said back in-- in August, “It would change my calculus. It would change my aquation-- equation, rather.” What would you have him do at this point?
SEN. MCCAIN: Well, for about two years as this situation has deteriorated in a very alarming fashion, affected the surrounding countries, destabilized Lebanon, destabilized Jordan, and has had implications and repercussions throughout the region, we have said that they need a no-fly zone which could be obtained without using U.S. manned aircraft. We could use patriot missiles-- patriot batteries and cruise missiles to take out their air and to supply the resistance with weapons. And, as you know, a flood of weapons is coming in from Russia and Iran. Iranians are on the ground in Syria, and it’s an unfair fight. And unless we change this balance of power by not using incrementalism, then there’s every risk of a stalemate that could go on for months and months while the jihadists flood in, while the sorting out the situation after he leaves becomes more and more complicated, and there’s also the possibility that he could enact a plan B which is to withdraw to the coast (Unintelligible) areas with a-- an enclave that stretches from the Golan Heights all throughout…
SEN. MCCAIN: … along the coast, and could be another long period of conflict.
GREGORY: But, Senator, as we-- the Bush library was dedicated this week, again the specter of Iraq and the legacy of Iraq was debated in this country. Are we not more skeptical about talk of more limited military action, no-fly zones, incrementalism, as you say, as well as the strength of the opposition? Aren’t there lessons from Iraq that need to be taken into mind here?
SEN. MCCAIN: Well, one of the lessons obviously, and we hear this a lot from the administration, is that we had false information about weapons of mass destruction with Iraq. In this case, there is significant evidence that the-- physical evidence of the use of chemical weapons. And by the way, the-- the administration has said, well, they want the U.N. to investigate. The only problem with that is Bashar wouldn’t let the U.N. in so it’s a-- a bit ludicrous. So I-- I-- the fact is that whether he has used those chemical weapons or not, he’s done virtually everything else that you-- atrocity that you can commit, and that should not be the gauge. But is-- would anyone be surprised if Bashar Assad did use chemical weapons in his desperation to hang on to power?
GREGORY: So what is the limit of what the United States, in your judgment, should do to put a limit on him?
SEN. MCCAIN: Well, as I said, a safe zone of arming the rebels, making sure that we help with the refugees and an international-- be prepared with an international force to go in and secure these stocks of chemical and perhaps biological weapons. There-- there are a number of caches of these chemical weapons. They cannot fall into the hands of the jihadists, otherwise we will end up seeing those weapons used in other places in the Middle East. It’s a very dangerous situation.
GREGORY: And U.S. troops should be part of that force?
SEN. MCCAIN: I don’t know. I think that, first of all, American people are weary, as you pointed out. They don’t want troops on the-- boots on the ground. I don’t want boots on the ground. I do want to give them the assistance which would give them a dramatic shift in the balance of power in Syria, but we have to, as an international group, plan and be ready operationally, not just plan but be ready operationally to go in and secure those areas. Now, if you could do it-- whatever the composition of that force is, is something I think we have to look at very carefully. But the worst thing the American-- the United States could do right now is put boots on the ground in Syria. That would-- that would turn the people against us. And just let me say the Syrian people are angry and bitter at the United States. I was in a refugee camp in Jordan, and there are thousands of people and kids, and this woman who’s a schoolteacher said, Senator McCain, you see these children here, they’re going to take revenge on those people who refuse to help them. They’re angry and bitter. And that legacy could last for a long time, too, unless we assist them.
GREGORY: Let me turn you quickly just to a couple of domestic items. This funding they came up at the week over the FAA and flight delays and new legislation to basically provide the administration with more flexibility to get the planes running on time again. What would you be prepared to do to replace the sequester or the most harmful effects of the sequester? Is that a model for what Washington ought to be doing about it?
SEN. MCCAIN: Well, I say with all due respect to my friends, it’s a little bit hypocritical on the same day when all of the focus was on the delays that we have in getting through airports. The Chief of Staff of the United States Army was saying that we are going to have-- if we don’t reverse this, we’re going to have a hollow army. We’ll be unable to defend the nation and it would take us 10 or 15 years to recover. I think we have our priorities a little bit skewed here. Look, I’m-- I’m forgiving the FAA flexibility, but I also want to give the military flexibility and I don’t want the sequestration cuts to be as steep as they are in-- on national defense. We’ve got a lot of savings we can make in national security, but right now we-- in the words of the Secretary of Defense and our uniformed service chiefs, we’re putting the security of this nation at risk.
GREGORY: I want to end on politics. You had your old friend and former colleague in the Senate, the Vice President Joe Biden, offering some political analysis about the 2008 race. Here’s part of what he said.
VICE PRESIDENT JOE BIDEN (Sedona, AZ): And the truth of the matter is, Barack knows I know, had the economy not collapsed around your ears, John, in the middle of, literally, just as you were-- as things were moving, you at least would have-- I think you probably would have won, but you-- it would have been incredibly, incredibly, incredibly closer. You inherited a really difficult time.
(End videotape)
GREGORY: If not for the economy, you would have been president, is that how you see it?
SEN. MCCAIN: No. Look, Joe Biden and I are very close friends, and I think it would have been a much closer race, but, I’ll tell you, he has-- President Obama ran a great race, and that-- campaigns matters. I appreciate the fact that my dear friend would say something like that, but I know that-- I doubt if the outcome would have been a lot different, but I can always hope it might have been.
GREGORY: All right. Senator, we’ll leave it there. More to come on the Syria debate. We appreciate you coming on this morning.
SEN. MCCAIN: Thank you.
GREGORY: All right. Turning now to Democratic Congressman Keith Ellison of Minnesota, and Republican Congressman Peter King of New York. Gentlemen, welcome to you.
REP. KEITH ELLISON (D-MN): Thank you.
GREGORY: I want to talk about the aftermath of the Boston bombings and the-- the surveillance work, the role of the FBI. But, first, let me get your comments, Congressman, on this prospect of a huge national security test now for President Obama. How do you see it?
REP. ELLISON: Well, you know, first of all, this action is the most despicable thing. You know, Americans have to rally together to stamp out terrorist acts like this. I’m proud of the law enforcement, proud of the first responders. But what I think we need to do is to really, really back law enforcement to make sure that we fully investigate this case and we don’t need to start identifying communities to surveil or to go after. We need to come together as a-- as a nation.
GREGORY: Let me get your comment before we get to that on Syria, what I was just discussing with Senator McCain.
REP. ELLISON: Yeah.
GREGORY: This is a huge test as well as the Boston bombings aftermath, but also the Syria being a huge test for President Obama. What-- what concerns you about what we’ve seen out of potential use of chemical weapons?
REP. ELLISON: Well, I’m absolutely concerned about that, but I believe the United States could play a greater role in dealing with the humanitarian crisis. There’s a-- there’s a very, very difficult humanitarian crisis as Senator McCain pointed out. I mean, we have spillage and refugees in Jordan, in Lebanon, in-- and currently displaced people in Syria. The suffering is intense. And I don’t think the world’s greatest superpower, the United States, can stand by and not do anything. Now we have done some things and the president deserves a lot of credit for that, but I think there’s perhaps a little bit more we could do on the humanitarian front.
GREGORY: We’re talking about a red line being crossed, Congressman, and whether the United States has any military options to back up what the president said, which is that you don’t cross it or there will be severe consequences.
REP. PETER KING (R-NY, Intelligence Committee): Yeah. Listen, the situation here is complex. My concern is al Qaeda has more influence than it should among the rebels and that if we assist the rebels, al Qaeda could take advantage of that. Having said that, the president did say that there’s a red line and once the United States lays out a red line, some action has to be taken. Now what that’s going to be, I was at the briefing with Senator Kerry the other day. He really didn’t lay that out. And I think the administration is right now trying to figure out what to do. I’m not trying to minimize it, but once he laid out the red line, something is going to have to be done.
GREGORY: Something militarily.
REP. KING: Well, either that or concerted action with allies, again…
GREGORY: But do somebody else besides the U.S. have to take the lead here? Is that where we are politically?
REP. KING: …if somebody else-- But again, I’m still concerned about who is going to take over the rebels. And we I think allowed this to go on too long where we didn’t have enough influence on the ground in dealing with the rebel forces.
REP. ELLISON: Well, red line does not mean boots on the ground, but there’s a lot of things we can do other than that. We have been providing nonlethal military aid. But I think more coordination and dealing with this humanitarian crisis I think is essential.
GREGORY: Let me turn to the aftermath of the Boston bombings where the focus has been this week is on the now dead older brother, Tamerlan Tsarnaev, who had trips back to the Chechnya region of the northern caucuses, was interviewed by the FBI as people will remember but then seemed to fall off the radar a little bit. Congressman, where are you critical of intelligence and the FBI’s role in this?
REP. KING: I think the FBI has done an outstanding job in solving this in those four-day-- four-day period. Having said that, I don’t think they did a full investigation beforehand. The fact is there were other items in his folder, in his file that they found. And I think they continued to give the benefit of the doubt in each instance and, therefore, just closed out that investigation. For instance, they never went to his mosque, never spoke to the imam, never spoke to a number of his relatives and, also, there were certain matters in his file that they chose to look the other way on or said there was nothing there.
GREGORY: What did they look the other way on?
REP. KING: His-- his name came up in several other instances and they said there was nothing there. I'm saying, if you have three independent references to someone possibly having terrorist connections, when do you stop saying it’s just a coincidence?
GREGORY: Well, there are reports now about his mother talking to him on the telephone that she was on a monitor list as well and that they may have been discussing potential jihad. Was the ball dropped here?
REP. ELLISON: Well, I mean, I don’t want to start assigning blame. I mean, every single day, the FBI, law enforcement protects this country. These terrorists, they just-- just got to get through once. And-- and-- and so, I mean, the fact is on an everyday basis, I feel really good about our nation’s law enforcement. But the fact is there will come a time when we can look back and see what lessons should be learned, what should we have done differently, and that’s a good, healthy process…
GREGORY: Well, let’s talk about the surveillance within the-- the Muslim community. I mean, that’s partly what you were talking about this week, Congressman King. You said this in the National Review and this is how they reported it, according to you, “Police have to be in the community, they have to build up as many sources as they can and they have to realize that the threat is coming from the Muslim community and increased surveillance there. We can’t be bound by political correctness.”
REP. KING: Absolutely. I know-- well, the NYPD in New-- is doing in New York with a thousand police officers focusing on this issue, knowing where the threat is coming from. Now most Muslims are outstanding people but the threat is coming from the Muslim community. Just yesterday Tom Friedman who is certainly no conservative, said “We must ask the question only Muslims can answer. What is going on in your community that a critical number of your youth believes that every American military action in the-- in the Middle East justifies a violent response?” It’s coming from the community. And when-- in previous times when certain elements in the community are the ones responsible for crime, the police focused on it. For instance in Boston, the FBI never spoke to the Boston police about the older brother. And afterwards there was-- basically, no intelligence files in Boston on these types of people-- these people inclined to terrorism. The FBI never even got to examining them.
GREGORY: Congressman, you’re a Muslim. This concerns you on civil libertarian grounds and other areas.
REP. ELLISON: Well, I’m an American, and I’m concerned about national safety, public safety, just like everyone is. But I think it’s ineffective law enforcement to go after a particular community. I think what we need to do is look at behavior and follow those leads where they would lead. So, like if-- if Tamerlan Tsarnaev is-- is evidencing dangerous behavior, by all means, go after him. But once you start saying we’re going to dragnet or surveil a community, what you do is you ignore dangerous threats that are not in that community and you go after people who don’t have anything to do with it. And so let me just finish up with this one point.
REP. KING: Sure.
REP. ELLISON: And-- and-- and so this-- this ricin attack, for example, that’s an act-- that’s an act of terrorism, that doesn’t come out of the Muslim community. We cannot-- we don’t have enough law enforcement resources to just go after one community and, remember, we went after a community in World War II. And the Japanese interment is a-- is a national stain on our-- on our country, and we are still apologizing for it. So…
REP. KING: No one is talking about interment. We’re talking about following the constitution. What the NYPD is doing-- yeah, they have thousand cops working on counterterrorism, 16 plots against New York have been stopped. If any of those had gone through, we’re going to have hundreds or thousands of people dead.
GREGORY: But where does political correctness get in a way with regard to surveilling potential terrorists in the Muslim community?
REP. KING: Why didn’t the FBI talk to the mosque, why didn’t they talk to the imam? I mean mosque, it’s-- it’s become more…
GREGORY: He’s an-- he was an illegal, permanent resident. Does that have something to do with in terms of what the-- what the FBI is capable of doing with Americans?
REP. KING: No. To be an American citizen, the FBI still has the right to ask questions about you. Just because you’re a citizen doesn’t mean they can’t ask questions.
GREGORY: But the question is based on what, based on the exercise of free-- free speech or actual evidence of them plotting?
REP. KING: I-- I think they’re afraid to somehow be called anti-Muslim or anti-Islam if they accept the reality that the element is coming from within the Muslim community. As in previous times, you had elements coming from certain communities. You know, Eric Holder said this keeps him awake at night…
REP. KING: …radical Islam among young people in the Muslim community. Tom-- Dennis McDonough said the same thing in 2011 when he went to a mosque in Virginia to say about the threats that have come to the Muslim community. It’s there.
GREGORY: Congressman, let me ask you. Jeff Goldberg, who-- who is-- The Atlantic journalist who has extensive reporting experience in the Middle East, said this on the program last week something that-- that the Muslim community and-- and other countries have to deal with. This is a portion of what he said.
(Videotape; Last Sunday)
MR. JEFFREY GOLDBERG (Columnist, Bloomberg View/Writer, The Atlantic): When you talk about what’s going on in the Muslim world, and we have to remember, of course, that the primary victims of Jihadism are-- are other Muslims, Muslims who don’t agree with-- with the more Jihadist elements, and so we have to ask ourselves and Muslim world has to ask ourselves-- ask themselves, you know, what are we doing to provide counter programming even on the internet? And-- and this is not something that the U.S. can fix or the-- the West can fix. It has to come from within Islam.
(End videotape)
REP. ELLISON: Let me assure you, Muslim leaders all across this country have roundly condemned this most recent act of terrorism and have condemned terrorism broadly and are in a-- in a number of ways in doing inter-- interfaith dialogue talking about emphasizing peace and connectedness with people, good works in-- within the community. I mean, the-- the reality is that this is going on and has been and it needs to continue to go on. But, I mean, that’s kind of the-- the-- the thing that I’m saying is that, you know, the-- the-- the community is facing this threat, but this is an American problem. There have been threats throughout this community-- this country, by-- from various sources. But, you know, the-- and Muslims and people across this nation need to think about public safety and threats and radicalism, not just-- not just one community.
GREGORY: Just a few seconds left, Congressman King. Remaining questions now, what are you really focused on that you’d like the intelligence community and the FBI to answer?
REP. KING: I think it’s important to know are there other people involved in this threat? Are there others that are still out there?
REP. ELLISON: Yeah.
REP. KING: Are there family members or people in-- in the community? That’s very important to find out. Also, what did cause them to radicalize? Was it done here? Was it done overseas? Was it done over the internet? What caused that to happen? How can we stop it in the future? Also ask why the FBI is not cooperating more with the law enforcement? Why they did not give vital evidence to the NYPD about another possible attack.
GREGORY: This is that you think a failure that needs to be learned from?
GREGORY: All right. Congressman-- congressmen, thank you both very much…
REP. ELLISON: Thank you very much, David.
GREGORY: …for being with us this morning.
REP. ELLISON: Thank you, Peter.
GREGORY: And we’ll continue.
REP. KING: Thank you.
GREGORY: And coming up here politics and presidential legacies just as all five living presidents gathered in Dallas this week for the dedication of the Bush Presidential Library, the current President faces a critical juncture as he looks at his own legacy as we approach the hundred-day mark of his second term. How is the team and the Obama agenda faring on issues like guns, immigration, national security and the economy? Political roundtable is here, as well as Tony Blair. Coming up after this break.
(Announcements)
GREGORY: It was a big night in Washington last night as journalists, celebrities, and politicians alike gathered for the annual White House Correspondents’ Association Dinner. The night was full of laughs. And here were a couple of our favorites.
PRESIDENT BARACK OBAMA: One senator who has reached across the aisle recently is Marco Rubio. But I don’t know about 2016. I mean, the guy has not even finished a single term in the Senate and he thinks he’s ready to be president. Kids these days.
MR. CONAN O'BRIEN: Also, I’d like to acknowledge that earlier this evening there was some confusion with the seating chart. For a moment, some-- someone accidentally sat Governor Chris Christie with the Republicans. That was awkward and I apologize.
PRESIDENT BARACK OBAMA: I, on the other hand, have run my last campaign. On Thursday, as Ed mentioned, I went to the opening of the Bush Presidential Library in Dallas. It was a wonderful event. And that inspired me to get started on my own legacy, which will actually begin by building another edifice right next to the Bush Library. Can we show that, please?
(End videotape)
GREGORY: And coming up, more from the dinner last night as well as my conversation with former British Prime Minister Tony Blair. But first our roundtable is here after this short commercial break.
(Announcements)
(Videotape, Last Night)
PRESIDENT BARACK OBAMA: My charm offensive has helped me learn some interesting things about what's going on in Congress. It turns out absolutely nothing. Some folks still don’t-- don’t think I spend enough time with Congress. Why don’t you get a drink with Mitch McConnell, they ask? Really? Why don’t you get a drink with Mitch McConnell?
(End videotape)
GREGORY: Why-- Mitch McConnell jokes, only really funny in Washington. We are back with our roundtable, joining me Former Counselor to President George W. Bush and former Undersecretary of State for Public Diplomacy and Public Affairs, Karen Hughes…
MS. KAREN HUGHES (Former Counselor to President George W. Bush/Under Secretary of State for Public Diplomacy, 2005-2007): I’d love to have a drink with Mitch McConnell.
GREGORY: …Yeah. I know. I too, yeah. Democratic Congressman from Texas, Joaquin Castro; our political director and chief White House correspondent, Chuck Todd; Republican Strategist, Mike Murphy, and Democratic Senator from Minnesota--huge Minnesota day on the program--Amy Klobuchar. Senator-- welcome to all of you. How did the president do last night?
SEN. AMY KLOBUCHAR (D-MN/Judiciary Committee): Well, I think he was incredible. You know, he likes to do these things. It’s fun. And I really look at this dinner as a chance for him to make fun of himself for-- in a town where there’s daggers on every corner for people to come together and have some fun. And he was-- he was tremendous. My favorite line was actually when he talked about now he wanted to have his presidential library and he wanted to have it in his birthplace, but he decided he better move it into his country.
GREGORY: Right. Here, and though, I mean, there-- these are grea-- these are actual opportunities for presidents and presidents, I think back to President Bush, usually do very well at these things, plus they can take on stuff that they’re actually legitimately mad about with some humor.
MS. HUGHES: With-- with a sense of humor. And…
GREGORY: Yeah.
MS. HUGHES: …humor and humility are in short supply…
GREGORY: Yeah.
MS. HUGHES: …in Washington.
GREGORY: Right. Exactly.
MS. HUGHES: So it’s always nice to see in abundance of those. And I thought the president’s remarks were funny last night.
GREGORY: Chuck, what did we-- what-- what-- what were his favorite targets? I-- I must say we played it at the top, the bit about if you want minority outreach, why don’t you start with this minority.
MR. TODD: By the way, is it contractually-- are we okay to praise Conan? Is that okay now…
(Cross talk)
MR. TODD: He was really funny, too.
GREGORY: I thought so. Yeah.
MR. TODD: But, no, I thought the-- you know, what-- what I wonder how many people realized at the end when he did his-- you know, there’s always this part at the end where they get serious for a minute, and it’s usually the part where president say, you know, I think the press has a good job to do and I understand what they have to do. He didn’t say that. He wasn’t very complimentary of the press. You know, we all can do better. He was-- it did seem-- I thought his pot shots joke wise and then the serious stuff about the internet, the rise of the internet media and social media…
GREGORY: Right.
MR. TODD: …and all that stuff. He hates it. Okay. He hates this part of the media. He really thinks that the sort of the buzzification, this isn’t just about BuzzFeed or Politico, and all the stuff, but he thinks that sort of coverage of political media has hurt political discourse. He hates it. And I think he was just trying to make that clear last night.
GREGORY: Senator, you know, we-- we’re also at a point, though, where some of these other big matters are-- are usually right-- right under the surface like Syria. You heard Senator McCain talking about his own call for action to do more after he thinks the administration has been late here getting into Syria after a couple of years. How did you react to that? What do you think the president’s next moves have to be?
SEN. KLOBUCHAR: Well, I’m much more focused on the future as Senator Gillibrand and Senator Graham…
GREGORY: Yeah.
SEN. KLOBUCHAR: …and I just came back from Jordan and Turkey and we met with the refugees, we met with the rebels. And I’m convinced that, first of all, the president knows that we can’t do this alone. He’s been good at reaching out to leaders. Just met with King Abdullah that we don’t want to put boots on the ground. Senator McCain made that very clear. But we need to up our game. We need to up our game with where the aid goes. We’ve learned that too much of it is going to Assad-controlled regions. That we have to make sure that we’re starting to do more with night goggles, armor, all kinds of things, and that we have to keep these possibilities that Senator McCain raised clearly on the front burner with the no-fly zone, with-- with the arming the rebels, but we cannot do this alone. And it is an incredible scene there what’s happening in Jordan…
GREGORY: Right.
SEN. KLOBUCHAR: …twenty-five hundred refugees a day coming in.
GREGORY: The-- what the interesting thing, Mike Murphy, as-- as a political matter…
MR. MURPHY: Mm-Hm.
GREGORY: …this is something that’s going to divide Democrats, but Republicans, too. And that’s one of the things that Senator…
MR. MIKE MURPHY (Republican Strategist): Mm-Hm.
GREGORY: …McCain has been speaking to.
MR. MURPHY: Yeah. No, it’s a complicated situation with a-- a lot of difficult politics around it. I’ve been kind of enjoying at least as an observer of Washington the red line because the red line has turned into about a mile wide. We’re now, maybe, in the middle of the red line or we’re across the red line, but it’s a problem for president. When you draw a red line, the world is watching, including the Iranians. The political problem is the country has total fatigue for this kind of thing and there’s a military problem. This is a lot easier to get into than get out of. Because, you know, what are the minimal things you try if they don’t work, does it lead to natural escalation? So, I think the Turks are going to be the key. You would need a big partner to really do it. And there’s no way we can do it alone.
GREGORY: Congressman, let me get you on the record on this. What are you thinking about?
REP. JOAQUIN CASTRO (D-TX): Well, I think, first, you know, the revolution of the rebellion has to be accepted by the people of Syria. It becomes a lot less effective in the long term, the more it’s driven by the United States of America. However much we may or may not want to get into it. It’s also clear that we have got to be careful in accepting the intelligence that we’re getting. We know from the past that we were a bit eager in other wars to get into, specifically Iraq. So we have got to make sure that once we’re going to get involved in that kind of serious way that our intelligence is right and that we have evidence to back it up.
MS. HUGHES: But I’m concerned the window of opportunity is closing. The people of Syria feel we have let them down. We are the world’s champion of freedom. They are fighting for their freedom, tens of thousands of them are being killed and they’re waiting for our help. And I think we have an obligation. No one is for boots on the ground. But we have an obligation to lead the world and try to intervene in a smart way through arming, you know, the-- the opposition that is not affiliated with al Qaeda. Al Qaeda is only strengthening and the situation is getting worse by the day. I’m concerned the window is closing.
GREGORY: And, Chuck, we’re going to own the problem one way or the other?
MR. TODD: Well, either way and that is-- that is the-- the concern, but I can tell you that there is regret about that red line comment because if you…
GREGORY: In the White House?
MR. TODD: ...in-- in the White House in this respect, you don’t draw, I mean, they meant it, they do mean it on the chemical weapons, but saying it creates this political conversation. They didn’t want to go public last week that they had this-- that-- that this early evidence yet. They weren’t ready. And yet they knew Congress was going to get this briefing and that it-- it was all going to get out, so they decided to go public with it last week because they felt they had no choice. And it was all going to start leaking out, yeah, the Israeli have (Unintelligible) intelligence, but they are not ready. There is no good answer, the Gulf states and-- and the big difference between here and Libya, by the way, is in Libya you had the Arab community, you had the Arab League on the record saying…
GREGORY: Right.
MR. TODD: …we got to stop this. The Arab League has been quiet on this and I think the United States would like to see that first before we jump.
SEN. KLOBUCHAR: The other difference with Libya is the no-fly zone. Libya didn’t have the capacity to hit back, Assad does. So when we do this, if we do this, we have to deal with other countries and we have to get the support from the region.
MR. MURPHY: But the problem is we always work the political stuff here, so we find a solution we can believe in. The question is, is that a solution linked to reality on the ground? We always look for the good guy rebels because we know the dictator is a jerk.
GREGORY: So…
MR. MURPHY: But good guy rebels could be hard to find here, say al Qaeda, Sharia law crowd that’s leading this fight.
GREGORY: Congressman, I’ve been thinking about what is the relationship between the Syria problem and how much time and energy that could occupy in-- in this White House? The president is focused on-- on his legacy he’s building in his second term and-- and immigration and then, of course, there is the economy and whether there is ever going to be a budget deal, so this debate about sequestration. So I look at those three areas and how they all come together.
REP. CASTRO: Yeah.
GREGORY: What is going to define this president’s second term?
REP. CASTRO: Well, I mean, I think there’s no question, David, that it’s-- it’s a full schedule, both foreign issues and domestic issues that the president is dealing with. He just got into his second term, though. So, he is not quite leaving yet. And I think he’s up-- he’s up to the task and the Congress is up to the task of dealing with these issues. I think that, you know, you’re going to see the president take some time to make sure the facts are right on Syria. When he makes a decision, he’ll act swiftly. I think the Congress is going to pass comprehensive immigration reform in 2013. I think they’ll bring the gun vote back. If not in 2013, then after the Republican primary before the general election in 2014 to put some pressure on those folks to vote a different way. So, I think on-- on all of these fronts, President Obama will leave his mark on some very big issues in our nation.
GREGORY: But, you know, Karen, you saw this firsthand. I mean, with President Bush coming in-- in a second term and-- and not succeeding on Social Security, the Iraq war, you know, using so much of his capital and there goes immigration and all the rest. I mean, he’s got-- the president has to coalesce around something that will define the second term rather soon.
MS. HUGHES: Well, the clock is ticking. And right now President Obama’s presidency is defined by two things, a health care law that’s proving more difficult to implement and-- and more costly than projected and massive build ups of debt and federal spending. And that is his legacy at this point. I do agree that immigration reform has a good chance of passing. I thought he was very shrewd to bring it up in the context of President George W. Bush’s Library opening and-- and to say that President Bush had it right on the immigration issue. But, you know, no day in the presidency is an easy day with…
MS. HUGHES: …with only one set of decisions. You have a lot of big things happening across the world and a lot of big troubling issues to-- to deal with.
GREGORY: Chuck, you wrote about this legacy issue for the president first read this week?
MR. TODD: Yeah, I know, it is. And Karen, I’m curious if you were to-- to sit down with President Obama, how long would you tell him that he had for a legislative agenda in a second term, how long did you…
MS. HUGHES: Probably a year.
MR. TODD: Yeah.
MS. HUGHES: Probably a year.
MR. TODD: That you have one year and I think that-- that’s what they’re operating on…
GREGORY: Yeah.
MR. TODD: …and-- and I think that the gun thing, you know, they-- they always knew they were going to lose it, just didn’t know they were going to lose so quickly. It does put more pressure on immigration to make sure it gets done and there would be this concern. And I think everybody, you know, there was this-- well, it was basically the New York Times, right? There’s New York Times, both Maureen Dowd and-- and others who just said, oh, wow, he’s losing his ability to get things done. The gun vote was just-- such a way to-- to show how he doesn’t know how to manage Washington, this town. And I think the gun vote was the wrong issue to pick on him on that. There-- there is other evidence that he struggles managing Washington. The gun vote was a different-- a different story. Immigration is going to be the real test.
GREGORY: Senator, how-- what is your counsel at this point? I know you were among the women from the Senate who met with him. There is a lot of outreach because one of the complaints on Capitol Hill is the president is not working, even his people enough to get some of the things he wants in an agenda.
SEN. KLOBUCHAR: Well, now that he’s put a Minnesotan in his chief of staff, Denis McDonough, always crazy. And I really think…
SEN. KLOBUCHAR: I-- I think that his outreach has been really good this year. People have genuinely liked meeting with him and believe that he wants to move forward on a debt deal to bring the debt down in a balanced way. I think that’s got to be part of his legacy as well to try to bring people together on that. The immigration bill, I-- it was an incredible week for the immigration bill. We started the week with people saying oh, we have to delay this because of Boston…
GREGORY: Yeah.
SEN. KLOBUCHAR: …and then you had people Like Speaker Boehner and Ryan come out and say you know what, this means we have to speed this up because there’s better security provisions in here. So I think it’s exciting. We had 23 witnesses on the judiciary committee and everyone from the head of the migrant workers to Grover Norquist supporting it.
GREGORY: All right. I want to come back to this issue of, well, it’s the-- President Bush’s legacy but the security threats facing President Obama as well. Earlier in the week, I was in Dallas covering the dedication of the Bush Presidential Library and I had a chance to catch up exclusively with former British Prime Minister Tony Blair to talk about his thoughts on the Middle East, the Bush legacy and some of the big foreign policy tests now facing President Obama.
(Videotape)
GREGORY: You are in this-- this pivot point politically of being so closely associated with President Clinton politically, the new Labor Party, at a time when he was refashioning the Democratic Party. And yet your legacy will forever also be entwined with President Bush and his response to the war on terror. It’s a-- it’s a very interesting place in political history.
MR. TONY BLAIR (British Prime Minister, 1997-2007): You know, there-- there was a British Prime Minister Harold Macmillan, the-- when he was once asked what-- what is the toughest thing about being prime minister, he said events, dear boy, events. And what happens is that something comes of a, you know, game-changing nature, world-changing nature like 9/11 and everything changes. So I-- I was very closely associated with President Clinton, still have a good and strong relationship with him because we are both progressive politicians of a centrist persuasion. When President Bush first came in, I mean, frankly, in-- in basic political terms, I really didn’t have a lot in common. After 9/11 though, I thought it was really important our two countries stood together and I thought it was important that we took on this-- this-- this new menace with-- with-- with strength.
GREGORY: It was Churchill who said during World War II always stay close to the Americans. And there was a moment in the Bush presidency before the invasion, just weeks before at that now infamous meeting in the Azores. And I’m told President Bush said to you at a very delicate time for you politically back home, called you Tony, presumably, said, back out if you need to, don’t do this, don’t stand by me when you have to go back and address parliament if it’s going to cost you your leadership. Tell me about that moment.
MR. BLAIR: He did say that. I mean, he-- he made it clear that, you know, he understood the-- the huge political difficulties I had and that-- that I shouldn’t, as it were, put my own premiership on the line. It was more important in-- in a way, to him, I think, that I stayed. But my attitude was that, you know, there are lots of things in politics where-- where you-- you’ll compromise and you’ll maybe back off exactly what you think you should do and, you know, these are often the run of the mill everyday types of issues. When it comes to issues of war and peace and-- and life and death, I think your-- your-- I came to the conclusion your proper obligation to your own country is to do what you think is right. And I thought it was right to be with the U.S. at that moment in time and, you know, if I ended up losing my premiership, that-- that was that but I didn’t want to-- to stay on a basis I wasn’t on this issue of this importance of this and decisiveness for the world. I-- I didn’t want to stay in this. I was going to be able to do what I thought was right and I-- I thought that, you know, the world had changed after 9/11 and-- and that we had to take these decisions together.
GREGORY: In this library, the president has decided not to separate Iraq-- out Iraq. Iraq is presented as part and parcel of the war on terrorism, which is how he saw it. But won’t history judge that as a false impression that this was a war of choice that became a misadventure in the eyes of so many?
MR. BLAIR: I think, you know, the controversy around that, I mean, around how you categorize it, will remain. But what I found was that, you see, removing Saddam happened within a matter of weeks. You then spent the next, you know, eight-- nine years in a different type of battle and that was a battle against precisely the forces that are trying to destabilize the Middle East today…
GREGORY: Mm-Hm.
MR. BLAIR: …al Qaeda on the one side, Iran on the other side, and this toxic cocktail, if you like, of religion, politics, ethnicity, tribalism. So, I mean, I never said the two things were linked in that direct sense, 9/11 and Iraq, I think the difficulties we ended up encountering in Iraq were difficulties that arose from precisely this-- this force of terror unleashed by religious extremism and I think that’s the, you know, frankly, what we still face today that if you see what’s happening in Syria today. That entirely encapsulates it as it does across North Africa, Yemen, further afield, countries like Pakistan and of course Iran.
GREGORY: It’s striking as the president was opening his library today, there emerged reports out of Syria that the Assad regime may have used chemical weapons, a red line for this administration. What lessons did you learn, did President Bush learn, that you hope President Obama takes into account?
MR. BLAIR: Well, I think the lessons are really tough, you see, and-- and-- and very difficult. And-- and I think the trouble is the lessons themselves are subject of great and heated debate. I mean, my view is that-- that in the end, the whole of the Middle East and beyond is undergoing this period of huge transition where you have these dictatorial regimes whose time is up. On the other hand, the battle for the future is between what I would call the modern-minded types of people, the people who took to the streets first in Egypt, who want what we want. But against them are various groups, Islamist groups, that I’m afraid don’t have the same concept of democracy or freedom that we do. And if any of them get-- get hold of the potential to-- to engage in mass destruction, we’ve got a huge problem on our hands.
GREGORY: And look what we’re dealing with in the United States, the Boston bombings, the prospect of home-grown terror.
MR. BLAIR: Yeah, as we found in the U.K.
GREGORY: Yeah, Britain has a lot of lessons to share about that.
MR. BLAIR: Yeah, no, of course. And the fact is I'm afraid, that this-- this ideology is being pumped around websites, is being encouraged by people in many different parts of the world and it’s-- and it’s there and it’s very hard for us to deal with. The first obligation of a government is to try and protect its people, but then you’ve got to-- you’ve got to cast out this ideology. I mean, I think this is very similar to the fight we faced in the 20th century against first of all fascism and then revolutionary communism. You know, it’s an ideology. It’s not got one command and control center, it's not a-- you know, you’re not talking about a country, but you are talking about an ideology based on a perversion of religion who-- which has an enormous force. If you don’t deal with this issue, this long-term question, this ideology based on-- on a perversion of the religion of Islam, you are going to end up fighting this for a long time.
GREGORY: You saw President Bush up close as a man during very difficult times for any leader. Talk about your relationship, what it was like to sit there today and this moment of finality even for a former president at the dedication of his library.
MR. BLAIR: Well, I thought it was a great (Unintelligible) for America today by the way. I mean, you had five presidents including President Obama, and all behaving with a sort of graciousness and-- and civility towards each other. I thought it was fantastic. And President Obama actually put his finger on it when he said it’s impossible to know George Bush and not like him. So, you know, often people say to me back home, they say, come on, you didn’t like him really, did you? And I say, you can totally disagree with him but as a human being he is a someone of immense character and genuine integrity. So, you know, you can say-- people have different views about decisions, but there’s a very few people who-- who don’t like him and respect him as a person.
GREGORY: Prime Minister, thank you very much.
MR. BLAIR: Thank you.
(End videotape)
GREGORY: Prime Minister, Tony Blair. When we come back, more on the Bush legacy with our roundtable, how history judge the 43rd president, plus 2016 politics. Is the country done with the Bushes? Somebody brought that up, pretty close to the family this week. It’s coming up after this.
(Announcements)
GREGORY: Back to this picture which is a rare sight in Dallas on Wednesday and is a wonderful celebration of the American presidency and Bill Clinton had this great line, Mike, where he said this is part of the eternal effort to rewrite presidential history which is, you know, the great truth…
MR. MURPHY: Sure.
GREGORY: …in all of these library openings.
MR. MURPHY: History is somewhat written in pencil and it takes a long time. I remember they once asked some decades ago, Chou-En Lai, the great communist leader in China, what he thought of the French revolution. He said, too early to tell. I kind of take that view in this stuff. But I tell you, there is a lot of smug kind of second-guessing, you know, revisionism, and we don’t yet-- know yet. What I’ll say about President Bush is, everything in the world changed in a day. The country was threatened a way it never had been before. And you can find a million little mistakes but I think the big decisions were right.
GREGORY: Karen, if you ever can get over Iraq in the public’s mind, how does he do it?
MS. HUGHES: Well, I think history has a way of right-sizing things, right? The-- the short term politics tends to magnify controversy and minimize accomplishments and what you heard was the beginning of that this week with Democratic presidents praising President Bush’s big accomplishments. Higher standards in our schools, millions of lives saved in Africa. I would have added prescription drug coverage for senior citizens that both parties had tried to get done. And George Bush got it done. Tax relief for every American that they’re still feeling today and I think by-- the huge accomplishment which was recognizing as President Obama praised his strength and resolve in the aftermath of 9/11 recognizing the gravity of the threat and making the tough decisions to help our nation confront it.
GREGORY: Senator, how do you see it?
SEN. KLOBUCHAR: Well, I-- I didn’t agree with his decision to go into Iraq. I think some of the fiscal decisions are clearly still haunting us today with the debt. But I will say working on this immigration bill back then I overlapped with President Bush for two years, he put together that coalition that’s going to succeed now.
GREGORY: Mm-Hm.
SEN. KLOBUCHAR: And it was very, very important. He was ahead of his time. Secondly, when that 35W bridge collapsed in Minneapolis six blocks from my house in the middle of a river, in the middle of a summer day, he was there a few days later. He made sure it got funded. We worked with him and that bi-- bridge got built within a year and you don’t forget that.
GREGORY: Chuck, Josh Bolten, the former chief of staff…
MR. TODD: Yeah.
GREGORY: …told me in an interview this week, he sort of took on Republicans saying what the Senator just said, those people who believe that there was fiscal insanity during the Bush years are wrong about that and Republicans ought to start supporting it because, you know, fiscal austerity and fiscal balance was not the priority after 9/11.
MR. TODD: You know, it’s funny in talking with some Bush officials during the run up to the library, they were briefing us, that seems to be the-- the issue that sort of got under the skin of some of you guys, Karen.
MS. HUGHES: But it’s not right. It’s not accurate.
MR. TODD: It’s the issue of the fiscal of Republican on Republican attack here…
MR. TODD: …on this front and these presidential libraries. By the way, the first draft of obituaries. It-- it must be a weird thing to be president because you’re sitting there and everybody’s wondering what are you going to say because it’s the same type of feeling. It’s almost like weird living eulogies. But you bring up the prescription drugs. You know, the Obama administration is looking at the pre-- prescription drug rollout which, by the way, all the run-up was, oh, my God, you guys can’t handle this, this is going to be chaotic, to model the healthcare rollout. After the prescription drug…
MR. TODD: And-- and before-- before it was done, people-- before you guys started doing it, there was all this concern. Do they know what they’re doing? Is this going to work? And seniors are going to be up in arms about it. And-- and so they’re actually using the prescription drug…
MS. BARBARA BUSH (Former First Lady of the United States): He-- he’s by far the best qualified men but, no. I really don’t. I-- I think it’s a great country. There are a lot of great families and it’s not just four families or whatever. There’s just-- there are other people out there that are very qualified, and we’ve had enough Bushes.
(End videotape)
GREGORY: Lord, it sounded like Jesse Jackson, stay out the bushes. I mean-- Karen, what did that mean? Come on, you don’t have to protect Jeb. You know, you…
MS. HUGHES: I think most moms can understand the instinct of a mom to protect yet another son from the spears of the-- of the political process.
GREGORY: Yeah.
MS. HUGHES: And, you know, I think that-- that’s exactly what it was. But Jeb Bush has big shoulders and-- and if he decides to run, I think he’d be a great president.
GREGORY: Well, that was interesting.
MR. MURPHY: That’s what we call New England encouragement. I’ll tell you this, I don’t know what Jeb’s going to do. I work for him by disclosure. But I think if he does decide to run, he will one day be president of the United States.
MS. HUGHES: And I will add that…
MR. TODD: Well, but I-- but I think, David…
MS. HUGHES: …Barbara Bush used to say when-- when Governor Bush was running, she-- she once predicted that-- that he couldn’t beat Ann Richards. We all know how that turned out. So.
REP. CASTRO: Well, I think-- I think part of the challenge for Jeb Bush, I think he would still be very formidable in the Republican primary. But there is a risk that the Republican primary has moved beyond him, has moved so far to the right that he wouldn’t be able to win that thing.
MR. TODD: He himself said that. He himself-- but Jeb Bush said this in 2012, “He thought-- I thought I was a conservative, and look at what’s going on here.”
GREGORY: Also a warning for Hillary Clinton.
MR. TODD: But I thought-- that’s right. She was channeling the whole-- and there is going to be a part of the country that says, wait a minute, what?
GREGORY: Yeah.
MR. TODD: Don’t we have new people?
GREGORY: All right.
MR. MURPHY: It’s going to be Hillary versus new, I think. And Jeb could move that primary, which is the best reason for him to run.
GREGORY: All right. Let me get a break in here. We’ll come back right after this.
GREGORY: …was going to be the nominee. All right. Thank you all very much for the discussion. Before you go, and we go, you could see my full PRESS Pass conversation this week when I sat down with four former advisors to President Bush at the dedication of the Bush Presidential Library and museum in Dallas. That’s on our blog, PRESSPass.nbcnews.com, some interesting reflections. That’s all for today. We’ll be back next week. If it’s Sunday, it’s MEET THE PRESS.
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* in the Software without restriction, including without limitation the rights
* to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
* copies of the Software, and to permit persons to whom the Software is
* furnished to do so, subject to the following conditions:
*
* The above copyright notice and this permission notice shall be included in
* all copies or substantial portions of the Software.
*
* THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
* IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
* FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
* AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
* LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
* OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
* THE SOFTWARE.
*
*===-----------------------------------------------------------------------===
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#error "Never use <clflushoptintrin.h> directly; include <immintrin.h> instead."
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#define __CLFLUSHOPTINTRIN_H
/* Define the default attributes for the functions in this file. */
#define __DEFAULT_FN_ATTRS __attribute__((__always_inline__, __nodebug__, __target__("clflushopt")))
static __inline__ void __DEFAULT_FN_ATTRS
_mm_clflushopt(char * __m) {
__builtin_ia32_clflushopt(__m);
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Rapper besucht US-Präsident Trumps West-Bindung
"Ich liebe diesen Kerl": Von den vielen merkwürdigen Auftritten im Weißen Haus unter Donald Trump war das einer der merkwürdigsten. Kanye West huldigt dem US-Präsidenten - und spekuliert darüber, sein Nachfolger zu werden.
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{
"pile_set_name": "OpenWebText2"
}
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Q:
Changing ListView.ShowItemToolTips raises ItemChecked events
Hi when I set ShowItemToolTips of a ListView with checkbox items to true in designer and change it to false in the code, the event ItemChecked is raised. The checked state itself is not changed though. But inside the (also raised) ItemCheck event the old value is not equal to the new value but the new value is the value that was previously visible. It seems like the items are re-inserted or reset in some way.
I tested this on two machines and projects. Why does this happen and how can I avoid it?
A:
I'll explain the "why", a workaround is hard to come by. Some control properties are very impactful and can have odd side-effects when you change them. Like ShowItemToolTips, changing it after the ListView is created requires Winforms to completely destroy the native control and recreate it from scratch. Under the hood, it is a style flag (LVS_EX_INFOTIP) that's specified in the CreateWindowEx() call. The Control.RecreateHandle() method ensures it is effective. You'll see the flicker that this causes if you look closely.
So for a brief moment, the native control exists without yet being initialized with the original checkbox states. Getting a flaky event for that is a bug, but it is the kind that was either never fixed because doing so was too difficult or was just never discovered because nobody ever changes the ShowItemToolTips property after the control was created. It is very uncommon to do so.
In general, this native control re-creation trick has been a significant bug generator in Winforms. And workarounds are hard to come by, they fit either in the "deal with it" or the "don't do it" category. With the latter one strongly recommended in this case.
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{
"pile_set_name": "StackExchange"
}
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2011 A Lyga
The 2011 A Lyga was the 22nd season of the A Lyga, the top-tier football league of Lithuania. The season began on 12 March 2011 and ended on 6 November 2011. Ekranas were the defending champions, having won their third consecutive title at the end of the 2010 season.
Teams
The league will see a change in the number of teams once again as twelve teams were granted a licence for 2011, one more than in the 2010 season.
FK Vėtra were expelled over financial troubles after 16 matches of the 2010 season; their records were annulled and the team was subsequently disbanded. From the remaining ten clubs, Atletas Kaunas, who finished in last place at the end of the season, were the only team not to apply for a 2011 top-level licence. Atletas therefore played at the second level in 2011.
Three new teams were admitted to the league, unbeaten 2010 I Lyga champions FBK Kaunas, seventh-placed team Atlantas Klaipėda and Dainava Alytus, a merger between I Lyga runners-up Alytis Alytus and third-placed city rivals Vidzgiris. FBK Kaunas and Atlantas made their return after two seasons in the lower divisions of the Lithuanian league system, while Dainava had their debut in the A Lyga, as neither of its predecessor clubs played at the Lithuanian top level in its history.
League table
Results
Teams played each other three times, either twice at home and once away or vice versa, for a total of 33 matches per team.
Matches 1–22
Matches 23–33
Top goalscorers
Including matches played on 6 November 2011; Source: Lietuvos futbolo statistika
References
External links
Official site
Category:LFF Lyga seasons
1
Lith
Lith
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{
"pile_set_name": "Wikipedia (en)"
}
|
Superbird-B3
Superbird-B3, known as Superbird-8 before launch, and DSN-1 (Kirameki-1) for its military payload, is a geostationary communications satellite operated by SKY Perfect JSAT Group and designed and manufactured by Mitsubishi Electric on the DS2000 platform.
It is intended to replace Superbird-B2 on the 162° East slot, offering Ku band and Ka band communication services to the Japanese market. It will also serve as one of the two planned X band military satellites of the DSN network, in this role, it will be known as DSN-1 (Kirameki-1).
Originally intended to be launched by an Ariane 5 ECA in the second half of fiscal year 2015, a mishap during transport to the launch site on March 2016 meant that it would be delayed up to two years.
History
JSAT along NEC, NTT Com and Maeda Corporation formed a joint venture called DSN Corporation. On January 15, 2013, DSN Corporation announced that it had closed a contract with the Ministry of Defense to execute the "Program to Upgrade and Operate X-Band Satellite Communications Functions, etc". The contract is a private finance initiative, where private funds, management and technical capabilities are used to upgrade and operate the Japanese military X band satellite network.
Based on this program, DSN Corporation will manufacture and launch two satellites plus perform the necessary upgrades to ground control stations. It will also operate, manage and maintain the facilities and equipment through fiscal years 2015 to 2030. The total program cost was estimated at ¥122,074,026,613.
The plan called for the launch of the first satellite on December 2015, with a start of operations in March 2016 and a termination of operations in April 2030. The second satellite was expected to launch in January 2017, starting operations in March 2017. The program and the operations of the second satellite were expected by March 2031.
JSAT role is the procurement and general management of the satellites. The first satellite, DSN-1, is actually an additional payload on one of JSAT's own satellites, Superbird-8. The second satellite, DSN-2 is a dedicated spacecraft.
On April 25, 2014 JSAT announced that it had placed an order with MELCO and its satellite platform DS2000 for its Superbird-8 satellite. It would replace Superbird-B2 and be positioned on the 162° East orbital slot.
On an earning revision, JSAT disclosed that they had confirmed container deformation after Superbird-8 arrived to its launch site. On July 2016, it was published that a May 25 mishap during air transport had delayed the satellite launch by an estimated two years. A dislodged tarpaulin had blocked the bleed valve on the satellite container and the spacecraft had suffer from over pressurization damage.
See also
DS2000 – The satellite bus on which Superbird-C2 is based.
SKY PerfecTV! – Satellite TV division of the same owner corporation and major user of Superbird-C2.
References
Category:Spacecraft launched in 2018
Category:Ariane commercial payloads
Category:Communications satellites in geostationary orbit
Category:Satellites using the DS2000 bus
Category:Communications satellites of Japan
Category:2018 in Japan
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{
"pile_set_name": "Wikipedia (en)"
}
|
The recovery of hydrocarbons from subterranean zones relies on the process of drilling wellbores. The process includes drilling equipment situated at surface, and a drill string extending from the surface equipment to a below-surface formation or subterranean zone of interest. The terminal end of the drill string includes a drill bit for drilling (or extending) the wellbore. The process also involves a drilling fluid system, which in most cases uses a drilling fluid (“mud”) that is pumped through the inside of piping of the drill string to cool and lubricate the drill bit. The mud exits the drill string via the drill bit and returns to surface carrying rock cuttings produced by the drilling operation. The mud also helps control bottom hole pressure and prevent hydrocarbon influx from the formation into the wellbore, which can potentially cause a blow out at surface.
Directional drilling is the process of steering the drilling of a well from vertical to intersect a target endpoint or follow a prescribed path. At the terminal end of the drill string is a bottom-hole-assembly (“BHA”) which comprises 1) the drill bit; 2) a steerable downhole mud motor of a rotary steerable system; 3) sensors of survey equipment used in logging-while-drilling (“LWD”) and/or measurement-while-drilling (“MWD”) to evaluate downhole conditions as drilling progresses; 4) means for telemetering data to surface; and 5) other control equipment such as stabilizers or heavy weight drill collars. The BHA is conveyed into the wellbore by a string of metallic tubulars (i.e. drill pipe). MWD equipment is used to provide downhole sensor and status information to surface while drilling in a near real-time mode. This information is used by a rig crew to make decisions about controlling and steering the well to optimize the drilling speed and trajectory based on numerous factors, including lease boundaries, existing wells, formation properties, and hydrocarbon size and location. The rig crew can make intentional deviations from the planned wellbore path as necessary based on the information gathered from the downhole sensors during the drilling process. The ability to obtain real-time MWD data allows for a relatively more economical and more efficient drilling operation.
One type of downhole telemetry known as mud pulse telemetry involves creating pressure waves (“pulses”) in the mud circulating through the drill string. Mud is circulated from surface to downhole using positive displacement pumps. The pressure pulses are created by a fluid pressure pulse generator in a downhole telemetry tool, which controllably changes the flow area and/or path of the mud as it passes through the pulse generator in a timed, coded sequence, thereby creating pressure differentials in the mud. The changes in flow area can be effected by a valve mechanism in the pulse generator. One such valve mechanism is a rotor and stator combination, wherein the rotor is coupled to a motor which is controlled to rotate the rotor relative to the stator between an opened position where there is no restriction of mud flowing through the valve and no pulse is generated, and a restricted flow position where there is restriction of mud flowing through the valve and a pressure pulse is generated.
The position of the rotor at any given time is conventionally determined by position sensors typically located on an output side of the motor. Such sensors can be prone to failure, and impose an expense and complexity to the downhole tool. However, determining the rotor position is important in order to ensure that the telemetry signal is corrected encoded; a misaligned rotor can cause errors in the encoded telemetry signal, or make it difficult or impossible to decode the telemetry signal at surface. Therefore, it is desirable to provide a new and useful method or apparatus for determining the rotor position in a fluid pressure pulse generator.
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{
"pile_set_name": "USPTO Backgrounds"
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Motability Enquiry
Our Motability specialists at Jardine Motors Mercedes-Benz are on hand to answer any of your questions and to help you every step of the way when getting a Mercedes-Benz Motability car.
For any questions about the Motability Scheme, such as how it works, your eligibility for the scheme, or the Mercedes-Benz Motability offers we have available, simply fill in this contact form detailing your enquiry and we’ll be in touch.
You can also book an appointment with us for a no-obligation session. During your appointment, we will answer all of your questions as well as explore the full range of options that are available to you under the Motability Scheme.
Fill in the contact form to request an appointment, selecting your nearest Jardine Motors Mercedes-Benz dealership, and one of our team will be in touch to arrange a time and date to suit you.
We work with a number of carefully selected credit providers who may be able to offer you finance for your purchase. We may receive a commission payment from the finance provider if you decide to enter into an agreement with them.
We work with a number of carefully selected credit providers who may be able to offer you finance for your purchase. We may receive a commission payment from the finance provider if you decide to enter into an agreement with them.
Welcome to Jardine Motor Group. To optimise your experience, cookie settings on the website are set to allow all cookies. By continuing your journey throughout the website, you consent to this. You can change these settings here.
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{
"pile_set_name": "Pile-CC"
}
|
Sense of coherence contributes to physical and mental health in general hospital patients in China.
The sense of coherence (SOC) may explain why some people become ill under stress whereas others remain healthy. SOC is strongly related to perceived health, particularly mental health. Little is known about the physical and mental health statuses associated with SOC among general hospital outpatients in China. This multicentre cross-sectional study analysed 491 outpatients from four large Chinese general hospitals located in Beijing, Shanghai, Chengdu and Kunming. Patients completed questionnaires examining their SOC (SOC-9), somatic symptom severity (PHQ-15), depression (PHQ-9), generalised anxiety disorder (GAD), health anxiety (WI-7), quality of life (QoL; SF-12) and socio-demographic and clinical characteristics. SOC was negatively correlated with daily-life impairment, symptom duration, somatic symptom severity, depression, GAD and health anxiety, but was positively correlated with age as well as physical and mental QoL. Using a multiple linear regression model, the three strongest correlates of SOC were mental QoL, depression and age. These three variables explained 52% of the variance. SOC may be an important contributor to both mental and physical health in Chinese general hospital outpatients, which is consistent with the results obtained for primary care patients in Western countries. Longitudinal studies are needed to investigate how SOC predicts physical and mental health statuses over time and how these statuses respond to treatment for low SOC.
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{
"pile_set_name": "PubMed Abstracts"
}
|
Your order number will remain valid for 4-5 days. You may download your purchase as often as you wish within that timeframe. Please do not share your number with others. All downloads are logged and checked for unauthorized access.
Sablique wants to become more voluptuous. She stuffs herself and talks to you about her growing body. She grows breasts and giant hips and gets stuck. She teases you with her new curves and wants you to cum all over her new fat rolls.
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{
"pile_set_name": "Pile-CC"
}
|
Crozscore:
Crozscore:
Software Description:
Globaldyne Systems is offering virtual desktops, that will transform personal computing.The problem with desktop computers today is that they only last 4 or 5 years, you have to be in front of them to use them, and they cost a lot of money to buy. With virtual desktops you move your desktop computer to the cloud and solve all three of these problems: they can be upgraded with the click of a few buttons and in a few seconds, they are in the cloud so they can be accessed from any computer, smartphone, or tablet in the world, and they cost much less and take less time to set up.
Software Description:
No back-and-forth emails, no double booking and only a few seconds to schedule an appointment with you. The idea is simple: you create your calendar, set your availability and then share it with your clients or co-workers, who can easily schedule an appointment. Thanks to the integration with all major calendars and time-zone synchronization, we can be sure that everything goes smoothly.
Software Description:
Accurants is a complete small business accounting software. The biggest advantage of Accurants is, that it's a cloud based software, which means there is no installation and it can be accessed from anywhere, anytime and from any device.
Accurants comes with multiple modules like Invoice management, Accounting, Time Tracker, Project management, Expenses management, Customer Relationship Management, Taxes, Email marketing, and Payroll management. All these modules are programmed perfectly to work independently as well as in combination.
Features:
Features:
Application Tracking
Lead Management
Customer Management
Contact Management
API
Email Integration
External Integrations
Scheduling
Calendar Management
Multi-User
Notifications
Google Apps Integration
Features:
Task Scheduling/Tracking
Lead Management
Customer Management
Project Management
Data Import
Accounts Receivable
Calendar Management
Forecasting
Payroll
Budgeting
Tax Management
Multi-User
Multi-Currency
Dashboard
Accounts Payable
Document Comparison
CRM Integration
Data Export
Expense Tracking
Billing/Invoicing
Summary:
Cost less and take less time to set up compared to traditional desktops
Access from any computer, smartphone, or tablet in the world
Upgrade with the click of a few buttons and in a few seconds
Summary:
A simple appointment scheduling tool.
Time zone synchronization.
Online calendars connection.
Pretty layout.
Time saving!
Summary:
No key features associated with this application.
Pricing:
Starting from: $25.00/month
Credit card required: No
Core-1: $25/month
Core-2: $35/month
Core-4: $65/month
Basic Plan
Free
Included in plan:
One click meeting scheduling
Personalized intro messages
Email notification for both parties
Unlimited number of appointments
Security
Up-to-date availability based on what you have in your calendar
Automatic appointments creation in integrated calendar service
Time zone synchronization
Manual availability settings
Automatic reminders about the appointments
Adjustable time-slots
No ads
Email reminders for you and your guest
Pro Plan
$10.001 user(s) / month
Included in plan:
All features from Basic Plan
Team dashboard (charts, reports, statistics)
Unlimited appointment types
Pro Plan
$96.001 user(s) / year
Included in plan:
All features from Basic Plan
Unlimited appointment types
Team dashboard (charts, reports, statistics)
Basic
$15.001 user(s) / month
Included in plan:
Invoice
Expenses
Project Management
Time Tracker
Plus
$45.001 user(s) / month
Included in plan:
Basic & CRM, Accounting
Enterprise
$75.001 user(s) / month
Included in plan:
Plus & CRM
FAQs:
No FAQs associated with this application.
FAQs:
What is this service generally used for?
Scheduling appointments
Managing calendars
Saving time
What are some applications this service is commonly used in tandem with?
Google Calendar
iCal
Outlook
other
Who are the main user groups of this service?
Everyone who wants to automate appointments scheduling and save a lot of time. Appoint.ly is used by marketing agencies, teachers, HR teams, CEOs, sport trainers and more!
|
{
"pile_set_name": "Pile-CC"
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We were literally talking about this yesterday waiting for a mechanic forever. xD
The current system needs work. As mentioned, the waiting time is too long, nobody wants to be sitting around for half an hour for a mechanic to show up.
I definitely appreciate that not everything needs to be instant, but to make this problem worse, it tells us how many mechanics are online - but what people don't know is that not all of them are allowed/trained to go out. This just makes it seem like the 10+ mechanics online are just ignoring us.
Having a shop item would solve this. Do I think this is always going to be needed? No. But I certainly think for now, and for a long time it's been needed.
As a friendly pointer, might I suggest you take these reports a little more seriously. You have broken a rule and your attitude suggests to me that you do not care.
Thanks to all involved, I see no reason to respond further.
You weren't gone that long... so, I won't comment on that.
You could've just DM'd me one more time to let me know you couldn't come back but instead kept me waiting for a while.
Don't really know what to say. I'd be happy with just a 'verbal' warning but up to staff.
Player(s) being reported: Theo Smalls (ID 13)
Date of interaction reported: 07/NOV/2019
Unix time stamp from HUD: 1573153936
Your characters name: Kai DeVito
Other player(s) involved: N/A
Specific rule(s) broken:
8. Non-Roleplay (NRP)
Actions that are unrealistic or promote poor quality roleplay are considered as non-roleplay.
Examples of actions that are considered as non-roleplay:
• Cop Baiting - Provoking a reaction from emergency services without a realistic reason.
• Mercy Killing - Asking to be killed by a friend (Killing a friend falls under deathmatching).
• Unrealistic stunt jumping or the use of an expensive vehicle to ram into other vehicles.
• Spawning a scripted work vehicle and using it for crimes or submerging any vehicle in water.
• Swimming in water for an unrealistic amount of time or without a destination during a chase.
Players who disconnect during roleplay must reconnect and inform other parties in order to resume roleplay. If you are unable to reconnect it may be excused after providing proof.
In a situation where a player gets away from an incident where they're being chased/pursued, they must wait 15 minutes before they can logout. Players should not instigate roleplay situations if they do not have time to play it through.
Players who ignore answering roleplay commands directed at them, e.g. /do.
In a situation where a player’s game crashes or the player is kicked from the server, they should be allowed to have the same advantages as they have had before their leave.
How did the player break the rule(s)?
The player timed out from in game, and initially made no attempt to alert me to him crashing. The player had earlier tried to add me on Discord to provide a video of whether the door was open on his screen or not. I gave him some time to let me know, however he did not and so I PM'd him after there was also no response in the ECRP General Chat.
He responded saying that his game had crashed, however he seemingly made no attempt to come back, and then stopped responded altogether, ignoring my messages. I waited a full 35-40 minutes as he had previously said he would return and nothing came of it.
Evidence of rule breach:
My video contains staff chat, I shall DM whoever is handling this.
My suggestion, in my opinion, makes this whole system much much better.
It allows people to leave messages without having to know the owner.
As mentioned in OP - its better to not necessarily declare the owner too easily.
Currently, if you're trying to get in touch or leave a message for an owner of a house, its impossible if you dont know who it is.
Having a way you can leave a message where they are alerted in chat (similar to ticket system maybe) would be extremely beneficial to the server, property owners, buyers as well as friends. You'd get this notification as you enter your home, that way there is no metagaming and may encourage people to check their home and mail more often.
This would certainly help with people trying to purchase houses or any other needs of contact.
Theres an argument for further information, however I dont think there should be names, phone numbers or emails so that owners can remain anonymous.
Personally, I prefer the way name changes are now. I do not believe it should return to the in game option it had before, as this often promotes a careless attitude towards changing names.
I can agree that there are plenty of reasons to change it, but unfortunately if its really worth it, then using credits is worth it.
If you live in a country that does not have the ability to perform international transactions, that's unfortunate. It's a shame but that should not restrict the progression of the server or these types of decisions. This new system, in my opinion, improves the server and should remain. I am not totally familiar with the options you may have, but you could attempt to get someone to gift you credits.
Either way, -1.
Player(s) being reported: ID 31
Date of interaction reported: 08/SEP/2019
Unix time stamp from HUD: 1567944831
Your characters name: Kai DeVito
Other player(s) involved: ID 2, 91 and 110 - I think they are all 'victims'. Police later showed up after one of them shot at 31 to defend themselves.
Specific rule(s) broken:
14. Deathmatch (DM)
Deathmatching is the act of attacking a player or their property without a proper roleplay reason.
Examples of valid reasons to attack another player:
• If they attempt to arrest or hurt you, an ally, or damage your property.
• If they report you to the police for a serious crime.
• If they are not in compliance with demands, attempt to escape, or call other players for help in a situation where they are required to display fear under fear roleplay rules.
A player cannot kill their victim if the victim is in compliance with the demands.
A player must allow their victim enough time to comply with the demands.
If a player informs you that your VOIP isn’t working, you must either fix your VOIP using appropriate commands or use text to deliver your demand(s).
Vehicles cannot be used to attack another player more than once including a failed attempt.
Attacking another player with no engagement in roleplay is not allowed.
Killing a player that has obeyed all orders and demands during a roleplay situation is allowed, with roleplay, only within 3 hours of:
Severe hostile or criminal action is taken against you, e.g. someone is robbing you at gunpoint. (Excluding police aiming a gun at you.)
Someone is attempting to take your life.
Someone is attempting to take the life of your close friend or ally, or if you have witnessed it happen.
You must explain your reason to kill to the player IC and have OOC evidence proving your reason.
How did the player break the rule(s)?
Player repeatedly used his vehicle to ram the players involved. He made multiple attempts to ram, drive away and drive back.
Evidence of rule breach:
I will need to provide this to Staff as it includes staff chat and so on. Apologies in advance for background noise (Netflix on 2nd monitor). There's also a slight break in the video as the first part is Shadowplay of last few minutes, then continued on live recording.
Budget is flexible and purely dependant on the property you are selling.
I am most likely only interested in a house, not an apartment. Preferably with at least one garage.
Feel free to contact me by phone too at: #3724977
As said above, you can't set multiple people with the same one.
Whilst I could see the argument for allowing multiple people with the names, I also see this problematic in terms of immersion when you get confused between people just based on their names, even though in character you would recognise them by more than just a hovering name
|
{
"pile_set_name": "Pile-CC"
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|
---
title: Jet Physics with Identified Particles at RHIC and LHC
---
Introduction
============
The measurement of particle identified high momentum spectra and two-particle correlations can be considered the next step in the characterization of the dense partonic phase created in relativistic heavy ion collisions at RHIC. Much emphasis is presently given to the similarities in the light and heavy quark behavior in the plasma, but these measurements are detailed in other contributions to this workshop [@dasilva; @harris]. Here I will mostly focus on the flavor dependence in light hadron production, i.e. hadrons consisting of u,d,s quarks. I will address in particular the question of baryon versus meson production through fragmentation and recombination as competing mechanisms. In order to determine the baryon production mechanism in AA collisions we need to understand the production in pp first. The main question is whether there is a difference between the light baryon production in the medium and in the vacuum. In the following section I will briefly review the latest particle identified pp results from STAR and then move on to results from AuAu collisions. The ambiguity in the production mechanism as deduced from single particle properties such as the suppression at high pt and elliptic flow v2 can be partially resolved by analyzing two particle correlations. I will show that early results of intermediate p$_{T}$ associated particle production are surprisingly featureless regarding flavor dependencies that were expected from perturbative QCD calculations in vacuum. In contrast, the single particle spectra suppression at high p$_{T}$ in AA seems very much affected by flavor suppression in the proton-proton system, in particular for strange particles. I will try to argue that this effect should be unique to the strange quark, only if the strange quark generation is gluon dominated and the heavy quark production is quark dominated. Many of the studies at RHIC lack the statistics to map out the transition from medium effects to pure vacuum fragmentation. I will show that these measurements are readily accessible at the LHC, in particular with the ALICE detector.
Why is pp so important ?
========================
The latest strange and non-strange hadron production results obtained in proton-proton collisions by STAR, were presented at this workshop [@heinz; @ruan]. They show that simple leading order fragmentation codes are not sufficient to describe the baryon production at RHIC energies. Next to leading order calculations do well as soon as quark separated fragmentation functions are used [@akk], in other words there are contributions in the baryon spectra from non-valence quark fragmentation. In a leading order calculation this fact can apparently be approximated by increasing the K-factor and the multiple parton scattering contribution to the underlying event [@bellwied1]. These effects are expected to be significantly less pronounced at higher incident energies [@eskola]. In other words, next to leading order contributions are more important at RHIC energies than at LHC energies.
One important new pp result is the break-down of the so called m$_{T}$-scaling [@gatoff; @schaffner] at sufficiently high transverse mass at RHIC. Fig.1a shows the measured spectra of all particle identified species obtained by STAR. After appropriate scaling of each spectrum the m$_{T}$-scaling plot (Fig.1b) can be devised. Clearly the m$_{T}$-scaling at lower m$_{T}$, which had previously been established through measurements at lower energies [@isr1; @isr2], can be confirmed. The noticeable deviation from simple scaling at sufficiently high m$_{T}$ (m$_{T}$ $>$ 3 GeV/c) is a new feature, though. The spectra seem to group into common baryon and meson curves at these momenta. This is a surprising effect in elementary pp collisions which is nevertheless described quantitatively in PYTHIA, as shown in Fig.2.
{width="2.in"} \[fig:1a\]
{width="2.in"} \[fig:1b\]
Figs.2a and 2b break down the effect, as modeled in PYTHIA, for gluon and quark jets. The combined spectrum (Fig.2c) is dominated by the gluon jets. According to PYTHIA the ratio of gluon to quark jets is about 2:1 at RHIC energies.
{width="1.5in"} \[fig:2a\]
{width="1.5in"} \[fig:2b\]
{width="1.5in"} \[fig:2c\]
One very interesting feature in the parton separated spectra (Figs.2a and 2b) is that apparently the gluon jet fragmentation leads to a baryon/meson difference at high m$_{T}$, whereas the quark jets show a mass ordering of the high m$_{T}$ spectra. Gluon fragmentation dominates at RHIC (and even more at LHC) energies, and based on PYTHIA the baryon/meson splitting effect in the kinematic spectra is due to the di-quark formation process which is a pre-requisite for baryon formation in LUND type string fragmentation [@lund-baryon]. The initial di-quark formation leads to a lowering of the $<$p$_{T}$$>$ for the baryons (the so called di-quark suppression factor), whereas for mesons the simple quark-antiquark hadronization does not affect the $<$pT$>$. This feature in the fragmentation of elementary gluon jets could be considered the seed of the baryon meson differences in AA collisions. The effect by itself is not big enough, though, to quantitatively describe the strong peak in the baryon/meson ratio at intermediate pt in AA, but the overall feature (a bump at intermediate p$_{T}$) can already be seen in pp collisions and might be simply enhanced by additional effects in AA. In AA one needs the combined effects of radial flow and quenching to ’pile-up’ the baryons over mesons in the intermediate p$_{T}$ range. Still it is important to note that the baryon/meson differences already have their origin in the basic fragmentation process in pp collisions. This measurement also hints at the validity of the fragmentation process as modeled by PYTHIA. It is my opinion that in its nature the diquark-quark formation process is similar to a three quark coalescence process and thus exhibits equivalent features.
Another conclusion from the pp modeling is that, although early pQCD calculations predicted a stronger drop in the anti-baryon over baryon ratio, our results are in accordance with PYTHIA calculations if one takes into account the strong gluon dominance at RHIC energies as shown in Fig.3.
![Measured Anti-$\Lambda$ over $\Lambda$ ratio compared to PYTHIA ratio from gluon and quark jets.[]{data-label="fig:3"}](fig3-lambdaratio.eps){width="2.5in"}
In order to unambiguously determine the predicted drop, which is due to the difference between quark and gluon distribution functions and the relative contribution of these partons to the baryon and anti-baryon production, one needs measurements at higher p$_{T}$. The momentum range of the spectra will be greatly enhanced at the LHC. Fig.4 shows a projection of p$_{T}$-ranges for identified spectra based on a scaled LHC pQCD calculation. Generally the light quark spectra will reach out to at least 20 GeV/c in the first year of running, which allows for a more unambiguous study of the flavor effects at high p$_{T}$.
![Annual hard process yields expected in the ALICE Calorimeter acceptance for minimum bias Pb-Pb collisions at 5.5 TeV.[]{data-label="fig:6"}](fig4-leading.ps){width="2.5in"}
![Annual hard process yields expected in the ALICE Calorimeter acceptance for minimum bias Pb-Pb collisions at 5.5 TeV.[]{data-label="fig:6"}](fig5.eps){width="2.5in"}
One interesting feature in the gluon dominated regime at RHIC and the LHC is that the $\gamma$-jet process is dominated by Compton scattering, which leads to a $\gamma$-quark-jet combination in the outgoing channel. This means not only is the tagged $\gamma$ the ’standard candle’ for the jet energy measurements, but it is also a good trigger for quark-jet events in the gluon dominated regime. The rate, based on early simulations using the ALICE calorimeter, is significantly limited compared to di-jet events, but one can still expect on the order 10,000 events with a $\gamma$ energy above 50 GeV. A similar quark-jet selection can be achieved by triggering on heavy mesons as leading particles. Projected rates for all jet measurements with the proposed ALICE EMCal are shown in Fig.5.
Flavor dependencies in identified high pt AA spectra
====================================================
One of the most surprising results of the past year was the apparent difference between R$_{AA}$ and R$_{CP}$ measurements, in particular for strange baryons. Figs.6 and 7 show a direct comparison of strange and non-strange baryons and mesons.
![Nuclear suppression factor (R$_{CP}$) as measured by STAR.[]{data-label="fig:6"}](fig6-raa.eps){width="2.in"}
![Nuclear suppression factor (R$_{CP}$) as measured by STAR.[]{data-label="fig:6"}](fig7-rcp.eps){width="2.in"}
The strong jet quenching effect at high p$_{T}$ and the slight baryon/meson splitting due to recombination at moderate p$_{T}$ as shown on the R$_{CP}$ plot is not visible in the R$_{AA}$ plot. The R$_{CP}$ suppression has been established for all particle species from pions to charmed mesons, and besides the already mentioned baryon/meson difference at intermediate p$_{T}$ the suppression is surprisingly flavor independent. The R$_{AA}$ pattern though exhibits a very strong flavor dependence, in particular for baryons. An enhancement of the high p$_{T}$ yield, rather than a suppression compared to the pp spectrum, actually increases as a function of the strangeness content in baryons. A similar enhancement pattern was previously measured for integrated particle yields, and is generally attributed to canonical suppression of strange quarks in small systems [@tounsi], but it is unexpected that apparently this effect of a small correlation volume in an equilibrated system should also affect the high p$_{T}$ particle production. Not only does it lead to an enhancement of the intermediate p$_{T}$ yield from pp to AA but there is also no evidence of quenching in the strange baryon R$_{AA}$ plot at high p$_{T}$. This effect is actually not seen in preliminary results of charmed meson suppression, so it could indeed be unique to the strange quarks. A measurement of a charmed baryon ($\Lambda_c$) is needed to unambiguously determine the difference between the quark flavors. Because of the difference between R$_{CP}$ and R$_{AA}$ the strange quark flavor effects need to have their origin in the particle production in the pp system. This is a good indicator that even intermediate p$_{T}$ strange baryons are predominantly produced through coalescence from a thermalized partonic system. In other words the initial gluon dominated scattering processes leads to thermalized strange quarks which coalesce into strange baryons. The effect of the correlation volume during hadronization is still dominant even at rather large (up to 3 GeV/c) transverse momentum. Beyond the intermediate p$_{T}$ range the spectrum gets quenched, but it is still enhanced in AA collisions compared to the pp system. The question is whether this strange particle production mechanism drives the pp to AA comparison even in the pure fragmentation regime above 7 GeV/c. The RHIC experiments do not have a big enough reach to establish an answer. Fig.4 shows that these measurements can be achieved at the LHC, though. We know from e$^{+}$e$^{-}$ experiments that the strangeness suppression factor in the quark condensate is about 0.4 [@e+e-], but this is just the relative quark production probability in the hadronization sea, which should also exist in the medium. In addition, the strangeness saturation factor increases from pp to AA by a factor two at RHIC energies based on measurements of integrated strange particle yields [@cleymans]. The factor in AA can be described quantitatively in lattic QCD [@gavai].
The difference between baryons and mesons in R$_{CP}$ (Fig.7), which is generally attributed to either recombination or an interplay between radial flow and jet quenching [@lamont], can also be described by the so-called Corona effect, which was shown elsewhere at this conference [@werner; @pantuev]. The principle here is that the formed medium consists of a dense core, which follows hydrodynamics and a corona of pp interactions dominated by multiple scattering. The main reason for such a distinction and the strong contribution from the corona is the relative diffuseness of the nuclear surface, which is not well described by hard spheres. The pp interactions can be modeled by codes such as EPOS which take into account the increased parton cascade activity in the low momentum sector. In these models effects such as baryon/meson splitting in v$_{2}$ occur because the corona, which carries very little v$_{2}$, has a much stronger contribution to the light particle spectrum than the heavy particle spectrum, so it pulls down the hydro v$_{2}$ for mesons to lower values than for baryons.
Finally one can measure identified two particle correlations at intermediate p$_{T}$ in order to detect flavor dependencies that are expected from simple fragmentation arguments. The correlations shown in Fig.8 show surprisingly little trigger particle flavor dependence. Again it seems that non-fragmentation processes, such as recombination, dominate in this p$_{T}$ range. There is evidence for long-range correlations in $\Delta\eta$ which could be due production mechanisms that do not exhibit the flavor dependencies of simple fragmentation. These correlations lead to a significant enhancement of the associated yield for any trigger species over the associated yields measured in pp, which are in agreement with the PYTHIA simulations shown in Fig.8b.
![High p$_T$ two particle correlations using identified trigger particles and charged hadron as associated particles. a.) measurements in 0-5% centrality Au-Au collisions in STAR, b.) PYTHIA simulations of the same correlations in pp collisions.[]{data-label="fig:7"}](fig8-complete.eps){width="3.in"}
Summary
=======
The interpretation of our pp collision results reveal that the baryon production yields require either multiple scattering through a soft particle production model such as EPOS or NLO corrections in pQCD models such as PYTHIA. It is interesting to note that the basic string fragmentation differences in baryon and meson production lead to a breakdown of the universal m$_{T}$-scaling of identified particle spectra. Apparently this breakdown is driven by the baryon production mechanism in gluon jets and manifests itself as a slope difference at high m$_{T}$ when comparing baryon to meson spectra. This basic effect in pp is not sufficient though to describe the large baryon over meson yield enhancement at intermediate p$_{T}$ in AA collisions.
Besides the baryon/meson difference there is a surprising absence of strong flavor effects in the particle to anti-particle ratios in AA, the identified two particle correlations in AA, and even the jet quenching in the medium. Thus, it is still an open question whether the partonic energy loss in AA shows the expected Casimir factor when comparing hadrons from a fragmenting gluon jet to a quark jet, i.e. is the energy loss really non-Abelian ?
The only strong flavor effect is in the strangeness sector. High p$_{T}$ strange baryon production in AA is enhanced instead of suppressed compared to pp . This could be due to simple canonical suppression in pp. This thermodynamic effect, which is due to a limited strangeness phase space occupancy, has been measured for the first time as a function of transverse momentum, and it is obvious that the effect is not limited to low momentum or simply bulk properties. Surprisingly the intermediate p$_{T}$ part scales well with the canonical suppression factors, which indicates that the hadronization mechanism of strange baryons, even at higher p$_{T}$, is driven by a correlation volume, which is distinctly different from charmed meson production. The D-meson yield and high p$_{T}$ suppression factors in AA are consistent with scaled hard scattering cross section, i.e. production from string fragmentation.
In identified two particle correlations in AA collisions we see a strongly enhanced associated particle yield compared to pp, independent of the trigger particle species. Long range $\Delta\eta$ correlations might account for that and they might be due to recombination [@hwa1]. A small baryon/meson trend can be found in those correlations but the effect is not very significant. Larger predicted effects for $\phi$ and $\Omega$ triggered correlations [@hwa2] are under investigation.
In summary, I believe that studies of the hadronization mechanism at RHIC and LHC energies in vacuum and in medium hold the key to the puzzle of baryonic matter formation in the universe. We need to first understand the basic baryon production mechanism(s) in pp (string fragmentation vs. recombination, di-quark formation ?). Then we need to determine whether the baryon production mechanism in AA collisions is modified from the vacuum production. For a more detailed study the high pt reach and the particle identification properties of the LHC detectors are crucial.
Acknowledgements {#acknowledgements .unnumbered}
================
I thank Helen Caines, Mark Heinz, and Klaus Werner for useful discussions.
[99]{}
C.L. DaSilva, contribution to these proceedings
J. Harris, contribution to these proceedings
M. Heinz, contribution to these proceedings
L. Ruan, contribution to these proceedings
S. Albino et al., hep-ph/0502188
R. Bellwied for the STAR collaboration, QM05 proceedings, nucl-ex/0511006
K. Eskola et al., Nucl. Phys. A713 (2003)
G. Gatoff and C. Y. Wong, Phys. Rev. D 46, 997 (1992)
J. Schaffner-Bielich et al., arXiv:nucl-th/0202054
P.V. Chliapnikov and V.A. Uvarov, Phys.Lett. B345, 313, 1995
M. Szczekowski, Phys.Lett. B359, 387, 1995
P. Eden, G. Gustafson, Z. Phys. C75, 41 (1997) and hep-ph/9606454
K. Redlich and A. Tounsi, Eur. Phys. J. [**C24**]{} (2002) 589
G. Abbiendi et al. (OPAL), Eur. Phys. J. C16, 407 (2000) and hep-ex/0001054
J. Cleymans, J. Phys. G28, 1575 (2002)
R.V. Gavai and S. Gupta, Phys. REv. D73, 014004 (2006)
J. Adams et al. (STAR), nucl-ex/0601042
K. Werner, contribution to these proceedings
V. Pantuev, contribution to these proceedings
C.B. Chiu, R. Hwa, Phys. Rev. C72, 034903 (2005)
R. Hwa, C.B. Yang, nucl-th/0602024
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È l’uomo del vento d’oro! Incredibile a Oestersund: anche Dominik Windisch trionfa ai Mondiali nella Mass Start di 15 km. Anche lui di Anterselva come Dorothea, si prende l’oro più pazzesco, sotto una nevicata che ha stravolto le condizioni di gara e sconvolto l’ultimo poligono. Dominik è stato perfetto perché non ha mai mollato, ha tenuto il suo ritmo ed è uscito in testa dall’ultimo poligono nel quale tutti gli avversari davanti, a cominciare dal leader di Coppa Johannes Boe, hanno sbagliato bersagli in serie (il norvegese addirittura 5). Dominik era entrato 11° a 55” ed è uscito dall’ultimo poligono primo: gli ultimi chilometri sono stati come una passerella trionfale. Dominik in 40’54”1 (3) batte il francese Antonin Guigonnat a 22”8 (3), bronzo all’austriaco Julian Eberhard a 23”3 (4), quarto il russo Loginov a 27”4 (5). Per il bronzo nella Sprint ai Giochi di PyeongChang 2018 (3 le medaglie in totale) è l’apoteosi dopo una delle gare più folli del biathlon, sport che si conferma imprevedibile.
Windisch con l’oro. Ap
Il ragazzo che è cresciuto insieme a Dorothea, dietro il fratello Markus, il mite Domme che arriva ultimo nelle gare giovanili ma non si arrendeva mai lo stesso, conquista un titolo maschile che all’Italia mancava dal 1997 con Willy Pallhuber. Per l’Italia è la quinta medaglia con 2 ori, 2 argenti e un bronzo. Lukas Hofer, argento con la Wierer, un 17° posto a 1’38”6. E’ la prima volta che l’Italia vince l’oro con uomini e donne lo stesso giorno. Bisogna crederci sempre, è la filosofia di Windisch: anche stavolta l’uomo del vento ha avuto ragione.
STRATOSFERICO - “Il biathlon azzurro non dimenticherà mai questo giorno, che fa rima con leggenda. Dopo il trionfo della Wierer arriva anche l’oro stratosferico di Dominik Windisch nella Mass Start mondiale. Sventola il tricolore a Oestersund. Orgogliosi di voi”: così, su Twitter, il presidente del Coni, Giovanni Malagò. “Storiche e strepitose vittorie italiane in Svezia! Auguri a Dorothea Wierer che ha vinto i mondiali di biathlon a Oestersund regalando all’Italia un oro emozionante. Complimenti di cuore anche all’altro oro italiano, Dominik Windish che trionfa, anche lui nella mass start. Successi ai quali si aggiunge quello di Lisa Vittozzi che è riuscita in un’impresa che ha del miracoloso. Sarò onorato e felice di festeggiarli e stringere loro la mano personalmente a Palazzo Chigi dove spero possano venire il più presto possibile”: così il sottosegretario alla presidenza con delega allo sport, Giancarlo Giorgetti.
PARLA DOMME - Dominik Windisch dice: “Sensazione fantastica, sono contento per la Nazione soprattutto perché ha vinto anche Dorothea e lei lo ha meritato perché ha fatto bene durante tutta la stagione. Questo Mondiale è non era andato comunque male per l’Italia, perché erano arrivate già tre medaglie e potevamo tornare a casa contenti, ma ovviamente finire così è ancora più bello e si va via con una sensazione bellissima, possiamo festeggiare a casa, ad Anterselva. Oggi era molto difficile sparare, ho cercato di concentrarmi soltanto su me stesso, anche perché in staffetta non era andata bene. Sono riuscito a gestire bene il vento, ma all’ultimo poligono per me non era così forte e sono stato fortunato. L’anno prossimo non vedo l’ora di gareggiare ai Mondiali perché saranno ad Anterselva e succede una volta nella carriera di un atleta di poter gareggiare in casa, per noi è come una mini Olimpiade. Vincere nello stesso giorno di Doro? Non scono scaramantico ma quasi comincio a crederci”.
MEDAGLIERE - Con il doppio oro di Dorothea Wierer e Dominik Windisch nella mass start, l’Italia chiude al terzo posto nel medagliere. Soprattutto, per la prima volta nella storia, l’Italia ha conquistato cinque medaglie nella stessa edizione. Oltre alle due medaglie odierne, l’Italia ha conquistato il bronzo nella staffetta mista (Vittozzi, Wierer, Hofer e Windisch) e due argenti: con con Lisa Vittozzi nell’individuale femminile e con la coppia Wierer-Hofer nella staffetta single mixed. Prima nel medagliere la Norvegia (5 ori, tre argenti e un bronzo), davanti alla Germania (2 ori, 2 argenti, 3 bronzi) e, appunto, l’Italia, davanti alla Svezia (1 oro, un argento, un bronzo).
Hofer, Vittozzi, Windisch e Wierer con gli organizzatori dei Mondiali di Anterselva 2020 e l’ambasciatore italiano in Svezia Mario Cospito
Classifica Mass Start uomini : 1. Windisch (Ita) 40’54”1 (3); 2. Guigonnat (Fra) a 22”8 (3); 3. Eberhard (Aut) a 23”3 (4); 4. Loginov (Rus) a 27”4 (5); 17. Hofer a 1’38”6 /7).
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There is a tendency both amongst Angelenos and New Yorkers to view the others’ city as the polar opposite of their own. New York is dense and space is oriented around the sidewalk and the train; Los Angeles is spread out and space is oriented around boulevards and freeways. New York is brutally cold in the winter and stiflingly hot in the summer; Los Angeles is just slightly too warm year-round. New York is built around a clearly defined urban core; Los Angeles is the place Dorothy Parker once derided as “72 suburbs in search of a city.”
This mythos contains some truths, but the overriding reality is that the similarities of these two cities far outweigh their differences. Both are home to peoples from around the world, modern testament to America’s dynamism as a melting pot. Both are cultural and economic engines on a global scale, the 2nd and 3rd largest urban economies in the world (Tokyo holds #1). And both contain a vast array of neighborhoods, each with its own distinctive character and culture.
LA also has a more ‘normal’ urban form than many observers think, which is manifested in its similarities to New York. Of course, LA doesn’t have the defined central municipality and boroughs as New York does, and there are many lifestyle differences between the two metros. But when you look at LA’s historic development patterns and the current functions of its various regions, they mirror those of New York City to a surprising degree. Most areas of the greater Los Angeles region can find direct analogs in New York and its surroundings. LA has its own iterations of Brooklyn, Central Park, Times Square, and more – and the social roles they all play here are similar.
There is a “there there” in LA, it just doesn’t present itself as obviously as it does in many other great cities. This article will serve as a guide for all those New Yorkers making the trek across the continent, either for a little while or permanently, and it may provide long-time Angelenos with a new way of thinking about the city as well. Additionally, given how much of the literature about this city is shaped by those from outside of it, it is my hope that this article will give those external writers a more familiar reference point as they grapple with this seemingly overwhelming metropolis.
(Note: It may help to open Google Maps for Los Angeles and New York City to follow along through this article.)
ManhattAngeles
Comparing Los Angeles to other cities can be difficult due to its unusual political boundaries. While many metro areas have a central primary city, such as San Francisco in the Bay Area, in LA there are major job and cultural centers such as Beverly Hills, West Hollywood, and Santa Monica which are centrally located but are legally their own municipalities, while distant suburbs at the edge of the San Fernando Valley are part of the City of LA. To make a true ‘apples to apples’ comparison between LA and other cities, we would need to define a legitimate core to the Los Angeles region – a ManhattAngeles, if you will.
I believe that the Manhattan of LA runs in a linear fashion westward from Downtown LA to Santa Monica. Its width encompasses Greater DTLA (including USC and Exposition Park), then moving westward it extends from the Santa Monica Mountains / Hollywood Hills in the north to roughly the 10 freeway in the south, widening as it approaches the coast to include Culver City and the beach cities south to LAX. It encompasses a few municipalities, but only some portions of the City of LA. Most of the remaining area within official City bounds, as well as some other proximate communities, constitute LA’s “outer boroughs”, to be described in the next section.
What defines a city’s center? Perhaps the best research on this subject when it comes to Los Angeles came from USC graduate student Samuel Krueger. With a focus on clusters of lifestyle and cultural elements, Krueger mapped what he called the “Wilshire - Santa Monica Corridor” – a linear belt of “centrality” running along those two boulevards from Downtown LA to Santa Monica. His data-driven approach was verified in that it correctly identified the “centers” of New York and Chicago, as well.
I accept Krueger’s core methodology, however I would add to it a consideration of job centers, high value homes, transit nodes, and hotbeds of real estate investment. Additionally, the means through which Angelenos move about says something about its different boroughs. Within a single borough, it is often most efficient to drive on surface streets rather than trek to and from the freeway; freeways are usually necessary for inter-borough transit. LA may be a region of freeways, but it is a city of boulevards.
Part of what makes ManhattAngeles such an interesting place in comparison to Manhattan is in fact how similar their historic development patterns are. Moving north up the island of Manhattan presents a very similar pattern of neighborhoods and development history as does moving west from DTLA toward the beach. New York was founded on the southern tip of the island and expanded northward over time. Its original business hub was in Lower Manhattan, and the newer hub is in Midtown. Los Angeles was founded in what is now Downtown and the core of the city expanded westward over time. Its original business district was Downtown, and the newer hub is on the Westside. Both cities’ patterns of expansion, divestment, and reinvestment, following broader trends in American culture and history, have left many parallel neighborhoods in analogous locations across their main urban cores – though all of these neighborhoods are a bit more smushed together in New York, of course.
Lower Manhattan was the original New York, back when Harlem was pastureland and Broadway was a Native American trail through the wilderness. It housed and continues to house the city’s government and other major legacy institutions. It is also home to the city’s original business district, centered around Wall Street. Over the course of the 20th Century, much of Lower Manhattan was to some extent abandoned in favor of the newer, cleaner, and bigger business, residential, and cultural districts further uptown. Over recent decades, this process has reversed to some extent, as Lower Manhattan has been revitalized with businesses, people, and cultural outlets.
This story may sound familiar to anyone who follows Los Angeles development patterns, or even read my “L.A. Urbanized” series on this site. Downtown LA too was largely abandoned and turned into a super-sized office park in the middle of the 20th Century. However, reinvestment over recent decades is turning this part of the city around. It is developing an array of neighborhoods largely analogous to those in Lower Manhattan. DTLA’s Financial District, Civic Center, and Chinatown have clear parallels in the southern tip of Manhattan. Over years to come, we may see DTLA’s South Park emerge as a West Coast Tribeca, and its Arts District as a California SoHo. The areas immediately west of DTLA (Westlake/MacArthur Park and Pico-Union, for example) are in some respects analogous to Manhattan’s Lower East Side as the arrival point for many of the city’s successive immigrant groups. The urban economist Joel Kotkin was making this comparison as early as 1997.
As we move a bit up the island of Manhattan and ‘up the island’ of ManhattAngeles we encounter more districts whose stories are similar to one another. Here we find neighborhoods with a fair bit of history and urban vibrancy, though not quite so dense as the cities’ original centers. Serving as cultural trendsetters with a historic vibe for their cities and the world beyond, neighborhoods such as Greenwich Village, Chelsea, Gramercy, and NoMad in New York share a lot of similarities as lifestyle centers with West Hollywood, the Sunset Strip, Beverly Grove, Mid-Wilshire, and Hancock Park in Los Angeles.
Moving further north to New York’s Korea Town, its analogue in LA is, well, Koreatown. Both are centrally located within the cities’ urban cores. They play prominent roles in the regions’ transit networks. And they are both secondary business and nightlife hubs; not quite so prominent as the major clusters on either side of them, but still notable in those regards.
The next stop on the northbound subway is at Times Square. Times Square is the icon of New York to an outsider, so it is no surprise that the place is fully overrun by tourists and associated shops, restaurants, and entertainment venues. Hollywood Boulevard and its “Walk of Fame” is, similarly, most outsiders’ primary image of Los Angeles. Accordingly, Hollywood Boulevard primarily serves a tourist audience. With its flashing lights, entertainment venues, throngs of people, and mixed feelings amongst locals, it is not hard to see the similarities between these two world famous destinations.
Venture a few blocks east of Times Square, however, and you’ll find yourself in Manhattan’s Midtown business district, which is probably the most important commercial agglomeration in the world. Ironically, many of the “Wall Street” banks are in fact headquartered here uptown, today. The city largely shifted its center of gravity uptown during the mid-20th Century, and though Lower Manhattan has recovered quite a bit, Midtown remains extremely vibrant as a business hub.
LA’s Westside developed as its own business hub over the course of the mid-20th Century as well. Many of New York’s most prestigious firms are based in Midtown, rather than the original city core; many of LA’s most prominent offices are based in Century City or Beverly Hills, rather than in Downtown. Offices in Westwood, Brentwood, and Santa Monica round out this robust, more recent business district. Moreover, this area also has much of the city’s high end housing stock, in a manner similar to Midtown Manhattan.
To the west of Times Square is Hell’s Kitchen, a neighborhood that used to be mostly industrial, but which has in recent years benefited from its Midtown proximity and has become a true lifestyle and creative hub. A similar pattern can be observed today in LA’s Culver City, which is emerging as a major creative office hub in its own right, located close to the existing Westside commercial core.
As you move further up Manhattan, you ultimately cross 59th Street, also known as Central Park South. This street acts in some respects as a dividing line, with the tonier and more residential Upper East and West Sides to its north, and the more commercial parts of the city to its south (though with no shortage of tony residential too). In Los Angeles, the same could be said of crossing west of the 405 freeway into the upscale residential neighborhoods such as Brentwood, Santa Monica, and the Pacific Palisades. The world to the west of the 405 is generally lower density and more residential in nature than the world to its east. These neighborhoods are home to many of the city’s elite, in a manner very similar to those on the Upper East and West Sides.
Both Manhattan and its Los Angeles counterpart are quite densely developed, but they are also both home to world famous open spaces. Those are New York’s Central Park, and LA’s expansive coastline of beaches. The most prominent of these is Santa Monica Beach, which together with its pier is a prominent draw for visitors from around the world and icon of the city, in a manner similar to Central Park. It also serves a similar function for its surrounding residential communities as Central Park does for its own. Much as Central Park serves as a focal point on the Upper East and West Sides, the beach and ocean is the open space around which much of the urban form and culture west of the 405 is organized.
Taken together, this “ManhattAngeles” represents a compelling “center” to the Los Angeles region nearly as much as Manhattan represents the center of New York. Those who would argue against this notion often say that LA is extremely polycentric, more so than is the case in other major cities. This line of reasoning is less convincing when we compare the rest of the metro area with New York outside of Manhattan. Manhattan has multiple ‘centers’ in its own right. Moreover, its outer boroughs and suburbs thereafter all serve important roles in the region as well, in a manner fairly similar to the arrangement in LA. The subsequent sections of this article will compare the two cities beyond their central cores, showing how their similarities of urban form continue.
The Outer Boroughs
New York’s outer boroughs are “suburbs” in some senses of the term, however in other respects they feel more like a part of the central city than do the more distant true suburbs beyond. The boroughs are deeply knit into the city’s economic and social fabric, and they entertain relatively few conflicts of identity as compared to the more distant suburbs (a topic I will return to in the subsequent section). In Los Angeles, there is a set of neighborhoods and municipalities that surround ManhattAngeles and function in a parallel manner to Brooklyn, Queens, the Bronx, and Staten Island.
The borough of Brooklyn conjures images of bearded hipsters, tattooed artists, and trendy shops and restaurant, rubbing up against much of the city’s diverse immigrant population and pockets of serious poverty. It feels decidedly different from Manhattan, though no one would say that it isn’t part of the city. The “East Side” of Los Angeles is very similar in many regards. I’ll take an expansive definition of the East Side, an area including Thai Town and Los Feliz east of Hollywood across the 101 freeway, Silver Lake, Echo Park, Atwater Village, Highland Park and the broader Northeast LA area, and moving southeast to include Boyle Heights and East Los Angeles. This area encompasses a vast range of peoples, income levels, and lifestyles. It is certainly the spiritual home to the city’s counterculture, bohemians, and “bobos”. Yet at the same time most of the people who live in this area have little to do with those cultures. They are living the American immigrant experience, centered around their own ethnic/cultural communities.
Developed mostly in the years after WWII, the San Fernando Valley was built essentially as the prototype for suburbia in America. Ranches were subdivided into “ranch-style” homes as “the Valley” became LA’s primary bedroom community. Over the decades, however, I would argue that The Valley has developed an urban form, its own commercial centers, and its own suburbs. These, taken together with its tight economic integration and City of LA governance, make it play much more of a city borough role than an outer suburban one.
Indeed, the Valley is the Queens borough of Los Angeles. It is located just across the ‘river’ from ManhattAngeles (filled in here by the Santa Monica Mountains and Hollywood Hills). People transit to and from The Valley by taking one of a few ‘bridges’ through the mountains: the 405, 101, or 5 freeways. In a manner similar to Queens, the Valley is home to a wide array of lifestyles and migrant groups. However both Queens and the Valley are generally more middle class and suburban in orientation than are Brooklyn or the East Side. They are also both major population centers, with almost half of City of LA residents living in the San Fernando Valley. Some parts of Queens today (such as Long Island City) are being developed as effective extensions of Manhattan across the river; Valley neighborhoods such as Studio City, North Hollywood, Sherman Oaks, and Encino are taking on a similar character themselves.
On the other side of ManhattAngeles is South LA. This is an area of the city which is too often overlooked, but which forms an essential component of LA’s civic identity. The clear parallel in New York is the Bronx. Both are home to a diverse set of immigrants and many lower income people. Both of their pasts have been characterized by challenges with crime and civil strife, by “redevelopment” projects, and by frictional relations with law enforcement.
Yet both communities have also been essential for their respective cities, providing housing at a lower cost for many of the people who do the work to keep these cities functioning, and serving as a cultural wellspring for musical and artistic styles that have defined these cities on the global map. Today, the impact of crime has lessened in these boroughs, and they have seen some new outside investment. There is a growing concern over gentrification in both boroughs, however it has not yet arrived there to the degree it has in the Brooklyns or Manhattans of both cities.
The final New York City borough is Staten Island. Generally more suburban in character and located across the harbor from the other boroughs, Staten Island is relatively less plugged in to the city center. Yet, with relatively affordable housing and straightforward access to Lower Manhattan by ferry, Staten Island serves as an effective bedroom community for many of the municipal employees and others who are quietly keeping the city running.
In Los Angeles, the San Gabriel Valley and the Gateway Cities at least historically served in a similar capacity. Their appropriateness for this role is evidenced by the location of several key Los Angeles County offices in this region. Over recent years, however, the transformation of these two areas into specific ethnic/cultural suburban enclaves: Chinese in the San Gabriel Valley and Latino in the Gateway Cities (see Chapter 3 of William Fulton’s The Reluctant Metropolis) has added a distinct character to these areas for which there are few comparisons in New York City.
Up to this point all of the neighborhoods of Los Angeles we’ve discussed, sprawled and diverse as they are, I would consider to be a part of the core ‘city’ of Los Angeles, akin to being within the city boundaries of New York City. Moving forward, we will take another step back to observe those areas which no longer feel like they are ‘in the city’, yet which still fall within the city’s broader metro area.
Suburbs and Exurbs
Moving further out from LA’s center and surrounding ‘boroughs’, we arrive at an outer ring of suburbs and exurbs which complete this metropolitan region. Some of these neighborhoods function mostly as bedroom communities for the more central parts of the city, while others have defined cultures and lifestyles of their own – which at times clash with those of the core city. Indeed, I think that the key differentiator between outer boroughs and true suburbs and exurbs is that many may believe these suburbs and exurbs are ‘not a part’ of the main city, but rather urban agglomerations of their own. I do not subscribe to that line of reasoning for Los Angeles and New York in particular, where the fundamental growth stories and economic systems of the city and suburbs are inextricably linked. However, where people are so far from the city that they begin to believe they are not a part of it, that is where true suburbia begins.
Head northeast from Manhattan through Queens, and after a while the city will fall away behind you, and you’ll find yourself amongst the sumptuous homes, greenery, and coastlines of Long Island’s North Shore. This is Gatsby-land; a place for wealthy New Yorkers to have their space just outside the city. Head northwest from ManhattAngeles through LA’s Queens, the San Fernando Valley, and you will arrive in LA’s Gatsby-land. It is a stretch of spacious and scenic communities generally oriented around the Santa Monica Mountains and the Malibu coastline, including Malibu itself, Calabasas, Hidden Hills, Agoura, and Westlake Village. This area is famed for being the home of the Kardashian clan. It is not much of a stretch to see the similarities between the fictional story of Jay Gatsby and the “reality” story of the Kardashians. LA’s South Bay beach cities and adjacent Palos Verdes play a similar role, as well.
Setting the Kardashians aside, most people choose to live here not because it is convenient to the rest of the city, but rather because it is decidedly out of the city. Here, social life is less mediated by larger civic institutions. In the manner of a small village, social life is organized around tight-knit community groups, or it is direct between individuals and families. Private residences often substitute for public space when it comes to parties or dinners or other such gatherings. The North Shore and LA’s equivalents are worlds unto themselves, retreats into small town life at the edge of the big city.
Moving deeper into Long Island, there is a long stretch of suburban neighborhoods. Notably, some of these serve as bedroom communities for Queens and other New York outer boroughs and suburbs. Moving deeper beyond LA’s San Fernando Valley, the suburban communities of Thousand Oaks, Simi Valley, Santa Clarita, and the Antelope Valley serve a similar function, providing relatively affordable and more spacious housing (at a greater distance) for people who work in the Valley and the rest of the city beyond.
Due north of Manhattan and the Bronx is Westchester County. Wealthy, well-educated, and at one time the home of many industrial tycoons, Westchester County finds its LA counterpart in the leafy streets of Pasadena and its surrounds. Both have a feeling of erudition in addition to affluence, with deep ties to local universities. Pasadena’s early development was driven largely by gilded age Midwestern magnates seeking a retreat during the freezing winters; Westchester’s early development was driven largely by gilded age Manhattan millionaires seeking a retreat during the hot and humid summer. Today, one can visit the historic Gamble House or Fenyes Mansion in Pasadena just as one can visit Kykuit or Lyndhurst in Westchester.
Across the Hudson River from Manhattan are the dense and industrially-oriented neighborhoods of the New Jersey waterfront. New York has always been a great port city, however today almost all of the shipping activity is concentrated on the New Jersey waterfront. In Los Angeles, industrial waterfront places such as Long Beach, Wilmington, and San Pedro play a very similar role – together processing nearly half the country’s oceanbound shipping, while supporting major population centers as well. This city-adjacent part of New Jersey has seen a boom of new residential and office development over recent years as prices in the city center have skyrocketed; the same has occurred in Long Beach.
Moving further inland from the New Jersey waterfront, you arrive at more typically suburban cities and towns, some of which are quite large. In Los Angeles, the equivalent region of the city is the inland suburban expanse of Orange County (not its coastline, which I will return to shortly). The reason this comparison is particularly sensible is because both places have an uncertain identity in relation to the centers of their metro areas. These New Jersey suburbs are across state lines from Manhattan, so can it they really be a part of New York? A similar reasoning goes for Orange County, which of course is not within Los Angeles County. Add to this some degree of cultural enmity in both cases. With many New Yorkers looking down on New Jersey and with Orange County’s history of being “across the Orange Curtain” from Los Angeles as a bastion of conservatism in California, it is clear why so many feel a divide. However, both northern New Jersey and Orange County are intricately linked into the dominant economic, social, cultural, and historical fabrics of their respective metro areas.
The strings of towns and cities feel interminable as you progress deeper and deeper west into New Jersey, even crossing another state boundary into northeastern Pennsylvania. The same experience is true as you continue east from the center of Los Angeles. LA’s “Inland Empire”, its stretch of development that extends forever eastward from the city, is akin to those westernmost suburbs of New York. The exurbs of San Bernardino and Riverside serve to anchor this distant region in a manner similar to Allentown and Trenton. All have largely industrial histories, and maintain a fair degree of that character to this day.
To the northeast of New York sits a series of exurbs with a fairly different orientation. The southwestern coast of Connecticut is one of the wealthier parts of the region. In particular, it serves as a home to the headquarters of several major corporations and financial institutions. Historically, many executives and well-paid employees have enjoyed its spacious suburban environment and spectacular coastline. Within the Greater Los Angeles area, the Orange County Coast and its surroundings have played a similar role as an exurban center of business within Southern California. Cities such as Newport Beach, Irvine, and Santa Ana are home to such businesses as PIMCO, Broadcom, First American Financial, and many regional headquarters.
Conclusion
At first glance, the differences between New York and Los Angeles as cities is starkly clear. New York builds up while Los Angeles builds out, and accordingly Angelenos are driving everywhere while New Yorkers are taking the subway and walking. It is clear that the spatial arrangement of the two cities and the means through which people move about them are quite different. However, on a more fundamental matter of which sorts of neighborhoods shape the city and how they developed and relate to each other, those differences begin to melt away. The experience of transporting yourself between neighborhoods is not the same, but the types of neighborhoods you’re moving between, and roughly the amount of travel time involved as well (even with traffic), are quite similar.
Both New York and Los Angeles boomed and expanded out from their historic cores, largely abandoned those original neighborhoods over the 20th Century, and have re-discovered and re-invested in them over the past few decades. The main thrust of this expansion moved north up Manhattan, and west across the LA Basin to form an area I call ManhattAngeles. The northward development of Manhattan was pursued along a similar timeline (however in different decades) to the westward development of ManhattAngeles, leaving both cities with comparable neighborhoods arranged in analogous patterns. Other urban and suburban growth spread in every which direction in both cases, creating a series of ‘boroughs’ that ring the core cities, and subsequent layers of suburbs and exurbs further out still.
Perhaps there is a set of underlying fundamentals which encourages parallel growth across these two megalopolises, as well as several others not addressed in this article. That notion may be well suited for further exploration. For now, it is my hope that this article has demonstrated that, despite their lifestyle differences, Los Angeles and New York are fundamentally similar animals. Los Angeles is not an impenetrably strange and exotic land, where none of the rules from back home apply, as many an outside writer might have you believe. Rather, it is the flip side to the same coin.
Jason Lopata works as a land use consultant with Craig Lawson & Co., LLC, helping real estate development projects in LA navigate the city approvals process. Jason previously spent time on the Business Team of LA Mayor Eric Garcetti. He also writes articles on globalization and urban development for Stratfor, the geopolitical analysis website. Jason received his bachelor’s degree from Stanford University and completed programs of study at the University of Oxford and at UCLA’s Anderson School of Management. While at Stanford, he founded and led the student real estate organization, and authored his senior thesis on Los Angeles development over the past 30 years. Read his earlier longform series "L.A. Urbanized." by clicking here.
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Why it is important to know how things happen to us
Below we have compiled many verses, mostly from Srimad-Bhagavatam and Bhagavad-gita for understanding why "good and bad" things happen to us, and more specifically how each of us individually reacts to such events as devotees or Vaisnavas. The ultimate goal of all action, according to our philosophy is to only act for the satisfaction of God, or Krishna, and in that way no personal karma is generated. OK, here we go….
Srimad-Bhagavatam 1.17.18
O greatest among human beings, it is very difficult to ascertain the particular miscreant who has caused our sufferings, because we are bewildered by all the different opinions of theoretical philosophers.
PURPORT
There are many theoretical philosophers in the world who put forward their own theories of cause and effect especially about the cause of suffering and its effect on different living beings. Generally there are six great philosophers: Kanada, the author of Vaisesika philosophy; Gautama, the author of logic; Patanjali, the author of mystic yoga; Kapila, the author of Sankhya philosophy; Jaimini, the author of Karma-mimamsa; and Vyasadeva, the author of Vedanta-darsana.
Although the bull, or the personality of religion, and the cow, the personality of the earth, knew perfectly well that the personality of Kali was the direct cause of their sufferings, still, as devotees of the Lord, they knew well also that without the sanction of the Lord no one could inflict trouble upon them. According to the Padma Purana, our present trouble is due to the fructifying of seedling sins, but even those seedling sins also gradually fade away by execution of pure devotional service. Thus even if the devotees see the mischief-mongers, they do not accuse them for the sufferings inflicted. They take it for granted that the mischief-monger is made to act by some indirect cause, and therefore they tolerate the sufferings, thinking them to be God-given in small doses, for otherwise the sufferings should have been greater.
Maharaja Pariksit wanted to get a statement of accusation against the direct mischief-monger, but they declined to give it on the abovementioned grounds. Speculative philosophers, however, do not recognize the sanction of the Lord; they try to find out the cause of sufferings in their own way, as will be described in the following verses. According to Srila Jiva Gosvami, such speculators are themselves bewildered, and thus they cannot know that the ultimate cause of all causes is the Supreme Lord, the Personality of Godhead.
Srimad-Bhagavatam 1.17.19
Some of the philosophers, who deny all sorts of duality, declare that one's own self is responsible for his personal happiness and distress. Others say that superhuman powers are responsible, while yet others say that activity is responsible, and the gross materialists maintain that nature is the ultimate cause.
PURPORT
As referred to above, philosophers like Jaimini and his followers establish that fruitive activity is the root cause of all distress and happiness, and that even if there is a superior authority, some superhuman powerful God or gods, He or they are also under the influence of fruitive activity because they reward result according to one's action. They say that action is not independent because action is performed by some performer; therefore, the performer himself is the cause of his own happiness or distress. In the Bhagavad-gita (6.5) also it is confirmed that by one's mind, freed from material affection, one can deliver himself from the sufferings of material pangs. So one should not entangle oneself in matter by the mind's material affections. Thus one's own mind is one's friend or enemy in one's material happiness and distress.
Atheistic, materialistic Sankhyaites conclude that material nature is the cause of all causes. According to them, combinations of material elements are the causes of material happiness and distress, and disintegration of matter is the cause of freedom from all material pangs. Gautama and Kanada find that atomic combination is the cause of everything, and impersonalists like Astavakra discover that the spiritual effulgence of Brahman is the cause of all causes. But in the Bhagavad-gita the Lord Himself declares that He is the source of impersonal Brahman, and therefore He, the Personality of Godhead, is the ultimate cause of all causes. It is also confirmed in the Brahma-samhita that Lord Krishna is the ultimate cause of all causes.
Srimad-Bhagavatam 1.17.20
There are also some thinkers who believe that no one can ascertain the cause of distress by argumentation, nor know it by imagination, nor express it by words. O sage amongst kings, judge for yourself by thinking over all this with your own intelligence.
PURPORT
The Vaisnavites, the devotees of the Lord, do believe, as above explained, that nothing can take place without the sanction of the Supreme Lord. He is the supreme director, for He confirms in the Bhagavad-gita (15.15) that He, as all-pervading Paramatma, stays in everyone's heart and keeps vigilance over all actions and witnesses all activities. The argument of the atheist that one cannot be punished for one's misdeeds unless proved before a qualified justice is refuted herein, for we accept the perpetual witness and constant companion of the living being. A living being may forget all that he might have done in his past or present life, but one must know that in the same tree of the material body, the individual soul and the Supreme Soul as Paramatma are sitting like two birds. One of them, the living being, is enjoying the fruits of the tree, whereas the Supreme Being is there to witness the activities. Therefore the Paramatma feature, the Supreme Soul, is actually the witness of all activities of the living being, and only by His direction can the living being remember or forget what he might have done in the past. He is, therefore, both the all-pervading impersonal Brahman and the localized Paramatma in everyone's heart. He is the knower of all past, present and future, and nothing can be concealed from Him. The devotees know this truth, and therefore they discharge their duties sincerely, without being overly anxious for rewards. Besides that, one cannot estimate the Lord's reactions, either by speculation or by scholarship. Why does He put some into difficulty and not others? ….
Srimad-Bhagavatam 1.17.22
The King (Pariksit) said: O you, who are in the form of a bull! You know the truth of religion, and you are speaking according to the principle that the destination intended for the perpetrator of irreligious acts is also intended for one who identifies the perpetrator. You are no other than the personality of religion.
PURPORT
A devotee's conclusion is that no one is directly responsible for being a benefactor or mischief-monger without the sanction of the Lord; therefore he does not consider anyone to be directly responsible for such action. But in both the cases he takes it for granted that either benefit or loss is God-sent, and thus it is His grace. In case of benefit, no one will deny that it is God-sent, but in case of loss or reverses one becomes doubtful about how the Lord could be so unkind to His devotee as to put him in great difficulty.
Jesus Christ was seemingly put into such great difficulty, being crucified by the ignorant, but he was never angry at the mischief-mongers. That is the way of accepting a thing, either favorable or unfavorable. Thus for a devotee the identifier is equally a sinner, like the mischief-monger. By God's grace, the devotee tolerates all reverses.
Maharaja Pariksit observed this, and therefore he could understand that the bull was no other than the personality of religion himself. In other words, a devotee has no suffering at all because so-called suffering is also God's grace for a devotee who sees God in everything. The cow and bull never placed any complaint before the King for being tortured by the personality of Kali, although everyone lodges such complaints before the state authorities. The extraordinary behavior of the bull made the King conclude that the bull was certainly the personality of religion, for no one else could understand the finer intricacies of the codes of religion.
Now what follows is what happens to "mischief mongers"…
The Hari-bhakti-vilasa cites the following quotation from Skanda Purana concerning the blaspheming of a Vaisnava: In this conversation between Markandeya and Bhagiratha, it is said: "My dear King, if one derides an exalted devotee, he loses the results of his pious activities, his opulence, his reputation and his sons. Vaisnavas are all great souls. Whoever blasphemes them falls down to the hell known as Maharaurava. He is also accompanied by his forefathers. Whoever kills or blasphemes a Vaisnava and whoever is envious of a Vaisnava or angry with him, or whoever does not offer him obeisances or feel joy upon seeing a Vaisnava, certainly falls into a hellish condition."
The Hari-bhakti-vilasa (10.314) also gives the following quotation from Dvaraka-mahatmya: In a conversation between Prahlada Maharaja and Bali Maharaja, it is said, "Those sinful people who blaspheme Vaisnavas, who are all great souls, are subjected very severely to the punishment offered by Yamaraja." In the Bhakti-sandarbha (313) there is a statement concerning the blaspheming of Lord Visnu. "One who criticizes Lord Visnu and His devotees loses all the benefits accrued in a hundred pious births. Such a person rots in the Kumbhipaka hell and is bitten by worms as long as the sun and moon exist. One should therefore not even see the face of a person who blasphemes Lord Visnu and His devotees. Never try to associate with such persons." In his Bhakti-sandarbha (265), Jiva Gosvami further quotes from Srimad-Bhagavatam (10.74.40): "If one does not immediately leave upon hearing the Lord or the Lord's devotee blasphemed, he falls down from devotional service." Similarly, Lord Siva's wife Sati states in Srimad-Bhagavatam (4.4.17): "If one hears an irresponsible person blaspheme the master and controller of religion, he should block his ears and go away if unable to punish him. But if one is able to kill, then one should by force cut out the blasphemer's tongue and kill the offender, and after that he should give up his own life."
Ok, now that is pretty scary information about offending a devotee or Lord Vishnu. That should set a humble tone for the following discussion.
1.) “Even the intelligent are bewildered in determining what is action and what is inaction. Now I shall explain to you what action is, knowing which you shall be liberated from all sins.” (Bg. 4.16)
2.) A person in the divine consciousness, although engaged in seeing, hearing, touching, smelling, eating, moving about, sleeping, and breathing, always knows within himself that he actually does nothing at all. Because while speaking, evacuating, receiving, opening or closing his eyes, he always knows that only the material senses are engaged with their objects and that he is aloof from them. (Bg. 5.8-9)
PURPORT
A person in Krishna consciousness is pure in his existence, and consequently he has nothing to do with any work which depends upon five immediate and remote causes: the doer, the work, the situation, the endeavor and fortune. This is because he is engaged in the loving transcendental service of Krishna. Although he appears to be acting with his body and senses, he is always conscious of his actual position, which is spiritual engagement. In material consciousness, the senses are engaged in sense gratification, but in Krishna consciousness the senses are engaged in the satisfaction of Krishna's senses. Therefore, the Krishna conscious person is always free, even though he appears to be engaged in things of the senses. Activities such as seeing, hearing, speaking, evacuating, etc., are actions of the senses meant for work. A Krishna consciousness person is never affected by the actions of the senses. He cannot perform any act except in the service of the Lord because he knows that he is the eternal servitor of the Lord.
3.) The bewildered spirit soul, under the influence of the three modes of material nature, thinks himself to be the doer of activities, which are in actuality carried out by nature. (Bg. 3.27)
4.) The embodied spirit, master of the city of his body, does not create activities, nor does he induce people to act, nor does he create the fruits of action. All this is enacted by the modes of material nature. (Bg. 5.14)
PURPORT
The living entity, as will be explained in the Seventh Chapter, is one in nature with the Supreme Lord, distinguished from matter, which is another nature – called inferior – of the Lord. Somehow, the superior nature, the living entity, has been in contact with material nature since time immemorial. The temporary body or material dwelling place which he obtains is the cause of varieties of activities and their resultant reactions. Living in such a conditional atmosphere, one suffers the results of the activities of the body by identifying himself (in ignorance) with the body. It is ignorance acquired from time immemorial that is the cause of bodily suffering and distress. As soon as the living entity becomes aloof from the activities of the body, he becomes free from the reactions as well. As long as he is in the city of body, he appears to be the master of it, but actually he is neither its proprietor nor controller of its actions and reactions. He is simply in the midst of the material ocean, struggling for existence. The waves of the ocean are tossing him, and he has no control over them. His best solution is to get out of the water by transcendental Krishna consciousness. That alone will save him from all turmoil.
5.) You have a right to perform your prescribed duty, but you are not entitled to the fruits of action. Never consider yourself to be the cause of the results of your activities, and never be attached to not doing your duty. (Bg. 2.47)
PURPORT
There are three considerations here: prescribed duties, capricious work, and inaction. Prescribed duties refer to activities performed while one is in the modes of material nature. Capricious work means actions without the sanction of authority, and inaction means not performing one's prescribed duties. The Lord advised that Arjuna not be inactive, but that he perform his prescribed duty without being attached to the result. One who is attached to the result of his work is also the cause of the action. Thus he is the enjoyer or sufferer of the result of such actions.
6.) Nature is said to be the cause of all material activities and effects, whereas the living entity is the cause of the various sufferings and enjoyments in this world. (Bg. 13.21)
PURPORT
The different manifestations of body and senses among the living entities are due to material nature. There are 8,400,000 different species of life, and these varieties are the creation of the material nature. They arise from the different sensual pleasures of the living entity, who thus desires to live in this body or that. When he is put into different bodies, he enjoys different kinds of happiness and distress. His material happiness and distress are due to his body, and not to himself as he is. In his original state there is no doubt of enjoyment; therefore that is his real state. Because of the desire to lord it over material nature, he is in the material world. In the spiritual world there is no such thing. The spiritual world is pure, but in the material world everyone is struggling hard to acquire victims who present different pleasures to the body. It might be more clear to state that this body is the effect of the senses. The senses are instruments for gratifying desire. Now, the sum total – body and instrument senses – are offered by material nature, and, as will be clear in the next verse, the living entity is blessed or damned with circumstances according to his past desire and activity. According to one's desires and activities, material nature places one in various residential quarters. The being himself is the cause of his attaining such residential quarters and his attendant enjoyment or suffering. Once placed in some particular kind of body, he comes under the control of nature because the body, being matter, acts according to the laws of nature. At that time, the living entity has no power to change that law. Suppose an entity is put into the body of a dog. As soon as he is put into the body of a dog, he must act like a dog. He cannot act otherwise. And if the living entity is put into the body of a hog, then he is forced to eat stool and act like a hog. Similarly, if the living entity is put into the body of a demigod, he must act according to his body. This is the law of nature. But in all circumstances, the Supersoul is with the individual soul. That is explained in the Vedas as follows: dvasuparna sayuja sakhaya. The Supreme Lord is so kind upon the living entity that He always accompanies the individual soul and in all circumstances is present as the Supersoul or Paramatma.
7.) One who can see that all activities are performed by the body, which is created of material nature, and sees that the self does nothing, actually sees. (Bg. 13.30)
PURPORT
This body is made by material nature under the direction of the Supersoul, and whatever activities are going on in respect to one's body are not his doing. Whatever one is supposed to do, either for happiness or for distress, one is forced to do because of the bodily constitution. The self, however, is outside all these bodily activities. This body is given according to one's past desires. To fulfill desires, one is given the body, with which he acts accordingly. Practically speaking, the body is a machine, designed by the Supreme Lord, to fulfill desires. Because of desires, one is put into difficult circumstances to suffer or to enjoy. This transcendental vision of the living entity, when developed, makes one separate from bodily activities. One who has such a vision is an actual seer.
8.) And that understanding which cannot distinguish between the religious way of life and the irreligious, between action that should be done and action that should not be done, that imperfect understanding, O son of Prtha, is in the mode of passion. (Bg. 18.31)
PURPORT
Intelligence in the mode of passion is always working perversely. It accepts religions which are not actually religions and rejects actual religion. All views and activities are misguided. Men of passionate intelligence understand a great soul to be a common man and accept a common man as a great soul. They think truth to be untruth and accept untruth as truth. In all activities they simply take the wrong path; therefore their intelligence is in the mode of passion.
Some conclusions: Let us review some of what has been stated above so that we can get a more clear understanding of what is actually going on in respect to each of us within our respective bodies, all the time.
1. A devotee's conclusion is that no one is directly responsible for being a benefactor or mischief-monger without the sanction of the Lord.
2. Even the intelligent are bewildered in determining what is action and what is inaction.
3. A person in the divine consciousness, although engaged in seeing, hearing, touching, smelling, eating, moving about, sleeping, and breathing, always knows within himself that he actually does nothing at all. (Bg. 5.8-9)
4. A person in Krishna consciousness is pure in his existence, and consequently he has nothing to do with any work which depends upon five immediate and remote causes: the doer, the work, the situation, the endeavor and fortune.
5. A Krishna consciousness person is never affected by the actions of the senses.
6. The bewildered spirit soul, under the influence of the three modes of material nature, thinks himself to be the doer of activities, which are in actuality carried out by nature. (Bg. 3.27)
7. The embodied spirit, master of the city of his body, does not create activities, nor does he induce people to act, nor does he create the fruits of action. All this is enacted by the modes of material nature. (Bg. 5.14)
8. The temporary body or material dwelling place which he obtains is the cause of varieties of activities and their resultant reactions. Living in such a conditional atmosphere, one suffers the results of the activities of the body by identifying himself (in ignorance) with the body.
9. As soon as the living entity becomes aloof from the activities of the body, he becomes free from the reactions as well. As long as he is in the city of body, he appears to be the master of it, but actually he is neither its proprietor nor controller of its actions and reactions. He is simply in the midst of the material ocean, struggling for existence.
10. You have a right to perform your prescribed duty, but you are not entitled to the fruits of action. Never consider yourself to be the cause of the results of your activities, and never be attached to not doing your duty. (Bg. 2.47)
11. Nature is said to be the cause of all material activities and effects, whereas the living entity is the cause of the various sufferings and enjoyments in this world. (Bg. 13.21)
12. When he is put into different bodies, he enjoys different kinds of happiness and distress. His material happiness and distress are due to his body, and not to himself as he is.
13. The being himself is the cause of his attaining such residential quarters and his attendant enjoyment or suffering.
14. One who can see that all activities are performed by the body, which is created of material nature, and sees that the self does nothing, actually sees. (Bg. 13.30)
Final conclusions
So this is quite a compilation of quotes, only from Bhagavad-gita in which Srila Prabhupada is explaining that this body we inhabit, does basically everything for us and to us. It digests the food we eat, totally unbeknown to us, it gives us illusory happiness and distress (these are completely foreign to the pure spirit soul, as spirit never mixes with matter), it creates a constant magic show to our consciousness thru imperfect senses in which we believe we are this or that human male or female body which belongs to such and such material family or such a race, was born in such a place, grew in another or the same place, developed "associates or friends" along the way, and has or is giving us at present so much happiness or distress. And none of the above is real in the same way watching a movie is also not real since it is only flickering beams of light upon some viewing screen. The movie can and will create emotion, like fear, love, hate, in the exact same way our senses present to us (the viewing soul within) the so called life that goes on outside our bodies as a daily affair. There was a movie once done by a Hollywood comic where he was put thru an entire series of life-like scenarios where he had some kind of wife, some kind of job, some place of residence, and while he was going about his daily "life" the whole thing was being generated by the movie makers behind the scenes – so in actuality none of what he thought was real, was real at all. It was only a very complicated movie set, but he was made to completely believe in it. The movie was called the Truman Story, starring Jim Carey. So how is this any different than what has been explained above in Bhagavad-gita?
The hero of the story (Jim Carey) finally figures it out one day by going behind one movie set that showed the ocean out in front of him, but was in reality just another illusion presented by the movie director.
This revelation he had is comparable to us when we finally realize we are not these bodies, but the consciousness within them. When that day comes, we will no longer be in illusion in that way, because once we know who we really are, as Srila Prabhupada so aptly states, the clutches of maya will no longer be an obstacle. It is a long road until that state of Krishna Consciousness arrives, but one important development upon that road is the above understanding of not identifying wrong doers with actions upon ourselves. When things happen to us, we have to understand it is coming initially from our own actions, with the Supreme Lord as Supersoul generating all the "movie sets" along the way.
Culture Camp
Jai Srila Prabhupada
What does an intelligent person do in Kali-yuga?
In the age of Kali, intelligent persons perform Sankirtana (congregational chanting) to worship Lord Chaitanya Mahaprabhu who constantly sings the holy names of Krishna. Although His complexion is not blackish, He is Lord Krishna Himself. He is accompanied by His associates, servants, weapons and confidential companions
Srimad Bhagavatam 11.5.32
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Does a person need any qualification to join Lord Chaitanya’s movement?
Everyone can join in His sankirtana movement. No previous qualification is necessary. Just by following His teachings, anyone can become a perfect human being. If a person is fortunate enough to be attracted by Lord Chaitanya, he is sure to be successful in his life’s mission.
Sri Chaitanya Charitamrita Adi-lila Preface
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Why is Sri Chaitanya Mahaprabhu called as the most munificent incarnation?
Lord Chaitanya Mahaprabhu is a wealthy capitalist possessing the touchstone of love of God. Not considering whether one is a proper or improper recipient, He gives His treasure to anyone and everyone. Thus He is the most munificent.
Sri Chaitanya Charitamrita Madhya-lila 2.81
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As followers, students, and disciples of His Divine Grace A.C. Bhaktivedanta Swami Prabhupada, Founder-Acharya of the International Society for Krishna Consciousness, also known as the Krishna Consciousness Movement, we welcome you to this new website to explain the position of His Divine Grace Srila Prabhupada, His original teachings, and His pure unblemished parampara and disciplic succession. Read More
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Enotno evropsko nebo (razprava)
Predsednica
Naslednja točka je vprašanje za ustni odgovor za Komisijo o vzpostavitvi enotnega evropskega neba s funkcionalnimi bloki zračnega prostora konč.), ki ga je predložil Paolo Costa v imenu odbora za promet in turizem - B6-0135/2007).
Gilles Savary
avtor. - (FR) Gospod predsednik, najprej moram predstaviti pisno vprašanje o SESAR, katerega avtor je Paolo Costa, ki me je prosil, naj vam vprašanje predstavim v njegovem imenu.
To je vprašanje za ustni odgovor za Komisijo z razpravo o oblikovanju funkcionalnih blokov zračnega prostora za vzpostavitev enotnega evropskega neba oziroma o namenu Komisije v zvezi z izvajanjem ali dosedanjim razvojem izvajanja paketa besedil, ki so bili decembra 2003 v spravnem postopku, in sicer paketa o enotnem nebu.
Eno od besedil obravnava oblikovanje funkcionalnih blokov zračnega prostora oziroma letalskih poti v različnih razredih zračnega prostora, da se optimizira poraba, zmanjšajo toplogredni plini in, če je mogoče, zmanjša preobremenjenost na najbolj zasedenih letališčih, vključno z možnostjo zmanjšanja stroškov zračnega prevoza. To je posebej občutljivo vprašanje s pridržki s strani držav članic, ki so vedno potrjevale svojo suverenost nad svojim zračnim prostorom. To zlasti velja za države članice in moja lastna država velike vojaške sile in bloke vojaškega zračnega prostora zadržuje na navidezno samovoljen način.
Gospod Costa je zaskrbljen, tako kot smo lahko pričakovali, da ni bil dosežen napredek v zvezi z besedilom o oblikovanju blokov zračnega prostora, enem od štirih besedil o enotnem nebu, saj so mu države članice močno nasprotovale. Gospod Costa zato Komisiji zastavlja naslednje vprašanje. Komisija je zdaj objavila sporočilo, ki pojasnjuje, da stroški neuspešnega oblikovanja funkcionalnih blokov zračnega prostora za vzpostavitev enotnega evropskega neba zajemajo približno 1 milijardo EUR. Gospod Costa je najprej zastavil vprašanje, ali je Komisija zadovoljna z razmerami in ali meni, da se uporaba uredbe (ES) št. 551/2004 o organiziranosti zračnega prostora zadovoljivo razvija. Kako si Komisija razlaga dejstvo, da od začetka veljavnosti uredbe niso začeli delovati nobeni novi bloki zračnega prostora?
Člen 10 uredbe določa razširitev organiziranosti zračnega prostora na spodnji zračni prostor ter od Komisije zahteva, da določi druge ukrepe, potrebne "glede na dosežen napredek". Kakšne spremembe obstoječe zakonodaje predlaga Komisija v zvezi s tem? Ali se Komisija strinja, da mora predložiti predlog v zvezi s tem še pred koncem leta 2008?
Gospod Costa v svojem ustnem vprašanju zastavlja vprašanje, ali se Komisija strinja, da je bil pristop od spodaj navzgor, pri čemer morajo pobudo za oblikovanje funkcionalnih blokov zračnega prostora pripraviti države članice, neuspešen in da mora zdaj Evropska unija oblikovati proaktivnejši pristop?
Upam, da sem ohranil duh vprašanja gospoda Coste Komisiji.
Jacques Barrot
podpredsednik Komisije. - (FR) Gospod Savary, hvala vam in gospodu Costi, ker menim, da je bilo to vprašanje zelo dobro pripravljeno in obravnava stvaren problem.
Reforma iz marca 2004 je bila namenjena organizaciji zračnega prometa v skladu z operativnimi zahtevami in ne nacionalnimi mejami. Zagotavlja krajšanje dolžine letov in preprečevanje nepotrebnega kroženja letal. Odgovoril bom na vsa vprašanja.
Prvo vprašanje zadeva stroške upravljanja zračnega prometa in posledice za enotno nebo. Vi in gospod Costa sta navedla ključen podatek, da stroški za neuspešno vzpostavitev enotnega neba znašajo 1 milijardo EUR, k čemur lahko dodam, da so v skladu z Evropsko organizacijo za varnost zračne plovbe možni prihranki večji, saj bi lahko prihranili 3 milijarde EUR. Poleg zmanjšanja stroškov letalskih prevoznikov bi bil dosežen prihranek v višini dveh milijard, če bi se izboljšala učinkovitost letalskih storitev.
Kot pravi gospod Savary, izvajanje enotnega evropskega neba ne napreduje dovolj hitro glede na pomembnost ciljev: konkurenčnost, trajnostni razvoj, boj proti podnebnim spremembam in spodbujanje varnosti v zraku. Ali moramo zato stati s prekrižanimi rokami in ne storiti ničesar? Ne. Sprejetje osnovnih pravil o enotnem trgu je Skupnosti prvič zagotovilo dejanska pooblastila na tem področju. Leta 2004 je bila izvedena reforma: ločitev med ureditvijo in zagotavljanjem storitev, certifikacija ponudnikov storitev v skladu z evropskimi predpisi, licence kontrolorjev zračnega prometa in niz tehničnih ukrepov, ki se sprejmejo s komitologijo. Nazadnje je bil sprožen industrijski projekt SESAR, pravi dodatek k enotnemu nebu.
Vendar moramo hitreje ukrepati. Komisija mora beležiti opravljeno delo. Decembra 2006 sem se posvetoval s skupino strokovnjakov na visoki ravni in letos julija so mi predstavili poročilo o obveznih reformah. Komisija bo letošnjo jesen predložila sporočilo v zvezi s tem.
Drugo vprašanje zadeva funkcionalne bloke zračnega prostora. Res je, da je Svet z reformo leta 2004 izbral pristop od spodaj navzgor, vključno z ukrepi nacionalnih vlad o oblikovanju blokov. Iskreno povedano ta pristop ni bil povsem zadovoljiv, saj je omejil možnosti za Komisijo in institucije Skupnosti, da zagotovijo dejansko oblikovanje blokov in nadaljevanje dela na lokalni ravni. Drug problem je, da ni bilo dovolj poudarjeno izboljšanje gospodarske učinkovitosti zagotovljenih storitev. V prvi polovici leta 2008 bomo poskušali uvesti pristop na podlagi učinkovitosti. S tem bi se določili posebni cilji učinkovitosti za ponudnike storitev ter v primeru neuspešnosti zagotovile pobude in intervencijske mehanizme. Menim, da bo pristop na podlagi učinkovitosti pospešil oblikovanje funkcionalnih blokov, ker bodo bistveni za uresničitev ciljev učinkovitosti. Razvijamo idejo organa za pregled uspešnosti in koordinatorja, odgovornega za hitrejši razvoj projektov. Osebno menim, da bi koordinator za vseevropska omrežja zelo prispeval k oblikovanju teh funkcionalnih blokov, ki jih potrebujemo.
Seveda s pospešitvijo oblikovanja in učinkovitosti funkcionalnih blokov ne bomo čakali do leta 2009. Upam, da vam bom lahko predložil pobudo sredi leta 2008. Na splošno velja, da so lahko bloki učinkoviti le, če se zgornji in spodnji zračni prostor obravnavata kot nedeljiva.
Četrto vprašanje zadeva pristop držav članic od spodaj navzgor, za katerega priznam, da je bil z določenih vidikov neuspešen. Moramo v tem primeru sprejeti popolnoma nasproten pristop? Nisem prepričan. Menim, da moramo poskusiti oblikovati boljši pristop od spodaj navzgor, vendar moramo za razvoj enotnega neba preiti na drugo stopnjo, ki temelji na uspešnosti in mehanizmih. Z državami članicami moramo dejavno sodelovati za spodbujanje politične zavezanosti in poudarjanje razvoja funkcionalnih blokov zračnega prostora.
Zato sem podprl to vprašanje. Tako sem dobil priložnost, da razložim glavne pobude, ki jih bomo sprejemali v skladu z zelo pomembnimi pripombami gospoda Savaryja.
Georg Jarzembowski
v imenu skupine PPE-DE. - (DE) Gospod predsednik, gospod podpredsednik Komisije, nikakor ne nasprotujemo temu, kar ste dosegli na področju učinkovitosti v zračnem prostoru, vendar je bil vaš odgovor precej jasen. Ta je izražal, da države članice niso izpolnile obveznosti. Države članice niso izpolnile obveznosti, ki so veljale od leta 2004, in sicer hitro oblikovanje funkcionalnih blokov zračnega prostora. Na eni strani to povzroča stroške v višini 3 milijard EU, ki ste jih navedli, na drugi strani pa onesnaževanje okolja.
Zdaj razpravljamo o uvedbi trgovanja z emisijami v zračnem prometu, in sicer o 3 % emisij zračnega prometa. Če bi bilo upravljanje letalskega prometa razumno, hitro in učinkovito, bi lahko zmanjšali porabo goriva do 12 %, kar bi bistveno zmanjšalo emisije CO2. Gospod podpredsednik, poštenjak ste, vendar moramo izpostaviti osnovni problem: države članice ne izpolnjujejo svojih obveznosti. Zato moramo vi kot Komisija in mi kot Parlament sporočiti državam članicam, da morajo to nadoknaditi. Po tolikšnem zaostanku morajo zelo pohiteti. Vendar to morda ne bo dovolj.
Zagroziti jim moramo tudi s spremembo pristopa od spodaj navzgor. Če države članice ne morejo doseči napredka v zvezi z zelo pomembnim vprašanjem varnosti v zračnem prometu in njegove učinkovitosti ter vplivu zračnega prometa na podnebje, pričakujemo, da Komisija leta 2008 ne bo le predložila poročila, da so se države članice izboljšale v smislu oblikovanja blokov zračnega prometa, ampak jim bo zagrozila. Zanesete se lahko na našo pomoč. Nato bomo morali spremeniti sistem in oblikovati bloke zračnega prostora na evropski ravni. Le tako lahko prepričamo države članice, da oblikujejo učinkovite in funkcionalne bloke zračnega prostora. Vem, kako težko je to, vendar prijazne besede ne bodo zalegle. Počasi se moramo naučiti ukrepati.
Brian Simpson
v imenu skupine PSE. - Gospod predsednik, v Parlamentu sem že tako dolgo, da se spominjam, ko je komisar de Palacio prvič predlagal enotno evropsko nebo in se je izraz "funkcionalni bloki zračnega prostora" prvič pojavil v besedišču EU. Po težkem začetku je bil leta 2004 dosežen napredek, ko je zakonodaja uzakonila te bloke zračnega prostora, vendar moram izpostaviti, da je bil napredek od takrat nevzdržno počasen, zlasti v zvezi s širitvijo blokov zračnega prostora, posebej glede nižjega zračnega prostora.
Gospod komisar, cenim, da je Komisija nameravala sodelovati z državami članicami in nedvomno so nekatere države članice pokazale, da so manj pripravljene izvajati to politiko pri hitrosti, ki si jo želimo ali smo jo dejansko predvideli, vendar je gotovo zdaj pravi čas, da se zadeve pospešijo in da Komisija čim prej predloži direktivo.
Od leta 2004 niso bili ustvarjeni nobeni novi bloki zračnega prostora in, kot so povedali prejšnji govorci, so stroški naše neuspešne vzpostavitve enotnega evropskega neba ocenjeni na 1 milijardo EUR. Poleg tega je treba veljavno zakonodajo posodobiti, saj se potniki še vedno dnevno spopadajo z zamudami v prometu zaradi staromodnega odnosa držav članic in, kot se zdi, nedejavnosti Komisije.
Potrpljenja zmanjkuje in ukrepanje je nujno. Neukrepanje ne pride v poštev, zato bo moja skupina podprla vprašanje za ustni odgovor, ki ga je gospod Costa predložil Parlamentu v imenu odbora za promet in turizem. Gospod komisar, vsi se staramo in si želimo dočakati enotno evropsko nebo.
Seán Ó Neachtain
v imenu skupine UEN. - (GA) Gospod predsednik, vprašati želim, ali se lahko šteje, da ta politika liberalizacije letalstva kakor koli pomaga nekaterim regijam in regionalnim letališčem. Poglejte, kaj se na primer dogaja na letališču Shannon v mojem volilnem okrožju na zahodnem Irskem. Odločitev letalske družbe Aer Lingus, da opusti lete v London, je negativno vplivala na regijo, ne nazadnje tudi z vidika gospodarstva. To je povsem v nasprotju s politiko irske vlade. Mislim torej, da bo ta svoboda na področju letalstva, kar zadeva evropske regije, prispevala k napredku močnih območij, tista območja, ki niso tako močna, pa bo oslabila. Zato Komisijo prosim, da obravnava na primer zadevo letališča Shannon in preuči, kako se lahko to politiko vodi skupaj s politiko regionalnega razvoja na takih območjih.
Vladimír Remek
v imenu skupine GUE/NGL. - (CS) Gospod predsednik, gospe in gospodje, pobuda "enotno evropsko nebo" potrjuje mojo izkušnjo kot zasebnega pilota, da je letalstvo šolski primer področja, ki zahteva nadnacionalno sodelovanje ne glede na državne meje.
Iz tega razloga in glede na potrebo po zagotovitvi največje varnosti v zračnem prometu, največje učinkovitosti in minimalne zamude letov podpiramo oblikovanje funkcionalnih blokov in posledično enotnega evropskega neba. Vendar ne smemo pozabiti, da tako kot razdrobljenost tudi odprava razdrobljenosti povzroča stroške. Ker je to zapleten sistem, v interesu stalnosti podpiram postopno vzpostavitev enotnega sistema za upravljanje operacij v skupnem zračnem prostoru.
Poleg tega bo poenotenje evropskega neba, za katerega danes obstaja 27 nacionalnih operacijskih sistemov, ogrozilo delovna mesta kontrolorjev zračnega prometa in drugih specialistov na tem področju. Kolikor vem, je bil v zvezi s tem vzpostavljen precej uspešen dolgoročen socialni dialog in menim, da je zato treba uskladiti navidez nasprotujoče si postopke. Prizadevamo si za varnejše in učinkovitejše lete; želimo, da so zamude letov minimalne in se čim bolj odpravijo nevarnosti neobičajnih dogodkov v zračnem prometu. Ogrožena so človeška življenja: življenja tistih, ki letijo, ter življenja in usode tistih, ki upravljajo zračni promet.
Kathy Sinnott
v imenu skupine IND/DEM. - Gospod predsednik, moti me predlog za pospešitev procesa vzpostavljanja odprtega neba. Zdi se, da se sploh ne priznajo težave v zvezi z odprtim nebom na regionalnih letališčih v Evropi, niti v pripravljalnem obdobju. Pri vzpostavljanju enotnega evropskega neba bosta nastali dve glavni vozlišči - zagotovo Heathrow in Frankfurt ali Charles de Gaulle - ki ju bo spremljala mreža podvozlišč.
Konkurenca med letališči, da v hierarhiji odprtega neba postanejo prvo- ali drugorazredna, se je v moji državi izkazala za smrtonosno. Letališču Shannon - vozlišče samo po sebi - in regionalnim letališčem, kot je Cork, primanjkuje poti, medtem ko je letališče Dublin kronično prenatrpano. Moja vlada stoji ob strani in ne stori ničesar, ker je princip odprtega neba ta, da se trg sam odloči, in trg, torej ne socialna odgovornost ali zdrav razum glede regionalnega in podeželskega razvoja, se odloča tako, da se povečuje dobiček, vendar to ne koristi ljudem.
Namesto da se prenaglimo glede odprtega neba, si ne glede na pozno uro vzemimo ves potreben čas za resno oceno učinka politike. Potem pa sprejmimo vse potrebne ukrepe za zagotovitev, da odprto nebo celotnih območij Evrope, kot sta zahodna in južna Irska, ne izolira od vitalne, gospodarske prihodnosti.
Reinhard Rack
(DE) Gospa predsednica, evropska prometna politika nas vse skrbi. Želimo izboljšati učinkovitost vseh vrst prevoza in zlasti zračnega prevoza, ne da bi pri tem povečali onesnaževanje okolja. Če je mogoče, bi radi izboljšali tudi okoljsko ravnotežje letenja.
S tem v zvezi smo imeli v Evropi veliko zamisli, na primer trgovanje z emisijami. Svoje cilje poskušamo doseči na primer z obdavčenjem letalskega goriva in podobno. Takšen pristop morda ni napačen, vendar je način za dosego našega cilja drugačen. Poiskati moramo pametnejše rešitve, kakor smo jih za cestni promet. Zamisel o odprtem evropskem nebu in enotnem evropskem nebu je pravilen pristop, čeprav se mora seveda izvesti. SESAR pomeni korak naprej, vendar moramo pri tem narediti več.
Naj se lotim zadnje točke, ker bomo o tej zadevi glasovali ta teden.
Preobremenjenost se ne pojavlja le na nebu, ampak tudi na tleh, zlasti na letališčih.
Zato odpravimo nesmiselne birokratske predpise o prenašanju tekočin na letališčih. S tem bomo prihranili veliko denarja in še več težav.
Ulrich Stockmann
(DE) Gospa predsednica, gospod komisar, vzpostavitev enotnega evropskega neba se nam zdi najpomembnejši projekt za prihodnost letalskega prometa. Komisija je v času vašega predhodnika vedno poudarjala njegovo pomembnost in tudi jaz sem prepričan, da je tako. Leta 2004 smo sprejeli paket pravil. Na nebu pa imamo še vedno nekakšno sestavljanko z 58 nacionalnimi bloki zračnega prostora, čeprav vemo, da v resnici potrebujemo le enega, ali, če smo radodarni, mogoče tri do šest.
Vemo, da takšna sestavljanka, številke katere so bile podane prejle, negativno vpliva na varnost in seveda tudi na gospodarstvo in potrošnike. Zavedamo se kopičenja in preobremenjenosti na nebu in dandanes dajemo veliko večji poudarek na emisije. Zdaj se zavedamo, da lahko pri tem naredimo velik korak naprej.
V svojem poročilu o napredku je Komisija ponazorila, kako počasi ukrepajo države članice kljub nekaterim pobudam, in predlagala nekaj načinov za izvajanje pritiska. S tem ne trdim, da je to nesmiselno, niti vam ne nameravam očitati, vendar smo že leta 2003 dejali, da pristop od spodaj navzgor ne bo deloval, ker smo že takrat domnevali, da se bodo države članice začele zapletati v razprave o področjih suverenosti v zvezi z zagotavljanjem storitev in da se morajo takšne ključne zadeve urejati z zakonodajnimi pravili od zgoraj navzdol.
Takrat smo menili, da bi lahko mogoče Eurocontrol predlagal pravila in podal predlog, ki bi temeljil preprosto na vsebini in funkcionalnosti, o kateri bi se lahko prepirale države članice, namesto da smo čakali, da so še same ustvarile nekakšno sestavljanko s pristopom od spodaj navzgor. Zdaj je pomembno, da resno razmislimo o ponovni preučitvi pravnega okvira. Le tako bi lahko izvedli resnični pritisk in omogočili potrebne spremembe.
Mieczysław Edmund Janowski
. - (PL) Gospa predsednica, gospod komisar, spomladi leta 2004, ko je Evropska unija sprejemala zadevno zakonodajo, je bilo govora o koristnosti, ki bi jo za civilno letalstvo imelo preoblikovanje predpisov o zračnem prometu in vojaško sodelovanje s civilnim sektorjem v zvezi s tem. Evropski sistem je bil takrat zelo razdrobljen, zaradi česar so nastali ozki koridorji zračnega prostora.
Zato se je zmanjšala varnost poletov, okrog 20 % letal je imelo zamude in porabilo se je več goriva, kar je negativno vplivalo na okolje. Ali je danes situacija kaj boljša, gospod komisar? Zakaj niso začeli delovati t. i. "funkcionalni bloki zračnega prostora"? Ali so za to krive le države članice? Ali mogoče naši zakoni niso v skladu z dejanskimi potrebami? Dobro bi bilo, če bi se takoj odzvali na ta vprašanja in izvedli popravne ukrepe zdaj, ne šele konec leta 2008.
Širitev zračnega prometa je izjemna. Zato so potrebni ustrezni pravni predpisi, ki pa ne smejo ostati le prazne besede. Potrebno je tudi ustrezno usposabljanje osebja. Za konec, gospod komisar, kako vidite to vprašanje v povezavi s sosedami EU?
Saïd El Khadraoui
(NL) Gospa predsednica, gospod komisar, gospe in gospodje, strinjam se s tem, kar so dejali drugi govorniki in dodajam, da se mora enotno evropsko nebo vzpostaviti čim prej. Jasno je, da mehki pristop uredbe 551/2004, ki naj bi države članice spodbudil k optimalni uporabi teh bolj funkcionalnih blokov zračnega prostora, ne deluje. Razlog za to je predvsem zadržanost veliko držav članic, ki ne želijo biti vpletene, poudarjajo svojo suverenost itd., vendar jim tega ne smemo dopustiti. Letalstvo je sektor, ki se mora na evropski ravni obravnavati zelo natančno in v interesu te industrije, uporabnikov, varnosti in okolja V času, ko so podnebne spremembe tako visoko na političnem dnevnem redu, gospod komisar, ne moremo dopuščati, da imajo letala nepotrebne obvoze, porabljajo ogromne količine goriva in tako naprej.
Preprosto nujno je, da to zadevo, skupaj z drugimi instrumenti, kot so SESAR, sistem za trgovanje z emisijami in podobno, pospešimo. Ne moremo še naprej dovoliti, da se zaradi neučinkovitega upravljanja našega zračnega prostora s celo vrsto nepotrebnih centrov kontrole zračnega prometa trošijo milijoni evrov. Tukaj se lahko postopki precej skrajšajo in to tudi želimo. Poleg tega bomo verjetno bomo kmalu dosegli meje zmogljivosti, ker se ta sektor hitro širi. Trenutni dvostranski odnosi za oblikovanje funkcionalnih blokov zračnega prostora niso dosegli skoraj ničesar, zato moramo resnično nekaj začeti ukrepati. Imenovanje koordinatorja in organa za pregled učinkovitosti se zdi primerno, vendar se obenem bojim, gospod komisar, da ta pristop od spodaj navzgor ne bo dovolj, izpopolnili smo ga po svojih najboljših močeh, zdaj pa si moramo prizadevati za nove zakonodajne pobude.
Silvia-Adriana Ţicău
(RO) Gospa predsednica, leta 2006 so podjetja z nizkimi stroški odprla 255 novih evropskih zračnih poti, kar pomeni 1 800 dodatnih poletov na teden. Razdrobitev zračnega prostora na nacionalni ravni s posebnimi operativnimi pravili in postopki lahko negativno vpliva na varnost prometne zmogljivosti, uvedbo novih tehnologij in stroške.
Ko potujejo iz enega zračnega sektorja v drugega, piloti spreminjajo frekvenco in vzpostavijo stik z naslednjim kontrolorjem zračnega prometa. Kontrola zračnega prometa je postal bistven element. Pred uvedbo novih funkcionalnih blokov je pomembno posvetovanje z vsemi zadevnimi strankami in učinkovito ukrepanje držav članic, da dosežejo integriran sistem upravljanja.
Medtem se mora vlagati v učinkovitejša letala in letališko infrastrukturo. Pristop Romunije in Bolgarije k EU pomeni dodatne funkcionalne bloke v zračnem prostoru Skupnosti, ki so pomembni zaradi črnomorske regije in sodelovanja na Balkanu.
Jacques Barrot
podpredsednik Komisije. - (FR) Gospa predsednica, podpiram neučakanost Parlamenta, ki jo tudi sam občutim. Dal vam bom zelo natančen, a zelo kratek odgovor. Gospe in gospodje, oktobra 2007 bo pripravljeno poročilo in do sredine leta 2008 drugi zakonodajni paket, zato resnično ne morete reči, da ničesar ne delamo. Na to vprašanje bomo torej skupaj natančno odgovorili.
Drugič: Verjetno sem že navajal koordinatorja, višjo politično osebnost, ki bo spodbujala uvedbo teh operacijskih blokov med državami članicami. Menim, da dosežki vseevropskih omrežij kažejo, da bi to lahko bil uporaben način za povečanje našega ukrepanja na tem področju.
V odgovoru na tretje vprašanje navajam sistem SESAR, ker ta sistem obstaja in je že skupno podjetje, ki združuje vse udeležence. Prepričan sem, da bomo z uvedbo SESAR spremenili vse svoje slabe navade, zaradi katerih smo vztrajali pri zračnih prostorih z nacionalnimi mejami, kar nima več smisla. Zato je moj odgovor na vprašanje, ki ga je zastavil gospod Costa in o katerem je razpravljal gospod Savary, zelo pozitiven, in pozorno sem poslušal, kaj želi Parlament. Pripravljen sem se odzvati po najboljših močeh.
Predsednica
Razprava je zdaj končana.
Pisna izjava (člen 142)
Zuzana Roithová
v pisni obliki. - (CS) Države članice so se strinjale z vzpostavitvijo skupnih blokov zračnega prostora za nadzor enotnega neba, ne glede na nacionalne meje. Pred tem sta se nad Nemčijo zaleteli dve letali in umrlo je 71 ljudi. Argumenti za enotno nebo so vse močnejši: za 28 000 dnevnih poletov imamo 57 kontrolnih točk, medtem ko imajo ZN le dve. Po treh letih nismo nič napredovali. EU še ni začela uporabljati vseh uredb iz leta 2004. Te uredbe naj bi integrirale zračni prostor v notranji trg storitev in omogočile osnovo za učinkovit operacijski sistem s poudarkom na varnosti, okolju in večji letalski zmogljivosti. Trenutno imamo 65 radarskih centrov z 31 sistemi, ki uporabljajo 22 računalniških omrežij, in pričakujemo, da se bo število letov v območju Evrope v desetih letih podvojilo.
Ali se državljani zavedajo, da njihove vlade in parlamenti v njihovo škodo ne upoštevajo koristi skupne Evrope? Zakaj proces vzpostavljanja skupnega zračnega prostora za civilne in vojaške polete nad združeno Evropo traja tako dolgo? Ali je to zaradi zadovoljevanja lokalnih gospodarskih interesov? Ali pa gre za zaščito nacionalne suverenosti na račun prometne varnosti in visokih cen? Danes želimo izvedeti, kako in kdaj bomo integrirali razvrščanje zgornjega zračnega prostora ter kako bomo skupaj upravljali spodnji zračni prostor v prihodnosti. Ali se lahko odkrito določijo ovire za vzpostavitev funkcionalnih blokov nad evropskim ozemljem? Ali je mogoče osvetliti politično voljo držav članic, da izpolnijo svoje obveznosti? Prav tako nas skrbi, da pristop od spodaj navzgor ne bo uspel, ker v treh letih države članice niso razvile funkcionalnih blokov, ki so potrebni za učinkovitejši nadzor neba.
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{
"pile_set_name": "EuroParl"
}
|
"I don't think we need the extra drive or motivation," Ferdinand explained at the pre-match press conference. "We were all disappointed with what happened last season and how we went out. But we won't harp on about it. We continue and start again afresh this season. New group, new season, new games. Last season is out of our minds and not something we need to use as motivation.
The Germans did well last year, the Spanish sides before that. It goes in cycles and hopefully we can start the cycle this season."
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{
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By -
LAHORE, Pakistan (Morning Star News) – A Christian with a mental disability in Pakistan has been arrested under the country’s blasphemy law after a Muslim neighbor outside his home overheard him arguing inside, sources said.
Francis Masih, older brother of 42-year-old Stephen Masih, said that Muslim neighbor Hafiz Mudassir on March 11 burst into their home in Imranpura, Wadiala, Sialkot District, beat the younger brother and accused him of speaking ill of the prophet of Islam after overhearing an argument.
At about 7 a.m. Stephen Masih, who belongs to a Pentecostal church, had become embroiled in a heated discussion with a Christian brother-in-law over fasting and praying during Lent when he lost his temper and started shouting loudly, Francis Masih said.
“This is when Mudassir barged into our house and started beating Stephen without any reason,” he told Morning Star News. “We told Mudassir that it was not right for him to intervene in our family issue, but he took offense and raised hue and cry in the street, alleging that Stephen had committed blasphemy.”
Soon a mob gathered outside their house, he said.
“Mudassir and Mohammad Rafiq, another neighbor, provoked them to attack Stephen,” Masih said. “They not only beat him up mercilessly but also attacked other family members who tried to save him.”
Someone called police, and they rescued Stephen Masih from the violent mob, he said.
“The police took my brother away, and it was after some time that we learned that he had been charged with blasphemy,” Masih said, adding that the family has not seen him since his arrest or heard about his condition. “We have been running from pillar to post, as we are very worried about his condition, especially since he was ruthlessly beaten up by the mob, but the police are not arranging our meeting. They keep telling us that he is safe and being taken care of.”
Their mother has not eaten enough or slept well since the arrest, he said.
“The police should show some mercy for the sake of my mother’s health and allow us a meeting,” Masih added.
Mudassir alleged in the First Information Report (FIR) registered at Badiana Police that he was standing outside his house when he heard Stephen Masih shouting derogatory words about Muhammad.
“I and another neighbor, Mohammad Rafiq, repeatedly asked Stephen to refrain from uttering blasphemous remarks, but he did not pay heed to our requests,” Mudassir said in the FIR. “This blasphemous act has caused immense agony to Muslims of the neighborhood, therefore Stephen should be punished as per the law.”
The FIR was registered under Section 295-C of Pakistan’s blasphemy law, which calls for the death penalty for defaming Muhammad.
The sub-inspector who registered the case, Mohammad Ashraf, told Morning Star News that police have yet to determine whether the accused’s mental capacity will be a factor.
“We are investigating the matter, but I cannot yet comment on the family’s claim that Stephen is mentally disabled,” he said. “It is up to the judge to decide once we present him in court.”
Condition Unknown
Francis Masih said his brother has been mentally disabled since birth, but that his condition worsened after the death of their father a little over 17 years ago.
“The entire locality knows about Stephen’s mental health status,” his brother said, adding that area residents used to tease him, provoking him into quarrels.
A doctor had advised them to admit him to a mental health facility, but their mother was unwilling to send him away, Masih said.
“And now we don’t even know where he is being kept and in what condition,” he said.
Lahore High Court attorney Sardar Mohammad Akhtar told Morning Star News that Section 84 of the Pakistan Penal Code states, “Nothing is an offense which is done by a person who, at the time of doing it, by reason of unsoundness of mind, is incapable of knowing the nature of the act, or that he is doing what is either wrong or contrary to law.”
Intent must be demonstrated for a blasphemy conviction.
Pakistan’s blasphemy laws have long polarized public opinion, with intense emotions leading to assassinations of senior politicians and judges who have advocated for repeal. Critics within Pakistan and in the international community point to the malicious use of the laws to harm minorities, while advocates say the self-proclaimed Islamic nature of the Pakistani state mandates such laws to justify its existence.
Although the U.S. Commission on International Religious Freedom (USCIRF) has long recommended Pakistan be designated as a Country of Particular Concern (CPC), the U.S. State Department had never done so until last November. On Nov. 28, the United States added Pakistan to its blacklist of countries that violate religious freedom, the government announced on Dec. 11.
Pakistan ranked fifth on Christian support organization Open Doors 2019 World Watch list of the 50 countries where it is most difficult to be a Christian.
If you would like to help persecuted Christians, visit https://morningstarnews.org/resources/aid-agencies/ for a list of organizations that can orient you on how to get involved.
If you or your organization would like to help enable Morning Star News to continue raising awareness of persecuted Christians worldwide with original-content reporting, please consider collaborating at https://morningstarnews.org/donate/?
###
© 2019 Morning Star News. Articles/photos may be reprinted with credit to Morning Star News.
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George Zimmerman Had Another Gun Incident
Not-guilty Trayvon Martin shooter George Zimmerman was taken into police custody after “an incident involving a gun” and another person, Click Orlando reports. Details are scarce so far, but “Lake Mary police say they were called to a house on Sprucewood Road Monday afternoon after a report that Zimmerman was involved in an altercation with another person with a threat involved.” The APreports that Zimmerman’s wife Shellie called the cops, claiming he threatened her and her father with a gun. She filed for divorce lastweek.
It’s been a hectic few months for the acquitted killer. After Shellie decided to get out, she cited George’s “reckless decisions” since the trial, which she said has him feeling “invincible,” in a nationally televised interview. George has been pulled over (twice!) for speeding, and he stopped by the gun manufacturer that made the weapon he used to kill Martin to pose for pictures. The pattern seems to beintensifying.
His lawyer Mark O’Mara, meanwhile, has signed on as a legal analyst at CNN. O’Mara may have more work to doyet.
Zimmerman’s brother Robert has already responded to the reports on Twitter, complete with an allusion to the Martincase:
[George is] trying to shut the garage door on me. He’s in his car, and he continually has his hand on his gun, and he keeps saying ‘Step closer.’ He’s just threatening all of us with his firearm. He’s gonna shootus.
He punched my dad in his nose … He accosted my father and then took my iPad out of my hands and smashed it and cut it with a pocketknife. There’s a Lake Mary city worker across the street that I believe saw almost all ofit.
He just showed up here, but my phone died, so I had to call you from my father’s phone. I’m really really afraid I don’t know what he’s capable of. I’m reallyscared.
The police are here. He’s in his truck. There are police here with their weaponsdrawn.
Operator: Does he seethem?
They’re telling his bodyguard to get out of the way. Dad, get behind the car. I don’t know if he’s going to start shooting at us ornot.
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{
"pile_set_name": "Pile-CC"
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|
<!DOCTYPE html>
<html lang="en">
<head>
<title>SpringBoot - validator</title>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
</head>
<body>
<p>当前时间：${.now?string("yyyy-MM-dd HH:mm:ss.sss")}</p>
<div class="body">
<form action="/saveUser" method="post">
<table>
<tbody>
<tr>
<td>姓名</td>
<td><input type="text" name="username" value="${user.username?if_exists}"></td>
</tr>
<tr>
<td>性别</td>
<td><input type="text" name="gender" value="${user.gender?if_exists}"></td>
</tr>
<tr>
<td>年龄</td>
<td><input type="text" name="age" value="${user.age?if_exists}"></td>
</tr>
<tr>
<td>生日</td>
<td><input type="text" name="birthday" value="${user.birthday?if_exists}"></td>
</tr>
<tr>
<td>邮箱</td>
<td><input type="text" name="email" value="${user.email?if_exists}"></td>
</tr>
<tr>
<td>网址</td>
<td><input type="text" name="url" value="${user.url?if_exists}"></td>
</tr>
<tr>
<td>身份证</td>
<td><input type="text" name="idcard" value="${other.idcard?if_exists}"></td>
</tr>
<tr>
<td>手机</td>
<td><input type="text" name="phone" value="${other.phone?if_exists}"></td>
</tr>
<tr>
<td colspan="2"><input type="submit" value="提交"></td>
</tr>
</tbody>
</table>
</form>
<div style="background-color: #F1F1F1;width: 80%;height: 200px">
user: ${user?if_exists}
<br>
other: ${other?if_exists}
<br>
<#if errorList?exists>
<ul>
<#list errorList as error>
<li>${error.field}-${error.message}</li>
</#list>
</ul>
</#if>
</div>
</div>
</body>
</html>
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{
"pile_set_name": "Github"
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|
Without failure, we can’t learn and progress. Plus, we wouldn’t be able to watch hilarious footage like this, so celebrate your failures proudly (just don’t forget to send us the footage :-).
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{
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|
Frank Lobman
Frank "The Animal" Lobman (born November 18, 1955) is a Surinamese-Dutch former kickboxer. He was five times the European kickboxing champion and had an astonishing 90% knockout ratio. He beat many notable fighters over his career, such as British Champion Steve Taberner (The Wigan Hammer), Bas Rutten and Ken Shamrock and fought in organizations such as Pancrase P.K.A. and K-1.
Biography
Frank was a prominent kickboxer in 1980s to the early 1990s. He trained often in rotterdam-crooswijk at schuttersveld where his Brother Hedwig Lobman taught Kyokushin karate. Several kickboxing matches were given in the early eighties with Lucien Carbin. In 1991 he beat Bas Rutten for a European kickboxing title. He announced his retirement fight in 2002 at the age 49. His last fight was a 20-year rematch with Jan Oosterbaan in Ahoy-2H2H, but he lost the fight due to a decision.
Frank was undefeated until his first fight with Peter Aerts.
Titles
5 time European Kick Boxing champion
I.K.B.F. European Heavyweight champion
E.M.T.A. European Heavyweight champion
Dutch Heavyweight champion
Kickboxing record
External links
mixed martial arts record
kickboxing achievements
pancrase profile
Aerts on Lobman
Category:1955 births
Category:Living people
Category:Dutch male kickboxers
Category:Surinamese male kickboxers
Category:Heavyweight kickboxers
Category:Dutch Muay Thai practitioners
Category:Surinamese Muay Thai practitioners
Category:Surinamese emigrants to the Netherlands
Category:Sportspeople from Rotterdam
Category:Sportspeople from Paramaribo
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{
"pile_set_name": "Wikipedia (en)"
}
|
Q:
Searching not exists in Neo4j via Cypher
I have some relations between persons in my graph.
my data (generate script below)
create (s:Person {name: "SUE"})
create(d:Person {name: "DAVID"})
create(j:Person {name: "JACK"})
create(m:Person {name: "MARY"})
create(js:Person {name: "JASON"})
create(b:Person {name: "BOB"})
create(a1:Adress {id:1})
create(a2:Adress {id:2})
create(a3:Adress {id:3})
create(a4:Adress {id:4})
create(a5:Adress {id:5})
merge (d)-[:MOTHER]->(s)
merge(j)-[:MOTHER]->(s)
merge(js)-[:MOTHER]->(m)
merge(b)-[:MOTHER]->(m)
merge(b)-[:CURRENT_ADRESS]->(a1)
merge(js)-[:CURRENT_ADRESS]->(a2)
merge(j)-[:CURRENT_ADRESS]->(a3)
merge(s)-[:CURRENT_ADRESS]->(a4)
merge(d)-[:CURRENT_ADRESS]->(a5)
;
I can get mothers who live with her child:
MATCH (p:Person)-[:CURRENT_ADRESS]->(a:Adress)<-[:CURRENT_ADRESS]-(t), (t)-[:MOTHER]->(p)
return p.name,t.name
p.name t.name
MARY JASON
but i want to get mothers who is not living with any child of her.
How can i do that in Cyper?
A:
Actually in your graph, everybody is living at a different address due to different identifiers.
Let's build a graph example introducing the sister which lives at the same address :
CREATE
(p:Person)-[:MOTHER]->(m:Person),
(p)-[:FATHER]->(f:Person),
(p)-[:SISTER]->(s:Person),
(p)-[:CURRENT_ADDRESS]->(a:Adress),
(m)-[:CURRENT_ADDRESS]->(b:Adress),
(f)-[:CURRENT_ADDRESS]->(c:Adress),
(s)-[:CURRENT_ADDRESS]->(a)
Now this is very simple, match family members that don't have a CURRENT_ADDRESS relationship in depth2 to the family member :
MATCH (p:Person)-[:MOTHER|:FATHER|:SISTER]->(familyMember)
WHERE NOT EXISTS((p)-[:CURRENT_ADDRESS*2]-(familyMember))
RETURN familyMember
|
{
"pile_set_name": "StackExchange"
}
|
Jonathan Swift’s satire Gulliver’s Travels, published in 1726, still has much to tell us about the way we live now and how politics is conduced across Europe. One image from the book, of the small, vain Lilliputians tying down Gulliver, resonates with recent comments from ministers in larger European countries on the rise of the “Hanseatic League 2.0”, an alignment of finance ministers from Ireland, the Netherlands and the Baltic and Nordic states. The name comes from the federation of towns and merchant guilds that exercised considerable economic power in northwestern Europe in the late middle ages.
Perhaps, unlike the Lilliputians, there are reasons for the European Commission and the larger European countries to take the Hanseatic countries, and their message, seriously. Indeed, in a bad year for politics and economics in Europe, the emergence of the Hanseatic countries is a new, positive development.
The first reason to focus on them is that they reflect the changing shape of the European Union. For some of the smaller European states – Ireland and the Netherlands, for example, the UK was a policy and political ally around which they could coalesce. Like the Hanseatics, Britain preferred a more liberal, decentralised conception of the EU and now Brexit means that small states need to club together in order to have a voice. Further, a consequence of EU enlargement has meant that older members of the EU such as Denmark have felt that their influence has been diluted. Grouping together with like-minded small states, many of whom share the same economic problems and viewpoints, helps to enhance their power.
Stress testing
A second reason is that the near-perpetual stress testing of Europe’s states through the euro-zone crisis has altered its political economy in that the need for high growth and stable state finances has been internalised in many small state capitals, though much less so, it seems, in larger countries. The Hanseatic view of the euro zone is that it should never again allow itself to be encumbered by debt, that focusing on economic growth is the best way to avoid another euro-zone crisis and to solve the underlying problems that provoke Europeans to opt for increasingly radical solutions at the ballot box.
Small states have some form here. The Nordic countries, Ireland and the Netherlands, together with the likes of Switzerland, Singapore and New Zealand, top the lists of most globalised, most innovative (Bloomberg Innovation Index), rule of law (World Bank) and democratic quality (Economist Intelligence Unit) league tables. They have a common emphasis on quality of life, and in crises have shown a singular ability to tackle big problems (for example, Sweden repairing its banking system, Ireland fixing its unemployment crisis and Denmark leading the world in renewable energy). This is indicative of the fact that small, advanced states, most of whom are European, have a ‘secret sauce’ when it comes to promoting economic growth and social stability. Other small states in, say, Eastern Europe can learn from this, but the larger countries should also take heed.
One example is Italy. In the past four months the exchanges between the European Commission and Italy on its budget deficit has been marked by the absence of a determined, detailed debate on a set of economic policies that could transform Italy’s trend rate of growth. Instead, the tone from Rome has sounded opportunistic while that from Brussels has been punitive. Fiscal policy as dictated from Brussels sounds a little too much like another Swift book, A Modest Proposal.
Italy’s growth rate
The Hanseatic League 2.0 countries have already issued a number of policy papers. A provocative one would be for them, in a constructive way, to present Italy with a set of suggestions on how to increase its growth rate, based on their experience. The education sector is an obvious example. Italy has a couple of universities in the top 200 in the world (Times Higher Education rakings) while the four Nordic countries have 13.
There is a third dynamic at work, which makes the perspective of the Hanseatic nations worthwhile. The marked geopolitical trend of the past year has been the growing schism between the United States and China and the way in which this is forcing the transition from a globalised to a multipolar world. The US and China are so far the dominant poles here.
This reality is leading to a slow change in mindset in Europe, such that it must less debate the merits of the Italian versus the French view of the world, but rather how Europe looks compared with both the US and China. Talk of a European army is part of this. While the Hanseatic League 2.0 countries do not have a manifesto, the kinds of things they value – economic openness, innovation and human development – are the factors that can empower the EU to hold its own relative to the US and China into 2019.
Michael O’Sullivan is the chief investment officer in the wealth management division at Credit Suisse and author of Ireland and the Global Question. David Skilling is director of Landfall Strategy
|
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"pile_set_name": "OpenWebText2"
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|
Yeah, maybe don’t go to the ground with Mackenzie Dern if you can help it.
The top women’s MMA prospect and Brazilian jiu-jitsu world champion twisted opponent Montana Stewart up in a nasty position Friday night and finished with a submission at 3:25 of the first round at Legacy FC 61 in Dallas. Dern tied up Stewart’s arm with an omoplata and then locked in a rear-naked choke simultaneously. Very high level stuff from her.
“I don’t know if she [tapped to] the shoulder or the choke, but I hope both were uncomfortable,” Dern told cageside reporter Ron Kruck afterward.
Dern (2-0) stayed standing a decent amount in the first round against Stewart, even landing some punches and two good knees to the mid-section. Stewart landed a couple of nice punches as well. But when it went to the ground, it was all Dern, of course. She’s the best female jiu-jitsu player in the world right now.
Dern, 23, didn’t have as much success with submissions in her pro debut back in July, beating Kenia Rosas by unanimous decision. She dominated that fight, but could not get the tap. The MMA Lab product made up for it here.
Afterward, Dern said she would like to fight again Dec. 2. She’s targeting a fast track to the UFC — as early as 2017 —but did miss weight 2.3 pounds Thursday. That’s something the very busy BJJ, and now MMA, star has to clean up in the future.
If Friday was any indication, that might be more difficult than the actual fight.
|
{
"pile_set_name": "Pile-CC"
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|
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