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https://learnzillion.com/lesson_plans/4654-multiply-fractions-by-whole-numbers-using-models	# Multiply fractions by whole numbers: using models teaches Common Core State Standards 111.7.3.I http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html teaches Common Core State Standards 111.26.3.E http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html teaches Common Core State Standards 111.27.3.B http://ritter.tea.state.tx.us/rules/tac/chapter111/index.html teaches Common Core State Standards CCSS.Math.Content.4.NF.B.4c http://corestandards.org/Math/Content/4/NF/B/4/c ## You have saved this lesson! Here's where you can access your saved items. Dismiss Card of In this lesson you will learn how to multiply fractions by whole numbers by using visual models. Related content	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9931216239929199, "perplexity": 22403.847113704698}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189242.54/warc/CC-MAIN-20170322212949-00625-ip-10-233-31-227.ec2.internal.warc.gz"}
https://www.atmos-chem-phys.net/18/11389/2018/	Journal cover Journal topic Atmospheric Chemistry and Physics An interactive open-access journal of the European Geosciences Union Journal topic Atmos. Chem. Phys., 18, 11389–11407, 2018 https://doi.org/10.5194/acp-18-11389-2018 Atmos. Chem. Phys., 18, 11389–11407, 2018 https://doi.org/10.5194/acp-18-11389-2018 Research article 14 Aug 2018 Research article \| 14 Aug 2018 # Spatial and seasonal variations of aerosols over China from two decades of multi-satellite observations – Part 1: ATSR (1995–2011) and MODIS C6.1 (2000–2017) Spatial and seasonal variations of aerosols over China from two decades of multi-satellite... Larisa Sogacheva1, Gerrit de Leeuw1, Edith Rodriguez1, Pekka Kolmonen1, Aristeidis K. Georgoulias2, Georgia Alexandri2, Konstantinos Kourtidis2, Emmanouil Proestakis3,4, Eleni Marinou5, Vassilis Amiridis3, Yong Xue6, and Ronald J. van der A7 Larisa Sogacheva et al. • 1Finnish Meteorological Institute (FMI), Climate Research Programme, Helsinki, Finland • 2Laboratory of Atmospheric Pollution and Pollution Control Engineering of Atmospheric Pollutants, Department of Environmental Engineering, Democritus University of Thrace, Xanthi, Greece • 3National Observatory Athens (NOA), Greece • 4Laboratory of Atmospheric Physics, Department of Physics, University of Patras, 26500, Greece • 5Deutsches Zentrum für Luft und Raumfahrt (DLR), Institut für Physik der Atmosphäre, Oberpfaffenhofen, Germany • 6Department of Electronics, Computing and Mathematics, College of Engineering and Technology, University of Derby, Derby DE22 1GB, UK • 7Royal Netherlands Meteorological Institute (KNMI), De Bilt, the Netherlands Correspondence: Larisa Sogacheva (larisa.sogacheva@fmi.fi) Abstract Aerosol optical depth (AOD) patterns and interannual and seasonal variations over China are discussed based on the AOD retrieved from the Along-Track Scanning Radiometer (ATSR-2, 1995–2002), the Advanced ATSR (AATSR, 2002–2012) (together ATSR) and the MODerate resolution Imaging Spectroradiometer (MODIS) aboard the Terra satellite (2000–2017). The AOD products used were the ATSR Dual View (ADV) v2.31 AOD and the MODIS/Terra Collection 6.1 (C6.1) merged dark target (DT) and deep blue (DB) AOD product. Together these datasets provide an AOD time series for 23 years, from 1995 to 2017. The difference between the AOD values retrieved from ATSR-2 and AATSR is small, as shown by pixel-by-pixel and monthly aggregate comparisons as well as validation results. This allows for the combination of the ATSR-2 and AATSR AOD time series into one dataset without offset correction. ADV and MODIS AOD validation results show similar high correlations with the Aerosol Robotic Network (AERONET) AOD (0.88 and 0.92, respectively), while the corresponding bias is positive for MODIS (0.06) and negative for ADV (−0.07). Validation of the AOD products in similar conditions, when ATSR and MODIS/Terra overpasses are within 90 min of each other and when both ADV and MODIS retrieve AOD around AERONET locations, show that ADV performs better than MODIS in autumn, while MODIS performs slightly better in spring and summer. In winter, both ADV and MODIS underestimate the AERONET AOD. Similar AOD patterns are observed by ADV and MODIS in annual and seasonal aggregates as well as in time series. ADV–MODIS difference maps show that MODIS AOD is generally higher than that from ADV. Both ADV and MODIS show similar seasonal AOD behavior. The AOD maxima shift from spring in the south to summer along the eastern coast further north. The agreement between sensors regarding year-to-year AOD changes is quite good. During the period from 1995 to 2006 AOD increased in the southeast (SE) of China. Between 2006 and 2011 AOD did not change much, showing minor minima in 2008–2009. From 2011 onward AOD decreased in the SE of China. Similar patterns exist in year-to-year ADV and MODIS annual AOD tendencies in the overlapping period. However, regional differences between the ATSR and MODIS AODs are quite large. The consistency between ATSR and MODIS with regards to the AOD tendencies in the overlapping period is rather strong in summer, autumn and overall for the yearly average; however, in winter and spring, when there is a difference in coverage between the two instruments, the agreement between ATSR and MODIS is lower. AOD tendencies in China during the 1995–2017 period will be discussed in more detail in Part 2 (a following paper: Sogacheva et al., 2018), where a method to combine AOD time series from ADV and MODIS is introduced, and combined AOD time series are analyzed. 1 Introduction The concentrations of aerosols in China have been relatively high over the last two decades (e.g., Wang et al., 2017; Zhang et al., 2017), and are rising as a consequence of economic development, industrialization, urbanization and the associated transport and traffic. Examples of other factors affecting interannual and seasonal variations of the aerosol optical depth (AOD) over China are the generation and transport of desert dust (e.g., Proestakis et al., 2018; Wang et al., 2008), seasonal biomass burning (e.g., Chen et al., 2017a) and meteorological conditions and large-scale circulation (Zhu et al., 2012). Both the direct production of aerosol particles and the emission of aerosol precursor gases, such as SO2, NO2 and volatile organic compounds (VOCs), contribute to the observed aerosol concentrations, which manifest themselves as particulate matter (PM) or AOD (Bouarar et al., 2017). PM2.5, the dry mass of aerosol particles with an ambient diameter smaller than 2.5 µm, is often used in air quality and health studies as a measure for aerosol concentrations. PM2.5 is a local quantity that is usually measured near the surface. In contrast, AOD is the column-integrated extinction coefficient, which is an optical property commonly used in climate studies; AOD can be measured from satellites or ground-based remote sensing. PM2.5 and AOD, although both used as a measure for the occurrence of aerosols, are very different aerosol properties which cannot be directly compared. Spatial variation, seasonal variability and time series have been observed from the analysis of ground-based networks measuring aerosol optical properties using sun photometers in, e.g., the Aerosol Robotic Network (AERONET, Holben et al., 1998), the China Aerosol Remote Sensing Network (CARSNET, Che et al., 2015), the Campaign on Atmospheric Aerosol Research network of China (CARE-China, Xin et al., 2015) and the Sun-sky radiometer Observation NETwork (SONET, Li et al., 2018) or hand-held sun photometers in the Chinese Sun Hazemeter (CSHNET, Wang et al., 2011) networks. These networks provide point measurements, which are representative for a limited area, and the coverage across China still leaves large gaps. Satellite observations, although less accurate, fill these gaps and provide a clear picture of spatial and temporal variations across the whole country. In de Leeuw et al. (2018), it was shown how the complementary use of three satellite-based radiometers, the Along-Track Scanning Radiometer ATSR-2 on ERS-2, the Advanced ATSR (AATSR) aboard the environmental satellite Envisat, and the MODerate resolution Imaging Spectroradiometer (MODIS) on Terra, results in two decades (1995–2015) of AOD observations over mainland China. This information was complemented with observations on the aerosol vertical structure from the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) between January 2007 and December 2015. The satellite data show the high aerosol concentrations over distinct regions in China such as the North China Plain (NCP) including the Beijing–Tianjin–Hebei (BTH) area, the Yangtze River Delta (YRD), the Pearl River Delta (PRD) and Sichuan Province/Chongqing, as well as the enhanced AOD over the Taklamakan Desert (TD). The two-decadal time series show the initial rise of the aerosol burden over China at the end of the 1990s, which was followed by AOD variations in response to policy measures to improve air quality via the reduction of emissions of both aerosol particles and their precursor gases such as SO2 and NO2 (e.g., van der A et al., 2017). After 2011, the AOD appears to decrease toward the end of the study period used in de Leeuw et al. (2018), i.e., the end of 2015. These observed temporal variations of the AOD have also been reported elsewhere, including recent analyses indicating a decline since about 2011 (Zhang et al., 2017; Zhao et al., 2017) with some variation in the reported pivot point. The question of whether the recent decrease in AOD is confirmed by an extension of the time series with the most recent data is addressed in the current paper and studied in more detail in Sogacheva et al. (2018) – hereafter referred as Part 2. Most of the aerosol studies over China are focused on the southeastern (SE) part of the country or on specific regions or cities in SE China. However, the economic situation and governmental policy measures to improve air quality by emission reduction obviously influence the temporal variations of the AOD in each province. This is due to the fact that differences in the emissions between provinces also occur due to the differences in regional policies on emission control and their implementation schedule (Jin et al., 2016; van der A et al., 2017). In addition, both meteorological conditions and large-scale circulation will vary from year to year and between different parts of China during each year. As a result, the aerosol properties and their spatial and temporal variations are expected to be different across China. As an illustration, Fig. 1 shows the AOD time series retrieved using the ATSR Dual View aerosol retrieval algorithm (ADV) version 2.31 (Kolmonen et al., 2016; Sogacheva et al., 2017), for the years 1995–2011, for two areas. One area covers mainland China, the other one only SE China (see Sect. 2 and Fig. 2 for specification of these regions). Clearly, the AOD over SE China is substantially higher than over mainland China, but the AOD also increases much faster over SE China. In addition, the interannual variations are quite similar, with minima and maxima occurring in the same years but with larger amplitudes over SE China. Figure 1Time series of ATSR-retrieved AOD at 550 nm over China for the years 1995–2011. Note that data are missing at the beginning of the ATSR-2 observation period in 1995 and 1996, and AATSR data start from August 2002. In this paper, the work presented in de Leeuw et al. (2018) is extended to obtain information on the occurrence of aerosols and their spatial and temporal variation over China with a focus on regional differences in annual and seasonal AOD behavior. In addition, the study period is extended by including 2016 and 2017 and the most recent update of the MODIS AOD data set, Collection 6.1 (C6.1), is used instead of C6. The C6.1 AOD validation results, the C6.1 vs. C6 comparison, the differences between the ADV and MODIS C6.1 seasonal AOD aggregates and the differences in AOD tendencies during the overlapping period (2000–2011) are discussed. The results from the ADV and MODIS AOD comparison will be utilized in Part 2 to construct a combined long-term AOD time series from ADV and MODIS for the period from 1995 to 2017. AOD tendencies over the selected regions will be estimated in Part 2 for the different periods characterized by changes in air pollution control policies in China (Jin et al., 2016; van der A et al., 2017). The structure of this paper is as follows. In Sect. 2, the study area, including the selection of the 10 regions, is described. In Sect. 3, satellite data are introduced, with a focus on the data coverage (Sect. 3.2), consistency between ATSR-2 and AATSR AOD (Sect. 3.3) and MODIS C6.1 and C6 AOD differences over China (Sect. 3.4). ATSR and MODIS validation results are discussed in Sect. 4. Section 5 focuses on the seasonal AOD variations and their differences for the selected regions across China. In Sect. 6, the main results are summarized as conclusions. 2 Study area and selection of different regions The study area, China, encompasses the same area as in de Leeuw et al. (2018), i.e., the area between 18–54 N and 73–135 E defined as $\mathrm{1}{}^{\circ }×\mathrm{1}{}^{\circ }$ grid cells with retrievals over land and constrained by the borders indicated by the black line in Fig. 2. The spatial variations of the AOD (Fig. 2) combined with geographical knowledge (cf. de Leeuw et al., 2018) and general knowledge of the locations of highly populated and industrialized urban centers in China was used to select regions with different characteristics for a more detailed study on the long-term variation of the seasonal and annual AOD. The results are expected to show differences in the AOD across China due to different climate conditions and differences in economic development. Such considerations resulted in the selection of 10 study areas as shown in Fig. 2: seven study areas (regions 1–7) in SE China (defined in this study as the over-land area between 20–41 N and 103–135 E), one covering the Tibetan Plateau (region 8), one over the Taklamakan Desert (region 9) and one over northeastern (NE) China (region 10). It is noted that all areas used in this study only consider the AOD over mainland China, i.e., AOD over the oceans or islands is not included. Figure 2Regions over mainland China selected for further study of seasonal, interannual and long-term behavior of the AOD, overlaid on the ATSR-retrieved (ADV version 2.31) 12-year aggregated AOD map. Mainland China is indicated by the black line. Figure shows the 10 selected regions over China and a larger area over SE China indicated by SE. Obviously, other choices are possible, such as those made by Luo et al. (2014) or Wang et al. (2017). The regions selected by Luo et al. (2014) are generally somewhat smaller than those in Fig. 2, although some were in slightly different regions to those in this study. However, overall the choices are similar and seem to cover major urban/industrial regions such as BTH, the YRD and the PRD, Sichuan/Chongqing and cleaner regions in the north (region 10 in Fig. 2) and southeast (region 3). Regions were also chosen to represent the Tibetan Plateau and Taklamakan Desert. Wang et al. (2017) selected seven regions in North China (north of 32 N), some of which partly overlap with the regions selected for the current study. Other studies on the seasonal variation over China were guided by the location of observational sites (e.g., Wang et al., 2011; Che et al., 2015; Wang et al., 2015). Another option may be to select regions by province (e.g., van der A et al., 2017); however, some provinces would cover a mix of high and low AOD regions, while other provinces would be too small for a statistically meaningful data set. 3 Satellite data ## 3.1 MODIS C6.1 DTDB and ATSR ADV version 2.31 The data used in this work were discussed in detail in de Leeuw et al. (2018). However, in the current study, the MODIS C6 DTDB merged AOD product (Sayer et al., 2014) was replaced with the recently released MODIS C6.1. In addition, MODIS/Terra data for 2016 and 2017 have been included in the analysis to provide information on the AOD evolution for the most recent years. In short, L3 (averaged on a grid of $\mathrm{1}{}^{\circ }×\mathrm{1}{}^{\circ }$) monthly AOD data retrieved from ATSR-2 (1995–2002) and AATSR (2002–2012) (together referred to as ATSR) using ADV version 2.31 (Kolmonen et al., 2016; Sogacheva et al., 2017; Veefkind et al., 1998) and MODIS/Terra AOD C6.1 merged DTDB (L3) monthly data (MOD08_M3, 2000–2017, https://ladsweb.modaps.eosdis.nasa.gov/, last access: 6 August 2018) were used together to cover the period from 1995 to 2017. Validation of the ADV and MODIS AOD products was performed for L2 (averaged on a grid of $\mathrm{0.1}{}^{\circ }×\mathrm{0.1}{}^{\circ }$) daily data, retrieved with the same corresponding ADV and MODIS algorithms as for L3. Hereafter, the ATSR ADV version 2.31 AOD product will be referred to as ADV, and the MODIS/Terra AOD C6.1 merged DTDB AOD product will be referred to as MODIS. In this study, the annually averaged AOD data were obtained by averaging monthly aggregated AOD data for each year. Furthermore, the seasonal means were obtained as averages of monthly aggregates for winter (DJF, including December, January and February), spring (MAM, including March, April and May), summer (JJA, including June, July and August) and autumn (SON, including September, October and November). Annual and seasonal linear AOD tendencies for both MODIS and ADV AOD for the overlapping period (2000–2011), when both ATSR and MODIS exist, were estimated using the least squares linear regression method (Chandler and Scott, 2011). ## 3.2 ADV and MODIS coverage over selected regions As introduced in de Leeuw et al. (2018), ATSR and MODIS have different temporal and spatial coverage over China. In brief, MODIS/Terra covers China in 1–2 days, while ATSR covers China in 4–5 days. The ADV datasets for the years 1995, 1996 and 2012 are incomplete. For 1995 and 1996, ADV AOD data are available for the second half of each year (June–December and July–December, respectively). However, all available ADV AOD data in 1995 and 1996 are used in the current study to construct the annual aggregates for comparison with other annual aggregates. Obviously, the 1995 and 1996 aggregates are not exact; therefore, the possible error related to the missing data has been estimated by comparison of the full-year (January to December) AOD composites with the half-year (July–December) AOD composites for the complete years (1997–2011). This comparison shows that when the half-year aggregate was used to present the full-year aggregate, the AOD was underestimated by −0.036 on average (with standard deviation of 0.02), or about 15 % of the yearly aggregated AOD value. In this study, the aggregated AOD values for the years 1995 and 1996 have not been corrected for the missing data and those years are included in the further analysis as they are. Another point worth mentioning is that the white area in the far west of the study area, where ATSR-2 did not provide data, was because the data collection was switched off for data transfer to the receiving station over that area. For 2012, the ADV AOD data are available until the connection with the satellite was lost on the 6 April. For MODIS/Terra, the AOD data record starts from the end of February 2000. Thus, the winter season for 2000 is missing. To estimate the spatial coverage of AOD, the fraction of the area where AOD is available has been calculated for all seasonal and annual aggregates for the selected regions (Table S1 in the Supplement). In spring (MAM), summer (JJA) and autumn (SON), the respective ADV coverage reaches 84 %, 91 % and 91 %, while MODIS coverage is 93 %, 93 % and 97 %, respectively, over mainland China. Throughout the year, both ADV and MODIS coverages are close to 100 %, except for region 9, where the ADV coverage is 62 %. For both ADV and MODIS, the Tibetan Plateau (region 8), the Taklamakan Desert (region 9) and NE China (region 10) are covered less than other regions, throughout the year. Regarding the seasons, the lowest AOD coverage is observed in winter (DJF), when northern and western China are covered with snow. As with most aerosol retrieval algorithms, MODIS and ADV have difficulty retrieving AOD over snow and ice (Hsu et al., 2013; Istomina et al., 2011; Kolmonen et al., 2016), in addition to year-round difficulty over bright surfaces such as the Taklamakan Desert. On average, in winter MODIS provides AOD values over 70 % of mainland China, while ADV AOD is available over 35 % of China. For certain years, ADV AOD is not available in the winter over regions 9 and 10; thus, it is not shown in the analysis (Sect. 5). However, as the annual AOD time series for ADV and MODIS in regions 9 and 10 show similar tendencies (discussed later in Sect. 5.3), we assume that missing (for some years) ADV AOD in winter does not considerably bias the results. Therefore, besides the difference in the validation results presented and discussed below (Sect. 4), which is likely due to the differences in the ADV and MODIS AOD retrieval approaches and their implementation, the difference in the ATSR and MODIS/Terra spatial and temporal coverage might influence the AOD composites. Another exercise might be performed, where AOD aggregates are built for collocated ADV and MODIS pixels, but this is beyond the scope of the current paper, where AOD aggregates for all available points in the ADV and MODIS standard products are analyzed and compared. ## 3.3 Consistency between ATSR-2 and AATSR AOD datasets The ATSR-2 and AATSR instrument characteristics are very similar (ATSR-1/2 User Guide, 1999; AATSR Product Handbook, 2007). The main potential reason for a difference would be offsets of the sensors' absolute calibration and small differences in band spectral response functions. Unfortunately, error characteristics of the two instruments are not available. Thus, we compare and validate the AOD products obtained from ATSR-2 and AATSR with the same retrieval algorithm (ADV V2.31). ATSR-2 was in an orbit ca. 30 min later than AATSR, which allows for the direct comparison of the retrieved collocated pixels. The number of collocations is limited by the cloud-free conditions for both overpasses needed for the retrieval. The AATSR AOD data series starts on the 20 May 2002. However, several data interruptions in June–July do not allow for the constructions of monthly aggregates. Thus, the comparison analysis between ATSR-2 and AATSR AOD is performed for August–December 2002. The period is limited by technical issues with the ATSR-2 pointing accuracy, which started in 2003. Pixel-by-pixel comparison between the ATSR-2 and AATSR L2 AOD is shown in Fig. 3 with (i) a scatter density plot of the difference between AATSR and ATSR-2 AODs as a function of AATSR and AOD and (ii) box plots with statistics related to certain AOD bins. For AOD < 0.5 (78.8 % of all retrieved pixels), the offset is close to 0, which means that there is practically no offset between ATSR-2 and AATSR AOD for low (<0.5) AOD. For an AOD between 0.5 and 1.5 (20.6 % of all retrieved pixels), the median values in chosen bins are slightly below 0, while the mean AATSR AOD is 0.05–0.12 lower than the mean ATSR-2 AOD. For an AOD > 1.5, AATSR AOD is considerably higher. However, only 0.6 % of the retrieved pixels fit into the AOD > 1.5 bin. Figure 3Scatterplot for AATSR AOD and the difference in AOD between AATSR and ATSR-2. For AATSR AOD bins, box plots (magenta) are shown, which include the following statistics: mean values as “+”, median values as “”, lower and upper quartiles (box), 9 % and 91 % as lower and upper whiskers. The percentages from all retrieved pixels in three AOD bins (AOD < 0.5, 0.5 <= AOD <= 1.5, AOD > 1.5) are shown in brown. Monthly AOD aggregates for August–December 2002 for China and globally over land are shown in Fig. 4. The monthly aggregates over China combined from L3 data show similar values for the two ATSR instruments, i.e., there are no systematic difference between ATSR-2 and AATSR AODs. ATSR-2 AOD is ca 0.035 higher in August and October, while AATSR is higher by a similar amount in September and by ca 0.02 in November. In December, AOD retrieved with the two instruments is similar. On a global scale, AOD retrieved from ATSR-2 is somewhat higher (ca. 0.01–0.03) than that from AATSR in all months except October, where the AOD difference is negligible. Error bars, which show 1σ standard deviation of AOD for each aggregate, closely overlap for all of the pairs that were compared. Figure 4AOD monthly aggregates for ATSR-2 (purple line) and AATSR (blue line) over China (green dots) and globally over land (red diamonds). The vertical dashed lines on each marker represent 1σ standard deviation. For an evaluation of the differences between the AOD retrieved from ATSR-2 and AATSR, data from the overlap period (August–December 2002) were validated using ground-based AOD from AERONET, which for that period are available over the BTH area from 2002 and over Taiwan (where AERONET measurements were started in 1998). The low density of AERONET stations during that period and the limited number of available collocations (5 for ATSR-2 and 17 for AATSR) does not allow for statistically significant conclusions on the AOD quality. Thus, we additionally added all available global locations for August–December 2002 for an evaluation exercise. The results in Fig. 5 show the correlation coefficient (R=0.89), and the low bias between AERONET and ATSR-2 AOD (Fig. 5, left). For AATSR the correlation is also high (0.86), with a small bias (0.01). AOD standard deviation is 0.008 and 0.005 and root mean square error is 0.12 and 0.13 for ATSR-2 and AATSR, respectively. Thus, the validation results confirm the similar performance of ADV for both sensors. Figure 5Density scatterplot of ATSR-2 AOD (a) and AATSR AOD (b) vs. AOD from AERONET stations globally for the period from August to December 2002. The filled circles are the averaged ATSR AOD binned in 0.1 AERONET AOD intervals (0.25 for AERONET AOD > 1.0) and the vertical lines on each circle represent the 1σ standard deviation. Statistics in the upper left corner indicate the correlation coefficient R, the bias, the standard deviation, the root mean square (rms) error and the number of data points (N). The color bar on the right indicates the number of data points in each bin. Thus, the AOD values retrieved from ATSR-2 and AATSR are consistent, as shown by pixel-by-pixel, monthly aggregates and validation results comparisons. Furthermore, most of the differences are within the measurement uncertainty (0.03, or 10 %) requirement of the Global Climate Observing System (GCOS, 2011); this makes it possible to combine ATSR-2 and AATSR AOD into one dataset without offset correction. ## 3.4 Comparison between MODIS merged DTDB C6.1 and C6 AOD In MODIS C6.1, the brightness temperatures biases and trending were significantly reduced compared to C6, which affected ice cloud detection over water surfaces (Moeller et al., 2017). The electronic crosstalk correction discussed in Wilson et al. (2017) was also made, which greatly improved the performance of the cloud mask. The difference between the C6.1 and C6 annual AOD over China averaged for the 2000–2011 period is shown in Fig. 6. This period was chosen because of the overlap between ATSR and MODIS, which is studied in the current paper. Over most of China, the difference between C6.1 and C6 is very small (within ±0.025), except for certain areas (Fig. 6). The annual aggregated C6.1 AOD over the Tibetan Plateau and over the area north of the Taklamakan Desert is 0.1–0.2 lower than for C6, while over Ningxia Province (ca. 35–37 N and 103–107 E) and the Sichuan Basin (ca. 28–30 N and 103–107 E) the AOD increased by 0.1–0.2. Figure 6b shows that the AOD differences over the TP and in the north are mostly due to the lower C6.1 AOD in the winter (DJF, about 0.15) and spring (MAM, up to 0.25), and that the differences over Ningxia are due to the much higher AOD in these seasons in C6.1. Over the Sichuan Basin the C6.1 and C6 AOD values are similar in all seasons except winter, when C6.1 is about 0.25 higher. Similar changes in the AOD between C6.1 and C6 are shown by Sayer (2017) for the period from 2000 to 2008 over China. With regards to coverage, over most of mainland China, the differences between C6.1 and C6 are very small, except over elevated areas such as the Tibetan Plateau, the Huangiu Gaoyuan Plateau and areas in the northeast and northwest of the country (Andrew Sayer, personal communication, 2017). However, the MODIS AOD coverage over other locations has increased in C6.1, which is concluded from the increasing number of points available for validation, as discussed in Sect. 4. Figure 6Difference between MODIS C6.1 and C6 DTDB merged AOD over China: annual averages for 2000–2011 (a) and seasonal averages for the same period (b), where DJF represents winter, MAM represents spring, JJA represents summer and SON represents autumn). Areas for which no data are available are shown in white. Table 1AOD validation results (number of points (N), correlation coefficient (R), bias, standard deviation (σ) and root mean square (rms) error) for ADV and MODIS (MOD) obtained for the regions (left column), where AERONET data are available. 4 ADV and MODIS AOD validation ## 4.1 General validation over China and validation results for selected regions MODIS C6.1 was validated over China with AERONET AOD (Fig. 7, right) for the sites available in the study area similar to C6 validation, as described in de Leeuw et al. (2018). Briefly, collocated satellite and AERONET data were used, i.e., satellite data within a radius of 0.125 around the AERONET site are averaged and compared with the averaged AERONET data measured within ±1 h of the satellite overpass time (Virtanen et al., 2018). C6.1 had about 5 % more matchups with AERONET. For C6.1 the validation results did not changed much, since the number of AERONET stations is limited over the areas where the changes in AOD in C6.1 compared to C6 are visible in the yearly and seasonal aggregates (Fig. 6). Figure 7Density scatterplot of ATSR ADV v2.31 AOD (a, reproduced from de Leeuw et al., 2018, Fig. 7), and MODIS C6.1 DTDB vs. AOD from AERONET stations in mainland China (b)for the years 2002–2011. The filled circles are the averaged ATSR AOD binned in 0.1 AERONET AOD intervals (0.25 for AERONET AOD > 1.0) and the vertical lines on each circle represent the 1σ standard deviation of the averages. Statistics in the upper left corner indicate the correlation coefficient R, the bias, the standard deviation, the root mean square (rms) error and the number of data points (N). The color bar on the right indicates the number of data points. ADV validation results (Fig. 7a, left) are adopted from de Leeuw et al. (2018). The main difference in ADV and MODIS performance, the bias, which is similar in absolute value but opposite in sign (0.06 for MODIS and −0.07 for ADV), changed little from C6 to C6.1 (Fig. 7). This difference in AOD bias is emphasized here because it explains the offset in the AOD between ADV and MODIS, as shown and discussed below, and will be used in Part 2 to construct the ADV and MODIS combined time series. We also checked whether the AOD validation results differ across China, where aerosol conditions change considerably from region to region, reflecting differences in primary and secondary aerosol sources, population density, industry, etc. Unfortunately, AERONET stations are sparsely located and long-term measurements have only been conducted for a few locations (see Table 1 and Fig. 1 in de Leeuw et al., 2018), mostly in SE China. The validation statistics for the selected regions, where AERONET AOD data are available, are shown in Table 1 (note the low number of validation points N in regions 5, 7, 8 and 10). For both ADV and MODIS, R was rather high (0.84–0.92) for all regions presented in the analysis, except for region 8, where the correlation with AERONET was much lower for both datasets (0.33 and 0.35, ADV and MODIS, respectively). In region 8, which includes the sparsely populated Tibetan Plateau, an area that is often covered with snow, AOD is very low; therefore, high uncertainties in AOD are expected related to the retrieval algorithms limitations (e.g., Kolmonen et al., 2016; Sayer et al., 2014). In region 5, both ADV and MODIS show a strong negative AOD bias (−0.30 and −0.15, respectively). A high positive AOD bias (0.16) is observed for MODIS in region 7. AOD was also validated for different aerosol types, classified according to the AOD value and the Ångström exponent (AE): “background” (AOD < 0.2), “fine-dominated” (AOD > 0.2, AE > 1) and “coarse-dominated” (AOD > 0.2, AE < 1) aerosols (Table 2). For “background” aerosols (26 % and 17 % of validation points are in that class for ADV and MODIS, respectively), the correlation between MODIS- retrieved and AERONET AOD was poor (R=0.17), while for ADV the correlation was better (R=0.59). For “fine-dominated” (59 % and 56 % of validation points for ADV and MODIS, respectively) and “coarse-dominated” (15 % and 27 % of validation points for ADV and MODIS, respectively) aerosols, the validation statistics for ADV and MODIS were similar. Both products showed high (>0.85) correlation with AERONET. Similar in absolute values but different in sign, AOD bias was calculated for “fine-dominated” (0.09 and 0.08, for ADV and MODIS, respectively) and “coarse-dominated” aerosol conditions (0.11 and 0.10, for ADV and MODIS, respectively). Table 2AOD validation results (number of points (N), correlation coefficient (R), bias, standard deviation (σ) and root mean square (rms) error) for ADV and MODIS (MOD) obtained for different aerosol types, classified with the AOD and the Ångström exponent (AE). ## 4.2 ADV and MODIS collocated points annual and seasonal validation The validation results presented in Fig. 7 show that MODIS AOD is positively biased, whilst ADV is negatively biased. However, since more validation points are available for MODIS than for ADV (Fig. 7 and Table 1), which is likely explained by better MODIS coverage (see the discussion on the ADV and MODIS coverage in Sect. 3.2), a direct comparison of the algorithms performance to show differences in the retrieved AOD cannot be made. Instead, the retrieval performance was evaluated using collocated ATSR–MODIS/Terra–AERONET data. In collocated points validation only AOD data were used, where both MODIS and ADV had achieved a successful retrieval within ±1 h over AERONET sites and the difference between the ADV and MODIS overpasses was below 90 min. In total, 255 collocated points were recognized for the 2002–2011 period. Figure 8Density scatterplots of collocated ATSR ADV v2.31 AOD and MODIS C6.1 DTDB merged AOD vs. AOD from AERONET stations in China for the years 2002–2011: all points (a) and seasonal statistics (b for ADV and c for MODIS). The color bar at the bottom indicates the number of data points. We also checked whether the difference in the ADV and MODIS AOD depends on the difference in overpass time between ATSR and MODIS/Terra. The comparison of the AOD for ADV–MODIS–AERONET collocated points is shown as a scatterplot of MODIS AOD vs. ADV AOD in Fig. 9. The color code indicates the difference in the exact overpass time between ADV and MODIS. For all collocated points, MODIS AOD is usually higher, with an offset of 0.2. This positive difference does not depend on the difference in overpass times between ATSR and MODIS/Terra; thus, the difference cannot be explained by the influence of the possible AOD daily cycle. Figure 9MODIS/Terra C6.1 DTDB merged AOD vs. ATSR ADV v2.31 AOD, for collocated ATSR–MODIS/Terra–AERONET data, as described in Sect. 4.1. The colors (scale at the right) indicate the difference between the MODIS/Terra and ATSR overpass times in minutes. 5 AOD seasonal variation The AOD over China does not only vary in space, seasonal variations are also observed, as briefly discussed in de Leeuw et al. (2018) based on MODIS/Terra C6 data. Seasonal AOD maps for ADV and MODIS C6.1, aggregated over the years 2000–2011, and ADV–MODIS difference maps for each season, are presented in Fig. 10. The spatial distribution of seasonally averaged AOD is similar to the spatial patterns of the annually averaged AOD. However, Fig. 10 shows some clear differences between ADV and MODIS, i.e., the MODIS AOD is often higher than that from ADV, and MODIS has better coverage over bright surfaces. The latter is particularly prominent for the winter season (DJF) when the north and west of China are covered with snow. As previously mentioned, like most aerosol retrieval algorithms, ADV has difficulty retrieving AOD over snow and ice, as well as year round over bright surfaces such as deserts. In seasons other than winter, ADV has reasonable coverage over most of China (see Table S1), except over the Taklamakan Desert where high dust episodes are missed. It is noted that MODIS also does not provide AOD over snow and ice (Levy et al., 2013; Hsu et al., 2013); however, over bright desert surfaces the DB algorithm does provide AOD (Hsu et al., 2004), which is included in the DBDT product used in this study. Nevertheless, as shown in Fig. 10, MODIS also misses AOD over the Tibetan Plateau along the southern border of China during all seasons, as well as along the northwest border in the winter. North of ca. 45 N both MODIS and ADV do not provide AOD data in the winter. Figure 10Seasonal AOD maps aggregated over the years 2000–2011 (top to bottom: DJF (winter), MAM (spring), JJA (summer) and SON (autumn)). (a, d, g, j): ATSR ADV v2.31 (adapted from de Leeuw et al., 2018, Fig. 11); (b, e, h, k): MODIS/Terra C6.1 merged DBDT; (c, f, i, l): difference maps ADV–MODIS. The AOD and difference scales are plotted at the bottom. Pixels for which no value was retrieved are plotted in white. Regarding the AOD seasonal variation, the maps in Fig. 10 show similar variations for the ADV and MODIS-retrieved AODs. For instance, for the PRD the AOD is highest in spring and lower in other seasons, whereas over the NCP (in the area from BTH to the YRD) the AOD is highest in summer. The ADV and MODIS AOD seasonal aggregates for different areas will be discussed in Sect. 5.1. ## 5.1 Seasonal variation by region for the 2000–2011 period AOD seasonal time series for China, SE China and each of the 10 regions over China, selected as described in Sect. 2, are shown in Fig. 11, for both ADV and MODIS. The data shown in Fig. 11 are averages over the three months in each season, and over the years 2000–2011, i.e., the overlapping period for ATSR and MODIS/Terra. These time series illustrate the overall behavior that emerged from the seasonal AOD maps in Fig. 10, i.e., a clear seasonal variation of the AOD over all regions, which is similar for both ADV and MODIS but with MODIS AOD somewhat higher than that from ADV. For all regions, the AOD is lowest in the winter, except for region 6 (Sichuan/Chongqing), where the minimum occurs in autumn. For all of mainland China, AOD is also slightly lower in autumn, as compared to winter. For all regions, the AOD is highest in spring, except for regions 1 and 5 where the maximum AOD is observed in the summer. In region 2, the AOD is similar in spring and summer. The difference in the seasonal variation of the AOD between regions 1 (NCP) and 5 and those further south in region 2 (YRD) and region 7 (PRD), which are all very large urban areas with a high population and large industrial development, is likely due to the different climatological zones. The NCP is situated in a temperate monsoon climate region, the YRD in a subtropical monsoon climate region and region 7 combines regions with a subtropical and a tropical monsoon climate, with strong differences in rain-season trends, i.e., precipitation and number of rain days (Song et al., 2011; Kourtidis et al., 2015; Stathopoulos et al., 2017). The East Asian summer monsoon (EASM) and the associated rain patterns over eastern China (Song et al., 2011) progress from the south in April to the YRD in the early summer and reach BTH in July. When the monsoon period ends in August, the rain belt moves back to the south. Precipitation obviously affects the AOD due to wash out of the aerosol particles, although on warm days with high relative humidity the aerosol particles swell and small (<100 nm) aerosol particles grow into the optically active size range. As a result, the particle size distribution shifts to larger particles and the aerosol scattering and associated AOD increase (Bian et al., 2014; Zhang et al., 2015). In region 10, in the northeast of China, which has a cooler climate that the EASM does not reach, the AOD maximum occurs in spring. Figure 11AOD seasonal time series averaged over the 2000–2011 period for ADV and MODIS (see legend for explanation) for China, SE China and the 10 selected regions as discussed in Sect. 2. Error bars shown on each seasonal data point are 1σ standard deviation. Figure 12Spatial distribution of the seasonal mean dust AOD, as determined from CALIPSO observations, aggregated over the period from January 2007 to December 2015. Adopted from Proestakis et al. (2018). Chinese borders are indicated by the black line. Another factor influencing the seasonal variation of the AOD is the dust emitted from the deserts, with the highest emission intensity in spring and summer (cf. Proestakis et al., 2018). The largest dust sources in China are the Taklamakan Desert and the Gobi (GD) Desert. Due to differences in topography, elevation, thermal conditions and atmospheric circulation, the GD has a much more important role than the TD in contributing to the dust concentrations in East Asia (Chen et al., 2017b). Figure 12, reproduced from Proestakis et al. (2018), who described how these products were obtained in detail, shows seasonal maps of dust AOD (DAOD) at 532 nm, based on CALIOP (Cloud Aerosol Lidar with Orthogonal Polarization; Winker et al., 2009) observations between January 2007 and December 2015. These maps clearly illustrate the effect of the dust generated over the TD, with very high DAOD in the spring (up to about 0.7) and summer, and much lower DAOD in the autumn and winter (about 0.2). In contrast, there is no clear dust signal over the northern part of the Gobi Desert, where surface dust concentrations are high (cf. Chen et al., 2017b), in either the CALIOP DAOD maps in Fig. 12 or the ADV and MODIS AOD maps in Fig. 10. In these satellite observations the dust appears to be confined south of 40 N. A noticeable feature is the distinct eastward pathway of dust aerosol transport, although the observed features vary strongly with season. The eastward dust aerosol pathway extends from the Taklamakan Desert over central China (Kuhlmann and Quaas, 2010), with DAOD values of up to 0.3 in the spring and much lower in other seasons (0.1), towards the Yellow Sea and the Pacific Ocean (Uno et al., 2009). This dust aerosol trans-Pacific belt extends over central China between 30 and 45 N, contributing (with dust aerosols) up to 50 % to the total aerosol load of the densely populated Beijing, Hebei, Tianjin and Shandong provinces (Proestakis et al., 2018). However, very low DAOD values are observed to the south of about 30 N throughout the year, i.e., south of the Yangtze River basin, indicating the very low dust aerosol transport to the south of the observed dust aerosol trans-Pacific belt. The YRD is also the area where the seasonal maximum shifts between spring and summer; north of the YRD are regions 1 and 5 with summer AOD maxima, as described above. Clearly, in spite of the relatively high DAOD over the TD in the summer and presumed sources over the GD, there appears to be little eastward transport. DAOD is also not responsible for the high summer AOD, with DAOD over the NCP in the order of 0.1. Another reason for the high AOD in summer might be agricultural fires during the summer harvest period in June in the NCP (Zhang et al., 2018), in addition to the mechanism proposed above in reaction to the migration of the EASM. ## 5.2 Long-term AOD seasonal variations for ATSR ADV (1995–2011) and MODIS (2000–2017) Figure 10 shows the spatial distribution of the multi-year averaged ADV and MODIS seasonal AOD for the years 2000–2011. However, this leaves out the pre-EOS period covered by ATSR-2 and the post-Envisat period covered by MODIS. Furthermore, interannual variations occur. In Fig. 13, the summer AOD datasets for China, SE China and the 10 selected regions are divided into three periods, i.e., pre-EOS with only ATSR-2 (1995–2000), post-Envisat with only MODIS/Terra (2011–2017) and the overlap period (2000–2011, shaded light green) when both algorithms provided valid AOD retrievals. Time series for other seasons and yearly aggregates are shown in the Supplement. The time series of the summer AOD over China (Fig. 13) show a small increase of the AOD over the years 1995–2011, with a somewhat larger tendency for MODIS than for ATSR, whereas from 2011 the MODIS data show a definite decrease. This behavior seems to be mainly determined by the AOD decrease in SE China (and regions 1–7 therein), where the AOD is substantially higher than in other parts of China, and tendencies until 2011 have a similar direction but are much stronger than over the west and north of China (regions 8–10). Here we estimate the AOD tendencies during the overlapping period, only to establish that ATSR and MODIS time series are similar; thus, they can be used to construct a combined long-term time series. AOD tendencies during the 1995–2017 period, as related to the changes in the emission control policy in China, are presented and discussed in detail in Part 2. For the overlapping period, linear fits were made using a MATLAB tool (https://se.mathworks.com/products/matlab.html, last access: 6 August 2018, and a detailed description of the statistics) to determine the variation of the AOD vs. time. AOD tendencies (dAOD) per decade, bias and slope for the linear regression lines, as well as the p value estimated using a t test and absolute error for linear fits are presented in Table S2 (for seasonal aggregates) and Table S3 (for annual aggregates) for all selected regions. For both China and SE China, the annual (Fig. S4) and seasonal (Fig. 13, Figs. S1–S3) time series for ADV and MODIS are very similar, albeit with an almost constant offset with MODIS high and ADV low. When looking at the long-term time series of the yearly averaged AOD for each of the 10 regions, this behavior is replicated, with some anomalous years for each of them. The possible exception is region 8 (the Tibetan Plateau). Here the AOD is very low in comparison to other regions, with practically no interannual variation or long-term tendency. AOD tendencies during the whole period (1995–2017) will be discussed in Part 2. Figure 13Time series of the summer-averaged AOD over China, SE China and each of the 10 selected regions, for ADV (1995–2011, green circles) and MODIS (2000–2017, red diamonds). The overlapping period is colored light green. AOD linear fits for the overlapping periods are shown for each instrument (green and red dashed lines for ADV and MODIS, respectively). Statistics for linear fits are shown in Table S2. Figure 14Scatterplot of the 2000–2011 yearly tendencies (a) derived from MODIS C6.1 DBDT vs. those derived from ATSR ADV v2.31, for China, SE China and the 10 selected areas (as specified in b) for the yearly (black dots) and seasonally averaged AOD (colored dots, see legend). Colored circles indicate if the p value < 0.05 for both ADV and MODIS (red), for ADV only (blue) or for MODIS only (green). ## 5.3 Comparison between ATSR ADV and MODIS seasonal AOD tendencies To compare the seasonal year-to-year behavior of the AOD retrieved with ATSR and MODIS, the AOD tendencies for the overlapping period (2000–2011) were estimated by fitting the time series with linear regression lines. The linear fit for AOD seasonal tendencies for the overlapping period for ADV and MODIS is shown in Fig. 13 and Figs. S1–S4, and the corresponding statistics are summarized in Table S2 and S3. For the overlapping period, positive AOD tendencies were observed with both instruments over China for all seasons, except for spring, when the AOD tendency was close to zero or slightly negative. In winter, the ADV-retrieved AOD shows a strong increase (between 1.31 and 1.51 per decade) in regions 4 to 7, which represent the south and east of SE China. Interestingly, along the east coast, the AOD tendency increases in winter from north to south, as shown with ADV. MODIS shows a strong (near 0.16) AOD increase in winter in regions 1 and 2. In spring, the AOD tendencies are very low for both instruments, showing an increase in the MODIS AOD and a decrease for ADV. The highest AOD increase was observed in region 7 for both ADV and MODIS (0.181 and 0.171 per decade, respectively). In summer, a strong AOD increase is observed in region 1 for both ADV and MODIS (0.503 and 0.422 per decade, respectively). The positive AOD tendencies were higher in SE China, reaching 0.168 and 0.154 for ADV and MODIS, respectively. In autumn, the AOD tendencies were smaller for both ADV and MODIS and agreed in sign for most of the selected regions, except for region 10. Note that the AOD tendencies were statistically significant for regions 1, 2, 4 and over SE China for MODIS only. The AOD tendencies for the overlapping period derived from MODIS are plotted in Fig. 14 vs. those derived from ATSR. This scatterplot includes tendencies for yearly and seasonal AOD aggregates (dots, see legend for colors) for China, SE China and for each of the 10 selected regions. The confidence for linear fits (p value) is indicated by the colored (with respect to p value for each instrument) circles around each symbol. The areas where both instruments show a similar tendency are denoted by a light red (both positive) and light blue (both negative) background. The same plot, but with symbols replaced with region numbers, is presented in Fig. 14b. Most of the ADV and MODIS AOD tendencies for corresponding periods are located in the colored (red and blue) areas, which confirm that ADV and MODIS show AOD tendencies that are similar in sign during the overlapping period. The grouping of the tendency points along the 1:1 line (line is not shown here) shows that the AOD tendencies derived for ADV and MODIS are also similar in an absolute sense. However, seasonal differences exist in the agreement between the ADV and MODIS AOD tendencies. The AOD tendencies derived from the two instruments are in good agreement in summer, autumn and annually (R is 0.87, 0.77 and 0.88, respectively). In winter and spring, the correlation coefficient is smaller (0.41). Thus, the consistency between ATSR and MODIS with regards to the AOD tendencies in the overlapping period is rather strong in the summer, the autumn and for the yearly average, while in the winter and spring, when there is a difference in coverage between the two instruments (Table S1), the agreement in the AOD tendencies is lower. 6 Summary and conclusions The current research is an extension of the study by de Leeuw et al. (2018), where ATSR-retrieved AOD using ADV v2.31 for the 1995–2011 period and the MODIS/Terra C6 DBDT merged AOD product for the 2000–2015 period were explored. In this paper, the MODIS/Terra C6 DBDT merged AOD product has been replaced with the recently released collection C6.1 and extended to include 2016 and 2017. The AOD annual anomaly maps are shown and discussed, and the analysis of the seasonal variability has been extended to 10 selected regions; the AOD tendencies for the overlapping period (2000–2011) for both ADV and MODIS are presented and compared. The main results and conclusions are summarized below. • The difference in AOD retrieved from ATSR-2 and AATSR is small, as shown by pixel-by-pixel, monthly means and validation results comparisons for the period from August to December 2002 over China and globally. Most of the differences fit to the measurement uncertainty requirement of the GCOS (0.03, or 10 %). This makes it possible to combine ATSR-2 and AATSR AOD time series into one dataset without offset correction. • Comparison with AERONET shows similar performance for both C6.1 and C6. The correlation coefficient increased slightly from 0.9 in C6 to 0.92 in C6.1, and the bias decreased slightly from 0.07 to 0.06. The AOD spatial coverage in C6.1 increased by ca. 5 % with respect to that in C6. • AOD validation with AERONET shows that the validation results depend on the sampling. If the sampling includes all available collocations with AERONET (1132 and 4964 points for ADV and MODIS, respectively), the validation statistics are slightly better for MODIS. The bias in both datasets is similar but with an opposite sign (0.06 for MODIS and −0.07 for ADV). However, for collocated points, when ATSR and MODIS overpasses are within ±90 min and AERONET data exist for validation, the correlation coefficient is closer between ADV and MODIS (0.92 and 0.93, respectively) for all collocated points. However, ADV performs better than MODIS in autumn, while MODIS performs slightly better in spring and summer. In winter, both ADV and MODIS underestimate AOD. For “fine-dominated” and “coarse-dominated” aerosols, validation statistics are similar for ADV and MODIS. Both products show high (>=0.85) correlation with AERONET. Similar in absolute values but different in sign, AOD bias is calculated for “fine-dominated” (−0.09 and 0.08, for ADV and MODIS, respectively) and for “coarse-dominated” (−0.11 and 0.10, for ADV and MODIS, respectively) aerosol conditions. • The AOD interannual variability over China was presented based on annual anomaly maps (with respect to the 2000–2011 averages). During the period from 1995 to 2006, AOD increased in SE China, while no significant changes in AOD were observed in the west or in the north. Between 2006 and 2011, AOD did not change much, showing minor minima in 2008–2009. From 2011 onward, AOD was observed to decrease in SE China. • Both ADV and MODIS show similar seasonal behavior, with spring AOD maxima in the south that shift from spring to summer along the eastern coast in a northerly direction. • Similar patterns are shown in year-to-year differences for ASTR ADV and MODIS AOD. For the overlapping period, positive AOD tendencies were observed with both instruments over China for all seasons, except for spring, when the AOD tendency was close to zero or slightly negative. More pronounced changes in AOD were confirmed for SE China. AOD changed faster in spring and autumn, compared to other seasons. • The consistency between ATSR and MODIS with regards to the AOD tendencies in the overlapping period was rather strong in summer, autumn and for the yearly average, while in winter and spring, when there was a difference in coverage between the two instruments, the agreement in AOD tendency was lower. The overall conclusion is that both ATSR ADV and MODIS individually show similar spatial and temporal AOD patterns over China. That conclusion is used as a main starting point in Part 2, where the combined long-term AOD time series over China and selected areas will be introduced for the 1995–2017 period. In Part 2, AOD tendencies in the combined time series will be estimated for the periods associated with changes in air pollution control policies in China. Data availability Data availability. The ATSR data used in this research are publicly available (after registration a password will be issued) at: http://www.icare.univ-lille1.fr/ (Finnish Meteorological Institute, 2018). MODIS data are publicly available at: https://ladsweb.modaps.eosdis.nasa.gov/ (NASA, 2018a). AERONET data are available at AERONET: https://aeronet.gsfc.nasa.gov/ (NASA, 2018b). Supplement Supplement. Author contributions Author contributions. The whole team designed the research. LS, AKG, ER and EP performed the analysis and prepared the figures and tables. LS and GL wrote the paper with comments/contributions from the whole team. Competing interests Competing interests. The authors declare that they have no conflict of interest. Acknowledgements Acknowledgements. Work presented in this paper was undertaken as part of the Marco Polo project supported by the EU, FP7 SPACE grant agreement no. 606953 and as part of the GlobEmission project ESA–ESRIN Data Users Element (DUE), project AO/1-6721/11/I-NB; it also contributes to the ESA/MOST DRAGON4 program. The ATSR algorithm (ADV/ASV) used in this work is improved with support from ESA as part of the Climate Change Initiative (CCI) project Aerosol_cci (ESA-ESRIN projects AO/1-6207/09/I-LG and ESRIN/400010987 4/14/1-NB). Further support was received from the Centre of Excellence in Atmospheric Science funded by the Finnish Academy of Sciences Excellence (project no. 272041). Many thanks are expressed to the NASA Goddard Space Flight Center (GSFC) Level 1 and Atmosphere Archive and Distribution System (LAADS) (http://ladsweb.nascom.nasa.gov, last access: 6 August 2018) for making the L3 MODIS/Terra C6.1 and C6 aerosol data available. 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https://link.springer.com/article/10.1007%2Fs10519-007-9179-7	Behavior Genetics , Volume 38, Issue 1, pp 55–66 # Evaluation of the Serotonergic Genes htr1A, htr1B, htr2A, and slc6A4 in Aggressive Behavior of Golden Retriever Dogs • L. van den Berg • M. Vos-Loohuis • M. B. H. Schilder • B. A. van Oost • H. A. W. Hazewinkel • C. M. Wade • E. K. Karlsson • A. E. Liinamo • P. A. J. Leegwater Open Access Original Research ## Abstract Aggressive behavior displays a high heritability in our study group of Golden Retriever dogs. Alterations in brain serotonin metabolism have been described in aggressive dogs before. Here, we evaluate whether four genes of the canine serotonergic system, coding for the serotonin receptors 1A, 1B, and 2A, and the serotonin transporter, could play a major role in aggression in Golden Retrievers. We performed mutation screens, linkage analysis, an association study, and a quantitative genetic analysis. There was no systematic difference between the coding DNA sequence of the candidate genes in aggressive and non-aggressive Golden Retrievers. An affecteds-only parametric linkage analysis revealed no strong major locus effect on human-directed aggression related to the candidate genes. An analysis of 41 single nucleotide polymorphisms (SNPs) in the 1 Mb regions flanking the genes in 49 unrelated human-directed aggressive and 49 unrelated non-aggressive dogs did not show association of SNP alleles, genotypes, or haplotypes with aggression at the candidate loci. We completed our analyses with a study of the effect of variation in the candidate genes on a collection of aggression-related phenotypic measures. The effects of the candidate gene haplotypes were estimated using the Restricted Maximum Likelihood method, with the haplotypes included as fixed effects in a linear animal model. We observed no effect of the candidate gene haplotypes on a range of aggression-related phenotypes, thus extending our conclusions to several types of aggressive behavior. We conclude that it is unlikely that these genes play a major role in the variation in aggression in the Golden Retrievers that we studied. Smaller phenotypic effects of these loci could not be ruled out with our sample size. ## Keywords Dog Aggression Serotonin Candidate gene Linkage Association ## Introduction Dogs have been living in close proximity to humans for at least 15,000 years (Clutton-Brock 1995). Behavior has been a strong selective factor in the domestication and breeding of dogs. According to the breed standard, Golden Retriever dogs should have a friendly character (http://www.goldenretrieverclub.nl; link accessed March 2007). However, there are reports of very aggressive Golden Retrievers (Galac and Knol 1997; Heath 1991). We recently described the behavioral phenotype of 110 Golden Retrievers referred to our clinic for aggression problems and 118 Golden Retrievers that were recruited because they were related to one or more of the aggressive dogs (van den Berg et al. 2006). The phenotypes were based on mail questionnaires and on personal interviews with dog owners. In a quantitative genetic study including 325 Golden Retrievers, we found a heritability of 0.8 for the traits of human-directed aggression and dog-directed aggression (Liinamo et al. 2007). The influence of serotonin (5-hydroxytryptamine, 5-HT) on aggressive behavior has been studied extensively (reviewed by Berman and Coccaro 1998; Gingrich and Hen 2001; Lesch and Merschdorf 2000). There is evidence for a role of the 5-HT system in canine aggression as well. For instance, Reisner and colleagues (1996) reported decreased levels of 5-hydroxyindoleacetic acid (the major metabolite of 5-HT) in cerebrospinal fluid of dominant aggressive dogs. Badino et al. (2004) found modifications of 5-HT receptor concentrations in brains of aggressive dogs. Domestication of silver foxes, which are taxonomically close relatives of dogs, seems to cause modifications in the 5-HT system (see Trut 2001 for a review). The role of 5-HT in canine aggression is further supported by two small clinical studies, where pharmacological or dietary intervention in the 5-HT system was shown to modulate aggressive behavior (DeNapoli et al. 2000; Dodman et al. 1996). Four genes that code for factors involved in serotonergic neurotransmission are particularly good candidates for the regulation of aggressive behavior: the serotonin receptor genes 1A (htr1A), 1B (htr1B), and 2A (htr2A), and the serotonin transporter gene (slc6A4). Serotonin receptor 1A plays a role in anxiety, stress response, and aggression (Olivier et al. 1995). Htr1A knockout mice show increased anxiety and stress response and an antidepressant-like phenotype (Heisler et al. 1998; Ramboz et al. 1998). In the above-mentioned studies of silver foxes, the researchers observed a lower density of 5-HT1A receptors in the hypothalamus of tame foxes compared to their wild counterparts (Popova et al. 1991). Many studies have suggested involvement of htr1B in the etiology of mental disorders. For instance, Huang et al. (2003) and Sanders et al. (2002) reported an association between one of the polymorphisms in the human HTR1B gene and alcoholism, suicidality, and obsessive-compulsive disorder. Knockout mice lacking htr1B display increased aggression (Saudou et al. 1994). A mutation in the human HTR2A gene is associated with altered 5-HT binding, which has been implicated in schizophrenia, suicidal behavior, impaired impulse control, and aggression history (Abdolmaleky et al. 2004; Bjork et al. 2002; Khait et al. 2005). Peremans and colleagues (2003) found an increased binding index of serotonin 2A receptors in cortical brain regions of impulsive aggressive dogs. A polymorphism in the promoter region of SLC6A4 influences serotonin transporter density in the brain and is associated with mental disorders in humans (Anguelova et al. 2003; Hariri et al. 2002; Lesch et al. 1996). Slc6A4 knockout mice show reduced aggression (Holmes et al. 2003). In this paper, we test the hypothesis that there is a strong effect of variation in these genes on the variation in aggression in Golden Retrievers. We performed mutation screens of the coding DNA sequence in unrelated aggressive Golden Retrievers. In addition, we used linkage analysis to determine the likelihood of the presence of a strong aggression locus in or close to the genes in several dog families. Third, we used 50 unrelated aggressive Golden Retrievers and 50 unrelated non-aggressive Golden Retrievers to search for association of alleles of 41 SNPs flanking the candidate genes with the trait of human-directed aggression. To complete our analyses, we evaluated the effects of variation in the genes on a range of aggression-related phenotypes using the same models as in Liinamo et al. (2007), extended to include the effects of the most common candidate gene haplotypes. ## Materials and methods ### Animals, DNA isolation, and phenotyping We have collected behavioral information of 328 privately owned Golden Retrievers. This group includes 162 dogs that were referred to our clinic because of their aggressive behavior (“probands”) and 166 relatives of 36 probands. DNA samples were available for 281 of these dogs. In addition, we collected DNA of a cohort of random privately owned Goldens that were born between July 2002 and February 2003. No phenotypes were available for these random dogs. Genomic DNA was isolated from whole blood leucocytes using a standard protocol (Miller et al.1988). For each type of analysis (mutation analysis, linkage analysis, association analysis, and quantitative genetic analysis) we selected a study group that was suited for the study design. The study groups are described in the Supplementary Information I. We have collected various quantitative measures of aggressiveness for the dogs (van den Berg et al. 2003a, 2006). In the linkage and association analysis we focused on one of these measures: the dog owners impression on human-directed aggression. Owner impressions were collected in a personal interview. We asked the owners if their dog was aggressive towards humans and the status of the dog was coded in three classes: non-aggressive (score 1), threatens (score 2), or bites (score 3). We focused on human-directed aggression because the majority of the probands were referred to our clinic for human-directed aggressive behavior. Owner impressions were available for all dogs and the quantitative genetic analyses showed that the heritability of this trait was high in our population of dogs (Liinamo et al. 2007). ### Mutation screening We analyzed the coding DNA sequence (CDS) of the four candidate genes in seven (htr1A and htr1B) or eight (htr2A and slc6A4) probands. The CDS were amplified and sequenced using overlapping primer pairs as described previously (van den Berg et al. 2004, 2005). Possible functional effects of polymorphisms were predicted with POLYPHEN (http://www.genetics.bwh.harvard.edu/cgi-bin/pph/polyphen.cgi). Effects of polymorphisms close to splice sites were predicted with three splice prediction programs: NetGene2 (Brunak et al. 1991), Splice Prediction by Neural Network (Reese et al. 1997), and SpliceSiteFinder (Shapiro and Senapathy 1987). We used nine families for linkage analysis (Figs. S1–S9 of Supplementary Information I). DNA samples were available for 31 affected and 65 unaffected dogs from these families. We converted the owner impression about human-directed aggression into a dichotomous variable for the linkage analysis (see Supplementary Information I). We have described polymorphic markers for the candidate genes before (van den Berg et al. 2003b, 2004, 2005). We selected three microsatellite markers and seven single nucleotide polymorphisms for linkage analysis (see Table 1). Microsatellite markers were genotyped after PCR on an ABI 3100 Genetic Analyzer (Applied Biosystems, Foster City, CA). PCR conditions were described by van den Berg et al. (2004, 2005). GENESCAN 3.7 software was used for genotype assessment. Single nucleotide polymorphism genotyping was performed by DNA sequencing of PCR products on the ABI 3100 Genetic Analyzer (van den Berg et al. 2004, 2005). The DNA sequence chromatograms were inspected using LASERGENE software (DNASTAR, Inc., Madison, WI USA). We combined several markers into haplotypes for the genes htr1B, htr2A, and slc6A4. For dogs that were heterozygous for multiple markers, we deduced the haplotypes from the data of relatives. If this was not possible, we assigned the most frequently observed possible haplotypes to these dogs. Table 1 Markers used for linkage analysis Genea Type of markerb Position of markerc Alleles observed (allele frequency)d Haplotypes observed (haplotype frequency)d htr1A (CA)n (UU160O12) 7370 297 (0.5) 303 (0.5) htr1B A/C SNPe 157 A (0.58) C (0.42) 143-A-G-T-G (0.20) 143-C-A-T-G (0.42) 143-A-G-C-C (0.06) 139-A-G-C-C (0.24) 139-A-G-T-G (0.05) 147-A-G-T-G (0.03) G/A SNP 246 G (0.58) A (0.42) T/C SNP 955 T (0.69) C (0.31) G/C SNP 1146 G (0.69) C (0.31) (GA)n (UU18L8) −68395 139 (0.29) 143 (0.68) 147 (0.03) htr2A C/T SNP IVS 2-10 C (0.85) T (0.15) 128-C (0.07) 130-C (0.41) 132-C (0.37) 132-T (0.15) (CA)n (UUHTR2AEX2) IVS2 + 1439 128 (0.07) 130 (0.41) 132 (0.52) slc6A4 C/T SNP 411 C (0.75) T (0.25) C-G (0.75) T-A (0.25) G/A SNP IVS9-12 G (0.75) A (0.25) ahtr1A, htr1B, htr2A = respectively serotonin receptor 1A, 1B, and 2A gene; slc6A4 = serotonin transporter gene bSNP = single nucleotide polymorphism. Names of microsatellite markers have been included in brackets cPosition refers to the coding sequence of the canine gene. We used the nomenclature recommended by den Dunnen and Antonarakis (2001): the A of the ATG start codon is designated number 1, the nucleotide 5′ to this A is numbered −1, and the nucleotide 3′ of the translation termination codon is 1. Positions in introns refer to the nearest exon. The nomenclature of the introns is based on the human gene structure. IVS = intervening sequence dAllele and haplotype frequencies were determined in a group of 27 (htr1A and htr2A), 31 (htr1B), or 26 (slc6A4) parents eThis polymorphism is nonsynonymous We performed a parametric affecteds-only linkage analysis to determine whether the candidate gene haplotypes were linked to aggressive behavior in the Golden Retriever families. Marker haplotype frequencies were determined in a group of 27 (htr1A and htr2A), 31 (htr1B), or 26 (slc6A4) parent dogs (see Supplementary Information I). The mode of inheritance of the aggressive phenotype in our families is unclear. We therefore analyzed the data under both autosomal dominant and autosomal recessive models. The penetrance of the genotype at risk was set at 0.01. In this way, affected dogs are assumed to have the risk allele and the software calculated likelihood that aggressive dogs share alleles by descent from a common ancestor. Unaffected dogs with the genotype at risk have no effect on the outcome of the calculation. We assumed that there were no phenocopies in the families and we assumed genetic homogeneity because all probands were related to each other within a limited number of generations (not shown). The frequency of the aggression allele was set at 0.1 to allow for multiple transmitting ancestors in the pedigrees. SUPERLINK software was used to calculate two-point logarithm of the odds (LOD) scores (Fishelson and Geiger 2002, 2004). In order to estimate the power of the pedigrees, we calculated the maximum obtainable LOD scores. Affected individuals were assigned haplotypes 2/2 in these calculations; unaffected parents were assigned haplotypes 1/2; and other unaffected individuals were assigned haplotypes 1/1. We assigned haplotypes 0/0 (unknown) to dogs from which we did not have a DNA sample. We assumed that there were four alleles of the hypothetical marker with equal allele frequencies. ### Association study To test for a more complex genetic effect of variants of the candidate genes, we performed an association study. Fifty aggressive Golden Retrievers were selected from our database. The main selection criteria were high estimated breeding values for human-directed aggression and as little interrelationship among the cases as possible. Non-aggressive dogs were selected for low estimated breeding values for both human- and dog-directed aggression. We avoided an excess of relationship within either the case or the control group. The non-aggressive group was completed with 25 dogs from the random group. A more detailed description of cases and controls is provided in Supplementary Information I. We genotyped a total number of 60,073 SNPs in these 100 Golden Retrievers using customized Affymetrix Genotyping Arrays. The SNPs were selected for the chip using a scoring system that optimized the SNPs accounting for low repeat content, low likelihood of SNPs in the assay probe sequences and their distribution over the genome as a whole (Lindblad-Toh 2007; personal communication). Twenty 32-mer probes interrogated each locus with genotyping calls made using the algorithm BRLMM (http://www.affymetrix.com) which analyses intensities for sets of probes that interrogate both forward and reverse sequences with perfect match and mismatched probes. Dogs with call rates of lower than 50% were discarded from the analysis. The total set of SNPs was filtered for genotype call probability, heterozygosity rate, and call rate across a large set of dogs, reducing the dataset to 26,625 SNPs. From this set, only SNPs within 1 Mb of the four candidate genes were used for the analysis described in this paper. There were 29 SNPs within 1 Mb of htr1A, 20 within 1 Mb of htr1B, 25 within 1 Mb of htr2A, and 20 within 1 Mb of slc6A4. From these SNPs, we selected 43 SNPs with a minor allele frequency >0.05 and call rates of >0.75. We used Haploview software version 4.0 (Barrett et al. 2005) for the analysis of the presence of Hardy-Weinberg equilibrium (HWE), the local association analysis, and the calculation of pairwise linkage disequilibrium (LD) between the SNPs. A HWE P-value cutoff of 0.001 was used. We used Bonferonni correction to account for multiple testing in the association analysis. Genotype frequencies in cases and controls were compared with Chi square tests using SPSS software. Two tailed Fisher’s exact tests were used when the number of expected cases was less than 5 in more than 20% of the categories. Haplotype blocks were formed using three methods in Haploview (confidence intervals, four gamete rule, and solid spine of LD). For all possible combinations we performed 10,000 permutations to obtain empirical P values for haplotype association tests. We used the genetic power calculator prepared by Purcell to estimate the power of the association analysis (http://www.pngu.mgh.harvard.edu/~purcell/gpc/). The following assumptions were made: high-risk allele frequency = 0.1; prevalence = 0.01. The mean pairwise D′ between the SNPs flanking a candidate gene was used as an estimate of the local D′ in these estimations. Calculations were performed for two different genotype relative risks: 2 (genotype relative risk Aa = 2; genotype relative risk AA = 4) and 5 (genotype relative risk Aa = 5; genotype relative risk AA = 10). ### Quantitative genetic analysis In addition to the owner impression on human-directed aggression and dog-directed aggression, we collected a variety of other aggression-related behavioral measures using the canine behavioral assessment and research questionnaire (CBARQ; Hsu and Serpell 2003). As described in Liinamo et al. (2007), these measures were of three types: original CBARQ items (27 items on the aggressiveness of the dog in various everyday situations), shortened CBARQ scores (scores based on questions that addressed stranger-directed, owner-directed, and strange dog-directed aggression), and CBARQ factors (scores based on questions about stranger-directed, owner-directed, and strange dog-directed, and familiar dog-directed aggression). For further explanation of the measures and the difference between shortened CBARQ scores and CBARQ factors, see Liinamo et al. (2007). The effects of the haplotypes of the serotonergic genes on the different aggression measures were estimated with Restricted Maximum Likelihood (REML) method (Patterson and Thompson 1971), using univariate analyses and an animal model with the VCE4.2.4 software (Groeneveld 1997). The analyses were an extension of the analyses outlined in Liinamo et al. (2007), using similar linear animal model methodology, but this time also including the haplotype classes of the dogs for the four studied loci as additional fixed effects in the model. For instance, the linear animal model that was assumed in the analyses for owner impression traits was: $$y_{ijklmno} = \mu + sex_{i} + age_{j} + htr1a_{k} + htr1b_{l} + htr2a_{m} + slc6a4_{n} + a_{o} + e_{o}$$ where y ijklmno is the observed value for the owner impression score for animal o; μ the general mean in the population; sex i the fixed effect of the reproductive status (i = 1–4, with 1 = intact male, 2 = castrated male, 3 = intact female, and 4 = castrated female); age j the fixed effect of the age j (j = 1–11, with 1 = 0.5–1 year old, 2 = 1–2 years old,…,10 = 9–10 years old, and 11 = over 10 years old); htr1a k , htr1b l , htr2a m , and slc6a4 n the fixed effects of the respective haplotype classes, a o the random additive genetic effect (i.e., polygenic breeding value) of the animal o, and e o the random residual effect related to the animal o. The age and reproductive status of the dogs had been recorded at the same time as the owner impressions. The haplotype classes were formed so that the most common haplotypes formed separate classes, the very rare haplotypes were all combined in one class, and the unknown haplotypes were classified as a separate class (see Table 4). ## Results ### Mutation screening of the coding DNA sequence The coding DNA sequence of each candidate gene was scanned for mutations in seven (htr1A and htr1B) or eight (htr2A and slc6A4) aggressive Golden Retrievers. Analysis of the CDS in non-aggressive Golden Retrievers has been described by van den Berg et al. (2004; 2005). There was no variation in the CDS of htr1A and htr2A in the Golden Retrievers. We observed five SNPs in the CDS of htr1B and one SNP in the CDS of slc6A4. The allele distribution of these SNPs in the two groups of Golden Retrievers did not indicate a role in aggressive behavior. In conclusion, there seems to be no systematic difference between the CDS of the candidate genes in aggressive and non-aggressive Golden Retrievers. We observed two alleles for htr1A marker UU160O12 (Table 1). The four SNPs in htr1B were fully in LD (D′ = 1). The SNPs displayed six haplotypes in the Goldens, three of which were rare (frequency <0.1). We detected four haplotypes of htr2A in the Golden Retrievers. The two SNPs in slc6A4 were fully in LD and formed two haplotypes in the dogs. In the nine families that we used for linkage analysis, haplotypes were deduced with certainty in 86% of the dogs for htr1B, 100% for htr2A, and 87% for slc6A4. We calculated the maximum achievable LOD score using hypothetical genotypes. The maximum LOD score generated by our pedigrees was 2.8 at recombination fraction θ = 0 assuming a dominant mode of inheritance (Table 2). Under a recessive model, the maximum LOD score was 5.3 at θ = 0. The families are therefore theoretically powerful enough to prove linkage under a recessive model and powerful enough to provide a good indication of the presence of linkage under a dominant model. There was no significant linkage of any of the candidate genes with the aggressive phenotype (Table 2). LOD scores varied from −1.0 to +0.26 assuming dominant inheritance and from −2.3 to −0.30 assuming recessive inheritance. The highest LOD scores were obtained for htr1A (+0.26 under a dominant model and −0.30 under a recessive model). Table 2 Results from the ODDS (LOD) scoresa Gene Autosomal dominant Autosomal recessive htr1A 0.26 −0.30 htr1B −0.72 −2.3 htr2A −1.0 −2.1 slc6A4 0.030 −1.2 Maximum 2.8 5.3 aLOD scores were calculated with the following assumptions: frequency of the “aggression allele” = 0.1; penetrance of the “aggression allele” = 0.01; θ = 0. Marker haplotype frequencies were deduced from a group of parents ### Association study Two dogs (one case and one control) were discarded from the association analysis because they had call rates lower than 50%. Mean call rates in the other 98 dogs were 92% for SNPs flanking htr1A, 94% for htr1B, 93% for htr2A, and 93% for slc6A4. There were 43 SNPs with a minor allele frequency >0.05 and call rates of >0.75 that occurred within 1 Mb of the candidate genes. The genotype frequencies of BICF2P1093362 for htr1B and BICF2P969902 for slc6A4 deviated from HWE in control dogs (P = 4.42E-14 and P = 5.242E-12, respectively). All but one dog in both case and control group had heterozygous genotypes for these SNPs. We concluded that the data for these two SNPs was artefactual and they were excluded from further analyses. The observed genotype frequencies of the other 41 SNPs were in HWE in controls (P values are listed in Table S2 in Supplementary Information II). The final SNP set used for the association analysis consisted of 12 SNPs flanking htr1A, 11 flanking htr1B, 8 flanking htr2A, and 10 flanking slc6A4 (Table 3). Table 3 Single nucleotide polymorphisms (SNPs) used for the association study, their allele frequencies in 49 aggressive cases and 49 control dogs, and results of chi-square tests for comparisons of case and control allele frequencies SNP namea Chromosomal location Chromosomal position (Mb)b Minor allele frequency in controls Corresponding allele frequency in cases χ2 P-value BICF2P546848 2 51.80 0.29 0.30 0.044 0.83 BICF2P1051894 2 51.96 0.073 0.028 1.6 0.21 BICF2P1398268 2 52.01 0.33 0.33 0.011 0.92 BICF2S23127755 2 52.14 0.23 0.21 0.078 0.78 BICF2P1200391 2 52.22 0.30 0.33 0.21 0.64 BICF2P590055 2 52.35 0.24 0.27 0.19 0.66 BICF2S22939125 2 52.44 0.48 0.53 0.54 0.46 BICF2S23215863 2 52.48 0.30 0.31 0.025 0.87 BICF2P25993 2 52.73 0.49 0.45 0.19 0.66 BICF2S23442706 2 52.76 0.19 0.28 1.8 0.18 Htr1A 2 52.88–52.88 BICF2P519607 2 53.22 0.27 0.24 0.17 0.68 BICF2P1341930 2 53.62 0.49 0.54 0.52 0.47 BICF2P1159241 12 41.11 0.12 0.13 0.012 0.91 BICF2P555130 12 41.59 0.13 0.21 2.1 0.15 BICF2S23326229 12 41.63 0.24 0.32 1.3 0.25 Htr1B 12 41.65–41.66 BICF2P670331 12 41.80 0.15 0.23 2.2 0.14 BICF2S23153760 12 41.84 0.039 0.12 3.2 0.073 BICF2P1426522 12 42.29 0.12 0.12 0.013 0.91 BICF2P27571 12 42.34 0.12 0.10 0.21 0.65 BICF2S23444066 12 42.39 0.12 0.11 0.032 0.86 TIGRP2P164447_rs8805986 12 42.51 0.038 0.12 3.6 0.059 BICF2P812153 12 42.57 0.033 0.12 4.8 0.029 BICF2P855402 12 42.62 0.021 0.12 6.9 0.0086 BICF2G630315581 22 6.383 0.10 0.14 0.83 0.36 BICF2G630315746 22 6.611 0.10 0.14 0.45 0.50 BICF2P1168502 22 6.973 0.10 0.11 0.0020 0.96 Htr2A 22 7.395–7.453 BICF2P164280 22 7.509 0.43 0.54 2.0 0.16 BICF2G630316047 22 7.709 0.44 0.53 1.7 0.19 BICF2S23125159 22 7.866 0.19 0.21 0.047 0.83 BICF2S23661838 22 8.207 0.31 0.36 0.59 0.44 BICF2S22954191 22 8.470 0.23 0.27 0.35 0.55 BICF2P813837 9 46.93 0.39 0.30 1.5 0.22 BICF2S23018060 9 47.06 0.33 0.37 0.22 0.64 BICF2S23551918 9 47.46 0.34 0.38 0.24 0.62 Slc6A4 9 47.55–47.57 BICF2S23325050 9 47.64 0.11 0.15 0.53 0.47 BICF2S23124809 9 47.79 0.18 0.22 0.38 0.54 BICF2P950384 9 47.88 0.11 0.12 0.032 0.86 BICF2S245135 9 48.02 0.27 0.25 0.074 0.79 BICF2S2347312 9 48.09 0.22 0.28 0.84 0.36 BICF2S23154457 9 48.13 0.31 0.24 1.2 0.28 BICF2S23141984 9 48.26 0.36 0.36 0.0070 0.93 ahtr1A, htr1B, htr2A = respectively serotonin receptor 1A, 1B, and 2A gene; slc6A4 = serotonin transporter gene. The genes are included in the table to show their position relative to the SNPs bSNP positions are based on the second version of the dog genome assembly, released in May 2005 (CanFam2.0) as can be viewed on http://www.broad.mit.edu/ftp/pub/papers/dog_genome/snps_canfam2/ Positions of the genes are based on the second version of the dog genome assembly (CanFam2.0) as displayed in NCBI Map Viewer for Canis familiaris http://www.ncbi.nlm.nih.gov/mapview/map_search.cgi?taxid=9615 The power of our association analysis depends on the local extent of LD. The mean r 2 between the SNPs flanking htr1A was 0.36 and the mean D′ between these SNPs was 0.89. Mean r 2 values were 0.23, 0.25, and 0.21 for htr1B, htr2A, and slc6A4, respectively. Mean D′ values were 0.80, 0.72, and 0.88 for htr1B, htr2A, and slc6A4, respectively. When the marker allele frequency is 0.1, the power to detect a variant with a relative risk of 5 with 49 cases and 49 controls would be 0.91 for htr1A, 0.85 for htr1B, 0.78 for htr2A, and 0.90 for slc6A4. Additional power estimations are provided in Fig. S10 in Supplementary Information II. The allele frequencies of the SNPs did not differ significantly between cases and controls after correction for multiple testing (Table 3). Genotype frequencies also did not display significant differences between cases and controls (see Table S2 in Supplementary Information II). We also analyzed the association of haplotypes with the phenotype. No significant associations were found (data not shown). In conclusion, there seemed to be no association between alleles, genotypes or haplotypes of SNPs that flank the candidate genes and human-directed aggression in the Golden Retrievers. ### Quantitative genetic analysis We completed our analyses with a study of the effect of variation in the candidate genes on a collection of aggression-related phenotypic measures. The haplotype effects were studied on owner impressions on human- and dog-directed aggression, the original CBARQ items related to stranger- and owner-directed aggression, the shortened CBARQ scores and the CBARQ factors. The haplotypes did not have a significant effect on any of the studied measures, i.e. the heritability estimates of the measures remained similar to the results presented in Liinamo et al. (2007) in spite of incorporation of the haplotypes in the mixed model. The results for owner impressions on human- and dog-directed aggression, which are the most reliable estimates due to the largest number of observations, are presented in Table 4. In conclusion, the large genetic variability between the dogs could not be explained by the serotonergic genes studied in this paper. Table 4 The effects of the studied genotypes (htr1A) or haplotypes (htr1B, htr2A, and slc6A4) on owner impressions of human-directed aggression and dog-directed aggression in 320 dogs Genotype or haplotype classa Number of animals Effect relative to class ‘unknown’ Human-directed aggression Dog-directed aggression htr1A Unknown 44 0.00 0.00 297/297 74 0.028 0.11 297/303 111 0.24 0.054 297/305 15 0.012 0.089 303/303 62 0.18 0.085 303/305 10 −0.11 −0.067 Other 4 −0.046 −0.17 htr1B Unknown 166 0.00 0.00 143-A-G-T-G/143-A-G-T-G 20 −0.73 0.28 143-A-G-T-G /143-C-A-T-G 8 −0.63 −0.19 143-A-G-T-G /139-A-G-C-C 19 0.11 0.19 143-C-A-T-G/143-C-A-T-G 41 −0.17 0.13 143-C-A-T-G /143-A-G-C-C 10 −0.021 0.059 143-C-A-T-G /139-A-G-C-C 30 0.0006 0.32 139-A-G-C-C/139-A-G-C-C 9 0.24 0.11 Other 17 0.15 0.36 htr2A Unknown 114 0.00 0.00 132-C/132-C 40 −0.15 −0.19 132-C/130-C 60 −0.27 −0.023 132-C/132-T 28 −0.22 0.073 132-C/128-C 15 −0.38 −0.43 130-C/130-C 21 −0.33 −0.072 130-C/132-T 22 0.10 −0.19 130-C/128-C 9 −0.52 −0.29 Other 11 0.33 −0.036 slc6A4 Unknown 103 0.00 0.00 C-G/C-G 116 0.025 −0.23 C-G/T-A 94 0.14 −0.23 Other 7 0.079 −0.10 None of the effects was significant aNote that there are additional alleles compared to Table 1 as a result of the larger study group. The htr1A class “other” contains genotypes 295/297 (n = 2 dogs) and 305/305 (n = 1 dog). For htr1B, the class “other” contains haplotypes 143-A-G-T-G/143-A-G-C-C (n = 3 dogs), 143-A-G-T-G/139-A-G-T-G (n = 1 dog), 143-A-G-T-G/147-A-G-T-G (n = 2 dogs), 143-A-G-C-C /139-A-G-C-C (n = 3 dogs), 143-A-G-C-C/147-A-G-T-G (n = 1 dog), 139-A-G-C-C /139-A-G-T-G (n = 3 dogs), and 143-C-A-T-G/139-A-G-T-G (n = 4 dogs). For htr2A, “other” contains haplotypes 0/130-C (n = 2 dogs), 0/132-T (n = 1 dog), 132-T /132-T (n = 6 dogs), and 132-T/128-C (n = 2 dogs). For slc6A4, “other” contains C-G/T-G (n = 1 dog) and T-A/T-A (n = 6 dogs). Unknown genotypes and haplotypes are the result of failure of genotyping or of the absence of a DNA sample (n = 44 dogs) ## Discussion We collected behavioral information and DNA samples of 281 dogs over a period of 10 years. Dogs were selected from this collection to evaluate four genes involved in serotonin metabolism by four methods: DNA sequence analysis of the coding region of the genes, genetic linkage analysis, genetic association analysis, and quantitative genetic analysis. The results indicate that it is unlikely that there is a major locus effect of one of the genes on aggression in the Golden Retrievers that we studied. The genetic study of the variation of aggression in Golden Retrievers is a promising tool to identify the molecular systems involved in aggression. The relative ease to find disease loci in the dog genome compared to the human genome is the result of the population structure of dog breeds. Within a breed, Lindblad-Toh and colleagues (2005) observed a limited number of common haplotypes per genomic region. In addition, LD in dog breeds extends over at least 50-fold greater distances than in human populations. These characteristics make the dog highly suited for molecular genetic studies of complex traits (Sutter and Ostrander 2004). We did not detect mutations in the CDS of the genes specific for aggressive dogs. All SNPs except A157C in htr1B were synonymous. This A157C variation, resulting in an isoleucine/leucine polymorphism of amino acid 53, was predicted to be functionally insignificant by POLYPHEN. The genes htr2A and slc6A4 contain SNPs close to splice sites (at position IVS2-10 and IVS9-12, respectively) that could theoretically affect splicing. However, the polymorphisms did not have a large effect on splice site prediction by three software programs. We performed mutation screening in a limited number of dogs and it is possible that we have missed rare alterations in the genes. Apart from this limitation, we conclude that there is no common variant acting on protein structure that contributes to the variation in aggression in our Golden Retriever sample. We used linkage analysis to evaluate the likelihood that there is a major aggression-influencing variant in the chromosomal regions surrounding the coding exons. The affecteds only parameters that we used in the calculations are a simplification with the assumption that all affected dogs of a family have the genotype at risk but unaffected dogs can have any genotype at the aggression locus. A LOD score of 3 is usually considered as evidence for linkage, whereas LOD scores below −2 exclude the gene. A power calculation with simulated genotypes was not feasible in this study due to the complexity of some pedigrees with multiple loops. Instead, we calculated the maximum achievable LOD scores to get an impression of the power embodied in the pedigrees. We assumed full informativeness of the markers in these calculations, but in reality, we expect the markers to have limited informativeness. Realistic obtainable LOD scores would then be lower than the maximum values that we presented in Table 2. These LOD scores are too low to obtain significant results, but they provide a means to set the obtained results into perspective. The LOD scores for htr1B and htr2A were low compared to the maximum obtainable scores. A major role of these genes is unlikely. The results for htr1A and slc6A4 are less conclusive. This is probably the result of the poor informativeness of the markers. For both genes, we observed only two alleles or haplotypes with high frequencies. Typing of additional markers might help to definitively exclude the genes. However, in the light of the observed low level of variation it is unlikely that htr1A and slc6A4 have a strong effect on aggression in the Golden Retriever families. Our linkage analysis does not account for genetic heterogeneity or phenocopies. We have thus only tested for a very strong major locus effect. In reality, the aggressiveness in the Golden Retrievers may be more complex. We therefore used a third study design to investigate the candidate genes: association analysis. For this analysis, we used data from a large-scale genotyping project in 100 Golden Retrievers. Our power calculations demonstrate that this sample size is expected to be sufficient to detect variants that confer a high relative risk for a range of marker allele frequencies. From the total set of 60,073 SNP genotypes, we selected 41 SNPs that flank the candidate genes. We found no association between alleles, genotypes or haplotypes of these SNPs flanking the candidate genes and human-directed aggression of the Golden Retrievers. We focused on human-directed aggression in the affecteds-only linkage analysis and the association study. In our quantitative genetic analysis, we studied additional types of aggression. There is no consensus in the literature on how aggression should be subdivided (Houpt and Willis 2001; Jacobs et al. 2003; Serpell and Jagoe 1995). There are indications that various types of aggression have a distinct genetic basis. For instance, selection of rats and silver foxes for reduced fear-induced aggression towards humans did not change predatory or inter-male aggression (Naumenko et al. 1989; Popova et al. 1993). This suggests that molecular genetic studies of aggressive behavior should focus on specific classes of aggression. However, reduced aggressiveness towards man in the rats and foxes was accompanied by reduced fear of novelties and irritable aggression, indicating that there is overlap between classes. As long as the genetic roots of aggressive behavior are poorly understood, it will remain impossible to design a classification that reflects the genetic basis. In conclusion, none of the four methods of analysis provided evidence for a strong effect of variants of the candidate genes on aggression in the Golden Retrievers that we studied. These results seem to contradict reports of the involvement of the candidate genes in the regulation of aggressive behavior. However, the study designs that we used are not powerful enough to detect variants of small effect. We can therefore not rule out the possibility that variation in the candidate genes has a smaller genetic effect on aggression. In addition, our results cannot be construed as evidence against a major role for these genes in aggression in other dog breeds. Possibly, other genes in the serotonin pathway play a role. With the completion of the dog genome project, genome-wide association studies have become feasible in dogs (Lindblad-Toh et al. 2005). This opens the opportunity for finding genes that have not been associated with aggression up to date. Such studies are in progress. ## Notes ### Acknowledgments The “Jubileumfonds Hoogleraren Diergeneeskunde” supported this work. We thank Laura Kwant, Frank van Steenbeek, and Tara Biagi for technical assistance, Harry van Engelen for collection of the blood samples, and the dog owners for their cooperation with our project. ### Open Access This article is distributed under the terms of the Creative Commons Attribution Noncommercial License which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited. ## Supplementary material 10519_2007_9179_MOESM1_ESM.doc (174 kb) (DOC 174 kb) ## References 1. Abdolmaleky HM, Faraone SV, Glatt SJ, Tsuang MT (2004) Meta-analysis of association between the T102C polymorphism of the 5HT2a receptor gene and schizophrenia. Schizophr Res 67:53–62 2. 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Sutter NB, Ostrander EA (2004) Dog star rising: the canine genetic system. Nat Rev Genet 5:900–910 45. Trut LN (2001) Experimental studies of early canid domestication. In: Ruvinsky A, Sampson J (eds) The genetics of the dog. CABI Publishing, New York, pp 15–41Google Scholar 46. Van den Berg L, Schilder MBH, Knol BW (2003a) Behavior genetics of canine aggression: behavioral phenotyping of Golden Retrievers by means of an aggression test. Behav Genet 33:469–483 47. Van den Berg L, Versteeg S, Van Oost BA (2003b) Isolation and characterization of the canine serotonin receptor 1A gene (htr1A). J Heredity 94:49–56 48. Van den Berg L, Imholz S, Versteeg SA, Leegwater PAJ, Zijlstra C, Bosma AA, Van Oost BA (2004) Isolation and characterization of the canine serotonin receptor 1B gene (htr1B). Gene 326:131–139 49. Van den Berg L, Kwant L, Hestand MS, van Oost BA, Leegwater PAJ (2005) Structure and variation of three canine genes involved in serotonin binding and transport: the serotonin receptor 1A gene (htr1A), serotonin receptor 2A gene (htr2A), and serotonin transporter gene (slc6A4). J Heredity 96(7):786–796 50. Van den Berg L, Schilder M, de Vries H, Leegwater PAJ, van Oost BA (2006) Phenotyping of aggressive behaviour in Golden Retriever dogs with a questionnaire. Behav Genet 36(6):882–902 © The Author(s) 2007 ## Authors and Affiliations • L. van den Berg • 1 • 2 • M. Vos-Loohuis • 1 • M. B. H. Schilder • 3 • B. A. van Oost • 4 • H. A. W. Hazewinkel • 1 • C. M. Wade • 5 • 6 • E. K. Karlsson • 5 • 5 • A. E. Liinamo • 7 • P. A. J. Leegwater • 1 1. 1.Department of Clinical Sciences of Companion Animals, Faculty of Veterinary MedicineUtrecht UniversityUtrechtThe Netherlands 2. 2.Department of Clinical Genetics, Section Medical GenomicsVU University Medical CenterAmsterdamThe Netherlands 3. 3.Department of Animals, Science and Society, Faculty of Veterinary MedicineUtrecht UniversityUtrechtThe Netherlands 4. 4.American University of the CaribbeanSt. MaartenThe Netherlands 5. 5.The Broad Institute of Harvard and MITCambridgeUSA 6. 6.Center for Human Genetic ResearchMassachusetts General HospitalBostonUSA 7. 7.Department of Animal ScienceHelsinki UniversityHelsinkiFinland	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7383254170417786, "perplexity": 10961.340735045836}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267159570.46/warc/CC-MAIN-20180923173457-20180923193857-00193.warc.gz"}
https://www.elastic.co/blog/kibana-5-0-0-alpha1	Kibana 5.0.0-alpha1 released \| Elastic Blog Releases Kibana 5.0.0-alpha1 released Kibana 5 is the best thing since sliced bread. There, I've said it. You know what? It's better than sliced bread. Kibana 5 is going to dethrone bread as the universal standard of goodness. And you can take a bite out of this bad boy right now: today we're sharing with the world the first alpha release of Kibana 5. If you're already salivating, pick up the Kibana 5.0.0-alpha1 from the downloads page. IMPORTANT: This is alpha software that will only work with Elasticsearch 5.0.0-alpha1. Please test it, but do not use it in production. So what's new in Kibana 5? A new design That's right, we redesigned it. Where Kibana 4 was dreary, Kibana 5 is bright and colorful. Where Kibana 4 wasted countless pixels on unnecessary navigation and chrome, Kibana 5 lets the borders fall away and brings a new focus on your data. Where Kibana ah forget it. Just see for yourself: First-class applications Since the plugin system was launched in 4.2, people have been building entire applications on top of Kibana. In Sense and Timelion, we created two such applications ourselves, but even they have been relegated to a tiny "app switcher" that is mostly hidden away in the toolbar. In Kibana 5, all applications are first-class citizens. Applications added by any plugin will appear in the main navigation alongside the Kibana favorites: discover, visualize, and dashboard. Packs, and a new plugin installer I'm sure you all loved installing every single plugin by hand as well as always remembering the exact plugin version that was compatible with your current version of Kibana. And off the top of your head, I bet you can recite exactly which organization name we arbitrarily chose to use for any given plugin of our own. But despite those "charms" of the existing plugin installer, we decided to make it a bit easier this time around anyway. In Kibana 5, one or more plugins can be bundled and installed as a single pack. Want to install a third party pack? Just give it a url: bin/kibana-plugin install https://example.com/mypack.zip Or how about one of our own - perhaps timelion's your cup of tea: bin/kibana-plugin install timelion Want security, monitoring, reporting, and graph? Grab them all as a single pack: bin/kibana-plugin install x-pack What is it not? Great question, me! Kibana 5 is not a rewrite from the ground up. We ripped that band-aid off long ago, and while necessary at the time, a massive overhaul of the entire application is no longer required to take a huge step forward like we have in Kibana 5. This alpha release is also not production ready. There are a bunch of known issues, and there are no doubt many more that we haven't discovered yet. There will be tons of commits coming into 5.0 over the next few weeks and months, and we'll probably break a few new things as well. This release isn't even feature-complete. We have a ton of features that we're still working on that we want to get into 5.0. Sense, for example. We're bringing that whole plugin into Kibana core, but that work isn't finished yet, so alpha1 is Senseless. What's next? Well, alpha2 of course! We're already working on it, and it's going to be even better than this. When Kibana 5.0 stable ships, these Kibana pre-releases will have bogarted the whole goodness leaderboard, and there will be no bread in sight. Too far with that analogy, eh? Anyway, we hope that you'll download this alpha and try it out. We'd love to get your feedback on our forums, irc, or even twitter, and please post any bugs you find directly to our github issues.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17672206461429596, "perplexity": 3594.257369114469}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347458095.68/warc/CC-MAIN-20200604192256-20200604222256-00280.warc.gz"}
https://nrich.maths.org/5951	### Biscuit Decorations Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated? ### Constant Counting You can make a calculator count for you by any number you choose. You can count by ones to reach 24. You can count by twos to reach 24. What else can you count by to reach 24? ### Skip Counting Find the squares that Froggie skips onto to get to the pumpkin patch. She starts on 3 and finishes on 30, but she lands only on a square that has a number 3 more than the square she skips from. # One of Thirty-six ##### Stage: 1 Challenge Level: Can you find the chosen number from this square using the clues below? 1. The number is odd. 2. It is a multiple of three. 3. It is smaller than $7\times 4$. 4. Its tens digit is even. 5. It is the greater of the two possibilities. You might like to print off this sheet of the problem.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3929876387119293, "perplexity": 1961.6810159602917}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084891980.75/warc/CC-MAIN-20180123151545-20180123171545-00706.warc.gz"}
https://www.r-bloggers.com/2019/08/detecting-outlier-samples-in-pca/	In this post, I present something I am currently investigating (feedback welcome!) and that I am implementing in my new package {bigutilsr}. This package can be used to detect outlier samples in Principal Component Analysis (PCA). remotes::install_github("privefl/bigutilsr") library(bigutilsr) I present three different statistics of outlierness and two different ways to choose the threshold of being an outlier for those statistics. ## A standard way to detect outliers ### Data X <- readRDS(system.file("testdata", "three-pops.rds", package = "bigutilsr")) pca <- prcomp(X, scale. = TRUE, rank. = 10) U <- pca$x library(ggplot2) theme_set(bigstatsr::theme_bigstatsr(0.8)) qplot(U[, 1], U[, 2]) + coord_equal() ### Measuring outlierness The standard way to detect outliers in genetics is the criterion of being “more than 6 standard deviations away from the mean”. apply(U, 2, function(x) which( abs(x - mean(x)) > (6 * sd(x)) )) ## integer(0) Here, there is no outlier according to this criterion. Let us make some fake one. U2 <- U U2[1, 1] <- 30 qplot(U2[, 1], U2[, 2]) + coord_equal() apply(U2, 2, function(x) which( abs(x - mean(x)) > (6 * sd(x)) )) ## integer(0) Still not an outlier.. U3 <- U2 U3[1, 1] <- 80 qplot(U3[, 1], U3[, 2]) + coord_equal() library(magrittr) apply(U3, 2, function(x) which( abs(x - mean(x)) > (6 * sd(x)) )) %>% Reduce(union, .) ## [1] 1 Now, the first sample is considered as an outlier by this criterion. ### A more robust variation Note that you might want to use median() instead of mean() and mad() instead of sd() because they are more robust estimators. This becomes ind.out <- apply(U3, 2, function(x) which( (abs(x - median(x)) / mad(x)) > 6 )) %>% Reduce(union, .) %>% print() ## [1] 1 516 We get a new outlier. col <- rep("black", nrow(U3)); col[ind.out] <- "red" qplot(U3[, 1], U3[, 3], color = I(col), size = I(2)) + coord_equal() ### A continuous view of this criterion This criterion flag an outlier if it is an outlier for at least one principal component (PC). This corresponds to using the max() (infinite) distance (in terms of number of standard deviations) from the mean. dist <- apply(U3, 2, function(x) abs(x - median(x)) / mad(x)) %>% apply(1, max) qplot(U3[, 1], U3[, 3], color = dist, size = I(3)) + coord_equal() + scale_color_viridis_c(trans = "log", breaks = c(1, 3, 6)) qplot(y = sort(dist, decreasing = TRUE)) + geom_hline(yintercept = 6, color = "red") ## Investigating two other criteria of outlierness ### Robust Mahalanobis distance Instead of using the infinite distance, Mahalanobis distance is a multivariate distance based on all variables (PCs here) at once. We use a robust version of this distance, which is implemented in packages {robust} and {robustbase} (Gnanadesikan and Kettenring 1972, Yohai and Zamar (1988), Maronna and Zamar (2002), Todorov, Filzmoser, and others (2009)) and that is reexported in {bigutilsr}. dist2 <- covRob(U3, estim = "pairwiseGK")$dist qplot(dist, sqrt(dist2)) cowplot::plot_grid( qplot(U3[, 1], U3[, 2], color = dist2, size = I(2)) + coord_equal() + scale_color_viridis_c(trans = "log", breaks = NULL), qplot(U3[, 3], U3[, 7], color = dist2, size = I(2)) + coord_equal() + scale_color_viridis_c(trans = "log", breaks = NULL), rel_widths = c(0.7, 0.4), scale = 0.95 ) This new criterion provides similar results for this data. These robust Mahalanobis distances are approximately Chi-square distributed, which enables deriving p-values of outlierness. pval <- pchisq(dist2, df = 10, lower.tail = FALSE) hist(pval) is.out <- (pval < (0.05 / length(dist2))) # Bonferroni correction sum(is.out) ## [1] 33 qplot(U3[, 3], U3[, 7], color = is.out, size = I(3)) + coord_equal() ### Local Outlier Factor (LOF) LOF statistic (Breunig et al. 2000) has been cited more than 4000 times. Instead of computing a distance from the center, it uses some local density of points. We make use of the fast K nearest neighbours implementation of R package {nabor} (Elseberg et al. 2012) to implement this statistic efficiently in {bigutilsr}. llof <- LOF(U3) # log(LOF) by default qplot(dist2, llof) The fake outlier that we introduced is now clearly an outlier. The other points, not so much. cowplot::plot_grid( qplot(U3[, 1], U3[, 2], color = llof, size = I(3)) + coord_equal() + scale_color_viridis_c(breaks = NULL), qplot(U3[, 3], U3[, 7], color = llof, size = I(3)) + coord_equal() + scale_color_viridis_c(breaks = NULL), rel_widths = c(0.7, 0.4), scale = 0.95 ) ## Choosing the threshold of being an outlier Threshold of 6 for the first criterion presented here may appear arbitrary. If the data you have is normally distributed, each sample (for each PC) has a probability of 2 * pnorm(-6) (2e-9) of being considered as an outlier by this criterion. Accounting for multiple testing, for 10K samples and 10 PCs, there is a chance of 1 - (1 - 2 * pnorm(-6))^100e3 (2e-4) of detecting at least one outlier. If choosing 5 as threshold, there is 5.6% chance of detecting at least one outlier when PCs are normally distributed. If choosing 3 instead, this probability is 1. ### Tukey’s rule Tukey’s rule (Tukey 1977) is a standard rule for detecting outliers. Here, we will apply it on the previously computed statistics. Note that we could use it directly on PCs, which is not much different from the robust version of the first criterion we introduced. x <- rnorm(10000) (tukey_up <- quantile(x, 0.75) + 1.5 * IQR(x)) ## 75% ## 2.70692 (tukey_low <- quantile(x, 0.25) - 1.5 * IQR(x)) ## 25% ## -2.725665 hist(x); abline(v = c(tukey_low, tukey_up), col = "red") mean(x < tukey_low \| x > tukey_up) ## [1] 0.0057 where IQR(x) is equal to quantile(x, 0.75) - quantile(x, 0.25) (the InterQuartile Range). However, there are two pitfalls when using Tukey’s rule: 1. Tukey’s rule assumes a normally distributed sample. When the data is skewed, it does not work that well. x <- rchisq(10000, df = 5) (tukey_up <- quantile(x, 0.75) + 1.5 * IQR(x)) ## 75% ## 12.42084 (tukey_low <- quantile(x, 0.25) - 1.5 * IQR(x)) ## 25% ## -3.232256 hist(x, "FD"); abline(v = c(tukey_low, tukey_up), col = "red") mean(x < tukey_low \| x > tukey_up) ## [1] 0.0294 To solve the problem of skewness, the medcouple (mc) has been introduced (Hubert and Vandervieren 2008) and is implemented in robustbase::adjboxStats(). 2. Tukey’s rule uses a fixed coefficient (1.5) that does not account for multiple testing, which means that for large samples, you will almost always get some outliers if using 1.5. To solve these two issues, we implemented tukey_mc_up() that accounts both for skewness and multiple testing by default. x <- rchisq(10000, df = 5) (tukey_up <- quantile(x, 0.75) + 1.5 * IQR(x)) ## 75% ## 12.48751 hist(x, "FD"); abline(v = tukey_up, col = "red") abline(v = print(tukey_mc_up(x, coef = 1.5)), col = "blue") ## [1] 16.74215 abline(v = print(tukey_mc_up(x)), col = "green") # accounts for multiple testing ## [1] 25.93299 Applying this corrected Tukey’s rule to our statistics: tukey_mc_up(dist) ## [1] 6.406337 qplot(dist2, llof) + geom_vline(xintercept = tukey_mc_up(dist2), color = "red") + geom_hline(yintercept = tukey_mc_up(llof), color = "red") ### Histogram’s gap This rule I come up with assumes that the “normal” data is somewhat grouped and the outliers have some gap (in the histogram, there is a bin with no value in it) with the rest of the data. For example, for dist, there is a gap just before 6, and we can derive an algorithm to detect this: hist(dist, breaks = nclass.scottRob) str(hist_out(dist)) ## List of 2 ## $x : num [1:515] 2.08 2.06 1.74 1.86 2.04 ... ##$ lim: num [1:2] -Inf 5.75 abline(v = hist_out(dist)$lim[2], col = "red") hist(dist2, breaks = nclass.scottRob) abline(v = hist_out(dist2)$lim[2], col = "red") hist(llof, breaks = nclass.scottRob) abline(v = hist_out(llof)$lim[2], col = "red") This criterion is convenient because it does not assume any distribution of the data, just that it is compact and that the outliers are not in the pack. It could be used in other contexts, e.g. choosing the number of outlier principal components: eigval <- pca$sdev^2 hist(eigval, breaks = "FD") # "FD" gives a bit more bins than scottRob abline(v = hist_out(eigval, breaks = "FD")$lim[2], col = "red") sum(eigval > hist_out(eigval, breaks = "FD")$lim[2]) ## [1] 3 pca_nspike(eigval) # directly implemented in {bigutilsr} ## [1] 3 Note the possible use of bootstrap to make hist_out() and pca_nspike() more robust. ## Conclusion Outlier detection is not an easy task, especially if you want the criterion of outlierness to be robust to several factors such as sample size and distribution of the data. Moreover, there is always some threshold to choose to separate outliers from non-ouliers. With one small example, we have seen several statistics to compute some degree of outlierness: 1. “6 standard deviations away from the mean” that somewhat assumes that PCs are normally distributed. Here, data is more a mixture of distributions (one for each cluster) than one normal distribution so that it might not work that well. 2. Mahalanobis distance that also assumes a (multivariate) normal distribution but that takes into account the correlation between PCs (that is not the identity because we use a robust estimation). 3. Local Outlier Factor (LOF) that does not assume any distribution and that finds points that are in empty areas (far from every other points) rather than points that are far from the center. One drawback is that this statistic has an hyper-parameter K (nearest neighbours); we combine three different values by default to make this statistic more robust to the choice of this parameter K. and several ways to decide the threshold of being an outlier according to those statistics: 1. Tukey’s rule, adjusting for skewness and multiple testing. 2. “Histogram’s gap” that finds a gap between outlier values and “normal” values based on a histogram. I have been investigating outlier detection in the past weeks. Any feedback and further input on this would be great. ## References Breunig, Markus M, Hans-Peter Kriegel, Raymond T Ng, and Jörg Sander. 2000. “LOF: Identifying Density-Based Local Outliers.” In ACM Sigmod Record, 29:93–104. 2. ACM. Elseberg, Jan, Stéphane Magnenat, Roland Siegwart, and Andreas Nüchter. 2012. “Comparison of Nearest-Neighbor-Search Strategies and Implementations for Efficient Shape Registration.” Journal of Software Engineering for Robotics 3 (1): 2–12. Gnanadesikan, Ramanathan, and John R Kettenring. 1972. “Robust Estimates, Residuals, and Outlier Detection with Multiresponse Data.” Biometrics. JSTOR, 81–124. Hubert, Mia, and Ellen Vandervieren. 2008. “An Adjusted Boxplot for Skewed Distributions.” Computational Statistics & Data Analysis 52 (12). Elsevier: 5186–5201. Maronna, Ricardo A, and Ruben H Zamar. 2002. “Robust Estimates of Location and Dispersion for High-Dimensional Datasets.” Technometrics 44 (4). Taylor & Francis: 307–17. Todorov, Valentin, Peter Filzmoser, and others. 2009. “An Object-Oriented Framework for Robust Multivariate Analysis.” Citeseer. Tukey, John W. 1977. Exploratory Data Analysis. Addison-Wesley. Yohai, Victor J, and Ruben H Zamar. 1988. “High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale.” Journal of the American Statistical Association 83 (402). Taylor & Francis: 406–13.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6844632029533386, "perplexity": 6180.953969676761}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964363216.90/warc/CC-MAIN-20211205191620-20211205221620-00075.warc.gz"}
https://deepai.org/publication/the-generalized-persistent-nerve-theorem	# The Generalized Persistent Nerve Theorem In this paper a parameterized generalization of a good cover filtration is introduced called an ϵ-good cover, defined as a cover filtration in which the reduced homology groups of the image of the inclusions between the intersections of the cover filtration at two scales ϵ apart are trivial. Assuming that one has an ϵ-good cover filtration of a finite simplicial filtration, we prove a tight bound on the bottleneck distance between the persistence diagrams of the nerve filtration and the simplicial filtration that is linear with respect to ϵ and the homology dimension. This bound is the result of a computable chain map from the nerve filtration to the space filtration's chain complexes at a further scale. Quantitative guarantees for covers that are not good are useful for when one is working a non-convex metric space, or one has more simplicial covers that are not the result of triangulations of metric balls. The Persistent Nerve Lemma is also a corollary of our theorem as good covers are 0-good covers. Lastly, a technique is introduced that symmetrizes the asymmetric interleaving used to prove the bound by shifting the nerve filtration's persistence module, improving the interleaving constant by a factor of 2. ## Authors • 3 publications • 6 publications • ### Embeddings of Persistence Diagrams into Hilbert Spaces Since persistence diagrams do not admit an inner product structure, a ma... 05/11/2019 ∙ by Peter Bubenik, et al. ∙ 0 • ### Filtration Simplification for Persistent Homology via Edge Contraction Persistent homology is a popular data analysis technique that is used to... 10/10/2018 ∙ by Tamal K. Dey, et al. ∙ 0 • ### Stable Signatures for Dynamic Metric Spaces via Zigzag Persistent Homology When studying flocking/swarming behaviors in animals one is interested i... 12/11/2017 ∙ by Woojin Kim, et al. ∙ 0 • ### Intrinsic persistent homology via density-based metric learning We address the problem of estimating intrinsic distances in a manifold f... 12/11/2020 ∙ by Eugenio Borghini, et al. ∙ 0 • ### A lower bound for essential covers of the cube Essential covers were introduced by Linial and Radhakrishnan as a model ... 05/28/2021 ∙ by Gal Yehuda, et al. ∙ 0 • ### On the entropy of coverable subshifts A coloration w of Z^2 is said to be coverable if there exists a rectangu... 12/19/2018 ∙ by Guilhem Gamard, et al. ∙ 0 • ### Combined Covers and Beth Definability In ESOP 2008, Gulwani and Musuvathi introduced a notion of cover and exp... 11/18/2019 ∙ by Diego Calvanese, et al. ∙ 0 ##### This week in AI Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. ## 1 Introduction The Nerve Theorem [1] is an important link between topological spaces and discrete geometric and topological algorithms. It is at the heart, either implicitly or explicitly, of many foundational algorithms in the rapidly growing field of topological data analysis. Example problems include surface reconstruction [2, 3, 4], function reconstruction [5], homology inference [6, 7, 8] , coordinate-free sensor network coverage [9, 10], shape analysis [11], data modeling [12, 13, 14], and clustering [15, 16]. A cover of a simplicial complex is a collection of subcomplexes such that . 111The notation is intended to help the reader remember that , (“double U”) is the union of the ’s. The nerve of is the abstract simplicial complex defined as follows NrvU:={non-empty σ⊆[n]∣⋂i∈σUi≠∅}. A cover is good if for every the simplicial complex is empty or contractible. The Nerve Theorem equates the homotopy type and thus homology of the covered simplicial complex to that of the nerve of a good cover . This theorem allows one to construct algorithms that compute topological properties of the nerve of a particular good cover and relate the output back to infer properties of the covered space. In persistence theory, one often works with filtered topological spaces: , where for all . The Persistent Nerve Lemma of Chazal and Oudot [2] proves that the Nerve Theorem extends in the most natural way to the persistence setting. In particular, it implies that the union filtration and the nerve filtration have the same persistent homology assuming is a good cover of for all . The requirement of good covers to ensure topological theoretical guarantees has significant algorithmic implications as it significantly reduces the spaces one can work in. Many algorithms in topological data analysis utilize a standard pipeline where one considers a nice sample of some space, builds a simplicial complex from this sample called the Čech complex, which is the nerve of metric balls, and uses the fact that this has the same topology of the metric balls. This means that algorithms depending on the Nerve Theorem can only be applied to spaces that admit covers by convex sets in Euclidean spaces or smooth manifolds of sufficiently large convexity radius [5] can be considered. Even one small hole in an intersection of cover elements can render nerve-based computational algorithms invalid as the theory rests upon some interpretation of this theorem. This also has implications for triangulations of covers of surfaces that have marginal measurement errors, because the errors can cause the cover elements to no longer be convex for example. Nerves are also in coverage testing for homological sensor networks [10, 9], however the idealized model of Euclidean balls as coverage regions differs significantly from the very jagged coverage regions measured in practice, particularly when taking into account the affect of physical obstacles on real-life sensors’ detection ranges. In this paper we introduce a parametrization of the good cover condition for simplicial cover filtrations called an -good cover, which roughly says that the homology of the cover elements’ intersections only persists for some amount of time. Our main result is as follows. Given a simplicial cover filtration that is an -good cover filtration of the corresponding covered simplicial filtration, there exists a constructive -interleaving between the -dimensional persistence modules of the a finite simplicial filtration and its covers’ nerve filtration, which implies a tight bound on the bottleneck distance between each modules persistence diagram. We assume no structure on the simplicial cover filtration other than that the simplicial complexes are finite. This persistence module interleaving notably results from a “pseudo” interleaving between chain complexes where we only require the maps compositions are chain homotopic to the identity chain maps between scales. Due to the spaces in question being finite simplicial complexes, the chain maps used to construct the homological interleaving are computable. A corollary of the Generalized Persistent Nerve Theorem is the algebraic Persistent Nerve Lemma for simplicial filtrations and covers. We also reduce the interleaving distance and thus the bottleneck distance bound by a factor of in Section 5 by considering a time-scale shifted nerve filtration assuming one knows an upper bound on the -goodness of the cover. #### History of the Problem In August , Govc and Skraba posted the solution to a very similar problem, among other results in their paper An Approximate Nerve Theorem to the arXiv. They originally assumed that the reduced homology of the -wise intersections of a simplicial cover filtrations’ cover elements are -interleaved with the module, a condition they call an -acyclic cover. Their paper arrived at an identical bound, up to differences in definitions. They restricted their hypotheses to a filtered simplicial complex that is induced by a cover on the complete complex. The cover filtration at each scale was thus defined by the simplicial filtration at that scale’s intersection with the cover. Unfortunately, this assumption is too restrictive to imply a simplicial version of the Persistent Nerve Lemma which was a primary goal of this research for us, as it does not account for covers which have no inherent relation to each other outside of inclusions. In September , we submitted our results for presentation at the 26th Fall Workshop on Computational Geometry, which notably implied the Persistent Nerve Lemma as a corollary, for our space assumptions, as originally desired. Soon afterwards, Govc and Skraba updated their arXiv submission relaxing their cover filtration assumption, and their paper has recently been accepted to a journal [17]. Though our papers both prove a similar result, the approaches are very different and utilize and develop different tools. Govc and Skraba utilized a construction from homological algebra called a spectral sequence, as well as their novel right and left persistence module interleavings to prove their theorem, which is actually a direct result of the the module interleavings they compute between the pages of the spectral sequences and the persistence modules of the nerve and space filtrations. In contrast, our proof technique focuses on constructing maps between the chain complexes of the nerve filtration, space filtration, and the barycentric decomposition of the so-called blow-up complex. We go from the homological -goodness condition to corresponding chain maps and chain homotopies between them among the chain complexes of the spaces of interest. This is more inline with the approach traditionally used to proof the Nerve Theorem and the homotopy version of the Persistent Nerve Lemma. Due to the fact that these chain maps are defined on chain complexes of simplicial complexes and regular CW-complexes, they are computable in practice. Our module interleaving and bottleneck distance bound results are a consequence of a chain-theoretic generalization of an interleaving only up to chain homotopy, rather than being purely one concerning persistent homology. There are also the novel contributions of the creation of chain map between the barycentric decomposition of the nerve of a cover and the space filtration at a further time scale, and the use a technique we call lifting to form a chain map into the barycentric decomposition of the blowup complex. The lack of existence of such a map is the reason the Nerve Theorem fails when the cover is not good, which gives credence to the notion that the maps we construct are “natural” choices. #### Related Work Apart from the Persistent Nerve Lemma and it’s original homotopy version, researchers have examined related problems concerning covers and their associated nerves with respect to persistence theory. Botnan and Spreemann [18] proved that if three cover filtrations are -interleaved, where two of the filtrations are good and sandwich the third in the interleaving, then the bottleneck distance between the persistence module of the nerve of one of the good cover filtrations and the arbitrary one is upper bounded by . Dey et al. [19] prove that for a cover whose elements are path-connected, the -dimensional homology of the map from the covered space to the nerve of the cover is surjective. Using this result, they also prove that if there exists a so-called cover map between two covers, then the -dimensional homology of the simplicial map resulting from the cover map between the covers’ nerves is surjective. ## 2 Background This is an overview of the combinatorial, topological and algebraic structures used in the paper to prove the Generalized Persistent Nerve Theorem. See Hatcher’s Algebraic Topology [20] for further reference on chain complexes and homology, and Chazal et al.’s The Structure and Stability of Persistence Modules [21] for more on persistence theory. ### 2.1 Simplicial Complexes A geometric simplex is the convex closure of a set of affinely independent points. A (geometric) simplicial complex is a collection of simplices such that for each simplex in , each of its subsimplices are in , and the intersection of two simplices is in or is empty. An abstract simplicial complex over a finite vertex set is a subset of the powerset closed under taking subsets. For a simplex , its dimension is . A simplex of dimension is called a -simplex of . The dimension of is the dimension of its largest simplex. Each finite abstract simplicial complex has a corresponding geometric simplicial complex. Consider the function , where . For each maximal of an abstract simplicial complex , its geometric realization is , i.e. the convex closure of the image of its vertices under . The geometric realization of is which is equipped with the subspace topology inherited from the Euclidean topology. This construction allows for discussion of topological properties of abstract simplicial complexes and is functorial in the sense that given two abstract simplicial complexes with a simplicial map between them, the geometric realization carries the simplicial map to a continuous structure-preserving map between the complexes’ realizations. CW-complexes are topogical structures that generalize the gluing procedures used to construct simplicial complexes. A CW-complex is defined inductively, starting with a collection of -cells, vertices, and then for natural , is the union of and some -cells whose boundaries are glued via continuous maps called attaching maps to the -cells of . A CW-complex is called finite if for some . As an example, the -sphere can be viewed as a CW-complex with one -cell and one -cell where the -cell’s boundary is attached to the -cell via the constant map. A simplicial complex is CW-complex under the obvious gluing procedure. Given two finite CW-complexes and , is a finite CW-complex with cells of the form , where and , and . A closed cover of a simplicial complex is a collection of simplicial complexes all defined over the same vertex set such that and is a subcomplex of of . A space is contractible if it has the homotopy type of a point. For example, all -simplices are contractible. A cover where every nonempty intersections of finitely many elements of is is called a good cover. Given a closed cover indexed over indexign set , the nerve of is the abstract simplicial complex NrvU={σ⊆A∣⋂i∈σUi≠∅ and #{σ}<∞}. The following is a version of the Nerve Theorem which relates the homotopy type of the nerve of a cover to that of the covered space. See Corollary 4G.3 in [20] for the more general topological formulation. ###### Theorem 1 (Nerve Theorem). If is a closed cover of a finite simplicial complex such that every non-empty intersection of finitely many of the elements in is contractible, then is homotopy equivalent to the geometric realization of the nerve, . ### 2.2 Chain Complexes and Homology We restrict ourselves to chain complexes and homology groups over to simplify boundary computations, but the constructions hold for general finite fields as well. Given a simplicial complex , and a non-negative integer , a simplicial -chain over is a formal sum of the form , where each and each is a unique -simplex of . Collectively these simplicial -chains form a vector space/abelian group over called the -dimensional chain group, denoted by , which has a natural basis consisting of the -simplices of . Formally, . For each there exists a linear map , called the simplicial boundary map, defined on a -simplex by , where is the -th face of or alternatively the simplex spanned by the vertices of with removed. The boundary map extends linearly to arbitrary -chains and has the property that , or for short. We denote the sequence of simplicial chain groups with the appropriate boundary maps as and call it the simplicial chain complex of . Given a CW-complex , we can similarly define the cellular chain complex , where each is naturally isomorphic to the vector space over over with a basis being the -cells in . For each basis -cell in , there is a boundary map , where is computed by the cellular boundary formula (see page 140 in Hatcher[20] for the exact formula). For a so-called regular CW-complex, which simplicial complexes and their products are, all the coefficients . Given two simplicial complexes and , a chain map is a collection of maps such that is a homomorphism and for all , i.e. the following diagram commutes. A continuous map induced by a map between the vertices of and yields a simplicial chain map , and a cellular map yields a cellular chain map . Given two chain maps , a chain homotopy between them is a a sequence of maps , such that , or for short, . This is equivalent to Diagram 2.2 commuting. We will drop the subscripts when the dimension is clear. If a chain homotopy exists between and , then and are said to be chain homotopic, written . Given a simplicial complex and its simplicial chain complex , the -dimensional simplicial homology group as . The rank of this groups is the number of linearly independent -dimensional holes in the space. Collectively, the homology groups of are denoted by . If two spaces have the same homotopy type, then their corresponding chain maps are chain homotopic, which then implies their homology groups are isomorphic in all dimensions. The reduced homology is the homology computed from the chain complex where one adjoins a copy of to . Functionally this means that so that the one-point space has trivial reduced homology groups over all dimensions. Given two finite CW-complexes and , there is a natural isomorphism , where is the tensor product. In particular, , where the basis of is the collection of products , where is a -cell in and is a -cell in for . Each basis elements is identified under the isomorphism with . The product chain complex has the boundary map defined on any basis element by and it extends linear to all chains. The cellular homology of a CW-complex is defined in the same manner as simplicial homology except instead with cellular chain complex groups and boundaries. In fact, for a finite simplicial complex , , which is a result of the cellular and simplicial chain complexes being canonically isomorphic — the -simplices are the -cells when is viewed as a CW-complex. ### 2.3 Filtrations and Persistence A filtration is a sequence of topological spaces such that if and only if . If a filtration consists of simplicial complexes, it is known as a simplicial filtration, and if each of the simplicial complexes is finite, it is known as a finite simplicial filtration. Filtrations often arise as the sublevel sets of a real-valued function on a topological space or simplicial complex. Persistent homology is the changes in the homology of a filtration as it ranges over the interval . To be precise, it is the computation of the “birth” and “death” scales of homological features under the homology maps induced by inclusion, , for all such that . The persistent homology data of a filtration is contained in its persistence module, denoted by , which consists of the spaces over all scales, and the aforementioned maps for . The birth and deaths scales of -dimensional homological features in a filtration are represented in a filtration’s -dimensional persistence diagram, denoted by . This is a multiset with elements being points in the plane , where and are the birth and death scales respectively of features, and for all with infinite multiplicity. When discussing the persistence diagrams collectively for all dimensions we write . The following theorem provides a condition under which we can say that two filtrations have identical persistence diagrams, often called the Persistence Equivalence Theorem — see chapter 26 of [22]. ###### Theorem 2 (Persistence Equivalence Theorem). Consider two filtrations , with point-wise finite dimensional persistence modules. If their persistence modules and are isomorphic then the filtrations have identical persistent homology and . Note that is isomorphic to if and only if there are natural isomorphisms for all . A persistence diagram is finite if it has finitely many off-diagonal points. The standard metric on the space of persistence diagrams is the bottleneck distance , which is efficiently computable for finite diagrams. For two finite diagrams and it is defined as dB(D,D′):=minϕ∈Φmaxp∈D∥p−ϕ(p)∥∞, where is the set of all bijections . Two finite persistent diagrams are equivalent if and only if the bottleneck distance between them is . A major result in topological data analysis is that the bottleneck distance stable with respect to perturbations of the function generating the diagram, which is known as the Stability Theorem [23]. Given two filtrations , , their persistence modules and are -interleaved if there exists collections of homomorphisms and , and , such that and , and these maps commute with all and for all . This is known as an additive interleaving. Persistence module interleavings and their persistence diagrams’ bottleneck distances are related by the Algebraic Stability Theorem (see [24, Thm 4.4]), ###### Theorem 3 (Algebraic Stability Theorem). Given two filtrations and such that for all , , if and are -interleaved then for all . Let be a collection of simplicial filtrations, where and for all and , is a finite subcomplex of an ambient simplicial complex. Let , the collection of simplicial complexes at scale from each filtration . For each non-empty , let yielding a simplicial filtration . Note that in this notation and . For a collection of filtrations there is an associated nerve filtration . For each scale the union of over the elements of is the simplicial complex defined as and the the union filtration with respect to is denoted by . For each , is a cover and thus we say that is a cover filtration of , or cover for short. We call a good cover filtration, or good cover for short, of if is a good cover of for all . The previous definitions allow for the statement of the Persistent Nerve Lemma which the main theorem of this paper generalizes. The following lemma was originally formulated by Frédéric Chazal and Steve Oudot in [2] as a generalization of the Nerve Theorem to filtrations. ###### Lemma 4. Let be two finite simplicial complexes with good covers, and respectively, such that for all . There exists homotopy equivalences and that commute with the topological inclusions and . Viewing each from a good cover filtration as a good cover of , Theorem 2 can be applied to the construction of the homotopy equivalences in the proof of Lemma 4 to achieve the following fundamental persistent homology result. ###### Theorem 5 (Persistent Nerve Lemma). Given a collection of finite simplicial filtrations where is a good cover filtration of , then . ## 3 The Generalized Persistent Nerve Theorem In the Persistent Nerve Lemma a primary assumption is that is a good cover of for all , i.e. is a good cover filtration of . However, there are common situations where a simplicial cover may not be good as shown in the figures below. In both cases these good cover violations are relatively small and intuitively ought to be able to be made insignificant for purposes of, for example, recovering the homotopy type of a triangulated space. Persistent homology is an ideal theory for quantifying what is meant by a small violation of the good cover condition. The following is our natural generalization of a good cover filtration. ###### Definition 6. A cover filtration is an -good cover of a filtration if for all non-empty , and all , . Though the definition of an -good covers is stated in terms of homology of the inclusions of cover intersections, it is in fact weaker than the assumption that is null-homotopic, which would align better with the traditional notion of a good cover. We choose to still use the term “good” despite this choice. The main goal of this paper is providing a theorem concerning persistent homology so nothing would be gained by working at the homotopy level. There is the following relation between the definitions of an -good cover and a good cover. If is a good finite simplicial cover then for each each non-empty intersection of cover elements of , is homotopy equivalent to a point. This implies that , so is a -good cover. However, the converse does not hold — the -skeleton of the Poincaré -sphere has trivial reduced homology groups but is not contractible. Recall the definition of the nerve filtration . The following theorem called the Generalized Persistent Nerve Theorem provides a tight bound of on the bottleneck distance between the -dimensional persistence diagrams of the nerve filtration and a simplicial cover filtration, given that is an -good cover filtration of . ###### Theorem 7 (Generalized Persistent Nerve Theorem). Given a finite collection of finite simplicial filtrations , where and all are subcomplexes of a sufficiently large simplicial complex, if is an -good cover filtration of , then dB(DgmK(W),DgmK(NrvU))≤(K+1)ε. As Theorem 7 is true for all dimensions it implies that for , as well as implying Theorem 5 (the Persistent Nerve Lemma) for the case of finite simplicial filtrations. See Appendix A for a construction that realizes the bottleneck distance bound over all dimensions. The Generalized Persistent Nerve Theorem can be seen as an extension of the Persistent Nerve Lemma analogous to how the Algebraic Stability Theorem for persistence modules extends the Persistence Equivalence Theorem to interleaved modules, by viewing -good cover filtrations as perturbations or approximations of good cover filtrations, the ideal object. This relationship is summarized in the following table. Equivalence Approximation Persistence Modules Persistence Equivalence Theorem Stability Theorem Nerves Persistent Nerve Lemma Gen. Persistent Nerve Theorem ## 4 Proof Construction Fix a cover filtration consisting of finite simplicial filtrations, where and all the are subcomplexes of some sufficiently large simplicial complex. Assume that is an -good cover filtration of the simplicial filtration . Fix a dimension for the remainder of the proof which will the be maximal dimension considered when discussing chain complexes, i.e. for any space and likewise for homology groups. The procedure to prove Theorem 7 is as follows. First we construct a diagram of chain complexes and chain maps that yield a -interleaving between the filtered chain complexes and for all . This chain complex interleaving is analogous to that defined previously between persistence diagrams, except one we only require the appropriate compositions be chain homotopic to the identity chain maps rather than equivalent. Applying homology to said chain complex diagram, the chain maps that are chain homotopic to the identity become homologically equivalent to identity maps so there is a true -interleaving between the persistence modules and for each . The theorem is proved then by applying the Algebraic Stability Theorem (Theorem 3). ### 4.1 The Nerve Diagram and Blowup Complex For each , define as the directed graph with vertex set , and edges of the form for any non-empty such . Note the vertices of this graph are in correspondence with the simplices of and thus form the -skeleton of the barycentric subdivision of , while the entire (undirected) graph is its -skeleton. The edges correspond to inclusions between intersections of cover elements of the form . can be given the structure of an abstract simplicial complex, where the -simplices are sequences of vertices such that for and , , there exists an edge . Some call this complex built from an acyclic graph or poset a flag complex. From now on we will use the notation to refer to the simplicial representation. A fact that will be important later on is that its geometric realization is homeomorphic as a topological space to . From and we define the finite CW-complex that glues together all the realizations of the simplices of paired with their corresponding cover elements’ intersection in . Bα:=⋃Nα∋σ=v0→⋯→vkk≥0Uαv0×\|σ\|. Note that this is the barycentric decomposition of the so-called (Mayer–Vietoris) blow-up complex central to the proof of the Nerve Theorem, called the realization of a diagram of spaces in Hatcher [20], and other more recent persistent homology research, e.g. Zomorodian and Carlsson’s work on localized homology [25]. Other readers familiar with combinatorial topology and discrete geometry may recognize this as the homotopy colimit of the categorical diagram between and Top constructed from the cover elements’ interesections’ correspondence with the vertices and the inclusions with the edges of . One may refer to Kozlov [26], p.262, for the relevant definition or Welker et al.’s treatise on homotopy colimits and their applications [27]. This is expanded upon in Appendix B. The associated filtration is denoted . By definition we have that for all . As the filtration organizes and combines the nerves and the covered simplicial complexes, it is easier to define maps from it rather than from . Using the filtration we will now reduce the proof to constructing a -interleaving between and as follows. There are natural projection maps for each , where and when It is well-known fact that that is a homotopy equivalence (see 4G.2 in [20]) for covers of paracompact spaces, so as finite simplicial complexes are paracompact. Moreover, two projections and commute with the inclusions and , yielding the following commutative homological diagram for all scales such that . (1) From Diagram 1 it follows that by Theorem 2. Define the filtration . There are also natural projection maps for each , where and . When is a good cover of , and by extension is a good cover filtration of , the projection maps are homotopy equivalences that commute with the filtration inclusions. This is a central component to the proof the Nerve Theorem and Lemma 4. However, under our assumptions, we do not have the homotopy equivalences resulting from the good cover condition, so instead we must find an interleaving between and to prove our theorem. As is homeomorphic to , this is sufficient. In the next section we will construct the chain maps mapping a basis chain in to a chain in which will result in an interleaving by symmetrizing. ### 4.2 The Chain Maps For the remainder of the proof we will not use the geometric realization vertical bars when discussing basis cellular chains corresponding to tensor products of geometric simplices viewed as cells to avoid cumbersome presentation. For an abstract -simplex where , the following two shorthands will be used, and . These are the geometric realizations of the restriction of to the first -vertices and the -th through -th vertices respectively. For notational simplicity, given some and some vertex , , where denotes the removal of vertex . For each non-empty , pick a vertex where , and note that for all . Consider the map which is the extension of the linear map sending each vertex of to to . This results in the chain map defined as follows. xv(σ):={xv if dimσ=0,0 otherwise. The following lemma will be used to show the existence of a chain homotopy between the inclusion chain maps and the vertex chain maps. ###### Lemma 8. Fix . Given non-empty , where , and is ’s corresponding vertex, consider the inclusion chain map and . There exists a chain homotopy from to . ###### Proof. We construct the chain homotopy by induction on dimension to prove that for all that there exists such that . In the base case we can consider . Now for some , assume there exists such that . Let be the -chain such that . Observe that for , for any -simplex , ∂k(z) =−(∂kck−1∂k)(σ)+(∂kiα,α+εv)(σ)−(∂kxv)(σ) =(ck−2∂k−1∂k)(σ)−(iα,α+εv∂k)(σ)+(xv∂k)(σ)+(∂kiα,α+εv)(σ)−(∂kxv)(σ) =0 The second line follows by the inductive hypothesis as is a -chain. The third line follows as and and are chain maps so they commute with the boundary operators. This proves that is a cycle so is a cycle, and as is an -good cover. There then must exist a boundary such that . Define . By the above calculations this choice of satisfies the inductive hypothesis so we are done. ∎ By Lemma 8, for a given and , there exists a chain homotopy, which we denote as , between the identity chain map and the constant chain map . By definition we have the equality . Denote for short for the remainder of the paper when referencing the For , define the map for a cellular basis element , where is a -cell and is a -cell corresponding to the geometric realization of the abstract -simplex in , as cα(τ⊗σ):=cασ(τ):=(cα+qεvq…cαv0)(τ). Note that this is well-defined despite ’s domain each being as for any basis cellular chain , is a simplex of for some by the definition of . Recall the two projections from the barycentric decomposition of the blow-up complex , and . For a cellular chain -chain , the projection-induced chain maps and are defined as follows, bα(τ⊗σ):={τ if dimσ=00 otherwise, and pα(τ⊗σ):={σ if dimτ=0,0 otherwise. Define the chain map for a basis -simplex to be the following qα(σ):={cα(xv0⊗(σ∖v0)) if dimσ≥1xv0 if dimσ=0. The chain maps and are induced by topological maps so they are chain maps by construction, while it is not immediately apparent it is a chain map. ###### Lemma 9. The map as defined above, where is a chain map for all dimensions less than or equal to . ###### Proof. Denote for this proof to make it clear what dimension is being worked in. We will prove that is a chain map by induction on the basis of for arbitrary and . These are the simplices of resulting from abstract simplices in of the form . In the base case, where , then for some vertex , so we have that . Now assume that for some , the following holds for any given basis -chain , . Now consider a basis -chain . We have the following equalities, defining . ∂qαk+1(σ′) =∂cα(xv0⊗(σ′∖v0)) =∂cα+kεvk+1cα(xv0⊗(σ′∖(v0∪vk+1))) =(cα+kεvk+1∂+iα+kε,α+(k+1)εvk+1+xαvk+1)(cα(xv0⊗(σ′∖(v0∪vk+1)))) =cα+kεvk+1∂cα(xv0⊗(σ′′∖v0))+cα(xv	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9756065011024475, "perplexity": 490.5093642663406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964362219.5/warc/CC-MAIN-20211202114856-20211202144856-00620.warc.gz"}
https://www.gamedev.net/forums/topic/418443-quaternion-based-camera-shows-odd-behaviour/	# Quaternion based camera shows odd behaviour This topic is 4452 days old which is more than the 365 day threshold we allow for new replies. Please post a new topic. ## Recommended Posts I'm trying to implement a camera into OpenGL (But since it is basically about quaternion math I posted it here.) using quaternions. I got it to do something, but the behaviour isn't quite right. For the camera I have 3 vectors: position, view and up. Position is actually a point, the camera position. View is the point it is looking at (so it's more like target, where direction = view - position.) and up is the up vector. I use the standard gluLookAt(vector3 position, vector3 view, vector3 up) function to position the camera based on these 3 vectors. It's a first-person camera, so as far as I can tell I should only have to update the view (or target) vector, and perhaps the up vector if I rotate over the z-axis. When I rotate around the y-axis (pointing up: {0.0, 1.0, 0.0}) the camera behaves well. However, when I do a full 360 degree rotation over time at a constant angle per frame, the rotation goes faster at some points than at others. This is odd, since I update it independent of the frame rate, and also the frame rate is quite constant. However, even weirder things happen when I try to rotate over the x or z-axis to produce a full 360 degree rotation. The camera starts out right, but it soon starts to rotate in different directions, which I cannot make any sense of. My sense of math is quite good, but quaternions are a first to me, and I have hardly any understanding of them yet. (complex numbers will be though at school in two weeks, but atm I don't know anything about them except they use i^2 = -1.) As far as I can tell all my OpenGL functions are implemented right, so the fault must be somewhere in the math. Who can spot it for me? Any help is greatly appreciated! The code is in C++, with some functions of the OpenGL API. CQuaternion and CVector3 are classes I wrote. /////////////////////////////////////////////////////////////////////////////////////////////// // QUATERNION OPERATORS /////////////////////////////////////////////////////////////////////////////////////////////// CQuaternion CQuaternion::operator/(float factor) { return CQuaternion(x / factor, y / factor, z / factor, w / factor); } void CQuaternion::operator/=(float factor) { x /= factor; y /= factor; z /= factor; w /= factor; } bool CQuaternion::operator==(CQuaternion q) { if (q.x == x && q.y == y && q.z == z && q.w == w) return true; return false; } bool CQuaternion::operator!=(CQuaternion q) { if (q.x == x && q.y == y && q.z == z && q.w == w) return false; return true; } /////////////////////////////////////////////////////////////////////////////////////////////// // MULTIPLIES QUATERNIONS (NON-COMMUTATIVE) /////////////////////////////////////////////////////////////////////////////////////////////// CQuaternion mult(CQuaternion q1, CQuaternion q2) { CQuaternion r; /r.x = q1.w q2.x + q1.x * q2.w + q1.y * q2.z - q1.z * q2.y; r.y = q1.w * q2.y - q1.x * q2.z + q1.y * q2.w + q1.z * q2.x; r.z = q1.w * q2.z + q1.x * q2.y - q1.y * q2.x + q1.z * q2.w; r.w = q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z;/ r.x = q1.x q2.w + q1.w * q2.x + q1.y * q2.z - q1.z * q2.y; r.y = q1.y * q2.w + q1.w * q2.y + q1.z * q2.x - q1.x * q2.z; r.z = q1.z * q2.w + q1.w * q2.z + q1.x * q2.y - q1.y * q2.x; r.w = q1.w * q2.w - q1.x * q2.x - q1.y * q2.y - q1.z * q2.z; return r; } /////////////////////////////////////////////////////////////////////////////////////////////// // RETURNS THE NORM OF A QUATERNION /////////////////////////////////////////////////////////////////////////////////////////////// float norm(CQuaternion q) { return sqrtf((q.x * q.x) + (q.y * q.y) + (q.z * q.z) + (q.w * q.w)); } /////////////////////////////////////////////////////////////////////////////////////////////// // NORMALIZES A QUATERNION /////////////////////////////////////////////////////////////////////////////////////////////// void normalize(CQuaternion &q) { q /= norm(q); } /////////////////////////////////////////////////////////////////////////////////////////////// // COMPUTES THE CONJUGATE OF A QUATERNION /////////////////////////////////////////////////////////////////////////////////////////////// CQuaternion conjugate(CQuaternion q) { return CQuaternion(-q.x, -q.y, -q.z, q.w); } /////////////////////////////////////////////////////////////////////////////////////////////// // CONVERSION FROM QUATERNION TO VECTOR3 /////////////////////////////////////////////////////////////////////////////////////////////// CVector3 quat_to_vector3(CQuaternion q) { return CVector3(q.x, q.y, q.z); } /////////////////////////////////////////////////////////////////////////////////////////////// // CONVERSION FROM VECTOR3 TO QUATERNION /////////////////////////////////////////////////////////////////////////////////////////////// CQuaternion vector3_to_quat(CVector3 v) { return CQuaternion(v.x, v.y, v.z, 0.0f); } /////////////////////////////////////////////////////////////////////////////////////////////// // ROTATES THE CAMERA AROUND THE PROVIDED AXIS /////////////////////////////////////////////////////////////////////////////////////////////// void CCamera::rotate(float angle, float x, float y, float z) { CQuaternion rotate, view; rotate.x = x * sin(angle / 2.0f); rotate.y = y * sin(angle / 2.0f); rotate.z = z * sin(angle / 2.0f); rotate.w = cos(angle / 2.0f); // this->view is the camera's view vector, as mentioned in the problem description view = vector3_to_quat(this->view); view = mult(mult(rotate, view), conjugate(rotate)); this->view = quat_to_vector3(view); } If a look at the behaviour is needed I can make an exe showing it. Just ask me for it :) [Edited by - Subotron on October 8, 2006 3:38:33 PM] ##### Share on other sites this->view is no longer the view vector as described, it is now more like a 'direction', this->view = target - position. This works better, since movement around the y-axis works. However, when I move around the x-axis, I still seem to suffer from gimbal lock, although I read quaternions should solve this (actually the most important reason I use them). Edit: fixed z-rotation. Figured my position didn't allow for z-rotation, and I was right... Also, I'm not sure if it is actually a 'gimbal lock' that's occuring. When I now try to rotate around the x-axis, only a half rotation is applied, and when the camera's view is either totally up or down, the rotation switches direction (so it is 'trapped' in a half circle, the motion of an old clock) [Edited by - Subotron on October 8, 2006 12:40:20 PM] ##### Share on other sites My favorite subject - the dreaded 'quaternion-based camera' :-) What kind of camera are you trying to implement exactly? Do you want a standard FPS or spectator camera as found in Quake or Unreal? Or something else? I think I already know the answer, but I'll wait and see, just to be sure. Also, if your code is based on a tutorial, could you post a link to it, and/or post the entirety of your camera code? ##### Share on other sites The code is based on these articles: http://www.gamedev.net/reference/articles/article1997.asp Actually, I don't really want to create FPS camera, but I thought it was a good start since I already have a working (except for gimbal lock) one using euler methods. 3rd person (with SLERP) is my goal, however I think the class should support both. FPS in the sense of Quake. The full camera class code: (doesn't feature any movement yet since I want the rotations to work first) class CCamera{private:protected: CVector3 pos; CVector3 view; CVector3 up;public: CCamera() { } ~CCamera() { } void set (float position_x, float position_y, float position_z, float view_x, float view_y, float view_z, float up_x, float up_y, float up_z); void look (); void rotate (float angle, float x, float y, float z); CVector3& get_position (); CVector3& get_view (); CVector3& get_up_vector (); CVector3 get_direction ();}; ///////////////////////////////////////////////////////////////////////////////////////////////// SETS THE CAMERA AT A GIVEN POSITION, VIEW AND UP VECTOR///////////////////////////////////////////////////////////////////////////////////////////////void CCamera::set(float position_x, float position_y, float position_z, float view_x, float view_y, float view_z, float up_x, float up_y, float up_z){ pos = CVector3(position_x, position_y, position_z); view = CVector3(view_x, view_y, view_z); up = CVector3(up_x, up_y, up_z);}///////////////////////////////////////////////////////////////////////////////////////////////// PLACES THE CAMERA IN THE SCENE///////////////////////////////////////////////////////////////////////////////////////////////void CCamera::look(){ gluLookAt(pos.x, pos.y, pos.z, view.x, view.y, view.z, up.x, up.y, up.z);}///////////////////////////////////////////////////////////////////////////////////////////////// ROTATES THE CAMERA AROUND THE PROVIDED AXIS///////////////////////////////////////////////////////////////////////////////////////////////void CCamera::rotate(float angle, float x, float y, float z){ CQuaternion rotate, view; rotate.x = x * sin(angle / 2.0f); rotate.y = y * sin(angle / 2.0f); rotate.z = z * sin(angle / 2.0f); rotate.w = cos(angle / 2.0f); view = vector3_to_quat(get_direction()); view = mult(mult(rotate, view), conjugate(rotate)); this->view = quat_to_vector3(view) + pos;}///////////////////////////////////////////////////////////////////////////////////////////////// RETURNS THE CAMERA'S POSITION///////////////////////////////////////////////////////////////////////////////////////////////CVector3& CCamera::get_position(){ return pos;}///////////////////////////////////////////////////////////////////////////////////////////////// RETURNS THE CAMERA'S VIEWPOINT///////////////////////////////////////////////////////////////////////////////////////////////CVector3& CCamera::get_view(){ return view;}///////////////////////////////////////////////////////////////////////////////////////////////// RETURNS THE CAMERA'S UP VECTOR///////////////////////////////////////////////////////////////////////////////////////////////CVector3& CCamera::get_up_vector(){ return up;}///////////////////////////////////////////////////////////////////////////////////////////////// GIVES THE DIRECTION THE CAMERA IS FACING///////////////////////////////////////////////////////////////////////////////////////////////CVector3 CCamera::get_direction(){ return view - pos;} Thanks a lot :) ##### Share on other sites You may be interested in other thread on similar topic there... i think the problem is similiar and i posted some pseudocode for it. ##### Share on other sites The requirements for each of the camera types you mention are somewhat different. Here are a few things to consider: 1. FPS/FPS-spectator The aforementioned tutorial notwithstanding, quaternions are in general entirely unnecessary for this type of camera, and in fact just get in the way. Gimbal lock is not a problem in this context, and in any case whether or not you use quaternions has absolutely nothing to do with whether you encounter gimbal lock. For this type of camera, Euler angles are actually a perfectly reasonable solution. Generally roll is ignored with this type of camera, so you are left with two angles, yaw and pitch, which you can update incrementally and then use to construct a matrix to submit to OpenGL. 2. 'Free' 6DOF This type of camera can be implemented equally effectively using vectors, matrices, or quaternions. The only reason I can think of at the moment to prefer the latter is if you're going to be doing a lot of interpolation. 3. 3rd-person I haven't had occasion to write a 'serious' third-person camera (i.e. with damping and collision avoidance), so I won't comment on this except to say that quaternions might be useful here for interpolation. (It seems though that such a camera could be implemented purely in terms of azimuth and elevation, in which case quaternions would probably be overkill.) Combining all these camera types into one class might be kind of tricky design-wise. If I were you I would implement each camera type individually using whatever methods are most appropriate to that type, and then think about what aspects could be factored out (and perhaps placed in a base class). ##### Share on other sites jyk, you catch my drift. Those are the types of camera I want to be able to use. The reason why I want more, is because I'm designing the class from an engine perspective. The 3 don't necessarily have to work next to eachother, but it should be possible to have 2 camera's, one FP and one 3rd person, so you can switch ingame. I would like to make one class allowing both, but I'm just happy if I can fix this bug, I will delve into the rest later (already have done some designing). Ok, this is the first time I hear quaternions don't actually do much for gimbal lock. I knew it was possible to still create one, but I thought this would be better. (think again) Still, I'd like to use them, both because I want to learn to use them (I have reason to believe I will be doing something with inverse kinematics later this year for school, and I am told quaternions might come in handy there) and because of the interpolation advantages. So well, I guess it's confirmed the problem is actually a gimbal lock? I really want to get that out, because even though Quake-style FPS doesn't suffer from it, I really don't want a bug stopping me from having full camera freedom... Could you please point out the problem to me, since I am really out of ideas :( ##### Share on other sites I'm not sure if I can easily identify the problem without digging through the code carefully (for one thing, I see the rotate() function, but I don't see where it's actually being used - you might post that as well). I will say that whenever you perform incremental rotations as you're doing here (which isn't really what you should be doing for this sort of camera, but anyway...), you will need to compensate for drift occasionally. In this case, that means normalizing the direction vector after you rotate it. Another thing that might help is to clean up the naming convention, which is currently somewhat misleading. The point at which you're looking is the target; 'view' is a fairly confusing name for it, and IMO should be reserved for the forward view vector. Also, there's no reason to track the 'view' in terms of the target; it just leads to unnecessary conversions back and forth between the two. Just store the forward vector for the camera and perform the operations on it directly. One last thing. IMO a camera should be thought of just like any other object; the only real functional difference is that with a camera you generally invert the matrix before submitting it to your API of choice (this is what gluLookAt() does, among other things). A first-person camera (whether FPS or 6DOF) is really then just an entity that attaches itself to the transform of an in-game object, be it a spaceship, airplane, or a humanoid character. In some cases the camera may need to be shifted or re-oriented somewhat in relation to the model, but the concept is the same. A third-person camera can be thought of as an object that is 'tethered' to another, and follows its target while obeying certain contraints. Anyway, the point here is not to think of a camera as something 'special' which requires special considerations, since really the math under discussion here can be applied to any in-game object. So anyway, I'm not exactly sure where the problem in your code is, but I have to admit I think the implementation is conceptually poor for a camera of this type; I understand you want to use quaternions, but you're not doing yourself any favors by using them where they're not an appropriate solution (IMO). I don't know what kind of time contraints you're up against, but if you have the time I would scratch that implementation and approach it differently. I can provide links to some references that might be useful if it would help. (How did this post get so long!?) ##### Share on other sites hehe thanks for the long post :) First of all, the rotate() function is called each frame: void apply_physics(float elapsed_time) { camera.rotate(elapsed_time, 1.0f, 0.0f, 0.0f); } I use the view and direction vector this way because gluLookAt uses (position, view, up), so I kind of stuck to that. It works in my head, but I can see it is confusing to others. I am planning on rewriting the gluLookAt though, in such a way that I don't need to convert anymore. I put this conversion in, because the 'view' (you call it target) is absolute, not relative to the position. Again, this will be changed later. But for now I have to substract (and later add) the position to it, else only rubbish happens... Quote: I will say that whenever you perform incremental rotations as you're doing here (which isn't really what you should be doing for this sort of camera, but anyway...) I'm not sure what you mean by this. What alternative is there? And what exactly do you mean with incremental rotations? I really want to understand all this well, and judging by all your posts on the subject (in other topics) you have a good understanding. I actually don't even know the difference between what I'm doing and axis-angle, since it seems to me the x, y, z (roll pitch jaw I guess) ARE an axis, and the other parameter is an angle... And yeah well, I have the time to rewrite my class, I'm actually in the process of rewriting the complete engine (not that it's that big at the moment) and I decided I would fix the camera, and quaternions seemed like a good idea, especially because I thought they would fix my gimbal problems, but also because of the interpolation advantages. But you're saying I shouldn't use them? Then when would be a good time to use them? :) Please understand, I always thought I understood how the camera worked, but at this point I feel like I'm totally in the dark again... ##### Share on other sites This is kind of a big topic, but I'll try and chip away at it a bit and see if I can help clear some things up. First of all, I'm wondering whether your main interest is to learn the underlying concepts, or to create a working game or game engine? If the former, then you're on the right track; if the latter, I could recommend some third-party libraries and code that would take care of a lot of this work for you. Meahwhile, back to the subject at hand. Let's start with the use of gluLookAt(). This function does two things: 1. Creates a transform matrix given a position, a target, and a reference up vector 2. Inverts this matrix so that it can be used as a view matrix Strictly speaking, this function is intended to be used when you have this particular information (position, target, and up) available, and nothing more. For example, in a simple demo scene you might use it to position the camera at a particular location and orient it so that it's looking at the object you wish to view. Now, people often use this function in other contexts because it's convenient, in that it hides the details of matrix construction and inversion from you. However (and this is IMO) if you want to understand what's going on it's better not to use this function unless 'look at' functionality is really what you want. In your case it's not. So what are the alternatives? It depends on the type of camera, but OpenGL provides glLoadMatrix(), glMultMatrix(), and glRotate*(), any and all of which can be used (depending on the circumstances) to set or modify the OpenGL modelview matrix. gluLookAt() is by no means the only option. I'll try to write some more later in another post, but post back if you have any specific questions about the above. 1. 1 2. 2 Rutin 21 3. 3 4. 4 A4L 15 5. 5 khawk 14 • 13 • 26 • 10 • 11 • 9 • ### Forum Statistics • Total Topics 633737 • Total Posts 3013612 ×	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28161826729774475, "perplexity": 1609.31051366716}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827769.75/warc/CC-MAIN-20181216143418-20181216165418-00066.warc.gz"}
http://peeterjoot.com/tag/bivector/	## Notes. Due to limitations in the MathJax-Latex package, all the oriented integrals in this blog post should be interpreted as having a clockwise orientation. [See the PDF version of this post for more sophisticated formatting.] ## Guts. Given a two dimensional generating vector space, there are two instances of the fundamental theorem for multivector integration \label{eqn:unpackingFundamentalTheorem:20} \int_S F d\Bx \lrpartial G = \evalbar{F G}{\Delta S}, and \label{eqn:unpackingFundamentalTheorem:40} \int_S F d^2\Bx \lrpartial G = \oint_{\partial S} F d\Bx G. The first case is trivial. Given a parameterizated curve $$x = x(u)$$, it just states \label{eqn:unpackingFundamentalTheorem:60} \int_{u(0)}^{u(1)} du \PD{u}{}\lr{FG} = F(u(1))G(u(1)) – F(u(0))G(u(0)), for all multivectors $$F, G$$, regardless of the signature of the underlying space. The surface integral is more interesting. Let’s first look at the area element for this surface integral, which is \label{eqn:unpackingFundamentalTheorem:80} d^2 \Bx = d\Bx_u \wedge d \Bx_v. Geometrically, this has the area of the parallelogram spanned by $$d\Bx_u$$ and $$d\Bx_v$$, but weighted by the pseudoscalar of the space. This is explored algebraically in the following problem and illustrated in fig. 1. fig. 1. 2D vector space and area element. ## Problem: Expansion of 2D area bivector. Let $$\setlr{e_1, e_2}$$ be an orthonormal basis for a two dimensional space, with reciprocal frame $$\setlr{e^1, e^2}$$. Expand the area bivector $$d^2 \Bx$$ in coordinates relating the bivector to the Jacobian and the pseudoscalar. With parameterization $$x = x(u,v) = x^\alpha e_\alpha = x_\alpha e^\alpha$$, we have \label{eqn:unpackingFundamentalTheorem:120} \Bx_u \wedge \Bx_v = \lr{ \PD{u}{x^\alpha} e_\alpha } \wedge \lr{ \PD{v}{x^\beta} e_\beta } = \PD{u}{x^\alpha} \PD{v}{x^\beta} e_\alpha e_\beta = \PD{(u,v)}{(x^1,x^2)} e_1 e_2, or \label{eqn:unpackingFundamentalTheorem:160} \Bx_u \wedge \Bx_v = \lr{ \PD{u}{x_\alpha} e^\alpha } \wedge \lr{ \PD{v}{x_\beta} e^\beta } = \PD{u}{x_\alpha} \PD{v}{x_\beta} e^\alpha e^\beta = \PD{(u,v)}{(x_1,x_2)} e^1 e^2. The upper and lower index pseudoscalars are related by \label{eqn:unpackingFundamentalTheorem:180} e^1 e^2 e_1 e_2 = -e^1 e^2 e_2 e_1 = -1, so with $$I = e_1 e_2$$, \label{eqn:unpackingFundamentalTheorem:200} e^1 e^2 = -I^{-1}, leaving us with \label{eqn:unpackingFundamentalTheorem:140} d^2 \Bx = \PD{(u,v)}{(x^1,x^2)} du dv\, I = -\PD{(u,v)}{(x_1,x_2)} du dv\, I^{-1}. We see that the area bivector is proportional to either the upper or lower index Jacobian and to the pseudoscalar for the space. We may write the fundamental theorem for a 2D space as \label{eqn:unpackingFundamentalTheorem:680} \int_S du dv \, \PD{(u,v)}{(x^1,x^2)} F I \lrgrad G = \oint_{\partial S} F d\Bx G, where we have dispensed with the vector derivative and use the gradient instead, since they are identical in a two parameter two dimensional space. Of course, unless we are using $$x^1, x^2$$ as our parameterization, we still want the curvilinear representation of the gradient $$\grad = \Bx^u \PDi{u}{} + \Bx^v \PDi{v}{}$$. ## Problem: Standard basis expansion of fundamental surface relation. For a parameterization $$x = x^1 e_1 + x^2 e_2$$, where $$\setlr{ e_1, e_2 }$$ is a standard (orthogonal) basis, expand the fundamental theorem for surface integrals for the single sided $$F = 1$$ case. Consider functions $$G$$ of each grade (scalar, vector, bivector.) From \ref{eqn:unpackingFundamentalTheorem:140} we see that the fundamental theorem takes the form \label{eqn:unpackingFundamentalTheorem:220} \int_S dx^1 dx^2\, F I \lrgrad G = \oint_{\partial S} F d\Bx G. In a Euclidean space, the operator $$I \lrgrad$$, is a $$\pi/2$$ rotation of the gradient, but has a rotated like structure in all metrics: \label{eqn:unpackingFundamentalTheorem:240} = e_1 e_2 \lr{ e^1 \partial_1 + e^2 \partial_2 } = -e_2 \partial_1 + e_1 \partial_2. • $$F = 1$$ and $$G \in \bigwedge^0$$ or $$G \in \bigwedge^2$$. For $$F = 1$$ and scalar or bivector $$G$$ we have \label{eqn:unpackingFundamentalTheorem:260} \int_S dx^1 dx^2\, \lr{ -e_2 \partial_1 + e_1 \partial_2 } G = \oint_{\partial S} d\Bx G, where, for $$x^1 \in [x^1(0),x^1(1)]$$ and $$x^2 \in [x^2(0),x^2(1)]$$, the RHS written explicitly is \label{eqn:unpackingFundamentalTheorem:280} \oint_{\partial S} d\Bx G = \int dx^1 e_1 \lr{ G(x^1, x^2(1)) – G(x^1, x^2(0)) } – dx^2 e_2 \lr{ G(x^1(1),x^2) – G(x^1(0), x^2) }. This is sketched in fig. 2. Since a 2D bivector $$G$$ can be written as $$G = I g$$, where $$g$$ is a scalar, we may write the pseudoscalar case as \label{eqn:unpackingFundamentalTheorem:300} \int_S dx^1 dx^2\, \lr{ -e_2 \partial_1 + e_1 \partial_2 } g = \oint_{\partial S} d\Bx g, after right multiplying both sides with $$I^{-1}$$. Algebraically the scalar and pseudoscalar cases can be thought of as identical scalar relationships. • $$F = 1, G \in \bigwedge^1$$. For $$F = 1$$ and vector $$G$$ the 2D fundamental theorem for surfaces can be split into scalar \label{eqn:unpackingFundamentalTheorem:320} \int_S dx^1 dx^2\, \lr{ -e_2 \partial_1 + e_1 \partial_2 } \cdot G = \oint_{\partial S} d\Bx \cdot G, and bivector relations \label{eqn:unpackingFundamentalTheorem:340} \int_S dx^1 dx^2\, \lr{ -e_2 \partial_1 + e_1 \partial_2 } \wedge G = \oint_{\partial S} d\Bx \wedge G. To expand \ref{eqn:unpackingFundamentalTheorem:320}, let \label{eqn:unpackingFundamentalTheorem:360} G = g_1 e^1 + g_2 e^2, for which \label{eqn:unpackingFundamentalTheorem:380} \lr{ -e_2 \partial_1 + e_1 \partial_2 } \cdot G = \lr{ -e_2 \partial_1 + e_1 \partial_2 } \cdot \lr{ g_1 e^1 + g_2 e^2 } = \partial_2 g_1 – \partial_1 g_2, and \label{eqn:unpackingFundamentalTheorem:400} d\Bx \cdot G = \lr{ dx^1 e_1 – dx^2 e_2 } \cdot \lr{ g_1 e^1 + g_2 e^2 } = dx^1 g_1 – dx^2 g_2, so \ref{eqn:unpackingFundamentalTheorem:320} expands to \label{eqn:unpackingFundamentalTheorem:500} \int_S dx^1 dx^2\, \lr{ \partial_2 g_1 – \partial_1 g_2 } = \int \evalbar{dx^1 g_1}{\Delta x^2} – \evalbar{ dx^2 g_2 }{\Delta x^1}. This coordinate expansion illustrates how the pseudoscalar nature of the area element results in a duality transformation, as we end up with a curl like operation on the LHS, despite the dot product nature of the decomposition that we used. That can also be seen directly for vector $$G$$, since \label{eqn:unpackingFundamentalTheorem:560} dA (I \grad) \cdot G = = dA I \lr{ \grad \wedge G }, since the scalar selection of $$I \lr{ \grad \cdot G }$$ is zero.In the grade-2 relation \ref{eqn:unpackingFundamentalTheorem:340}, we expect a pseudoscalar cancellation on both sides, leaving a scalar (divergence-like) relationship. This time, we use upper index coordinates for the vector $$G$$, letting \label{eqn:unpackingFundamentalTheorem:440} G = g^1 e_1 + g^2 e_2, so \label{eqn:unpackingFundamentalTheorem:460} \lr{ -e_2 \partial_1 + e_1 \partial_2 } \wedge G = \lr{ -e_2 \partial_1 + e_1 \partial_2 } \wedge G \lr{ g^1 e_1 + g^2 e_2 } = e_1 e_2 \lr{ \partial_1 g^1 + \partial_2 g^2 }, and \label{eqn:unpackingFundamentalTheorem:480} d\Bx \wedge G = \lr{ dx^1 e_1 – dx^2 e_2 } \wedge \lr{ g^1 e_1 + g^2 e_2 } = e_1 e_2 \lr{ dx^1 g^2 + dx^2 g^1 }. So \ref{eqn:unpackingFundamentalTheorem:340}, after multiplication of both sides by $$I^{-1}$$, is \label{eqn:unpackingFundamentalTheorem:520} \int_S dx^1 dx^2\, \lr{ \partial_1 g^1 + \partial_2 g^2 } = \int \evalbar{dx^1 g^2}{\Delta x^2} + \evalbar{dx^2 g^1 }{\Delta x^1}. As before, we’ve implicitly performed a duality transformation, and end up with a divergence operation. That can be seen directly without coordinate expansion, by rewriting the wedge as a grade two selection, and expanding the gradient action on the vector $$G$$, as follows \label{eqn:unpackingFundamentalTheorem:580} dA (I \grad) \wedge G = = dA I \lr{ \grad \cdot G }, since $$I \lr{ \grad \wedge G }$$ has only a scalar component. fig. 2. Line integral around rectangular boundary. ## Theorem 1.1: Green’s theorem [1]. Let $$S$$ be a Jordan region with a piecewise-smooth boundary $$C$$. If $$P, Q$$ are continuously differentiable on an open set that contains $$S$$, then \begin{equation} \int dx dy \lr{ \PD{y}{P} – \PD{x}{Q} } = \oint P dx + Q dy. \end{equation} ## Problem: Relationship to Green’s theorem. If the space is Euclidean, show that \ref{eqn:unpackingFundamentalTheorem:500} and \ref{eqn:unpackingFundamentalTheorem:520} are both instances of Green’s theorem with suitable choices of $$P$$ and $$Q$$. I will omit the subtleties related to general regions and consider just the case of an infinitesimal square region. ### Start proof: Let’s start with \ref{eqn:unpackingFundamentalTheorem:500}, with $$g_1 = P$$ and $$g_2 = Q$$, and $$x^1 = x, x^2 = y$$, the RHS is \label{eqn:unpackingFundamentalTheorem:600} \int dx dy \lr{ \PD{y}{P} – \PD{x}{Q} }. On the RHS we have \label{eqn:unpackingFundamentalTheorem:620} \int \evalbar{dx P}{\Delta y} – \evalbar{ dy Q }{\Delta x} = \int dx \lr{ P(x, y_1) – P(x, y_0) } – \int dy \lr{ Q(x_1, y) – Q(x_0, y) }. This pair of integrals is plotted in fig. 3, from which we see that \ref{eqn:unpackingFundamentalTheorem:620} can be expressed as the line integral, leaving us with \label{eqn:unpackingFundamentalTheorem:640} \int dx dy \lr{ \PD{y}{P} – \PD{x}{Q} } = \oint dx P + dy Q, which is Green’s theorem over the infinitesimal square integration region. For the equivalence of \ref{eqn:unpackingFundamentalTheorem:520} to Green’s theorem, let $$g^2 = P$$, and $$g^1 = -Q$$. Plugging into the LHS, we find the Green’s theorem integrand. On the RHS, the integrand expands to \label{eqn:unpackingFundamentalTheorem:660} \evalbar{dx g^2}{\Delta y} + \evalbar{dy g^1 }{\Delta x} = dx \lr{ P(x,y_1) – P(x, y_0)} + dy \lr{ -Q(x_1, y) + Q(x_0, y)}, which is exactly what we found in \ref{eqn:unpackingFundamentalTheorem:620}. ### End proof. fig. 3. Path for Green’s theorem. We may also relate multivector gradient integrals in 2D to the normal integral around the boundary of the bounding curve. That relationship is as follows. ## Theorem 1.2: 2D gradient integrals. \begin{equation} \begin{aligned} \int J du dv \rgrad G &= \oint I^{-1} d\Bx G = \int J \lr{ \Bx^v du + \Bx^u dv } G \\ \int J du dv F \lgrad &= \oint F I^{-1} d\Bx = \int J F \lr{ \Bx^v du + \Bx^u dv }, \end{aligned} \end{equation} where $$J = \partial(x^1, x^2)/\partial(u,v)$$ is the Jacobian of the parameterization $$x = x(u,v)$$. In terms of the coordinates $$x^1, x^2$$, this reduces to \begin{equation} \begin{aligned} \int dx^1 dx^2 \rgrad G &= \oint I^{-1} d\Bx G = \int \lr{ e^2 dx^1 + e^1 dx^2 } G \\ \int dx^1 dx^2 F \lgrad &= \oint G I^{-1} d\Bx = \int F \lr{ e^2 dx^1 + e^1 dx^2 }. \end{aligned} \end{equation} The vector $$I^{-1} d\Bx$$ is orthogonal to the tangent vector along the boundary, and for Euclidean spaces it can be identified as the outwards normal. ### Start proof: Respectively setting $$F = 1$$, and $$G = 1$$ in \ref{eqn:unpackingFundamentalTheorem:680}, we have \label{eqn:unpackingFundamentalTheorem:940} \int I^{-1} d^2 \Bx \rgrad G = \oint I^{-1} d\Bx G, and \label{eqn:unpackingFundamentalTheorem:960} \int F d^2 \Bx \lgrad I^{-1} = \oint F d\Bx I^{-1}. Starting with \ref{eqn:unpackingFundamentalTheorem:940} we find \label{eqn:unpackingFundamentalTheorem:700} \int I^{-1} J du dv I \rgrad G = \oint d\Bx G, to find $$\int dx^1 dx^2 \rgrad G = \oint I^{-1} d\Bx G$$, as desireed. In terms of a parameterization $$x = x(u,v)$$, the pseudoscalar for the space is \label{eqn:unpackingFundamentalTheorem:720} I = \frac{\Bx_u \wedge \Bx_v}{J}, so \label{eqn:unpackingFundamentalTheorem:740} I^{-1} = \frac{J}{\Bx_u \wedge \Bx_v}. Also note that $$\lr{\Bx_u \wedge \Bx_v}^{-1} = \Bx^v \wedge \Bx^u$$, so \label{eqn:unpackingFundamentalTheorem:760} I^{-1} = J \lr{ \Bx^v \wedge \Bx^u }, and \label{eqn:unpackingFundamentalTheorem:780} I^{-1} d\Bx = I^{-1} \cdot d\Bx = J \lr{ \Bx^v \wedge \Bx^u } \cdot \lr{ \Bx_u du – \Bx_v dv } = J \lr{ \Bx^v du + \Bx^u dv }, so the right acting gradient integral is \label{eqn:unpackingFundamentalTheorem:800} \int J du dv \grad G = \int \evalbar{J \Bx^v G}{\Delta v} du + \evalbar{J \Bx^u G dv}{\Delta u}, which we write in abbreviated form as $$\int J \lr{ \Bx^v du + \Bx^u dv} G$$. For the $$G = 1$$ case, from \ref{eqn:unpackingFundamentalTheorem:960} we find \label{eqn:unpackingFundamentalTheorem:820} \int J du dv F I \lgrad I^{-1} = \oint F d\Bx I^{-1}. However, in a 2D space, regardless of metric, we have $$I a = – a I$$ for any vector $$a$$ (i.e. $$\grad$$ or $$d\Bx$$), so we may commute the outer pseudoscalars in \label{eqn:unpackingFundamentalTheorem:840} \int J du dv F I \lgrad I^{-1} = \oint F d\Bx I^{-1}, so \label{eqn:unpackingFundamentalTheorem:850} -\int J du dv F I I^{-1} \lgrad = -\oint F I^{-1} d\Bx. After cancelling the negative sign on both sides, we have the claimed result. To see that $$I a$$, for any vector $$a$$ is normal to $$a$$, we can compute the dot product \label{eqn:unpackingFundamentalTheorem:860} \lr{ I a } \cdot a = \gpgradezero{ I a a } = a^2 \gpgradezero{ I } = 0, since the scalar selection of a bivector is zero. Since $$I^{-1} = \pm I$$, the same argument shows that $$I^{-1} d\Bx$$ must be orthogonal to $$d\Bx$$. ### End proof. Let’s look at the geometry of the normal $$I^{-1} \Bx$$ in a couple 2D vector spaces. We use an integration volume of a unit square to simplify the boundary term expressions. • Euclidean: With a parameterization $$x(u,v) = u\Be_1 + v \Be_2$$, and Euclidean basis vectors $$(\Be_1)^2 = (\Be_2)^2 = 1$$, the fundamental theorem integrated over the rectangle $$[x_0,x_1] \times [y_0,y_1]$$ is \label{eqn:unpackingFundamentalTheorem:880} \int dx dy \grad G = \int \Be_2 \lr{ G(x,y_1) – G(x,y_0) } dx + \Be_1 \lr{ G(x_1,y) – G(x_0,y) } dy, Each of the terms in the integrand above are illustrated in fig. 4, and we see that this is a path integral weighted by the outwards normal. fig. 4. Outwards oriented normal for Euclidean space. • Spacetime: Let $$x(u,v) = u \gamma_0 + v \gamma_1$$, where $$(\gamma_0)^2 = -(\gamma_1)^2 = 1$$. With $$u = t, v = x$$, the gradient integral over a $$[t_0,t_1] \times [x_0,x_1]$$ of spacetime is \label{eqn:unpackingFundamentalTheorem:900} \begin{aligned} \int dt dx \grad G &= \int \gamma^1 dt \lr{ G(t, x_1) – G(t, x_0) } + \gamma^0 dx \lr{ G(t_1, x) – G(t_1, x) } \\ &= \int \gamma_1 dt \lr{ -G(t, x_1) + G(t, x_0) } + \gamma_0 dx \lr{ G(t_1, x) – G(t_1, x) } . \end{aligned} With $$t$$ plotted along the horizontal axis, and $$x$$ along the vertical, each of the terms of this integrand is illustrated graphically in fig. 5. For this mixed signature space, there is no longer any good geometrical characterization of the normal. fig. 5. Orientation of the boundary normal for a spacetime basis. • Spacelike: Let $$x(u,v) = u \gamma_1 + v \gamma_2$$, where $$(\gamma_1)^2 = (\gamma_2)^2 = -1$$. With $$u = x, v = y$$, the gradient integral over a $$[x_0,x_1] \times [y_0,y_1]$$ of this space is \label{eqn:unpackingFundamentalTheorem:920} \begin{aligned} \int dx dy \grad G &= \int \gamma^2 dx \lr{ G(x, y_1) – G(x, y_0) } + \gamma^1 dy \lr{ G(x_1, y) – G(x_1, y) } \\ &= \int \gamma_2 dx \lr{ -G(x, y_1) + G(x, y_0) } + \gamma_1 dy \lr{ -G(x_1, y) + G(x_1, y) } . \end{aligned} Referring to fig. 6. where the elements of the integrand are illustrated, we see that the normal $$I^{-1} d\Bx$$ for the boundary of this region can be characterized as inwards. fig. 6. Inwards oriented normal for a Dirac spacelike basis. # References [1] S.L. Salas and E. Hille. Calculus: one and several variables. Wiley New York, 1990. ## Some experiments in youtube mathematics videos A couple years ago I was curious how easy it would be to use a graphics tablet as a virtual chalkboard, and produced a handful of very rough YouTube videos to get a feel for the basics of streaming and video editing (much of which I’ve now forgotten how to do). These were the videos in chronological order: • Introduction to Geometric (Clifford) Algebra.Introduction to Geometric (Clifford) algebra. Interpretation of products of unit vectors, rules for reducing products of unit vectors, and the axioms that justify those rules. • Geometric Algebra: dot, wedge, cross and vector products.Geometric (Clifford) Algebra introduction, showing the relation between the vector product dot and wedge products, and the cross product. • Solution of two line intersection using geometric algebra. • Linear system solution using the wedge product.. This video provides a standalone introduction to the wedge product, the geometry of the wedge product and some properties, and linear system solution as a sample application. In this video the wedge product is introduced independently of any geometric (Clifford) algebra, as an antisymmetric and associative operator. You’ll see that we get Cramer’s rule for free from this solution technique. • Exponential form of vector products in geometric algebra.In this video, I discussed the exponential form of the product of two vectors. I showed an example of how two unit vectors, each rotations of zcap orthonormal $$\mathbb{R}^3$$ planes, produce a “complex” exponential in the plane that spans these two vectors. • Velocity and acceleration in cylindrical coordinates using geometric algebra.I derived the cylindrical coordinate representations of the velocity and acceleration vectors, showing the radial and azimuthal components of each vector. I also showed how these are related to the dot and wedge product with the radial unit vector. • Duality transformations in geometric algebra.Duality transformations (pseudoscalar multiplication) will be demonstrated in $$\mathbb{R}^2$$ and $$\mathbb{R}^3$$. A polar parameterized vector in $$\mathbb{R}^2$$, written in complex exponential form, is multiplied by a unit pseudoscalar for the x-y plane. We see that the result is a vector normal to that vector, with the direction of the normal dependent on the order of multiplication, and the orientation of the pseudoscalar used. In $$\mathbb{R}^3$$ we see that a vector multiplied by a pseudoscalar yields the bivector that represents the plane that is normal to that vector. The sign of that bivector (or its cyclic orientation) depends on the orientation of the pseudoscalar. The order of multiplication was not mentioned in this case since the $$\mathbb{R}^3$$ pseudoscalar commutes with any grade object (assumed, not proved). An example of a vector with two components in a plane, multiplied by a pseudoscalar was also given, which allowed for a visualization of the bivector that is normal to the original vector. • Math bait and switch: Fractional integer exponents.When I was a kid, my dad asked me to explain fractional exponents, and perhaps any non-positive integer exponents, to him. He objected to the idea of multiplying something by itself $$1/2$$ times. I failed to answer the question to his satisfaction. My own son is now reviewing the rules of exponentiation, and it occurred to me (30 years later) why my explanation to Dad failed. Essentially, there’s a small bait and switch required, and my dad didn’t fall for it. The meaning that my dad gave to exponentiation was that $$x^n$$ equals $$x$$ times itself $$n$$ times. Using this rule, it is easy to demonstrate that $$x^a x^b = x^{a + b}$$, and this can be used to justify expressions like $$x^{1/2}$$. However, doing this really means that we’ve switched the definition of exponential, defining an exponential as any number that satisfies the relationship: $$x^a x^b = x^{a+b}$$, where $$x^1 = x$$. This slight of hand is required to give meaning to $$x^{1/2}$$ or other exponentials where the exponential argument is any non-positive integer. Of these videos I just relistened to the wedge product episode, as I had a new lone comment on it, and I couldn’t even remember what I had said. It wasn’t completely horrible, despite the low tech. I was, however, very surprised how soft and gentle my voice was. When I am talking math in person, I get very animated, but attempting to manage the tech was distracting and all the excitement that I’d normally have was obliterated. I’d love to attempt a manim based presentation of some of this material, but suspect if I do something completely scripted like that, I may not be a very good narrator. ## Fundamental theorem of geometric calculus for line integrals (relativistic.) [This post is best viewed in PDF form, due to latex elements that I could not format with wordpress mathjax.] Background for this particular post can be found in ## Motivation. I’ve been slowly working my way towards a statement of the fundamental theorem of integral calculus, where the functions being integrated are elements of the Dirac algebra (space time multivectors in the geometric algebra parlance.) This is interesting because we want to be able to do line, surface, 3-volume and 4-volume space time integrals. We have many $$\mathbb{R}^3$$ integral theorems \label{eqn:fundamentalTheoremOfGC:40a} \int_A^B d\Bl \cdot \spacegrad f = f(B) – f(A), \label{eqn:fundamentalTheoremOfGC:60a} \int_S dA\, \ncap \cross \spacegrad f = \int_{\partial S} d\Bx\, f, \label{eqn:fundamentalTheoremOfGC:80a} \int_S dA\, \ncap \cdot \lr{ \spacegrad \cross \Bf} = \int_{\partial S} d\Bx \cdot \Bf, \label{eqn:fundamentalTheoremOfGC:100a} \int_S dx dy \lr{ \PD{y}{P} – \PD{x}{Q} } = \int_{\partial S} P dx + Q dy, \label{eqn:fundamentalTheoremOfGC:120a} \int_V dV\, \spacegrad f = \int_{\partial V} dA\, \ncap f, \label{eqn:fundamentalTheoremOfGC:140a} \int_V dV\, \spacegrad \cross \Bf = \int_{\partial V} dA\, \ncap \cross \Bf, \label{eqn:fundamentalTheoremOfGC:160a} \int_V dV\, \spacegrad \cdot \Bf = \int_{\partial V} dA\, \ncap \cdot \Bf, and want to know how to generalize these to four dimensions and also make sure that we are handling the relativistic mixed signature correctly. If our starting point was the mess of equations above, we’d be in trouble, since it is not obvious how these generalize. All the theorems with unit normals have to be handled completely differently in four dimensions since we don’t have a unique normal to any given spacetime plane. What comes to our rescue is the Fundamental Theorem of Geometric Calculus (FTGC), which has the form \label{eqn:fundamentalTheoremOfGC:40} \int F d^n \Bx\, \lrpartial G = \int F d^{n-1} \Bx\, G, where $$F,G$$ are multivectors functions (i.e. sums of products of vectors.) We’ve seen ([2], [1]) that all the identities above are special cases of the fundamental theorem. Do we need any special care to state the FTGC correctly for our relativistic case? It turns out that the answer is no! Tangent and reciprocal frame vectors do all the heavy lifting, and we can use the fundamental theorem as is, even in our mixed signature space. The only real change that we need to make is use spacetime gradient and vector derivative operators instead of their spatial equivalents. We will see how this works below. Note that instead of starting with \ref{eqn:fundamentalTheoremOfGC:40} directly, I will attempt to build up to that point in a progressive fashion that is hopefully does not require the reader to make too many unjustified mental leaps. ## Multivector line integrals. We want to define multivector line integrals to start with. Recall that in $$\mathbb{R}^3$$ we would say that for scalar functions $$f$$, the integral \label{eqn:fundamentalTheoremOfGC:180b} \int d\Bx\, f = \int f d\Bx, is a line integral. Also, for vector functions $$\Bf$$ we call \label{eqn:fundamentalTheoremOfGC:200} \int d\Bx \cdot \Bf = \inv{2} \int d\Bx\, \Bf + \Bf d\Bx. a line integral. In order to generalize line integrals to multivector functions, we will allow our multivector functions to be placed on either or both sides of the differential. ## Definition 1.1: Line integral. Given a single variable parameterization $$x = x(u)$$, we write $$d^1\Bx = \Bx_u du$$, and call \label{eqn:fundamentalTheoremOfGC:220a} \int F d^1\Bx\, G, a line integral, where $$F,G$$ are arbitrary multivector functions. We must be careful not to reorder any of the factors in the integrand, since the differential may not commute with either $$F$$ or $$G$$. Here is a simple example where the integrand has a product of a vector and differential. ## Problem: Circular parameterization. Given a circular parameterization $$x(\theta) = \gamma_1 e^{-i\theta}$$, where $$i = \gamma_1 \gamma_2$$, the unit bivector for the $$x,y$$ plane. Compute the line integral \label{eqn:fundamentalTheoremOfGC:100} \int_0^{\pi/4} F(\theta)\, d^1 \Bx\, G(\theta), where $$F(\theta) = \Bx^\theta + \gamma_3 + \gamma_1 \gamma_0$$ is a multivector valued function, and $$G(\theta) = \gamma_0$$ is vector valued. The tangent vector for the curve is \label{eqn:fundamentalTheoremOfGC:60} \Bx_\theta = -\gamma_1 \gamma_1 \gamma_2 e^{-i\theta} = \gamma_2 e^{-i\theta}, with reciprocal vector $$\Bx^\theta = e^{i \theta} \gamma^2$$. The differential element is $$d^1 \Bx = \gamma_2 e^{-i\theta} d\theta$$, so the integrand is \label{eqn:fundamentalTheoremOfGC:80} \begin{aligned} \int_0^{\pi/4} \lr{ \Bx^\theta + \gamma_3 + \gamma_1 \gamma_0 } d^1 \Bx\, \gamma_0 &= \int_0^{\pi/4} \lr{ e^{i\theta} \gamma^2 + \gamma_3 + \gamma_1 \gamma_0 } \gamma_2 e^{-i\theta} d\theta\, \gamma_0 \\ &= \frac{\pi}{4} \gamma_0 + \lr{ \gamma_{32} + \gamma_{102} } \inv{-i} \lr{ e^{-i\pi/4} – 1 } \gamma_0 \\ &= \frac{\pi}{4} \gamma_0 + \inv{\sqrt{2}} \lr{ \gamma_{32} + \gamma_{102} } \gamma_{120} \lr{ 1 – \gamma_{12} } \\ &= \frac{\pi}{4} \gamma_0 + \inv{\sqrt{2}} \lr{ \gamma_{310} + 1 } \lr{ 1 – \gamma_{12} }. \end{aligned} Observe how care is required not to reorder any terms. This particular end result is a multivector with scalar, vector, bivector, and trivector grades, but no pseudoscalar component. The grades in the end result depend on both the function in the integrand and on the path. For example, had we integrated all the way around the circle, the end result would have been the vector $$2 \pi \gamma_0$$ (i.e. a $$\gamma_0$$ weighted unit circle circumference), as all the other grades would have been killed by the complex exponential integrated over a full period. ## Problem: Line integral for boosted time direction vector. Let $$x = e^{\vcap \alpha/2} \gamma_0 e^{-\vcap \alpha/2}$$ represent the spacetime curve of all the boosts of $$\gamma_0$$ along a specific velocity direction vector, where $$\vcap = (v \wedge \gamma_0)/\Norm{v \wedge \gamma_0}$$ is a unit spatial bivector for any constant vector $$v$$. Compute the line integral \label{eqn:fundamentalTheoremOfGC:240} \int x\, d^1 \Bx. Observe that $$\vcap$$ and $$\gamma_0$$ anticommute, so we may write our boost as a one sided exponential \label{eqn:fundamentalTheoremOfGC:260} x(\alpha) = \gamma_0 e^{-\vcap \alpha} = e^{\vcap \alpha} \gamma_0 = \lr{ \cosh\alpha + \vcap \sinh\alpha } \gamma_0. The tangent vector is just \label{eqn:fundamentalTheoremOfGC:280} \Bx_\alpha = \PD{\alpha}{x} = e^{\vcap\alpha} \vcap \gamma_0. Let’s get a bit of intuition about the nature of this vector. It’s square is \label{eqn:fundamentalTheoremOfGC:300} \begin{aligned} \Bx_\alpha^2 &= e^{\vcap\alpha} \vcap \gamma_0 e^{\vcap\alpha} \vcap \gamma_0 \\ &= -e^{\vcap\alpha} \vcap e^{-\vcap\alpha} \vcap (\gamma_0)^2 \\ &= -1, \end{aligned} so we see that the tangent vector is a spacelike unit vector. As the vector representing points on the curve is necessarily timelike (due to Lorentz invariance), these two must be orthogonal at all points. Let’s confirm this algebraically \label{eqn:fundamentalTheoremOfGC:320} \begin{aligned} x \cdot \Bx_\alpha &= \gpgradezero{ e^{\vcap \alpha} \gamma_0 e^{\vcap \alpha} \vcap \gamma_0 } \\ &= \gpgradezero{ e^{-\vcap \alpha} e^{\vcap \alpha} \vcap (\gamma_0)^2 } \\ &= \gpgradezero{ \vcap } \\ &= 0. \end{aligned} Here we used $$e^{\vcap \alpha} \gamma_0 = \gamma_0 e^{-\vcap \alpha}$$, and $$\gpgradezero{A B} = \gpgradezero{B A}$$. Geometrically, we have the curious fact that the direction vectors to points on the curve are perpendicular (with respect to our relativistic dot product) to the tangent vectors on the curve, as illustrated in fig. 1. fig. 1. Tangent perpendicularity in mixed metric. ### Perfect differentials. Having seen a couple examples of multivector line integrals, let’s now move on to figure out the structure of a line integral that has a “perfect” differential integrand. We can take a hint from the $$\mathbb{R}^3$$ vector result that we already know, namely \label{eqn:fundamentalTheoremOfGC:120} \int_A^B d\Bl \cdot \spacegrad f = f(B) – f(A). It seems reasonable to guess that the relativistic generalization of this is \label{eqn:fundamentalTheoremOfGC:140} \int_A^B dx \cdot \grad f = f(B) – f(A). Let’s check that, by expanding in coordinates \label{eqn:fundamentalTheoremOfGC:160} \begin{aligned} \int_A^B dx \cdot \grad f &= \int_A^B d\tau \frac{dx^\mu}{d\tau} \partial_\mu f \\ &= \int_A^B d\tau \frac{dx^\mu}{d\tau} \PD{x^\mu}{f} \\ &= \int_A^B d\tau \frac{df}{d\tau} \\ &= f(B) – f(A). \end{aligned} If we drop the dot product, will we have such a nice result? Let’s see: \label{eqn:fundamentalTheoremOfGC:180} \begin{aligned} \int_A^B dx \grad f &= \int_A^B d\tau \frac{dx^\mu}{d\tau} \gamma_\mu \gamma^\nu \partial_\nu f \\ &= \int_A^B d\tau \frac{dx^\mu}{d\tau} \PD{x^\mu}{f} + \int_A^B d\tau \sum_{\mu \ne \nu} \gamma_\mu \gamma^\nu \frac{dx^\mu}{d\tau} \PD{x^\nu}{f}. \end{aligned} This scalar component of this integrand is a perfect differential, but the bivector part of the integrand is a complete mess, that we have no hope of generally integrating. It happens that if we consider one of the simplest parameterization examples, we can get a strong hint of how to generalize the differential operator to one that ends up providing a perfect differential. In particular, let’s integrate over a linear constant path, such as $$x(\tau) = \tau \gamma_0$$. For this path, we have \label{eqn:fundamentalTheoremOfGC:200a} \begin{aligned} \int_A^B dx \grad f &= \int_A^B \gamma_0 d\tau \lr{ \gamma^0 \partial_0 + \gamma^1 \partial_1 + \gamma^2 \partial_2 + \gamma^3 \partial_3 } f \\ &= \int_A^B d\tau \lr{ \PD{\tau}{f} + \gamma_0 \gamma^1 \PD{x^1}{f} + \gamma_0 \gamma^2 \PD{x^2}{f} + \gamma_0 \gamma^3 \PD{x^3}{f} }. \end{aligned} Just because the path does not have any $$x^1, x^2, x^3$$ component dependencies does not mean that these last three partials are neccessarily zero. For example $$f = f(x(\tau)) = \lr{ x^0 }^2 \gamma_0 + x^1 \gamma_1$$ will have a non-zero contribution from the $$\partial_1$$ operator. In that particular case, we can easily integrate $$f$$, but we have to know the specifics of the function to do the integral. However, if we had a differential operator that did not include any component off the integration path, we would ahve a perfect differential. That is, if we were to replace the gradient with the projection of the gradient onto the tangent space, we would have a perfect differential. We see that the function of the dot product in \ref{eqn:fundamentalTheoremOfGC:140} has the same effect, as it rejects any component of the gradient that does not lie on the tangent space. ## Definition 1.2: Vector derivative. Given a spacetime manifold parameterized by $$x = x(u^0, \cdots u^{N-1})$$, with tangent vectors $$\Bx_\mu = \PDi{u^\mu}{x}$$, and reciprocal vectors $$\Bx^\mu \in \textrm{Span}\setlr{\Bx_\nu}$$, such that $$\Bx^\mu \cdot \Bx_\nu = {\delta^\mu}_\nu$$, the vector derivative is defined as \label{eqn:fundamentalTheoremOfGC:240a} \partial = \sum_{\mu = 0}^{N-1} \Bx^\mu \PD{u^\mu}{}. Observe that if this is a full parameterization of the space ($$N = 4$$), then the vector derivative is identical to the gradient. The vector derivative is the projection of the gradient onto the tangent space at the point of evaluation.Furthermore, we designate $$\lrpartial$$ as the vector derivative allowed to act bidirectionally, as follows \label{eqn:fundamentalTheoremOfGC:260a} R \lrpartial S = R \Bx^\mu \PD{u^\mu}{S} + \PD{u^\mu}{R} \Bx^\mu S, where $$R, S$$ are multivectors, and summation convention is implied. In this bidirectional action, the vector factors of the vector derivative must stay in place (as they do not neccessarily commute with $$R,S$$), but the derivative operators apply in a chain rule like fashion to both functions. Noting that $$\Bx_u \cdot \grad = \Bx_u \cdot \partial$$, we may rewrite the scalar line integral identity \ref{eqn:fundamentalTheoremOfGC:140} as \label{eqn:fundamentalTheoremOfGC:220} \int_A^B dx \cdot \partial f = f(B) – f(A). However, as our example hinted at, the fundamental theorem for line integrals has a multivector generalization that does not rely on a dot product to do the tangent space filtering, and is more powerful. That generalization has the following form. ## Theorem 1.1: Fundamental theorem for line integrals. Given multivector functions $$F, G$$, and a single parameter curve $$x(u)$$ with line element $$d^1 \Bx = \Bx_u du$$, then \label{eqn:fundamentalTheoremOfGC:280a} \int_A^B F d^1\Bx \lrpartial G = F(B) G(B) – F(A) G(A). ### Start proof: Writing out the integrand explicitly, we find \label{eqn:fundamentalTheoremOfGC:340} \int_A^B F d^1\Bx \lrpartial G = \int_A^B \lr{ \PD{\alpha}{F} d\alpha\, \Bx_\alpha \Bx^\alpha G + F d\alpha\, \Bx_\alpha \Bx^\alpha \PD{\alpha}{G } } However for a single parameter curve, we have $$\Bx^\alpha = 1/\Bx_\alpha$$, so we are left with \label{eqn:fundamentalTheoremOfGC:360} \begin{aligned} \int_A^B F d^1\Bx \lrpartial G &= \int_A^B d\alpha\, \PD{\alpha}{(F G)} \\ &= \evalbar{F G}{B} \evalbar{F G}{A}. \end{aligned} ## More to come. In the next installment we will explore surface integrals in spacetime, and the generalization of the fundamental theorem to multivector space time integrals. # References [1] Peeter Joot. Geometric Algebra for Electrical Engineers. Kindle Direct Publishing, 2019. [2] A. Macdonald. Vector and Geometric Calculus. CreateSpace Independent Publishing Platform, 2012. ## Lorentz transformations in Space Time Algebra (STA) [If mathjax doesn’t display properly for you, click here for a PDF of this post] ## Motivation. One of the remarkable features of geometric algebra are the complex exponential sandwiches that can be used to encode rotations in any dimension, or rotation like operations like Lorentz transformations in Minkowski spaces. In this post, we show some examples that unpack the geometric algebra expressions for Lorentz transformations operations of this sort. In particular, we will look at the exponential sandwich operations for spatial rotations and Lorentz boosts in the Dirac algebra, known as Space Time Algebra (STA) in geometric algebra circles, and demonstrate that these sandwiches do have the desired effects. ## Theorem 1.1: Lorentz transformation. The transformation \label{eqn:lorentzTransform:580} x \rightarrow e^{B} x e^{-B} = x’, where $$B = a \wedge b$$, is an STA 2-blade for any two linearly independent four-vectors $$a, b$$, is a norm preserving, that is \label{eqn:lorentzTransform:600} x^2 = {x’}^2. ### Start proof: The proof is disturbingly trivial in this geometric algebra form \label{eqn:lorentzTransform:40} \begin{aligned} {x’}^2 &= e^{B} x e^{-B} e^{B} x e^{-B} \\ &= e^{B} x x e^{-B} \\ &= x^2 e^{B} e^{-B} \\ &= x^2. \end{aligned} ### End proof. In particular, observe that we did not need to construct the usual infinitesimal representations of rotation and boost transformation matrices or tensors in order to demonstrate that we have spacetime invariance for the transformations. The rough idea of such a transformation is that the exponential commutes with components of the four-vector that lie off the spacetime plane specified by the bivector $$B$$, and anticommutes with components of the four-vector that lie in the plane. The end result is that the sandwich operation simplifies to \label{eqn:lorentzTransform:60} x’ = x_\parallel e^{-B} + x_\perp, where $$x = x_\perp + x_\parallel$$ and $$x_\perp \cdot B = 0$$, and $$x_\parallel \wedge B = 0$$. In particular, using $$x = x B B^{-1} = \lr{ x \cdot B + x \wedge B } B^{-1}$$, we find that \label{eqn:lorentzTransform:80} \begin{aligned} x_\parallel &= \lr{ x \cdot B } B^{-1} \\ x_\perp &= \lr{ x \wedge B } B^{-1}. \end{aligned} When $$B$$ is a spacetime plane $$B = b \wedge \gamma_0$$, then this exponential has a hyperbolic nature, and we end up with a Lorentz boost. When $$B$$ is a spatial bivector, we end up with a single complex exponential, encoding our plane old 3D rotation. More general $$B$$’s that encode composite boosts and rotations are also possible, but $$B$$ must be invertible (it should have no lightlike factors.) The rough geometry of these projections is illustrated in fig 1, where the spacetime plane is represented by $$B$$. fig 1. Projection and rejection geometry. What is not so obvious is how to pick $$B$$’s that correspond to specific rotation axes or boost directions. Let’s consider each of those cases in turn. ## Theorem 1.2: Boost. The boost along a direction vector $$\vcap$$ and rapidity $$\alpha$$ is given by \label{eqn:lorentzTransform:620} x’ = e^{-\vcap \alpha/2} x e^{\vcap \alpha/2}, where $$\vcap = \gamma_{k0} \cos\theta^k$$ is an STA bivector representing a spatial direction with direction cosines $$\cos\theta^k$$. ### Start proof: We want to demonstrate that this is equivalent to the usual boost formulation. We can start with decomposition of the four-vector $$x$$ into components that lie in and off of the spacetime plane $$\vcap$$. \label{eqn:lorentzTransform:100} \begin{aligned} x &= \lr{ x^0 + \Bx } \gamma_0 \\ &= \lr{ x^0 + \Bx \vcap^2 } \gamma_0 \\ &= \lr{ x^0 + \lr{ \Bx \cdot \vcap} \vcap + \lr{ \Bx \wedge \vcap} \vcap } \gamma_0, \end{aligned} where $$\Bx = x \wedge \gamma_0$$. The first two components lie in the boost plane, whereas the last is the spatial component of the vector that lies perpendicular to the boost plane. Observe that $$\vcap$$ anticommutes with the dot product term and commutes with he wedge product term, so we have \label{eqn:lorentzTransform:120} \begin{aligned} x’ &= \lr{ x^0 + \lr{ \Bx \cdot \vcap } \vcap } \gamma_0 e^{\vcap \alpha/2 } e^{\vcap \alpha/2 } + \lr{ \Bx \wedge \vcap } \vcap \gamma_0 e^{-\vcap \alpha/2 } e^{\vcap \alpha/2 } \\ &= \lr{ x^0 + \lr{ \Bx \cdot \vcap } \vcap } \gamma_0 e^{\vcap \alpha } + \lr{ \Bx \wedge \vcap } \vcap \gamma_0. \end{aligned} Noting that $$\vcap^2 = 1$$, we may expand the exponential in hyperbolic functions, and find that the boosted portion of the vector expands as \label{eqn:lorentzTransform:260} \begin{aligned} \lr{ x^0 + \lr{ \Bx \cdot \vcap} \vcap } \gamma_0 e^{\vcap \alpha} &= \lr{ x^0 + \lr{ \Bx \cdot \vcap} \vcap } \gamma_0 \lr{ \cosh\alpha + \vcap \sinh \alpha} \\ &= \lr{ x^0 + \lr{ \Bx \cdot \vcap} \vcap } \lr{ \cosh\alpha – \vcap \sinh \alpha} \gamma_0 \\ &= \lr{ x^0 \cosh\alpha – \lr{ \Bx \cdot \vcap} \sinh \alpha} \gamma_0 + \lr{ -x^0 \sinh \alpha + \lr{ \Bx \cdot \vcap} \cosh \alpha } \vcap \gamma_0. \end{aligned} We are left with \label{eqn:lorentzTransform:320} \begin{aligned} x’ &= \lr{ x^0 \cosh\alpha – \lr{ \Bx \cdot \vcap} \sinh \alpha} \gamma_0 + \lr{ \lr{ \Bx \cdot \vcap} \cosh \alpha -x^0 \sinh \alpha } \vcap \gamma_0 + \lr{ \Bx \wedge \vcap} \vcap \gamma_0 \\ &= \begin{bmatrix} \gamma_0 & \vcap \gamma_0 \end{bmatrix} \begin{bmatrix} \cosh\alpha & – \sinh\alpha \\ -\sinh\alpha & \cosh\alpha \end{bmatrix} \begin{bmatrix} x^0 \\ \Bx \cdot \vcap \end{bmatrix} + \lr{ \Bx \wedge \vcap} \vcap \gamma_0, \end{aligned} which has the desired Lorentz boost structure. Of course, this is usually seen with $$\vcap = \gamma_{10}$$ so that the components in the coordinate column vector are $$(ct, x)$$. ## Theorem 1.3: Spatial rotation. Given two linearly independent spatial bivectors $$\Ba = a^k \gamma_{k0}, \Bb = b^k \gamma_{k0}$$, a rotation of $$\theta$$ radians in the plane of $$\Ba, \Bb$$ from $$\Ba$$ towards $$\Bb$$, is given by \label{eqn:lorentzTransform:640} x’ = e^{-i\theta} x e^{i\theta}, where $$i = (\Ba \wedge \Bb)/\Abs{\Ba \wedge \Bb}$$, is a unit (spatial) bivector. ### Start proof: Without loss of generality, we may pick $$i = \acap \bcap$$, where $$\acap^2 = \bcap^2 = 1$$, and $$\acap \cdot \bcap = 0$$. With such an orthonormal basis for the plane, we can decompose our four vector into portions that lie in and off the plane \label{eqn:lorentzTransform:400} \begin{aligned} x &= \lr{ x^0 + \Bx } \gamma_0 \\ &= \lr{ x^0 + \Bx i i^{-1} } \gamma_0 \\ &= \lr{ x^0 + \lr{ \Bx \cdot i } i^{-1} + \lr{ \Bx \wedge i } i^{-1} } \gamma_0. \end{aligned} The projective term lies in the plane of rotation, whereas the timelike and spatial rejection term are perpendicular. That is \label{eqn:lorentzTransform:420} \begin{aligned} x_\parallel &= \lr{ \Bx \cdot i } i^{-1} \gamma_0 \\ x_\perp &= \lr{ x^0 + \lr{ \Bx \wedge i } i^{-1} } \gamma_0, \end{aligned} where $$x_\parallel \wedge i = 0$$, and $$x_\perp \cdot i = 0$$. The plane pseudoscalar $$i$$ anticommutes with $$x_\parallel$$, and commutes with $$x_\perp$$, so \label{eqn:lorentzTransform:440} \begin{aligned} x’ &= e^{-i\theta/2} \lr{ x_\parallel + x_\perp } e^{i\theta/2} \\ &= x_\parallel e^{i\theta} + x_\perp. \end{aligned} However \label{eqn:lorentzTransform:460} \begin{aligned} \lr{ \Bx \cdot i } i^{-1} &= \lr{ \Bx \cdot \lr{ \acap \wedge \bcap } } \bcap \acap \\ &= \lr{\Bx \cdot \acap} \bcap \bcap \acap -\lr{\Bx \cdot \bcap} \acap \bcap \acap \\ &= \lr{\Bx \cdot \acap} \acap +\lr{\Bx \cdot \bcap} \bcap, \end{aligned} so \label{eqn:lorentzTransform:480} \begin{aligned} x_\parallel e^{i\theta} &= \lr{ \lr{\Bx \cdot \acap} \acap + \lr{\Bx \cdot \bcap} \bcap } \gamma_0 \lr{ \cos\theta + \acap \bcap \sin\theta } \\ &= \acap \lr{ \lr{\Bx \cdot \acap} \cos\theta \lr{\Bx \cdot \bcap} \sin\theta } \gamma_0 + \bcap \lr{ \lr{\Bx \cdot \acap} \sin\theta + \lr{\Bx \cdot \bcap} \cos\theta } \gamma_0, \end{aligned} so \label{eqn:lorentzTransform:500} x’ = \begin{bmatrix} \acap & \bcap \end{bmatrix} \begin{bmatrix} \cos\theta & – \sin\theta \\ \sin\theta & \cos\theta \end{bmatrix} \begin{bmatrix} \Bx \cdot \acap \\ \Bx \cdot \bcap \\ \end{bmatrix} \gamma_0 + \lr{ x \wedge i} i^{-1} \gamma_0. Observe that this rejection term can be explicitly expanded to \label{eqn:lorentzTransform:520} \lr{ \Bx \wedge i} i^{-1} \gamma_0 = x – \lr{ \Bx \cdot \acap } \acap \gamma_0 \lr{ \Bx \cdot \acap } \acap \gamma_0. This is the timelike component of the vector, plus the spatial component that is normal to the plane. This exponential sandwich transformation rotates only the portion of the vector that lies in the plane, and leaves the rest (timelike and normal) untouched. ## Problem: Verify components relative to boost direction. In the proof of thm. 1.2, the vector $$x$$ was expanded in terms of the spacetime split. An alternate approach, is to expand as \label{eqn:lorentzTransform:340} \begin{aligned} x &= x \vcap^2 \\ &= \lr{ x \cdot \vcap + x \wedge \vcap } \vcap \\ &= \lr{ x \cdot \vcap } \vcap + \lr{ x \wedge \vcap } \vcap. \end{aligned} Show that \label{eqn:lorentzTransform:360} \lr{ x \cdot \vcap } \vcap = \lr{ x^0 + \lr{ \Bx \cdot \vcap} \vcap } \gamma_0, and \label{eqn:lorentzTransform:380} \lr{ x \wedge \vcap } \vcap = \lr{ \Bx \wedge \vcap} \vcap \gamma_0. Let $$x = x^\mu \gamma_\mu$$, so that \label{eqn:lorentzTransform:160} \begin{aligned} x \cdot \vcap &= \gpgradeone{ x^\mu \gamma_\mu \cos\theta^b \gamma_{b 0} } \\ &= x^\mu \cos\theta^b \gpgradeone{ \gamma_\mu \gamma_{b 0} } . \end{aligned} The $$\mu = 0$$ component of this grade selection is \label{eqn:lorentzTransform:180} \gpgradeone{ \gamma_0 \gamma_{b 0} } = -\gamma_b, and for $$\mu = a \ne 0$$, we have \label{eqn:lorentzTransform:200} \gpgradeone{ \gamma_a \gamma_{b 0} } = -\delta_{a b} \gamma_0, so we have \label{eqn:lorentzTransform:220} \begin{aligned} x \cdot \vcap &= x^0 \cos\theta^b (-\gamma_b) + x^a \cos\theta^b (-\delta_{ab} \gamma_0 ) \\ &= -x^0 \vcap \gamma_0 x^b \cos\theta^b \gamma_0 \\ &= – \lr{ x^0 \vcap + \Bx \cdot \vcap } \gamma_0, \end{aligned} where $$\Bx = x \wedge \gamma_0$$ is the spatial portion of the four vector $$x$$ relative to the stationary observer frame. Since $$\vcap$$ anticommutes with $$\gamma_0$$, the component of $$x$$ in the spacetime plane $$\vcap$$ is \label{eqn:lorentzTransform:240} \lr{ x \cdot \vcap } \vcap = \lr{ x^0 + \lr{ \Bx \cdot \vcap} \vcap } \gamma_0, as expected. For the rejection term, we have \label{eqn:lorentzTransform:280} x \wedge \vcap = x^\mu \cos\theta^s \gpgradethree{ \gamma_\mu \gamma_{s 0} }. The $$\mu = 0$$ term clearly contributes nothing, leaving us with: \label{eqn:lorentzTransform:300} \begin{aligned} \lr{ x \wedge \vcap } \vcap &= \lr{ x \wedge \vcap } \cdot \vcap \\ &= x^r \cos\theta^s \cos\theta^t \lr{ \lr{ \gamma_r \wedge \gamma_{s}} \gamma_0 } \cdot \lr{ \gamma_{t0} } \\ &= x^r \cos\theta^s \cos\theta^t \gpgradeone{ \lr{ \gamma_r \wedge \gamma_{s} } \gamma_0 \gamma_{t0} } \\ &= -x^r \cos\theta^s \cos\theta^t \lr{ \gamma_r \wedge \gamma_{s}} \cdot \gamma_t \\ &= -x^r \cos\theta^s \cos\theta^t \lr{ -\gamma_r \delta_{st} + \gamma_s \delta_{rt} } \\ &= x^r \cos\theta^t \cos\theta^t \gamma_r x^t \cos\theta^s \cos\theta^t \gamma_s \\ &= \Bx \gamma_0 – (\Bx \cdot \vcap) \vcap \gamma_0 \\ &= \lr{ \Bx \wedge \vcap} \vcap \gamma_0, \end{aligned} as expected. Is there a clever way to demonstrate this without resorting to coordinates? ## Problem: Rotation transformation components. Given a unit spatial bivector $$i = \acap \bcap$$, where $$\acap \cdot \bcap = 0$$ and $$i^2 = -1$$, show that \label{eqn:lorentzTransform:540} \lr{ x \cdot i } i^{-1} = \lr{ \Bx \cdot i } i^{-1} \gamma_0 = \lr{\Bx \cdot \acap } \acap \gamma_0 + \lr{\Bx \cdot \bcap } \bcap \gamma_0, and \label{eqn:lorentzTransform:560} \lr{ x \wedge i } i^{-1} = \lr{ \Bx \wedge i } i^{-1} \gamma_0 = x – \lr{\Bx \cdot \acap } \acap \gamma_0 \lr{\Bx \cdot \bcap } \bcap \gamma_0. Also show that $$i$$ anticommutes with $$\lr{ x \cdot i } i^{-1}$$ and commutes with $$\lr{ x \wedge i } i^{-1}$$. This problem is left for the reader, as I don’t feel like typing out my solution. The first part of this problem can be done in the tedious coordinate approach used above, but hopefully there is a better way. For the last (commutation) part of the problem, here is a hint. Let $$x \wedge i = n i$$, where $$n \cdot i = 0$$. The result then follows easily. ## Curvilinear coordinates and gradient in spacetime, and reciprocal frames. [If mathjax doesn’t display properly for you, click here for a PDF of this post] ## Motivation. I started pondering some aspects of spacetime integration theory, and found that there were some aspects of the concepts of reciprocal frames that were not clear to me. In the process of sorting those ideas out for myself, I wrote up the following notes. In the notes below, I will introduce the many of the prerequisite ideas that are needed to express and apply the fundamental theorem of geometric calculus in a 4D relativistic context. The focus will be the Dirac’s algebra of special relativity, known as STA (Space Time Algebra) in geometric algebra parlance. If desired, it should be clear how to apply these ideas to lower or higher dimensional spaces, and to plain old Euclidean metrics. ### On notation. In Euclidean space we use bold face reciprocal frame vectors $$\Bx^i \cdot \Bx_j = {\delta^i}_j$$, which nicely distinguishes them from the generalized coordinates $$x_i, x^j$$ associated with the basis or the reciprocal frame, that is \label{eqn:reciprocalblog:640} \Bx = x^i \Bx_i = x_j \Bx^j. On the other hand, it is conventional to use non-bold face for both the four-vectors and their coordinates in STA, such as the following standard basis decomposition \label{eqn:reciprocalblog:660} x = x^\mu \gamma_\mu = x_\mu \gamma^\mu. If we use non-bold face $$x^\mu, x_\nu$$ for the coordinates with respect to a specified frame, then we cannot also use non-bold face for the curvilinear basis vectors. To resolve this notational ambiguity, I’ve chosen to use bold face $$\Bx^\mu, \Bx_\nu$$ symbols as the curvilinear basis elements in this relativistic context, as we do for Euclidean spaces. ## Definition 1.1: Standard Dirac basis. The Dirac basis elements are $$\setlr{ \gamma_0, \gamma_1, \gamma_2, \gamma_3 }$$, satisfying \label{eqn:reciprocalblog:1940} \gamma_0^2 = 1 = -\gamma_k^2, \quad \forall k = 1,2,3, and \label{eqn:reciprocalblog:740} \gamma_\mu \cdot \gamma_\nu = 0, \quad \forall \mu \ne \nu. A conventional way of summarizing these orthogonality relationships is $$\gamma_\mu \cdot \gamma_\nu = \eta_{\mu\nu}$$, where $$\eta_{\mu\nu}$$ are the elements of the metric $$G = \text{diag}(+,-,-,-)$$. ## Definition 1.2: Reciprocal basis for the standard Dirac basis. We define a reciprocal basis $$\setlr{ \gamma^0, \gamma^1, \gamma^2, \gamma^3}$$ satisfying $$\gamma^\mu \cdot \gamma_\nu = {\delta^\mu}_\nu, \forall \mu,\nu \in 0,1,2,3$$. ## Theorem 1.1: Reciprocal basis uniqueness. This reciprocal basis is unique, and for our choice of metric has the values \label{eqn:reciprocalblog:1960} \gamma^0 = \gamma_0, \quad \gamma^k = -\gamma_k, \quad \forall k = 1,2,3. Proof is left to the reader. ## Definition 1.3: Coordinates. We define the coordinates of a vector with respect to the standard basis as $$x^\mu$$ satisfying \label{eqn:reciprocalblog:1980} x = x^\mu \gamma_\mu, and define the coordinates of a vector with respect to the reciprocal basis as $$x_\mu$$ satisfying \label{eqn:reciprocalblog:2000} x = x_\mu \gamma^\mu, ## Theorem 1.2: Coordinates. Given the definitions above, we may compute the coordinates of a vector, simply by dotting with the basis elements \label{eqn:reciprocalblog:2020} x^\mu = x \cdot \gamma^\mu, and \label{eqn:reciprocalblog:2040} x_\mu = x \cdot \gamma_\mu, ### Start proof: This follows by straightforward computation \label{eqn:reciprocalblog:840} \begin{aligned} x \cdot \gamma^\mu &= \lr{ x^\nu \gamma_\nu } \cdot \gamma^\mu \\ &= x^\nu \lr{ \gamma_\nu \cdot \gamma^\mu } \\ &= x^\nu {\delta_\nu}^\mu \\ &= x^\mu, \end{aligned} and \label{eqn:reciprocalblog:860} \begin{aligned} x \cdot \gamma_\mu &= \lr{ x_\nu \gamma^\nu } \cdot \gamma_\mu \\ &= x_\nu \lr{ \gamma^\nu \cdot \gamma_\mu } \\ &= x_\nu {\delta^\nu}_\mu \\ &= x_\mu. \end{aligned} ## Derivative operators. We’d like to determine the form of the (spacetime) gradient operator. The gradient can be defined in terms of coordinates directly, but we choose an implicit definition, in terms of the directional derivative. ## Definition 1.4: Directional derivative and gradient. Let $$F = F(x)$$ be a four-vector parameterized multivector. The directional derivative of $$F$$ with respect to the (four-vector) direction $$a$$ is denoted \label{eqn:reciprocalblog:2060} \lr{ a \cdot \grad } F = \lim_{\epsilon \rightarrow 0} \frac{ F(x + \epsilon a) – F(x) }{ \epsilon }, where $$\grad$$ is called the space time gradient. ## Theorem 1.3: Gradient. The standard basis representation of the gradient is \label{eqn:reciprocalblog:2080} \grad = \gamma^\mu \partial_\mu, where \label{eqn:reciprocalblog:2100} \partial_\mu = \PD{x^\mu}{}. ### Start proof: The Dirac gradient pops naturally out of the coordinate representation of the directional derivative, as we can see by expanding $$F(x + \epsilon a)$$ in Taylor series \label{eqn:reciprocalblog:900} \begin{aligned} F(x + \epsilon a) &= F(x) + \epsilon \frac{dF(x + \epsilon a)}{d\epsilon} + O(\epsilon^2) \\ &= F(x) + \epsilon \PD{\lr{x^\mu + \epsilon a^\mu}}{F} \PD{\epsilon}{\lr{x^\mu + \epsilon a^\mu}} \\ &= F(x) + \epsilon \PD{\lr{x^\mu + \epsilon a^\mu}}{F} a^\mu. \end{aligned} The directional derivative is \label{eqn:reciprocalblog:920} \begin{aligned} \lim_{\epsilon \rightarrow 0} \frac{F(x + \epsilon a) – F(x)}{\epsilon} &= \lim_{\epsilon \rightarrow 0}\, a^\mu \PD{\lr{x^\mu + \epsilon a^\mu}}{F} \\ &= a^\mu \PD{x^\mu}{F} \\ &= \lr{a^\nu \gamma_\nu} \cdot \gamma^\mu \PD{x^\mu}{F} \\ &= a \cdot \lr{ \gamma^\mu \partial_\mu } F. \end{aligned} ## Curvilinear bases. Curvilinear bases are the foundation of the fundamental theorem of multivector calculus. This form of integral calculus is defined over parameterized surfaces (called manifolds) that satisfy some specific non-degeneracy and continuity requirements. A parameterized vector $$x(u,v, \cdots w)$$ can be thought of as tracing out a hypersurface (curve, surface, volume, …), where the dimension of the hypersurface depends on the number of parameters. At each point, a bases can be constructed from the differentials of the parameterized vector. Such a basis is called the tangent space to the surface at the point in question. Our curvilinear bases will be related to these differentials. We will also be interested in a dual basis that is restricted to the span of the tangent space. This dual basis will be called the reciprocal frame, and line the basis of the tangent space itself, also varies from point to point on the surface. Fig 1a. One parameter curve, with illustration of tangent space along the curve. Fig 1b. Two parameter surface, with illustration of tangent space along the surface. One and two parameter spaces are illustrated in fig. 1a, and 1b. The tangent space basis at a specific point of a two parameter surface, $$x(u^0, u^1)$$, is illustrated in fig. 1. The differential directions that span the tangent space are \label{eqn:reciprocalblog:1040} \begin{aligned} d\Bx_0 &= \PD{u^0}{x} du^0 \\ d\Bx_1 &= \PD{u^1}{x} du^1, \end{aligned} and the tangent space itself is $$\mbox{Span}\setlr{ d\Bx_0, d\Bx_1 }$$. We may form an oriented surface area element $$d\Bx_0 \wedge d\Bx_1$$ over this surface. Fig 2. Two parameter surface. Tangent spaces associated with 3 or more parameters cannot be easily visualized in three dimensions, but the idea generalizes algebraically without trouble. ## Definition 1.5: Tangent basis and space. Given a parameterization $$x = x(u^0, \cdots, u^N)$$, where $$N < 4$$, the span of the vectors \label{eqn:reciprocalblog:2120} \Bx_\mu = \PD{u^\mu}{x}, is called the tangent space for the hypersurface associated with the parameterization, and it’s basis is $$\setlr{ \Bx_\mu }$$. Later we will see that parameterization constraints must be imposed, as not all surfaces generated by a set of parameterizations are useful for integration theory. In particular, degenerate parameterizations for which the wedge products of the tangent space basis vectors are zero, or those wedge products cannot be inverted, are not physically meaningful. Properly behaved surfaces of this sort are called manifolds. Having introduced curvilinear coordinates associated with a parameterization, we can now determine the form of the gradient with respect to a parameterization of spacetime. ## Theorem 1.4: Gradient, curvilinear representation. Given a spacetime parameterization $$x = x(u^0, u^1, u^2, u^3)$$, the gradient with respect to the parameters $$u^\mu$$ is \label{eqn:reciprocalblog:2140} \grad = \sum_\mu \Bx^\mu \PD{u^\mu}{}, where \label{eqn:reciprocalblog:2160} \Bx^\mu = \grad u^\mu. The vectors $$\Bx^\mu$$ are called the reciprocal frame vectors, and the ordered set $$\setlr{ \Bx^0, \Bx^1, \Bx^2, \Bx^3 }$$ is called the reciprocal basis.It is convenient to define $$\partial_\mu \equiv \PDi{u^\mu}{}$$, so that the gradient can be expressed in mixed index representation \label{eqn:reciprocalblog:2180} \grad = \Bx^\mu \partial_\mu. This introduces some notational ambiguity, since we used $$\partial_\mu = \PDi{x^\mu}{}$$ for the standard basis derivative operators too, but we will be careful to be explicit when there is any doubt about what is intended. ### Start proof: The proof follows by application of the chain rule. \label{eqn:reciprocalblog:960} \begin{aligned} &= \gamma^\alpha \PD{x^\alpha}{F} \\ &= \gamma^\alpha \PD{x^\alpha}{u^\mu} \PD{u^\mu}{F} \\ &= \lr{ \grad u^\mu } \PD{u^\mu}{F} \\ &= \Bx^\mu \PD{u^\mu}{F}. \end{aligned} ## Theorem 1.5: Reciprocal relationship. The vectors $$\Bx^\mu = \grad u^\mu$$, and $$\Bx_\mu = \PDi{u^\mu}{x}$$ satisfy the reciprocal relationship \label{eqn:reciprocalblog:2200} \Bx^\mu \cdot \Bx_\nu = {\delta^\mu}_\nu. ### Start proof: \label{eqn:reciprocalblog:1020} \begin{aligned} \Bx^\mu \cdot \Bx_\nu &= \PD{u^\nu}{x} \\ &= \lr{ \gamma^\alpha \PD{x^\alpha}{u^\mu} } \cdot \lr{ \PD{u^\nu}{x^\beta} \gamma_\beta } \\ &= {\delta^\alpha}_\beta \PD{x^\alpha}{u^\mu} \PD{u^\nu}{x^\beta} \\ &= \PD{x^\alpha}{u^\mu} \PD{u^\nu}{x^\alpha} \\ &= \PD{u^\nu}{u^\mu} \\ &= {\delta^\mu}_\nu . \end{aligned} ### End proof. It is instructive to consider an example. Here is a parameterization that scales the proper time parameter, and uses polar coordinates in the $$x-y$$ plane. ## Problem: Compute the curvilinear and reciprocal basis. Given \label{eqn:reciprocalblog:2360} x(t,\rho,\theta,z) = c t \gamma_0 + \gamma_1 \rho e^{i \theta} + z \gamma_3, where $$i = \gamma_1 \gamma_2$$, compute the curvilinear frame vectors and their reciprocals. The frame vectors are all easy to compute \label{eqn:reciprocalblog:1180} \begin{aligned} \Bx_0 &= \PD{t}{x} = c \gamma_0 \\ \Bx_1 &= \PD{\rho}{x} = \gamma_1 e^{i \theta} \\ \Bx_2 &= \PD{\theta}{x} = \rho \gamma_1 \gamma_1 \gamma_2 e^{i \theta} = – \rho \gamma_2 e^{i \theta} \\ \Bx_3 &= \PD{z}{x} = \gamma_3. \end{aligned} The $$\Bx_1$$ vector is radial, $$\Bx^2$$ is perpendicular to that tangent to the same unit circle, as plotted in fig 3. Fig3: Tangent space direction vectors. All of these particular frame vectors happen to be mutually perpendicular, something that will not generally be true for a more arbitrary parameterization. To compute the reciprocal frame vectors, we must express our parameters in terms of $$x^\mu$$ coordinates, and use implicit integration techniques to deal with the coupling of the rotational terms. First observe that \label{eqn:reciprocalblog:1200} \gamma_1 e^{i\theta} = \gamma_1 \lr{ \cos\theta + \gamma_1 \gamma_2 \sin\theta } = \gamma_1 \cos\theta – \gamma_2 \sin\theta, so \label{eqn:reciprocalblog:1220} \begin{aligned} x^0 &= c t \\ x^1 &= \rho \cos\theta \\ x^2 &= -\rho \sin\theta \\ x^3 &= z. \end{aligned} We can easily evaluate the $$t, z$$ gradients \label{eqn:reciprocalblog:1240} \begin{aligned} \grad t &= \frac{\gamma^1 }{c} \\ \grad z &= \gamma^3, \end{aligned} but the $$\rho, \theta$$ gradients are not as easy. First writing \label{eqn:reciprocalblog:1260} \rho^2 = \lr{x^1}^2 + \lr{x^2}^2, we find \label{eqn:reciprocalblog:1280} \begin{aligned} 2 \rho \grad \rho = 2 \lr{ x^1 \grad x^1 + x^2 \grad x^2 } &= 2 \rho \lr{ \cos\theta \gamma^1 – \sin\theta \gamma^2 } \\ &= 2 \rho \gamma^1 \lr{ \cos\theta – \gamma_1 \gamma^2 \sin\theta } \\ &= 2 \rho \gamma^1 e^{i\theta}, \end{aligned} so \label{eqn:reciprocalblog:1300} \grad \rho = \gamma^1 e^{i\theta}. For the $$\theta$$ gradient, we can write \label{eqn:reciprocalblog:1320} \tan\theta = -\frac{x^2}{x^1}, so \label{eqn:reciprocalblog:1340} \begin{aligned} \inv{\cos^2 \theta} \grad \theta &= -\frac{\gamma^2}{x^1} – x^2 \frac{-\gamma^1}{\lr{x^1}^2} \\ &= \inv{\lr{x^1}^2} \lr{ – \gamma^2 x^1 + \gamma^1 x^2 } \\ &= \frac{\rho}{\rho^2 \cos^2\theta } \lr{ – \gamma^2 \cos\theta – \gamma^1 \sin\theta } \\ &= -\frac{1}{\rho \cos^2\theta } \gamma^2 \lr{ \cos\theta + \gamma_2 \gamma^1 \sin\theta } \\ &= -\frac{\gamma^2 e^{i\theta} }{\rho \cos^2\theta }, \end{aligned} or \label{eqn:reciprocalblog:1360} \grad\theta = -\inv{\rho} \gamma^2 e^{i\theta}. In summary, \label{eqn:reciprocalblog:1380} \begin{aligned} \Bx^0 &= \frac{\gamma^0}{c} \\ \Bx^1 &= \gamma^1 e^{i\theta} \\ \Bx^2 &= -\inv{\rho} \gamma^2 e^{i\theta} \\ \Bx^3 &= \gamma^3. \end{aligned} Despite being a fairly simple parameterization, it was still fairly difficult to solve for the gradients when the parameterization introduced coupling between the coordinates. In this particular case, we could have solved for the parameters in terms of the coordinates (but it was easier not to), but that will not generally be true. We want a less labor intensive strategy to find the reciprocal frame. When we have a full parameterization of spacetime, then we can do this with nothing more than a matrix inversion. ## Theorem 1.6: Reciprocal frame matrix equations. Given a spacetime basis $$\setlr{\Bx_0, \cdots \Bx_3}$$, let $$[\Bx_\mu]$$ and $$[\Bx^\nu]$$ be column matrices with the coordinates of these vectors and their reciprocals, with respect to the standard basis $$\setlr{\gamma_0, \gamma_1, \gamma_2, \gamma_3 }$$. Let \label{eqn:reciprocalblog:2220} A = \begin{bmatrix} [\Bx_0] & \cdots & [\Bx_{3}] \end{bmatrix} X = \begin{bmatrix} [\Bx^0] & \cdots & [\Bx^{3}] \end{bmatrix}. The coordinates of the reciprocal frame vectors can be found by solving \label{eqn:reciprocalblog:2240} A^\T G X = 1, where $$G = \text{diag}(1,-1,-1,-1)$$ and the RHS is an $$4 \times 4$$ identity matrix. ### Start proof: Let $$\Bx_\mu = {a_\mu}^\alpha \gamma_\alpha, \Bx^\nu = b^{\nu\beta} \gamma_\beta$$, so that \label{eqn:reciprocalblog:140} A = \begin{bmatrix} {a_\nu}^\mu \end{bmatrix}, and \label{eqn:reciprocalblog:160} X = \begin{bmatrix} b^{\nu\mu} \end{bmatrix}, where $$\mu \in [0,3]$$ are the row indexes and $$\nu \in [0,N-1]$$ are the column indexes. The reciprocal frame satisfies $$\Bx_\mu \cdot \Bx^\nu = {\delta_\mu}^\nu$$, which has the coordinate representation of \label{eqn:reciprocalblog:180} \begin{aligned} \Bx_\mu \cdot \Bx^\nu &= \lr{ {a_\mu}^\alpha \gamma_\alpha } \cdot \lr{ b^{\nu\beta} \gamma_\beta } \\ &= {a_\mu}^\alpha \eta_{\alpha\beta} b^{\nu\beta} \\ &= {[A^\T G B]_\mu}^\nu, \end{aligned} where $$\mu$$ is the row index and $$\nu$$ is the column index. ## Problem: Matrix inversion reciprocals. For the parameterization of \ref{eqn:reciprocalblog:2360}, find the reciprocal frame vectors by matrix inversion. We expanded $$\Bx_1$$ explicitly in \ref{eqn:reciprocalblog:1200}. Doing the same for $$\Bx_2$$, we have \label{eqn:reciprocalblog:1201} \Bx_2 = -\rho \gamma_2 e^{i\theta} = -\rho \gamma_2 \lr{ \cos\theta + \gamma_1 \gamma_2 \sin\theta } = – \rho \lr{ \gamma_2 \cos\theta + \gamma_1 \sin\theta}. Reading off the coordinates of our frame vectors, we have \label{eqn:reciprocalblog:1400} X = \begin{bmatrix} c & 0 & 0 & 0 \\ 0 & C & -\rho S & 0 \\ 0 & -S & -\rho C & 0 \\ 0 & 0 & 0 & 1 \\ \end{bmatrix}, where $$C = \cos\theta$$ and $$S = \sin\theta$$. We want \label{eqn:reciprocalblog:1420} Y = {\begin{bmatrix} c & 0 & 0 & 0 \\ 0 & -C & S & 0 \\ 0 & \rho S & \rho C & 0 \\ 0 & 0 & 0 & -1 \\ \end{bmatrix}}^{-1} = \begin{bmatrix} \inv{c} & 0 & 0 & 0 \\ 0 & -C & \frac{S}{\rho} & 0 \\ 0 & S & \frac{C}{\rho} & 0 \\ 0 & 0 & 0 & -1 \\ \end{bmatrix}. We can read off the coordinates of the reciprocal frame vectors \label{eqn:reciprocalblog:1440} \begin{aligned} \Bx^0 &= \inv{c} \gamma_0 \\ \Bx^1 &= -\cos\theta \gamma_1 + \sin\theta \gamma_2 \\ \Bx^2 &= \inv{\rho} \lr{ \sin\theta \gamma_1 + \cos\theta \gamma_2 } \\ \Bx^3 &= -\gamma_3. \end{aligned} Factoring out $$\gamma^1$$ from the $$\Bx^1$$ terms, we find \label{eqn:reciprocalblog:1460} \begin{aligned} \Bx^1 &= -\cos\theta \gamma_1 + \sin\theta \gamma_2 \\ &= \gamma^1 \lr{ \cos\theta + \gamma_1 \gamma_2 \sin\theta } \\ &= \gamma^1 e^{i\theta}. \end{aligned} Similarly for $$\Bx^2$$, \label{eqn:reciprocalblog:1480} \begin{aligned} \Bx^2 &= \inv{\rho} \lr{ \sin\theta \gamma_1 + \cos\theta \gamma_2 } \\ &= \frac{\gamma^2}{\rho} \lr{ \sin\theta \gamma_2 \gamma_1 – \cos\theta } \\ &= -\frac{\gamma^2}{\rho} e^{i\theta}. \end{aligned} This matches \ref{eqn:reciprocalblog:1380}, as expected, but required only algebraic work to compute. There will be circumstances where we parameterize only a subset of spacetime, and are interested in calculating quantities associated with such a surface. For example, suppose that \label{eqn:reciprocalblog:1500} x(\rho,\theta) = \gamma_1 \rho e^{i \theta}, where $$i = \gamma_1 \gamma_2$$ as before. We are now parameterizing only the $$x-y$$ plane. We will still find \label{eqn:reciprocalblog:1520} \begin{aligned} \Bx_1 &= \gamma_1 e^{i \theta} \\ \Bx_2 &= -\gamma_2 \rho e^{i \theta}. \end{aligned} We can compute the reciprocals of these vectors using the gradient method. It’s possible to state matrix equations representing the reciprocal relationship of \ref{eqn:reciprocalblog:2200}, which, in this case, is $$X^\T G Y = 1$$, where the RHS is a $$2 \times 2$$ identity matrix, and $$X, Y$$ are $$4\times 2$$ matrices of coordinates, with \label{eqn:reciprocalblog:1540} X = \begin{bmatrix} 0 & 0 \\ C & -\rho S \\ -S & -\rho C \\ 0 & 0 \end{bmatrix}. We no longer have a square matrix problem to solve, and our solution set is multivalued. In particular, this matrix equation has solutions \label{eqn:reciprocalblog:1560} \begin{aligned} \Bx^1 &= \gamma^1 e^{i\theta} + \alpha \gamma^0 + \beta \gamma^3 \\ \Bx^2 &= -\frac{\gamma^2}{\rho} e^{i\theta} + \alpha’ \gamma^0 + \beta’ \gamma^3. \end{aligned} where $$\alpha, \alpha’, \beta, \beta’$$ are arbitrary constants. In the example we considered, we saw that our $$\rho, \theta$$ parameters were functions of only $$x^1, x^2$$, so taking gradients could not introduce any $$\gamma^0, \gamma^3$$ dependence in $$\Bx^1, \Bx^2$$. It seems reasonable to assert that we seek an algebraic method of computing a set of vectors that satisfies the reciprocal relationships, where that set of vectors is restricted to the tangent space. We will need to figure out how to prove that this reciprocal construction is identical to the parameter gradients, but let’s start with figuring out what such a tangent space restricted solution looks like. ## Theorem 1.7: Reciprocal frame for two parameter subspace. Given two vectors, $$\Bx_1, \Bx_2$$, the vectors $$\Bx^1, \Bx^2 \in \mbox{Span}\setlr{ \Bx_1, \Bx_2 }$$ such that $$\Bx^\mu \cdot \Bx_\nu = {\delta^\mu}_\nu$$ are given by \label{eqn:reciprocalblog:2260} \begin{aligned} \Bx^1 &= \Bx_2 \cdot \inv{\Bx_1 \wedge \Bx_2} \\ \Bx^2 &= -\Bx_1 \cdot \inv{\Bx_1 \wedge \Bx_2}, \end{aligned} provided $$\Bx_1 \wedge \Bx_2 \ne 0$$ and $$\lr{ \Bx_1 \wedge \Bx_2 }^2 \ne 0$$. ### Start proof: The most general set of vectors that satisfy the span constraint are \label{eqn:reciprocalblog:1580} \begin{aligned} \Bx^1 &= a \Bx_1 + b \Bx_2 \\ \Bx^2 &= c \Bx_1 + d \Bx_2. \end{aligned} We can use wedge products with either $$\Bx_1$$ or $$\Bx_2$$ to eliminate the other from the RHS \label{eqn:reciprocalblog:1600} \begin{aligned} \Bx^1 \wedge \Bx_2 &= a \lr{ \Bx_1 \wedge \Bx_2 } \\ \Bx^1 \wedge \Bx_1 &= – b \lr{ \Bx_1 \wedge \Bx_2 } \\ \Bx^2 \wedge \Bx_2 &= c \lr{ \Bx_1 \wedge \Bx_2 } \\ \Bx^2 \wedge \Bx_1 &= – d \lr{ \Bx_1 \wedge \Bx_2 }, \end{aligned} and then dot both sides with $$\Bx_1 \wedge \Bx_2$$ to produce four scalar equations \label{eqn:reciprocalblog:1640} \begin{aligned} a \lr{ \Bx_1 \wedge \Bx_2 }^2 &= \lr{ \Bx^1 \wedge \Bx_2 } \cdot \lr{ \Bx_1 \wedge \Bx_2 } \\ &= \lr{ \Bx_2 \cdot \Bx_1 } \lr{ \Bx^1 \cdot \Bx_2 } \lr{ \Bx_2 \cdot \Bx_2 } \lr{ \Bx^1 \cdot \Bx_1 } \\ &= \lr{ \Bx_2 \cdot \Bx_1 } (0) \lr{ \Bx_2 \cdot \Bx_2 } (1) \\ &= – \Bx_2 \cdot \Bx_2 \end{aligned} \label{eqn:reciprocalblog:1660} \begin{aligned} – b \lr{ \Bx_1 \wedge \Bx_2 }^2 &= \lr{ \Bx^1 \wedge \Bx_1 } \cdot \lr{ \Bx_1 \wedge \Bx_2 } \\ &= \lr{ \Bx^1 \cdot \Bx_2 } \lr{ \Bx_1 \cdot \Bx_1 } \lr{ \Bx^1 \cdot \Bx_1 } \lr{ \Bx_1 \cdot \Bx_2 } \\ &= (0) \lr{ \Bx_1 \cdot \Bx_1 } (1) \lr{ \Bx_1 \cdot \Bx_2 } \\ &= – \Bx_1 \cdot \Bx_2 \end{aligned} \label{eqn:reciprocalblog:1680} \begin{aligned} c \lr{ \Bx_1 \wedge \Bx_2 }^2 &= \lr{ \Bx^2 \wedge \Bx_2 } \cdot \lr{ \Bx_1 \wedge \Bx_2 } \\ &= \lr{ \Bx_2 \cdot \Bx_1 } \lr{ \Bx^2 \cdot \Bx_2 } \lr{ \Bx_2 \cdot \Bx_2 } \lr{ \Bx^2 \cdot \Bx_1 } \\ &= \lr{ \Bx_2 \cdot \Bx_1 } (1) \lr{ \Bx_2 \cdot \Bx_2 } (0) \\ &= \Bx_2 \cdot \Bx_1 \end{aligned} \label{eqn:reciprocalblog:1700} \begin{aligned} – d \lr{ \Bx_1 \wedge \Bx_2 }^2 &= \lr{ \Bx^2 \wedge \Bx_1 } \cdot \lr{ \Bx_1 \wedge \Bx_2 } \\ &= \lr{ \Bx_1 \cdot \Bx_1 } \lr{ \Bx^2 \cdot \Bx_2 } \lr{ \Bx_1 \cdot \Bx_2 } \lr{ \Bx^2 \cdot \Bx_1 } \\ &= \lr{ \Bx_1 \cdot \Bx_1 } (1) \lr{ \Bx_1 \cdot \Bx_2 } (0) \\ &= \Bx_1 \cdot \Bx_1. \end{aligned} Putting the pieces together we have \label{eqn:reciprocalblog:1740} \begin{aligned} \Bx^1 &= \frac{ – \lr{ \Bx_2 \cdot \Bx_2 } \Bx_1 + \lr{ \Bx_1 \cdot \Bx_2 } \Bx_2 }{\lr{\Bx_1 \wedge \Bx_2}^2} \\ &= \frac{ \Bx_2 \cdot \lr{ \Bx_1 \wedge \Bx_2 } }{\lr{\Bx_1 \wedge \Bx_2}^2} \\ &= \Bx_2 \cdot \inv{\Bx_1 \wedge \Bx_2} \end{aligned} \label{eqn:reciprocalblog:1760} \begin{aligned} \Bx^2 &= \frac{ \lr{ \Bx_1 \cdot \Bx_2 } \Bx_1 – \lr{ \Bx_1 \cdot \Bx_1 } \Bx_2 }{\lr{\Bx_1 \wedge \Bx_2}^2} \\ &= \frac{ -\Bx_1 \cdot \lr{ \Bx_1 \wedge \Bx_2 } } {\lr{\Bx_1 \wedge \Bx_2}^2} \\ &= -\Bx_1 \cdot \inv{\Bx_1 \wedge \Bx_2} \end{aligned} ## Lemma 1.1: Distribution identity. Given k-vectors $$B, C$$ and a vector $$a$$, where the grade of $$C$$ is greater than that of $$B$$, then \label{eqn:reciprocalblog:2280} \lr{a \wedge B} \cdot C = a \cdot \lr{ B \cdot C }. See [1] for a proof. ## Theorem 1.8: Higher order tangent space reciprocals. Given an $$N$$ parameter tangent space with basis $$\setlr{ \Bx_0, \Bx_1, \cdots \Bx_{N-1} }$$, the reciprocals are given by \label{eqn:reciprocalblog:2300} \Bx^\mu = (-1)^\mu \lr{ \Bx_0 \wedge \cdots \check{\Bx_\mu} \cdots \wedge \Bx_{N-1} } \cdot I_N^{-1}, where the checked term ($$\check{\Bx_\mu}$$) indicates that all terms are included in the wedges except the $$\Bx_\mu$$ term, and $$I_N = \Bx_0 \wedge \cdots \Bx_{N-1}$$ is the pseudoscalar for the tangent space. ### Start proof: I’ll outline the proof for the three parameter tangent space case, from which the pattern will be clear. The motivation for this proof is a reexamination of the algebraic structure of the two vector solution. Suppose we have a tangent space basis $$\setlr{\Bx_0, \Bx_1}$$, for which we’ve shown that \label{eqn:reciprocalblog:1860} \begin{aligned} \Bx^0 &= \Bx_1 \cdot \inv{\Bx_0 \wedge \Bx_1} \\ &= \frac{\Bx_1 \cdot \lr{\Bx_0 \wedge \Bx_1} }{\lr{ \Bx_0 \wedge \Bx_1}^2 }. \end{aligned} If we dot with $$\Bx_0$$ and $$\Bx_1$$ respectively, we find \label{eqn:reciprocalblog:1800} \begin{aligned} \Bx_0 \cdot \Bx^0 &= \Bx_0 \cdot \frac{ \Bx_1 \cdot \lr{ \Bx_0 \wedge \Bx_1 } }{\lr{ \Bx_0 \wedge \Bx_1}^2 } \\ &= \lr{ \Bx_0 \wedge \Bx_1 } \cdot \frac{ \Bx_0 \wedge \Bx_1 }{\lr{ \Bx_0 \wedge \Bx_1}^2 }. \end{aligned} We end up with unity as expected. Here the “factored” out vector is reincorporated into the pseudoscalar using the distribution identity \ref{eqn:reciprocalblog:2280}. Similarly, dotting with $$\Bx_1$$, we find \label{eqn:reciprocalblog:0810} \begin{aligned} \Bx_1 \cdot \Bx^0 &= \Bx_1 \cdot \frac{ \Bx_1 \cdot \lr{ \Bx_0 \wedge \Bx_1 } }{\lr{ \Bx_0 \wedge \Bx_1}^2 } \\ &= \lr{ \Bx_1 \wedge \Bx_1 } \cdot \frac{ \Bx_0 \wedge \Bx_1 }{\lr{ \Bx_0 \wedge \Bx_1}^2 }. \end{aligned} This is zero, since wedging a vector with itself is zero. We can perform such an operation in reverse, taking the square of the tangent space pseudoscalar, and factoring out one of the basis vectors. After this, division by that squared pseudoscalar will normalize things. For a three parameter tangent space with basis $$\setlr{ \Bx_0, \Bx_1, \Bx_2 }$$, we can factor out any of the tangent vectors like so \label{eqn:reciprocalblog:1880} \begin{aligned} \lr{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 }^2 &= \Bx_0 \cdot \lr{ \lr{ \Bx_1 \wedge \Bx_2 } \cdot \lr{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 } } \\ &= (-1) \Bx_1 \cdot \lr{ \lr{ \Bx_0 \wedge \Bx_2 } \cdot \lr{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 } } \\ &= (-1)^2 \Bx_2 \cdot \lr{ \lr{ \Bx_0 \wedge \Bx_1 } \cdot \lr{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 } }. \end{aligned} The toggling of sign reflects the number of permutations required to move the vector of interest to the front of the wedge sequence. Having factored out any one of the vectors, we can rearrange to find that vector that is it’s inverse and perpendicular to all the others. \label{eqn:reciprocalblog:1900} \begin{aligned} \Bx^0 &= (-1)^0 \lr{ \Bx_1 \wedge \Bx_2 } \cdot \inv{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 } \\ \Bx^1 &= (-1)^1 \lr{ \Bx_0 \wedge \Bx_2 } \cdot \inv{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 } \\ \Bx^2 &= (-1)^2 \lr{ \Bx_0 \wedge \Bx_1 } \cdot \inv{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 }. \end{aligned} ### End proof. In the fashion above, should we want the reciprocal frame for all of spacetime given dimension 4 tangent space, we can state it trivially \label{eqn:reciprocalblog:1920} \begin{aligned} \Bx^0 &= (-1)^0 \lr{ \Bx_1 \wedge \Bx_2 \wedge \Bx_3 } \cdot \inv{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 \wedge \Bx_3 } \\ \Bx^1 &= (-1)^1 \lr{ \Bx_0 \wedge \Bx_2 \wedge \Bx_3 } \cdot \inv{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 \wedge \Bx_3 } \\ \Bx^2 &= (-1)^2 \lr{ \Bx_0 \wedge \Bx_1 \wedge \Bx_3 } \cdot \inv{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 \wedge \Bx_3 } \\ \Bx^3 &= (-1)^3 \lr{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 } \cdot \inv{ \Bx_0 \wedge \Bx_1 \wedge \Bx_2 \wedge \Bx_3 }. \end{aligned} This is probably not an efficient way to compute all these reciprocals, since we can utilize a single matrix inversion to solve them in one shot. However, there are theoretical advantages to this construction that will be useful when we get to integration theory. ### On degeneracy. A small mention of degeneracy was mentioned above. Regardless of metric, $$\Bx_0 \wedge \Bx_1 = 0$$ means that this pair of vectors are colinear. A tangent space with such a pseudoscalar is clearly undesirable, and we must construct parameterizations for which the area element is non-zero in all regions of interest. Things get more interesting in mixed signature spaces where we can have vectors that square to zero (i.e. lightlike). If the tangent space pseudoscalar has a lightlike factor, then that pseudoscalar will not be invertible. Such a degeneracy will will likely lead to many other troubles, and parameterizations of this sort should be avoided. This following problem illustrates an example of this sort of degenerate parameterization. ## Problem: Degenerate surface parameterization. Given a spacetime plane parameterization $$x(u,v) = u a + v b$$, where \label{eqn:reciprocalblog:480} a = \gamma_0 + \gamma_1 + \gamma_2 + \gamma_3, \label{eqn:reciprocalblog:500} b = \gamma_0 – \gamma_1 + \gamma_2 – \gamma_3, show that this is a degenerate parameterization, and find the bivector that represents the tangent space. Are these vectors lightlike, spacelike, or timelike? Comment on whether this parameterization represents a physically relevant spacetime surface. To characterize the vectors, we square them \label{eqn:reciprocalblog:1080} a^2 = b^2 = \gamma_0^2 + \gamma_1^2 + \gamma_2^2 + \gamma_3^2 = 1 – 3 = -2, so $$a, b$$ are both spacelike vectors. The tangent space is clearly just $$\mbox{Span}\setlr{ a, b } = \mbox{Span}\setlr{ e, f }$$ where \label{eqn:reciprocalblog:1100} \begin{aligned} e &= \gamma_0 + \gamma_2 \\ f &= \gamma_1 + \gamma_3. \end{aligned} Observe that $$a = e + f, b = e – f$$, and $$e$$ is lightlike ($$e^2 = 0$$), whereas $$f$$ is spacelike ($$f^2 = -2$$), and $$e \cdot f = 0$$, so $$e f = – f e$$. The bivector for the tangent plane is \label{eqn:reciprocalblog:1120} a b } = (e + f) (e – f) } = e^2 – f^2 – 2 e f } = -2 e f, where \label{eqn:reciprocalblog:1140} e f = \gamma_{01} + \gamma_{21} + \gamma_{23} + \gamma_{03}. Because $$e$$ is lightlike (zero square), and $$e f = – f e$$, the bivector $$e f$$ squares to zero \label{eqn:reciprocalblog:1780} \lr{ e f }^2 = -e^2 f^2 = 0, which shows that the parameterization is degenerate. This parameterization can also be expressed as \label{eqn:reciprocalblog:1160} x(u,v) = u ( e + f ) + v ( e – f ) = (u + v) e + (u – v) f, a linear combination of a lightlike and spacelike vector. Intuitively, we expect that a physically meaningful spacetime surface involves linear combinations spacelike vectors, or combinations of a timelike vector with spacelike vectors. This beastie is something entirely different. ### Final notes. There are a few loose ends above. In particular, we haven’t conclusively proven that the set of reciprocal vectors $$\Bx^\mu = \grad u^\mu$$ are exactly those obtained through algebraic means. For a full parameterization of spacetime, they are necessarily the same, since both are unique. So we know that \ref{eqn:reciprocalblog:1920} must equal the reciprocals obtained by evaluating the gradient for a full parameterization (and this must also equal the reciprocals that we can obtain through matrix inversion.) We have also not proved explicitly that the three parameter construction of the reciprocals in \ref{eqn:reciprocalblog:1900} is in the tangent space, but that is a fairly trivial observation, so that can be left as an exercise for the reader dismissal. Some additional thought about this is probably required, but it seems reasonable to put that on the back burner and move on to some applications. # References [1] Peeter Joot. Geometric Algebra for Electrical Engineers. Kindle Direct Publishing, 2019. ## Maxwell’s equation Lagrangian (geometric algebra and tensor formalism) [Click here for a PDF of this post with nicer formatting] Maxwell’s equation using geometric algebra Lagrangian. ## Motivation. In my classical mechanics notes, I’ve got computations of Maxwell’s equation (singular in it’s geometric algebra form) from a Lagrangian in various ways (using a tensor, scalar and multivector Lagrangians), but all of these seem more convoluted than they should be. Here we do this from scratch, starting with the action principle for field variables, covering: • Derivation of the relativistic form of the Euler-Lagrange field equations from the covariant form of the action, • Derivation of Maxwell’s equation (in it’s STA form) from the Maxwell Lagrangian, • Relationship of the STA Maxwell Lagrangian to the tensor equivalent, • Relationship of the STA form of Maxwell’s equation to it’s tensor equivalents, • Relationship of the STA Maxwell’s equation to it’s conventional Gibbs form. • Show that we may use a multivector valued Lagrangian with all of $$F^2$$, not just the scalar part. It is assumed that the reader is thoroughly familiar with the STA formalism, and if that is not the case, there is no better reference than [1]. ## Theorem 1.1: Relativistic Euler-Lagrange field equations. Let $$\phi \rightarrow \phi + \delta \phi$$ be any variation of the field, such that the variation $$\delta \phi = 0$$ vanishes at the boundaries of the action integral \label{eqn:maxwells:2120} S = \int d^4 x \LL(\phi, \partial_\nu \phi). The extreme value of the action is found when the Euler-Lagrange equations \label{eqn:maxwells:2140} 0 = \PD{\phi}{\LL} – \partial_\nu \PD{(\partial_\nu \phi)}{\LL}, are satisfied. For a Lagrangian with multiple field variables, there will be one such equation for each field. ### Start proof: To ease the visual burden, designate the variation of the field by $$\delta \phi = \epsilon$$, and perform a first order expansion of the varied Lagrangian \label{eqn:maxwells:20} \begin{aligned} \LL &\rightarrow \LL(\phi + \epsilon, \partial_\nu (\phi + \epsilon)) \\ &= \LL(\phi, \partial_\nu \phi) + \PD{\phi}{\LL} \epsilon + \PD{(\partial_\nu \phi)}{\LL} \partial_\nu \epsilon. \end{aligned} The variation of the Lagrangian is \label{eqn:maxwells:40} \begin{aligned} \delta \LL &= \PD{\phi}{\LL} \epsilon + \PD{(\partial_\nu \phi)}{\LL} \partial_\nu \epsilon \\ &= \PD{\phi}{\LL} \epsilon + \partial_\nu \lr{ \PD{(\partial_\nu \phi)}{\LL} \epsilon } \epsilon \partial_\nu \PD{(\partial_\nu \phi)}{\LL}, \end{aligned} which we may plug into the action integral to find \label{eqn:maxwells:60} \delta S = \int d^4 x \epsilon \lr{ \PD{\phi}{\LL} \partial_\nu \PD{(\partial_\nu \phi)}{\LL} } + \int d^4 x \partial_\nu \lr{ \PD{(\partial_\nu \phi)}{\LL} \epsilon }. The last integral can be evaluated along the $$dx^\nu$$ direction, leaving \label{eqn:maxwells:80} \int d^3 x \evalbar{ \PD{(\partial_\nu \phi)}{\LL} \epsilon }{\Delta x^\nu}, where $$d^3 x = dx^\alpha dx^\beta dx^\gamma$$ is the product of differentials that does not include $$dx^\nu$$. By construction, $$\epsilon$$ vanishes on the boundary of the action integral so \ref{eqn:maxwells:80} is zero. The action takes its extreme value when \label{eqn:maxwells:100} 0 = \delta S = \int d^4 x \epsilon \lr{ \PD{\phi}{\LL} \partial_\nu \PD{(\partial_\nu \phi)}{\LL} }. The proof is complete after noting that this must hold for all variations of the field $$\epsilon$$, which means that we must have \label{eqn:maxwells:120} 0 = \PD{\phi}{\LL} \partial_\nu \PD{(\partial_\nu \phi)}{\LL}. ### End proof. Armed with the Euler-Lagrange equations, we can apply them to the Maxwell’s equation Lagrangian, which we will claim has the following form. ## Theorem 1.2: Maxwell’s equation Lagrangian. Application of the Euler-Lagrange equations to the Lagrangian \label{eqn:maxwells:2160} \LL = – \frac{\epsilon_0 c}{2} F \cdot F + J \cdot A, where $$F = \grad \wedge A$$, yields the vector portion of Maxwell’s equation \label{eqn:maxwells:2180} \grad \cdot F = \inv{\epsilon_0 c} J, which implies \label{eqn:maxwells:2200} \grad F = \inv{\epsilon_0 c} J. This is Maxwell’s equation. ### Start proof: We wish to apply all of the Euler-Lagrange equations simultaneously (i.e. once for each of the four $$A_\mu$$ components of the potential), and cast it into four-vector form \label{eqn:maxwells:140} 0 = \gamma_\nu \lr{ \PD{A_\nu}{} – \partial_\mu \PD{(\partial_\mu A_\nu)}{} } \LL. Since our Lagrangian splits nicely into kinetic and interaction terms, this gives us \label{eqn:maxwells:160} 0 = \gamma_\nu \lr{ \PD{A_\nu}{(A \cdot J)} + \frac{\epsilon_0 c}{2} \partial_\mu \PD{(\partial_\mu A_\nu)}{ (F \cdot F)} }. The interaction term above is just \label{eqn:maxwells:180} \gamma_\nu \PD{A_\nu}{(A \cdot J)} = \gamma_\nu \PD{A_\nu}{(A_\mu J^\mu)} = \gamma_\nu J^\nu = J, but the kinetic term takes a bit more work. Let’s start with evaluating \label{eqn:maxwells:200} \begin{aligned} \PD{(\partial_\mu A_\nu)}{ (F \cdot F)} &= \PD{(\partial_\mu A_\nu)}{ F } \cdot F + F \cdot \PD{(\partial_\mu A_\nu)}{ F } \\ &= 2 \PD{(\partial_\mu A_\nu)}{ F } \cdot F \\ &= 2 \PD{(\partial_\mu A_\nu)}{ (\partial_\alpha A_\beta) } \lr{ \gamma^\alpha \wedge \gamma^\beta } \cdot F \\ &= 2 \lr{ \gamma^\mu \wedge \gamma^\nu } \cdot F. \end{aligned} We hit this with the $$\mu$$-partial and expand as a scalar selection to find \label{eqn:maxwells:220} \begin{aligned} \partial_\mu \PD{(\partial_\mu A_\nu)}{ (F \cdot F)} &= 2 \lr{ \partial_\mu \gamma^\mu \wedge \gamma^\nu } \cdot F \\ &= – 2 (\gamma^\nu \wedge \grad) \cdot F \\ &= – 2 \gpgradezero{ (\gamma^\nu \wedge \grad) F } \\ &= – 2 \gpgradezero{ \gamma^\nu \grad F – \gamma^\nu \cdot \grad F } \\ &= – 2 \gamma^\nu \cdot \lr{ \grad \cdot F }. \end{aligned} Putting all the pieces together yields \label{eqn:maxwells:240} 0 = J – \epsilon_0 c \gamma_\nu \lr{ \gamma^\nu \cdot \lr{ \grad \cdot F } } = J – \epsilon_0 c \lr{ \grad \cdot F }, but \label{eqn:maxwells:260} \begin{aligned} &= \grad F – \grad \wedge F \\ &= &= \end{aligned} so the multivector field equations for this Lagrangian are \label{eqn:maxwells:280} \grad F = \inv{\epsilon_0 c} J, as claimed. ## Problem: Correspondence with tensor formalism. Cast the Lagrangian of \ref{eqn:maxwells:2160} into the conventional tensor form \label{eqn:maxwells:300} \LL = \frac{\epsilon_0 c}{4} F_{\mu\nu} F^{\mu\nu} + A^\mu J_\mu. Also show that the four-vector component of Maxwell’s equation $$\grad \cdot F = J/(\epsilon_0 c)$$ is equivalent to the conventional tensor form of the Gauss-Ampere law \label{eqn:maxwells:320} \partial_\mu F^{\mu\nu} = \inv{\epsilon_0 c} J^\nu, where $$F^{\mu\nu} = \partial^\mu A^\nu – \partial^\nu A^\mu$$ as usual. Also show that the trivector component of Maxwell’s equation $$\grad \wedge F = 0$$ is equivalent to the tensor form of the Gauss-Faraday law \label{eqn:maxwells:340} \partial_\alpha \lr{ \epsilon^{\alpha \beta \mu \nu} F_{\mu\nu} } = 0. To show the Lagrangian correspondence we must expand $$F \cdot F$$ in coordinates \label{eqn:maxwells:360} \begin{aligned} F \cdot F &= ( \grad \wedge A ) \cdot ( \grad \wedge A ) \\ &= \lr{ (\gamma^\mu \partial_\mu) \wedge (\gamma^\nu A_\nu) } \cdot \lr{ (\gamma^\alpha \partial_\alpha) \wedge (\gamma^\beta A_\beta) } \\ &= \lr{ \gamma^\mu \wedge \gamma^\nu } \cdot \lr{ \gamma_\alpha \wedge \gamma_\beta } (\partial_\mu A_\nu ) (\partial^\alpha A^\beta ) \\ &= \lr{ {\delta^\mu}_\beta {\delta^\nu}_\alpha {\delta^\mu}_\alpha {\delta^\nu}_\beta } (\partial_\mu A_\nu ) (\partial^\alpha A^\beta ) \\ &= – \partial_\mu A_\nu \lr{ \partial^\mu A^\nu \partial^\nu A^\mu } \\ &= – \partial_\mu A_\nu F^{\mu\nu} \\ &= – \inv{2} \lr{ \partial_\mu A_\nu F^{\mu\nu} + \partial_\nu A_\mu F^{\nu\mu} } \\ &= – \inv{2} \lr{ \partial_\mu A_\nu \partial_\nu A_\mu } F^{\mu\nu} \\ &= \inv{2} F_{\mu\nu} F^{\mu\nu}. \end{aligned} With a substitution of this and $$A \cdot J = A_\mu J^\mu$$ back into the Lagrangian, we recover the tensor form of the Lagrangian. To recover the tensor form of Maxwell’s equation, we first split it into vector and trivector parts \label{eqn:maxwells:1580} \grad \cdot F + \grad \wedge F = \inv{\epsilon_0 c} J. Now the vector component may be expanded in coordinates by dotting both sides with $$\gamma^\nu$$ to find \label{eqn:maxwells:1600} \inv{\epsilon_0 c} \gamma^\nu \cdot J = J^\nu, and \label{eqn:maxwells:1620} \begin{aligned} \gamma^\nu \cdot \lr{ \grad \cdot F } &= \partial_\mu \gamma^\nu \cdot \lr{ \gamma^\mu \cdot \lr{ \gamma_\alpha \wedge \gamma_\beta } \partial^\alpha A^\beta } \\ &= \lr{ {\delta^\mu}_\alpha {\delta^\nu}_\beta {\delta^\nu}_\alpha {\delta^\mu}_\beta } \partial_\mu \partial^\alpha A^\beta \\ &= \partial_\mu \lr{ \partial^\mu A^\nu \partial^\nu A^\mu } \\ &= \partial_\mu F^{\mu\nu}. \end{aligned} Equating \ref{eqn:maxwells:1600} and \ref{eqn:maxwells:1620} finishes the first part of the job. For the trivector component, we have \label{eqn:maxwells:1640} 0 = \grad \wedge F = (\gamma^\mu \partial_\mu) \wedge \lr{ \gamma^\alpha \wedge \gamma^\beta } \partial_\alpha A_\beta = \inv{2} (\gamma^\mu \partial_\mu) \wedge \lr{ \gamma^\alpha \wedge \gamma^\beta } F_{\alpha \beta}. Wedging with $$\gamma^\tau$$ and then multiplying by $$-2 I$$ we find \label{eqn:maxwells:1660} 0 = – \lr{ \gamma^\mu \wedge \gamma^\alpha \wedge \gamma^\beta \wedge \gamma^\tau } I \partial_\mu F_{\alpha \beta}, but \label{eqn:maxwells:1680} \gamma^\mu \wedge \gamma^\alpha \wedge \gamma^\beta \wedge \gamma^\tau = -I \epsilon^{\mu \alpha \beta \tau}, which leaves us with \label{eqn:maxwells:1700} \epsilon^{\mu \alpha \beta \tau} \partial_\mu F_{\alpha \beta} = 0, as expected. ## Problem: Correspondence of tensor and Gibbs forms of Maxwell’s equations. Given the identifications \label{eqn:lorentzForceCovariant:1500} F^{k0} = E^k, and \label{eqn:lorentzForceCovariant:1520} F^{rs} = -\epsilon^{rst} B^t, and \label{eqn:maxwells:1560} J^\mu = \lr{ c \rho, \BJ }, the reader should satisfy themselves that the traditional Gibbs form of Maxwell’s equations can be recovered from \ref{eqn:maxwells:320}. The reader is referred to Exercise 3.4 “Electrodynamics, variational principle.” from [2]. ## Problem: Correspondence with grad and curl form of Maxwell’s equations. With $$J = c \rho \gamma_0 + J^k \gamma_k$$ and $$F = \BE + I c \BB$$ show that Maxwell’s equation, as stated in \ref{eqn:maxwells:2200} expand to the conventional div and curl expressions for Maxwell’s equations. To obtain Maxwell’s equations in their traditional vector forms, we pre-multiply both sides with $$\gamma_0$$ \label{eqn:maxwells:1720} \gamma_0 \grad F = \inv{\epsilon_0 c} \gamma_0 J, and then select each grade separately. First observe that the RHS above has scalar and bivector components, as \label{eqn:maxwells:1740} \gamma_0 J = c \rho + J^k \gamma_0 \gamma_k. In terms of the spatial bivector basis $$\Be_k = \gamma_k \gamma_0$$, the RHS of \ref{eqn:maxwells:1720} is \label{eqn:maxwells:1760} \gamma_0 \frac{J}{\epsilon_0 c} = \frac{\rho}{\epsilon_0} – \mu_0 c \BJ. For the LHS, first note that \label{eqn:maxwells:1780} \begin{aligned} &= \gamma_0 \lr{ \gamma_0 \partial^0 + \gamma_k \partial^k } \\ &= \partial_0 – \gamma_0 \gamma_k \partial_k \\ &= \inv{c} \PD{t}{} + \spacegrad. \end{aligned} We can express all the the LHS of \ref{eqn:maxwells:1720} in the bivector spatial basis, so that Maxwell’s equation in multivector form is \label{eqn:maxwells:1800} \lr{ \inv{c} \PD{t}{} + \spacegrad } \lr{ \BE + I c \BB } = \frac{\rho}{\epsilon_0} – \mu_0 c \BJ. Selecting the scalar, vector, bivector, and trivector grades of both sides (in the spatial basis) gives the following set of respective equations \label{eqn:maxwells:1840} \spacegrad \cdot \BE = \frac{\rho}{\epsilon_0} \label{eqn:maxwells:1860} \inv{c} \partial_t \BE + I c \spacegrad \wedge \BB = – \mu_0 c \BJ \label{eqn:maxwells:1880} \spacegrad \wedge \BE + I \partial_t \BB = 0 \label{eqn:maxwells:1900} I c \spacegrad \cdot B = 0, which we can rewrite after some duality transformations (and noting that $$\mu_0 \epsilon_0 c^2 = 1$$), we have \label{eqn:maxwells:1940} \spacegrad \cdot \BE = \frac{\rho}{\epsilon_0} \label{eqn:maxwells:1960} \spacegrad \cross \BB – \mu_0 \epsilon_0 \PD{t}{\BE} = \mu_0 \BJ \label{eqn:maxwells:1980} \spacegrad \cross \BE + \PD{t}{\BB} = 0 \label{eqn:maxwells:2000} \spacegrad \cdot B = 0, which are Maxwell’s equations in their traditional form. ## Problem: Alternative multivector Lagrangian. Show that a scalar+pseudoscalar Lagrangian of the following form \label{eqn:maxwells:2220} \LL = – \frac{\epsilon_0 c}{2} F^2 + J \cdot A, which omits the scalar selection of the Lagrangian in \ref{eqn:maxwells:2160}, also represents Maxwell’s equation. Discuss the scalar and pseudoscalar components of $$F^2$$, and show why the pseudoscalar inclusion is irrelevant. The quantity $$F^2 = F \cdot F + F \wedge F$$ has both scalar and pseudoscalar components. Note that unlike vectors, a bivector wedge in 4D with itself need not be zero (example: $$\gamma_0 \gamma_1 + \gamma_2 \gamma_3$$ wedged with itself). We can see this multivector nature nicely by expansion in terms of the electric and magnetic fields \label{eqn:maxwells:2020} \begin{aligned} F^2 &= \lr{ \BE + I c \BB }^2 \\ &= \BE^2 – c^2 \BB^2 + I c \lr{ \BE \BB + \BB \BE } \\ &= \BE^2 – c^2 \BB^2 + 2 I c \BE \cdot \BB. \end{aligned} Both the scalar and pseudoscalar parts of $$F^2$$ are Lorentz invariant, a requirement of our Lagrangian, but most Maxwell equation Lagrangians only include the scalar $$\BE^2 – c^2 \BB^2$$ component of the field square. If we allow the Lagrangian to be multivector valued, and evaluate the Euler-Lagrange equations, we quickly find the same results \label{eqn:maxwells:2040} \begin{aligned} 0 &= \gamma_\nu \lr{ \PD{A_\nu}{} – \partial_\mu \PD{(\partial_\mu A_\nu)}{} } \LL \\ &= \gamma_\nu \lr{ J^\nu + \frac{\epsilon_0 c}{2} \partial_\mu \lr{ (\gamma^\mu \wedge \gamma^\nu) F + F (\gamma^\mu \wedge \gamma^\nu) } }. \end{aligned} Here some steps are skipped, building on our previous scalar Euler-Lagrange evaluation experience. We have a symmetric product of two bivectors, which we can express as a 0,4 grade selection, since \label{eqn:maxwells:2060} \gpgrade{ X F }{0,4} = \inv{2} \lr{ X F + F X }, for any two bivectors $$X, F$$. This leaves \label{eqn:maxwells:2080} \begin{aligned} 0 &= J + \epsilon_0 c \gamma_\nu \gpgrade{ (\grad \wedge \gamma^\nu) F }{0,4} \\ &= J + \epsilon_0 c \gamma_\nu \gpgrade{ -\gamma^\nu \grad F + (\gamma^\nu \cdot \grad) F }{0,4} \\ &= J + \epsilon_0 c \gamma_\nu \gpgrade{ -\gamma^\nu \grad F }{0,4} \\ &= J – \epsilon_0 c \gamma_\nu \lr{ \gamma^\nu \cdot \lr{ \grad \cdot F } + \gamma^\nu \wedge \grad \wedge F }. \end{aligned} However, since $$\grad \wedge F = \grad \wedge \grad \wedge A = 0$$, we see that there is no contribution from the $$F \wedge F$$ pseudoscalar component of the Lagrangian, and we are left with \label{eqn:maxwells:2100} \begin{aligned} 0 &= J – \epsilon_0 c (\grad \cdot F) \\ &= J – \epsilon_0 c \grad F, \end{aligned} which is Maxwell’s equation, as before. # References [1] C. Doran and A.N. Lasenby. Geometric algebra for physicists. Cambridge University Press New York, Cambridge, UK, 1st edition, 2003. [2] Peeter Joot. Quantum field theory. Kindle Direct Publishing, 2018. ## Mathematica notebooks updated, and a bivector addition visualization. February 10, 2019 math and physics play No comments , , , This blog now has a copy of all my Mathematica notebooks (as of Feb 10, 2019), complete with a chronological index. I hadn’t updated that index since 2014, and it was quite stale. I’ve also added an additional level of per-directory indexing. For example, you can now look at just the notebooks for my book, Geometric Algebra for Electrical Engineers. That was possible before, but you would have had to clone the entire git repository to be able to do so easily. This update includes a new notebook written today, which has a Manipulate visualization of 3D bivector addition that is kind of fun. Bivector addition, at least in 3D, can be done graphically almost like vector addition. Instead of trying to add the planes (which can be done, as in the neat illustration in Geometric Algebra for Computer Science), you can do the task more simply by connecting the normals head to tail, where each of the normals are scaled by the area of the bivector (i.e. it’s absolute magnitude). The resulting bivector has an area equal to the length of that sum of normals, and a “direction” perpendicular to that resulting normal. This fun little Manipulate lets you interactively visualize this process, by changing the radius of a set of summed bivectors, each oriented in a different direction, and observing the effects of doing so. Of course, you can interpret this visualization as nothing more than a representation of addition of cross products, if you were to interpret the vector representing a cross product as an oriented area with a normal equal to that cross product (where the normal’s magnitude equals the area, as in this bivector addition visualization.) This works out nicely because of the duality relationship between the cross and wedge product, and the duality relationship between 3D bivectors and their normals. ## Potential solutions to the static Maxwell’s equation using geometric algebra [Click here for a PDF of this post with nicer formatting] When neither the electromagnetic field strength $$F = \BE + I \eta \BH$$, nor current $$J = \eta (c \rho – \BJ) + I(c\rho_m – \BM)$$ is a function of time, then the geometric algebra form of Maxwell’s equations is the first order multivector (gradient) equation \label{eqn:staticPotentials:20} \spacegrad F = J. While direct solutions to this equations are possible with the multivector Green’s function for the gradient \label{eqn:staticPotentials:40} G(\Bx, \Bx’) = \inv{4\pi} \frac{\Bx – \Bx’}{\Norm{\Bx – \Bx’}^3 }, the aim in this post is to explore second order (potential) solutions in a geometric algebra context. Can we assume that it is possible to find a multivector potential $$A$$ for which \label{eqn:staticPotentials:60} F = \spacegrad A, is a solution to the Maxwell statics equation? If such a solution exists, then Maxwell’s equation is simply \label{eqn:staticPotentials:80} \spacegrad^2 A = J, which can be easily solved using the scalar Green’s function for the Laplacian \label{eqn:staticPotentials:240} G(\Bx, \Bx’) = -\inv{\Norm{\Bx – \Bx’} }, a beastie that may be easier to convolve than the vector valued Green’s function for the gradient. It is immediately clear that some restrictions must be imposed on the multivector potential $$A$$. In particular, since the field $$F$$ has only vector and bivector grades, this gradient must have no scalar, nor pseudoscalar grades. That is \label{eqn:staticPotentials:100} This constraint on the potential can be avoided if a grade selection operation is built directly into the assumed potential solution, requiring that the field is given by \label{eqn:staticPotentials:120} However, after imposing such a constraint, Maxwell’s equation has a much less friendly form \label{eqn:staticPotentials:140} Luckily, it is possible to introduce a transformation of potentials, called a gauge transformation, that eliminates the ugly grade selection term, and allows the potential equation to be expressed as a plain old Laplacian. We do so by assuming first that it is possible to find a solution of the Laplacian equation that has the desired grade restrictions. That is \label{eqn:staticPotentials:160} \begin{aligned} \spacegrad^2 A’ &= J \\ \end{aligned} for which $$F = \spacegrad A’$$ is a grade 1,2 solution to $$\spacegrad F = J$$. Suppose that $$A$$ is any formal solution, free of any grade restrictions, to $$\spacegrad^2 A = J$$, and $$F = \gpgrade{\spacegrad A}{1,2}$$. Can we find a function $$\tilde{A}$$ for which $$A = A’ + \tilde{A}$$? Maxwell’s equation in terms of $$A$$ is \label{eqn:staticPotentials:180} \begin{aligned} J &= \spacegrad^2 (A’ + \tilde{A}) \end{aligned} or \label{eqn:staticPotentials:200} This non-homogeneous Laplacian equation that can be solved as is for $$\tilde{A}$$ using the Green’s function for the Laplacian. Alternatively, we may also solve the equivalent first order system using the Green’s function for the gradient. \label{eqn:staticPotentials:220} Clearly $$\tilde{A}$$ is not unique, as we can add any function $$\psi$$ satisfying the homogeneous Laplacian equation $$\spacegrad^2 \psi = 0$$. In summary, if $$A$$ is any multivector solution to $$\spacegrad^2 A = J$$, that is \label{eqn:staticPotentials:260} A(\Bx) = \int dV’ G(\Bx, \Bx’) J(\Bx’) = -\int dV’ \frac{J(\Bx’)}{\Norm{\Bx – \Bx’} }, then $$F = \spacegrad A’$$ is a solution to Maxwell’s equation, where $$A’ = A – \tilde{A}$$, and $$\tilde{A}$$ is a solution to the non-homogeneous Laplacian equation or the non-homogeneous gradient equation above. ### Integral form of the gauge transformation. Additional insight is possible by considering the gauge transformation in integral form. Suppose that \label{eqn:staticPotentials:280} A(\Bx) = -\int_V dV’ \frac{J(\Bx’)}{\Norm{\Bx – \Bx’} } – \tilde{A}(\Bx), is a solution of $$\spacegrad^2 A = J$$, where $$\tilde{A}$$ is a multivector solution to the homogeneous Laplacian equation $$\spacegrad^2 \tilde{A} = 0$$. Let’s look at the constraints on $$\tilde{A}$$ that must be imposed for $$F = \spacegrad A$$ to be a valid (i.e. grade 1,2) solution of Maxwell’s equation. \label{eqn:staticPotentials:300} \begin{aligned} F &= \spacegrad A \\ &= -\int_V dV’ \lr{ \spacegrad \inv{\Norm{\Bx – \Bx’} } } J(\Bx’) – \spacegrad \tilde{A}(\Bx) \\ &= \int_V dV’ \lr{ \spacegrad’ \inv{\Norm{\Bx – \Bx’} } } J(\Bx’) – \spacegrad \tilde{A}(\Bx) \\ &= \int_V dV’ \spacegrad’ \frac{J(\Bx’)}{\Norm{\Bx – \Bx’} } – \int_V dV’ \frac{\spacegrad’ J(\Bx’)}{\Norm{\Bx – \Bx’} } – \spacegrad \tilde{A}(\Bx) \\ &= \int_{\partial V} dA’ \ncap’ \frac{J(\Bx’)}{\Norm{\Bx – \Bx’} } – \int_V \frac{\spacegrad’ J(\Bx’)}{\Norm{\Bx – \Bx’} } \end{aligned} Where $$\ncap’ = (\Bx’ – \Bx)/\Norm{\Bx’ – \Bx}$$, and the fundamental theorem of geometric calculus has been used to transform the gradient volume integral into an integral over the bounding surface. Operating on Maxwell’s equation with the gradient gives $$\spacegrad^2 F = \spacegrad J$$, which has only grades 1,2 on the left hand side, meaning that $$J$$ is constrained in a way that requires $$\spacegrad J$$ to have only grades 1,2. This means that $$F$$ has grades 1,2 if \label{eqn:staticPotentials:320} = \int_{\partial V} dA’ \frac{ \gpgrade{\ncap’ J(\Bx’)}{0,3} }{\Norm{\Bx – \Bx’} }. The product $$\ncap J$$ expands to \label{eqn:staticPotentials:340} \begin{aligned} \ncap J &= &= \ncap \cdot (-\eta \BJ) + \gpgradethree{\ncap (-I \BM)} \\ &=- \eta \ncap \cdot \BJ -I \ncap \cdot \BM, \end{aligned} so \label{eqn:staticPotentials:360} = -\int_{\partial V} dA’ \frac{ \eta \ncap’ \cdot \BJ(\Bx’) + I \ncap’ \cdot \BM(\Bx’)}{\Norm{\Bx – \Bx’} }. Observe that if there is no flux of current density $$\BJ$$ and (fictitious) magnetic current density $$\BM$$ through the surface, then $$F = \spacegrad A$$ is a solution to Maxwell’s equation without any gauge transformation. Alternatively $$F = \spacegrad A$$ is also a solution if $$\lim_{\Bx’ \rightarrow \infty} \BJ(\Bx’)/\Norm{\Bx – \Bx’} = \lim_{\Bx’ \rightarrow \infty} \BM(\Bx’)/\Norm{\Bx – \Bx’} = 0$$ and the bounding volume is taken to infinity. # References ## Generalizing Ampere’s law using geometric algebra. The question I’d like to explore in this post is how Ampere’s law, the relationship between the line integral of the magnetic field to current (i.e. the enclosed current) \label{eqn:flux:20} \oint_{\partial A} d\Bx \cdot \BH = -\int_A \ncap \cdot \BJ, generalizes to geometric algebra where Maxwell’s equations for a statics configuration (all time derivatives zero) is \label{eqn:flux:40} \spacegrad F = J, where the multivector fields and currents are \label{eqn:flux:60} \begin{aligned} F &= \BE + I \eta \BH \\ J &= \eta \lr{ c \rho – \BJ } + I \lr{ c \rho_\txtm – \BM }. \end{aligned} Here (fictitious) the magnetic charge and current densities that can be useful in antenna theory have been included in the multivector current for generality. My presumption is that it should be possible to utilize the fundamental theorem of geometric calculus for expressing the integral over an oriented surface to its boundary, but applied directly to Maxwell’s equation. That integral theorem has the form \label{eqn:flux:80} \int_A d^2 \Bx \boldpartial F = \oint_{\partial A} d\Bx F, where $$d^2 \Bx = d\Ba \wedge d\Bb$$ is a two parameter bivector valued surface, and $$\boldpartial$$ is vector derivative, the projection of the gradient onto the tangent space. I won’t try to explain all of geometric calculus here, and refer the interested reader to [1], which is an excellent reference on geometric calculus and integration theory. The gotcha is that we actually want a surface integral with $$\spacegrad F$$. We can split the gradient into the vector derivative a normal component \label{eqn:flux:160} \spacegrad = \boldpartial + \ncap (\ncap \cdot \spacegrad), so \label{eqn:flux:100} \int_A d^2 \Bx \spacegrad F = \int_A d^2 \Bx \boldpartial F + \int_A d^2 \Bx \ncap \lr{ \ncap \cdot \spacegrad } F, so \label{eqn:flux:120} \begin{aligned} \oint_{\partial A} d\Bx F &= \int_A d^2 \Bx \lr{ J – \ncap \lr{ \ncap \cdot \spacegrad } F } \\ &= \int_A dA \lr{ I \ncap J – \lr{ \ncap \cdot \spacegrad } I F } \end{aligned} This is not nearly as nice as the magnetic flux relationship which was nicely split with the current and fields nicely separated. The $$d\Bx F$$ product has all possible grades, as does the $$d^2 \Bx J$$ product (in general). Observe however, that the normal term on the right has only grades 1,2, so we can split our line integral relations into pairs with and without grade 1,2 components \label{eqn:flux:140} \begin{aligned} \oint_{\partial A} \gpgrade{d\Bx F}{0,3} &= \int_A dA \gpgrade{ I \ncap J }{0,3} \\ \oint_{\partial A} \gpgrade{d\Bx F}{1,2} &= \int_A dA \lr{ \gpgrade{ I \ncap J }{1,2} – \lr{ \ncap \cdot \spacegrad } I F }. \end{aligned} Let’s expand these explicitly in terms of the component fields and densities to check against the conventional relationships, and see if things look right. The line integrand expands to \label{eqn:flux:180} \begin{aligned} d\Bx F &= d\Bx \lr{ \BE + I \eta \BH } = d\Bx \cdot \BE + I \eta d\Bx \cdot \BH + d\Bx \wedge \BE + I \eta d\Bx \wedge \BH \\ &= d\Bx \cdot \BE – \eta (d\Bx \cross \BH) + I (d\Bx \cross \BE ) + I \eta (d\Bx \cdot \BH), \end{aligned} the current integrand expands to \label{eqn:flux:200} \begin{aligned} I \ncap J &= I \ncap \lr{ \frac{\rho}{\epsilon} – \eta \BJ + I \lr{ c \rho_\txtm – \BM } } \\ &= \ncap I \frac{\rho}{\epsilon} – \eta \ncap I \BJ – \ncap c \rho_\txtm + \ncap \BM \\ &= \ncap \cdot \BM + \eta (\ncap \cross \BJ) – \ncap c \rho_\txtm + I (\ncap \cross \BM) + \ncap I \frac{\rho}{\epsilon} – \eta I (\ncap \cdot \BJ). \end{aligned} We are left with \label{eqn:flux:220} \begin{aligned} \oint_{\partial A} \lr{ d\Bx \cdot \BE + I \eta (d\Bx \cdot \BH) } &= \int_A dA \lr{ \ncap \cdot \BM – \eta I (\ncap \cdot \BJ) } \\ \oint_{\partial A} \lr{ – \eta (d\Bx \cross \BH) + I (d\Bx \cross \BE ) } &= \int_A dA \lr{ \eta (\ncap \cross \BJ) – \ncap c \rho_\txtm + I (\ncap \cross \BM) + \ncap I \frac{\rho}{\epsilon} -\PD{n}{} \lr{ I \BE – \eta \BH } }. \end{aligned} This is a crazy mess of dots, crosses, fields and sources. We can split it into one equation for each grade, which will probably look a little more regular. That is \label{eqn:flux:240} \begin{aligned} \oint_{\partial A} d\Bx \cdot \BE &= \int_A dA \ncap \cdot \BM \\ \oint_{\partial A} d\Bx \cross \BH &= \int_A dA \lr{ – \ncap \cross \BJ + \frac{ \ncap \rho_\txtm }{\mu} – \PD{n}{\BH} } \\ \oint_{\partial A} d\Bx \cross \BE &= \int_A dA \lr{ \ncap \cross \BM + \frac{\ncap \rho}{\epsilon} – \PD{n}{\BE} } \\ \oint_{\partial A} d\Bx \cdot \BH &= -\int_A dA \ncap \cdot \BJ \\ \end{aligned} The first and last equations could have been obtained much more easily from Maxwell’s equations in their conventional form more easily. The two cross product equations with the normal derivatives are not familiar to me, even without the fictitious magnetic sources. It is somewhat remarkable that so much can be packed into one multivector equation: \label{eqn:flux:260} \oint_{\partial A} d\Bx F = I \int_A dA \lr{ \ncap J – \PD{n}{F} }. # References [1] A. Macdonald. Vector and Geometric Calculus. CreateSpace Independent Publishing Platform, 2012. ## Solving Maxwell’s equation in freespace: Multivector plane wave representation [Click here for a PDF of this post with nicer formatting] The geometric algebra form of Maxwell’s equations in free space (or source free isotopic media with group velocity $$c$$) is the multivector equation \label{eqn:planewavesMultivector:20} \lr{ \spacegrad + \inv{c}\PD{t}{} } F(\Bx, t) = 0. Here $$F = \BE + I c \BB$$ is a multivector with grades 1 and 2 (vector and bivector components). The velocity $$c$$ is called the group velocity since $$F$$, or its components $$\BE, \BH$$ satisfy the wave equation, which can be seen by pre-multiplying with $$\spacegrad – (1/c)\PDi{t}{}$$ to find \label{eqn:planewavesMultivector:n} \lr{ \spacegrad^2 – \inv{c^2}\PDSq{t}{} } F(\Bx, t) = 0. Let’s look at the frequency domain solution of this equation with a presumed phasor representation \label{eqn:planewavesMultivector:40} F(\Bx, t) = \textrm{Re} \lr{ F(\Bk) e^{-j \Bk \cdot \Bx + j \omega t} }, where $$j$$ is a scalar imaginary, not necessarily with any geometric interpretation. Maxwell’s equation reduces to just \label{eqn:planewavesMultivector:60} 0 = -j \lr{ \Bk – \frac{\omega}{c} } F(\Bk). If $$F(\Bk)$$ has a left multivector factor \label{eqn:planewavesMultivector:80} F(\Bk) = \lr{ \Bk + \frac{\omega}{c} } \tilde{F}, where $$\tilde{F}$$ is a multivector to be determined, then \label{eqn:planewavesMultivector:100} \begin{aligned} \lr{ \Bk – \frac{\omega}{c} } F(\Bk) &= \lr{ \Bk – \frac{\omega}{c} } \lr{ \Bk + \frac{\omega}{c} } \tilde{F} \\ &= \lr{ \Bk^2 – \lr{\frac{\omega}{c}}^2 } \tilde{F}, \end{aligned} which is zero if $$\Norm{\Bk} = \ifrac{\omega}{c}$$. Let $$\kcap = \ifrac{\Bk}{\Norm{\Bk}}$$, and $$\Norm{\Bk} \tilde{F} = F_0 + F_1 + F_2 + F_3$$, where $$F_0, F_1, F_2,$$ and $$F_3$$ are respectively have grades 0,1,2,3. Then \label{eqn:planewavesMultivector:120} \begin{aligned} F(\Bk) &= \lr{ 1 + \kcap } \lr{ F_0 + F_1 + F_2 + F_3 } \\ &= F_0 + F_1 + F_2 + F_3 + \kcap F_0 + \kcap F_1 + \kcap F_2 + \kcap F_3 \\ &= F_0 + F_1 + F_2 + F_3 + \kcap F_0 + \kcap \cdot F_1 + \kcap \cdot F_2 + \kcap \cdot F_3 + \kcap \wedge F_1 + \kcap \wedge F_2 \\ &= \lr{ F_0 + \kcap \cdot F_1 } + \lr{ F_1 + \kcap F_0 + \kcap \cdot F_2 } + \lr{ F_2 + \kcap \cdot F_3 + \kcap \wedge F_1 } + \lr{ F_3 + \kcap \wedge F_2 }. \end{aligned} Since the field $$F$$ has only vector and bivector grades, the grades zero and three components of the expansion above must be zero, or \label{eqn:planewavesMultivector:140} \begin{aligned} F_0 &= – \kcap \cdot F_1 \\ F_3 &= – \kcap \wedge F_2, \end{aligned} so \label{eqn:planewavesMultivector:160} \begin{aligned} F(\Bk) &= \lr{ 1 + \kcap } \lr{ F_1 – \kcap \cdot F_1 + F_2 – \kcap \wedge F_2 } \\ &= \lr{ 1 + \kcap } \lr{ F_1 – \kcap F_1 + \kcap \wedge F_1 + F_2 – \kcap F_2 + \kcap \cdot F_2 }. \end{aligned} The multivector $$1 + \kcap$$ has the projective property of gobbling any leading factors of $$\kcap$$ \label{eqn:planewavesMultivector:180} \begin{aligned} (1 + \kcap)\kcap &= \kcap + 1 \\ &= 1 + \kcap, \end{aligned} so for $$F_i \in F_1, F_2$$ \label{eqn:planewavesMultivector:200} (1 + \kcap) ( F_i – \kcap F_i ) = (1 + \kcap) ( F_i – F_i ) = 0, leaving \label{eqn:planewavesMultivector:220} F(\Bk) = \lr{ 1 + \kcap } \lr{ \kcap \cdot F_2 + \kcap \wedge F_1 }. For $$\kcap \cdot F_2$$ to be non-zero $$F_2$$ must be a bivector that lies in a plane containing $$\kcap$$, and $$\kcap \cdot F_2$$ is a vector in that plane that is perpendicular to $$\kcap$$. On the other hand $$\kcap \wedge F_1$$ is non-zero only if $$F_1$$ has a non-zero component that does not lie in along the $$\kcap$$ direction, but $$\kcap \wedge F_1$$, like $$F_2$$ describes a plane that containing $$\kcap$$. This means that having both bivector and vector free variables $$F_2$$ and $$F_1$$ provide more degrees of freedom than required. For example, if $$\BE$$ is any vector, and $$F_2 = \kcap \wedge \BE$$, then \label{eqn:planewavesMultivector:240} \begin{aligned} \lr{ 1 + \kcap } \kcap \cdot F_2 &= \lr{ 1 + \kcap } \kcap \cdot \lr{ \kcap \wedge \BE } \\ &= \lr{ 1 + \kcap } \lr{ \BE \kcap \lr{ \kcap \cdot \BE } } \\ &= \lr{ 1 + \kcap } \kcap \lr{ \kcap \wedge \BE } \\ &= \lr{ 1 + \kcap } \kcap \wedge \BE, \end{aligned} which has the form $$\lr{ 1 + \kcap } \lr{ \kcap \wedge F_1 }$$, so the solution of the free space Maxwell’s equation can be written \label{eqn:planewavesMultivector:260} \boxed{ F(\Bx, t) = \textrm{Re} \lr{ \lr{ 1 + \kcap } \BE\, e^{-j \Bk \cdot \Bx + j \omega t} } , } where $$\BE$$ is any vector for which $$\BE \cdot \Bk = 0$$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9963210225105286, "perplexity": 3257.799754693209}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704804187.81/warc/CC-MAIN-20210126233034-20210127023034-00096.warc.gz"}
https://catwolf.org/qs?id=cb6980f4-7385-4116-afff-96b64700bd55&x=x	#### Automatically power on Android when the charger is connected 96002 visibility 18 arrow_circle_up 0 arrow_circle_down Is it possible to automatically power on the device once the charger is connected given that the device is initially turned off? 18 arrow_circle_up 0 arrow_circle_down The battery charging graphic is displayed by /system/bin/playlpm file on Samsung devices. If you are root, you can edit this file to: #!/system/bin/sh /system/bin/reboot And be sure to add those permissions to the file: chmod 0755 /system/bin/playlpm chown root.shell /system/bin/playlpm Your device will now boot when plugged by IET_DEMO • Thanks @IET_DEMO , Do you know solutions for cyanogenmod devices to do this? • Hi, I have a Cyanogenmod device , do you know how can I do this on cyanogenmod ? Thanks • This only works on Samsung devices. [This](http://forum.cyanogenmod.org/topic/68291-auto-start-boot-power-on-when-charger-connected/) may be useful for you • If you're trying to do this, make sure you don't have carriage returns in your playlpm file or it won't work. 18 arrow_circle_up 0 arrow_circle_down So, there are many ways to do so. The most proper one, as always supported by Google (and more and more by others, e.g. nvidia from nougat) is this fastboot command fastboot oem off-mode-charge 0 Otherwise, you can either hijack the charging binary (not guaranteed to be possible on all devices, but just requires root) or patch your ramdisk (theoretically universal, but will require an unlocked bootloader). For the first solution, you'll have to find somewhere in your system partition (usually the bin folder) where the program in charge of the battery animation and all resides. Some common names: • Motorola: charge_only_mode • Mediatek: kpoc_charger or ipod • Htc: chargemon or zchgd • Samsung: playlpm or lpm • Sony: chargemon or battery_charging • Most(?) AOSP-based roms: healthd Once found, you can just replace it with a script such as that above by IET_DEMO. Touching the kernel is instead something I don't feel like explaining and recommending if you don't know what you are doing. Just for the records then, I'd just like to underline that offline charging exists because the boot process is fairly energy intensive, and especially on older phones without even fast charging the power draw from the system could be higher than that on the plug. by mirh 18 arrow_circle_up 0 arrow_circle_down Just got this working for ZTE Force (Boost Force, Sprint Force, etc). I used IET_DEMO's answer, but replaced the file located at /system/bin/battery_charging with this code: #!/system/bin/sh /system/bin/reboot • Hi, I have a Cyanogenmod device , do you know how can I do this on cyanogenmod ? Thanks 18 arrow_circle_up 0 arrow_circle_down For some older Samsung devices, this can be accomplished through NoMoarPowah!: NoMoarPowah! can automatically reboot into Android when charging is done. Either when fully charged, or when the battery level reaches 15% and Android has enough juice to run. You need root and you probably don't want to do it unless you really know what you're doing, since I would expect this to modify important system files. It looks like this has been removed from the Play Store, but you can probably find the APK hosted elsewhere. (I don't have a trusted link offhand.) 18 arrow_circle_up 0 arrow_circle_down fastboot oem off-mode-charge 0 is the genuine method if your device supports. It's Google's recommended method but not all OEMs/vendors implement the command in bootloader. Or on some devices it's reset on next reboot. If off-mode-charge is disabled, bootloader won't pass androidboot.mode=charger commandline parameter to kernel when charger is inserted, so device boots normally. Otherwise when ro.bootmode property is set to charger on boot, init doesn't continue the normal boot process. Instead limited number of services are started and charging animation is displayed. So you can instruct init to reboot the device whenever charger mode is detected. Create a new .rc file or edit any existing one: # /system/etc/init/off_mode_charge.rc on charger setprop sys.powerctl reboot,leaving-off-mode-charging Or execute reboot binary: on charger exec - -- /system/bin/reboot leaving-off-mode-charging But if SELinux is enforcing, stock policy may not let init execute /system/bin/reboot. So use Magisk's context (or whatever rooting solution you use): on charger exec u:r:magisk:s0 -- /system/bin/reboot Don't forget to set permissions on *.rc file (chown 0.0, chmod 0644, chcon u:object_r:system_file:s0). It's also possible to continue boot process instead of restarting the device by replacing class_start charger with trigger late-init in /init.rc file: on charger #class_start charger trigger late-init Or by setting property sys.boot_from_charger_mode: on charger setprop sys.boot_from_charger_mode 1 • This method should work on all devices irrespective of OEM as it doesn't depend on vendor-specific charging binaries like playlpm, battery_charging, chargeonlymode, zchgd, kpoc_charger and so on. • Also replacing binaries of important services like healthd - which take care of a lot of things related to battery, storage etc. - is not a good idea. In this case if the service runs both in charger and normal mode, device may get into bootloop. • On non-System-as-Root devices it's not necessary to modify /system partition (e.g. if you don't want to break dm-verity for OTA updates to work). Simply unpack boot.img and edit /init.rc file in ramdisk. • Though unnecessary, it's also possible to execute an init.d script from .rc file. For reference see How to run an executable on boot? and How to power off when charger is removed?. RELATED: • nice, many thanks for systemless solution! will test this weekend! • @JeffLuyet thanks for the path correction. You can ask a new question if something isn't properly addressed in existing questions/answers. I just saw your proposed edit by-chance. No notification is sent. // I don't know exactly why it didn't work for you. I have been playing with init's .rc file at least since Android 7. And it always worked. Usually SELinux is the most problematic part. You should have seen at kernel logs (dmesg) right after first failed attempt. init logs its events to kernel log. That's how the problem can be identified. 18 arrow_circle_up 0 arrow_circle_down If you want to do the opposite, shutdown when charge, use this: "Auto ShutDown when no charge" https://play.google.com/store/apps/details?id=com.zeroFactorial.probattle good for my car's device and also had button broken • In powered off state device's behavior on hardware events like power button and charger obviously depends on lower level code including SoC/PMIC firmware and bootloaders. But I haven't seen an Android device on which bootloader handles charging entirely itself without involving OS (not sure if there were in 2012). Bootloader hands over charge to Android kernel and even init is started. The only difference is that /data (and possibly other filesystems) are not mounted and a limited set of services is started as compared to normal userspace.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.21694868803024292, "perplexity": 6397.141378971406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662521041.0/warc/CC-MAIN-20220518021247-20220518051247-00725.warc.gz"}
https://chemistry.stackexchange.com/questions/67382/why-is-phenol-soluble-in-sodium-carbonate-but-not-in-sodium-bicarbonate	# Why is phenol soluble in sodium carbonate but not in sodium bicarbonate? The original question was basically to predict which of sodium carbonate or sodium bicarbonate can be used to distinguish between phenol and benzene. I was sure that phenol neither reacts nor dissolves in $\ce{NaHCO3}$ but I was not sure about the $\ce{Na2CO3}$. By searching on Google I found that phenol is soluble in sodium carbonate. I am curious to know why this is, even though phenol doesn't liberate $\ce{CO2}$. • $\ce{NaHCO3}$ is less basic than $\ce{Na2CO3}$. Phenol is weakly acidic. – DHMO Jan 30 '17 at 11:29 The liberation of $\ce{CO2}$ from $\ce{Na2CO3}$ requires two protonation steps. \begin{align} \ce{CO3^2- + HA &<=> HCO3- + A-}\\ \ce{HCO3- + HA &<=> CO2 ^ + H2O + A-} \end{align} Neglecting the concentrations, the position of these equilibria will depend on the acid strength of $\ce{HA}$. If $\ce{HA}$ is a stronger acid than $\ce{HCO3-}$, for example, the first equilibrium will favour the products. This is the case for phenol, which has a $\mathrm{p}K_\mathrm{a}$ of $9.95$, whereas $\ce{HCO3-}$ has a $\mathrm{p}K_\mathrm{a}$ of $10.32$. Therefore, as long as you don't have too much phenol, it will exist in the soluble phenolate form: $$\ce{PhOH + CO3^2- <=>> PhO- + HCO3-}$$ The solubility of phenol does not necessitate that it releases carbon dioxide. Now, the second protonation. If you want to quantitatively determine whether $\ce{CO2}$ will actually be liberated, you need more data than the $\mathrm{p}K_\mathrm{a}$ values, since quite a significant amount of $\ce{CO2}$ can exist in the aqueous form. However, one thing is certain: if you want to produce $\ce{CO2 (g)}$ you first have to protonate $\ce{HCO3-}$ to form $\ce{H2CO3}$ (which dissociates to give $\ce{CO2 (aq)}$). This is not possible with phenol, since $\ce{H2CO3}$ has a $\mathrm{p}K_\mathrm{a}$ of $6.3$ (even after correcting for dissolved $\ce{CO2}$).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8872836828231812, "perplexity": 1186.1314591334137}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370506673.7/warc/CC-MAIN-20200402045741-20200402075741-00304.warc.gz"}
https://arxiv.org/abs/1507.06723	astro-ph.EP (what is this?) (what is this?) # Title:Discovery and Validation of Kepler-452b: A 1.6-Re Super Earth Exoplanet in the Habitable Zone of a G2 Star Abstract: We report on the discovery and validation of Kepler-452b, a transiting planet identified by a search through the 4 years of data collected by NASA's Kepler Mission. This possibly rocky 1.63$^{+0.23}_{-0.20}$ R$_\oplus$ planet orbits its G2 host star every 384.843$^{+0.007}_{0.012}$ days, the longest orbital period for a small (R$_p$ < 2 R$_\oplus$) transiting exoplanet to date. The likelihood that this planet has a rocky composition lies between 49% and 62%. The star has an effective temperature of 5757$\pm$85 K and a log g of 4.32$\pm$0.09. At a mean orbital separation of 1.046$^{+0.019}_{-0.015}$ AU, this small planet is well within the optimistic habitable zone of its star (recent Venus/early Mars), experiencing only 10% more flux than Earth receives from the Sun today, and slightly outside the conservative habitable zone (runaway greenhouse/maximum greenhouse). The star is slightly larger and older than the Sun, with a present radius of 1.11$^{+0.15}_{-0.09}$ R$_\odot$ and an estimated age of 6 Gyr. Thus, Kepler-452b has likely always been in the habitable zone and should remain there for another 3 Gyr. Comments: 19 pages, 16 figures Subjects: Earth and Planetary Astrophysics (astro-ph.EP) Journal reference: The Astronomical Journal 150 : 56 (2015) DOI: 10.1088/0004-6256/150/2/56 Cite as: arXiv:1507.06723 [astro-ph.EP] (or arXiv:1507.06723v1 [astro-ph.EP] for this version) ## Submission history From: Jon Jenkins [view email] [v1] Fri, 24 Jul 2015 02:05:15 UTC (4,020 KB)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.26617637276649475, "perplexity": 7398.473767253051}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583771929.47/warc/CC-MAIN-20190121090642-20190121112642-00225.warc.gz"}
http://mathhelpforum.com/calculus/220789-need-help-improper-integral.html	# Math Help - Need help with improper integral 2. ## Re: Need help with improper integral What do you need help with? The set up, or actually proving it converges? 3. ## Re: Need help with improper integral He needs to prove it, which won't be very easy since we can't find any anti derivatives.. I would consider looking into some of the convergence test for improper integrals.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8868486285209656, "perplexity": 1120.32944404771}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207927863.72/warc/CC-MAIN-20150521113207-00120-ip-10-180-206-219.ec2.internal.warc.gz"}
https://dec.dearbornschools.org/mod/glossary/showentry.php?eid=6545	#### SL.2.1c Comprehension and Collaboration: Ask for clarification and further explanation as needed about the topics and texts under discussion.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9815909266471863, "perplexity": 3528.363253078335}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499845.10/warc/CC-MAIN-20230131055533-20230131085533-00576.warc.gz"}
http://math.stackexchange.com/questions/291281/diffeomorphic-riemannian-manifolds-and-volume-forms	Diffeomorphic riemannian manifolds and volume forms Maybe the question will be stupid, but I'm a beginner in riemannian geometry... We have two riemannian manifolds $(M,g)$, $(\overline M,\overline g)$ and a diffeomorphism $F:M\rightarrow\overline M$ between them. If $dV_g$ and $dV_\overline g$ are the riemannian volume forms of $M$ and $\overline M$ respectively, is it true that $F^(dV_\overline g)_p=det(DF_p)(dV_g)_p$ $\forall p\in M$ ? - Please, don't get offended with my question, but did you tried to do the calculation? Maybe you could provide us with some of your efforts? – Tomás Jan 31 '13 at 11:15 Sorry... It's a nonsense! In abstract terms there is no reason why this is true. – Frankenstein Jan 31 '13 at 13:43 Recall that $$DF_p : T_p M \rightarrow T_{\bar{p}} \bar{M}$$ how do you define its determinant?? However, its true that if you consider an $n$-form $\omega$ on $\mathbb{R}^n$ and a smooth map $\Phi : \mathbb{R}^n \rightarrow \mathbb{R}^n$ there is a formula $$(\Phi^ \omega)_x = \det(d \Phi(x)) \omega_{\Phi(x)} .$$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8023198843002319, "perplexity": 278.36226456006705}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422118973352.69/warc/CC-MAIN-20150124170253-00164-ip-10-180-212-252.ec2.internal.warc.gz"}
https://www.springerprofessional.de/integral-equations-on-time-scales/10999610	scroll identifier for mobile main-content ## Über dieses Buch This book offers the reader an overview of recent developments of integral equations on time scales. It also contains elegant analytical and numerical methods. This book is primarily intended for senior undergraduate students and beginning graduate students of engineering and science courses. The students in mathematical and physical sciences will find many sections of direct relevance. The book contains nine chapters and each chapter is pedagogically organized. This book is specially designed for those who wish to understand integral equations on time scales without having extensive mathematical background. ## Inhaltsverzeichnis ### Chapter 1. Elements of the Time Scale Calculus This chapter is devoted to a brief exposition of the time scale calculus that provide the framework for the study of integral equations on time scales. Svetlin G. Georgiev ### Chapter 2. Introductory Concepts of Integral Equations on Time Scales A delta integral equation (or in short integral equation) is the equation in which the unknown function $$\displaystyle {\phi (x)}$$ appears inside a delta integral sign. Svetlin G. Georgiev ### Chapter 3. Generalized Volterra Integral Equations In this chapter we investigate generalized Volterra integral equations. They are described different methods for finding a solution as an infinite series such as: the Adomian decomposition method, the modified decomposition method, the noise terms phenomenon, the differential equations method and the successive iterations method. It is given a procedure for conversion of generalized Volterra integral equations of the first kind to generalized Volterra integral equations of the second kind. They are provided existence and uniqueness of the solution. Svetlin G. Georgiev ### Chapter 4. Generalized Volterra Integro-Differential Equations In this chapter we describe the Adomian decomposition method for generalized Volterra integro-differential equations of the second kind. Svetlin G. Georgiev ### Chapter 5. Generalized Fredholm Integral Equations In this chapter we adapt the Adomian decomposition method, the modified decomposition method, the noise term phenomenon, the direct computation method and the successive approximation method for generalized Fredholm integral equations. Svetlin G. Georgiev ### Chapter 6. Hilbert-Schmidt Theory of Generalized Integral Equations with Symmetric Kernels Assume that K(xy) is continuous and Hermitian symmetric on $$[a, b]\times [a, b].$$ Svetlin G. Georgiev ### Chapter 7. The Laplace Transform Method This chapter is devoted on applications of the Laplace transform on time scales to dynamic equations, generalized Volterra integral equations and generalized Volterra integro-differential equations. Svetlin G. Georgiev ### Chapter 8. The Series Solution Method In this chapter we describe the series solution method for generalized Volterra integral equations and generalized Volterra integro-differential equations. Svetlin G. Georgiev ### Chapter 9. Non-linear Generalized Integral Equations The generalized Volterra integral equation. Svetlin G. Georgiev ### Backmatter Weitere Informationen ## BranchenIndex Online Die B2B-Firmensuche für Industrie und Wirtschaft: Kostenfrei in Firmenprofilen nach Lieferanten, Herstellern, Dienstleistern und Händlern recherchieren. ## Whitepaper - ANZEIGE - ### Best Practices für die Mitarbeiter-Partizipation in der Produktentwicklung Unternehmen haben das Innovationspotenzial der eigenen Mitarbeiter auch außerhalb der F&E-Abteilung erkannt. Viele Initiativen zur Partizipation scheitern in der Praxis jedoch häufig. Lesen Sie hier - basierend auf einer qualitativ-explorativen Expertenstudie - mehr über die wesentlichen Problemfelder der mitarbeiterzentrierten Produktentwicklung und profitieren Sie von konkreten Handlungsempfehlungen aus der Praxis.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9823890328407288, "perplexity": 2896.257277259379}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583658702.9/warc/CC-MAIN-20190117041621-20190117063621-00080.warc.gz"}
https://puzzling.stackexchange.com/questions/85961/the-joke-office/85963	# The joke office Alice and Bob are supposed to get form A at the joke office. Forms A, B, C, D and E are each at exactly one of the following five terminals. At one Terminal is only one form. Terminal 1: Here there are form B. Terminal 2: Here there are form C or E. Terminal 3: Here there are form D. Terminal 4: Here there are form A, C or E. Terminal 5: Here there are form A. Bob is at a loss when he reads the signs at the counters. Alice remembers what the janitor is said: "Exactly one statement on the terminals is wrong, the four other statements are true." Question: At which terminal is form A available? • Is switch the right word, or were you looking for "counter" or "terminal" ? – Falco Jul 9 '19 at 11:20 • Yes, terminal is better. – Matti Jul 9 '19 at 11:32 • You should specify that at each terminal there is exactly one form, otherwise there are alternate solutions, for example with B at 1, C and E at 2, D at 3 and A at 5. – Magma Jul 9 '19 at 14:03 Notation: (P,Q,R,S,T) denotes that form P is in Switch 1, Q in Switch 2, etc. If Switch 1 is wrong, then (?,C/E,D,C/E,A), only choice left for ? is B -> contradiction If Switch 2 is wrong, then (B,?,D,C/E,A), only choices left for ? are C and E -> contradiction If Switch 3 is wrong, then (B,C/E,?,C/E,A), only choice left for ? is D -> contradiction If Switch 4 is wrong, then (B,C/E,D,?,A), only choices left for ? are C and E -> contradiction If Switch 5 is wrong, then (B,C/E,D,A/C/E,?), one scenario can be (B,C/E,D,A,C/E) -> possible Form A: Switch 4; Wrong Sign: Switch 5 Form A is available at Switch 4. Assume Switch 1 was incorrect. This means that form B must be somewhere else. But there is no other sign which references form B, so that would mean more than one sign was incorrect (contradiction!). If we assume Switch 3 was incorrect, we’d get the same result. So one of Switches 2, 4, or 5 are wrong. It can’t be 4, because then B or D would have to be there too and those have already been placed. Assuming that Switch 2 was wrong would put A at Switch 2, but then Switch 5 would also be wrong. Therefore Switch 5 must be wrong, so all of the others are right, and since Switch 4 is the only place with mention to A, it must be there. • you sniped me with only the answer, but i have the full explanation first. let the judge decide! good game! – Omega Krypton Jul 8 '19 at 12:24 Let us assume for contradiction sake Switch 5 was correct. If Switch 1 and 3 are correct only C and E are left for Switches 2 and 4 which would thus be correct, too. Similarly if Switches 2 and 4 are correct only B and D are left for Switch 1 and 3 and either both or none of them is correct. Thus, there is no way that Switch 5 is correct and exactly one of the remaining switches incorrect. This implies that Switch 5 must be the incorrect one. The only Switch remaining which could possibly contain Form A is Switch 4. • Hi! Welcome to the Puzzling Stack Exchange (PSE)! Great job on your first answer! I'm glad you have learnt to use the spoiler tag >! and have even answered the question correctly — and pretty nicely too with a thorough explanation! — so well done! Take the tour if you have not already, just to get a clearer understanding of what this site is all about, as well as the community thriving on it. Also, check out the Help Center to know how you may contribute to this community. Apart from that, enjoy! :) – Mr Pie Jul 9 '19 at 9:57 Terminal 4 is wrong as it must contain either Forms C or E, thusly Bob should go to Terminal 5 to retrieve Form A	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7650471925735474, "perplexity": 1120.488510055658}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704800238.80/warc/CC-MAIN-20210126135838-20210126165838-00234.warc.gz"}
https://gitter.im/cypress-io/cypress?at=5f338b31f3d6d26b0d8dfa95	## Where communities thrive • Join over 1.5M+ people • Join over 100K+ communities • Free without limits ##### Activity • 07:12 lmiller1990 edited #15316 • 06:38 JessicaSachs on runner-ct-ui-improvements wip: nav bar external link fix (compare) • 06:32 JessicaSachs on runner-ct-ui-improvements wip: nav bar (compare) • 06:27 muralimohan3628 opened #15319 • 06:26 muralimohan3628 opened #15318 • 05:56 Ppkd2021 commented #15317 • 05:48 Ppkd2021 opened #15317 • 05:45 cypress[bot] commented #15314 • 05:37 dmtrKovalenko commented #15314 • 05:36 dmtrKovalenko commented #15314 • 05:31 dmtrKovalenko commented #15314 • 05:17 cypress-bot[bot] commented #15316 • 05:17 lmiller1990 opened #15316 • 05:17 lmiller1990 review_requested #15316 • 05:13 lmiller1990 on vite-react-issues fix: add support file and unmou… (compare) • 05:09 lmiller1990 on unmount-after-each-spec-vite fix: ensure to call unmount aft… (compare) • 04:56 lmiller1990 on vite-react-issues • 04:45 lmiller1990 on see-if-ci-fails • 04:28 lmiller1990 commented #9563 • 04:24 cypress[bot] commented #15314 Hello, getCookie() and getCookies() return an array. How can I cy.log('key=value') string from that returned array? 9 replies Michael @michael-siek Hi, is there anyway that I could modify the output from (Results)? avinashkrishna613 @avinashkrishna613 Hi, I have to test my login functionality. On clickikng login button, i should do authentication and return a token. I was using auth0 with react Ondskan56 @Ondskan56 Hey all, the issue with '.get' that scrolls the screen is really annoying and it seems that it hasn't been fixed since 2017. Is this on the roadmap? Are you aware of this issue and you think on a solution? any feedback is appreciated cypress-io/cypress#871 I tried some of the workaround and they work on some of my tests but they don't work on all of them. I find it really difficult using Cypress with this issue. JonathanDagan @JonathanDagan Is there a way to have the test execute all of the assertions and if one fails fail the test but if an assertion that has assertions after it fails the test would still fail but would show the results of the other assertions? melibe23 @melibe23 Hi, I am still not able to fix this (I honestly tried everything and I am feeling so stupid by now), I left the question here: https://stackoverflow.com/questions/63360027 it is related to cy.stub, google events and new pages loading Mitch Lillie @MitchLillie Hi all. I'm having a super mysterious issue getting Cypress running in Jenkins inside a Docker container. I'm using the official cypress/included image. It seems to be able to visit a page, but not actually find or manipulate on that page. Turning on the debug logging, it appears to simply hang forever, always at the same place. We've tried increasing the memory to 6gb, disabling shm in Chrome, using Electron, but nothing seems to work. Does anyone have any experience or insight? amr wahdan @amrwahdan3 suddenly having trouble getting tests to run in windows. i get Unable to Read property 'name' of undefined and it says this is the line(s): const runEachSpec = (spec, index, length, estimated) => { if (!options.quiet) { displaySpecHeader(spec.name, index + 1, length, estimated) } what could be the issue? started failing yesterday 4 replies Sergio A Gomez Hi everyone, I'm trying to upload a file of 100 Mb using cy.get('[type="file"]').attachFile('filename.xlsx') but cypress is throwing the following error: 'cy.fixture() timed out waiting 30000ms to receive a fixture. No fixture was ever sent by the server'. I've already checked that the file is in cypress/fixtures folder executing : cy.exec(dir \${Cypress.config('fixturesFolder')}) to list all files in fixtures folders and it is there. I've also tried with a smaller file and it worked in this case. By another hand, I tried to increased timeout but it didn't work. I used cy.fixture('filename.xlsx', 'binary', { timeout: 120000}) and I got the same error. Do you know if there is a limitation of file size using fixture command? Darren-Ivey @Darren-Ivey I am looking into Cypress to replace Selenium. I really like Cypress, but the browser support is quite limited. I'd like to know if the lack of support for IE and Safari impacts anyone? Are if there is any way around this limitation? Thanks! Gleb Bahmutov @bahmutov shaymaasab @shaymaasab hey i made a test and i ran it many times but now iam facing this problem its emergency :( maximum call stack size exceeded Ming Han Chung So horribly newb question. If I make a task 'db:reset': (user, table) => {} is that the correct way to declare two args? Say i'm calling cy.task('db:reset'. {user: 'Jim', table: 'Users'}) 7 replies or is it like 'db:reset': (user) => {} and then u call user.user user.table Santiago Agüero @saaguero Hi guys, how are you? In Gitlab I'm running into the problem I cannot adjust/change the setting shm_size, which causes Cypress tests against Chrome hang forever... I think this is a recurring problem. What are you using to overcome this scenario in Gitlab? Dana Woodman @danawoodman Does anyone know how to support import aliases in plugin files? We have WebPack aliases in our Next.js project (eg ~/server) and I'd like to import this code into a plugin file. I know I can use WebPack preprocessor for test files, but how do I tell Cypress to respect my aliases in plugin files themselves? Don't see anything on docs or Google about this. Use case is to have a "reset db" plugin that calls our server code to seed the DB using our models directly. Is this possible or should I try something else? Dana Woodman @danawoodman For now I'll use exec but it seems like a plugin is the "correct" way to do this? QA1980 @QA1980 Has anyone encountered this error when you run test to the dashboard ? thanks Sapan Shah @sapandegreed Hi, Does anyone know how to deal with infinite scrolling in cypress? I want to keep scrolling the page until the desired data is found. Thanks! symphony @symphony2014 Hi guys, when I run cypress , there was so many pages depend on top object, but in the container of cypress, top target to "http://localhost:8080/__/#/tests/__all"? anyway or workaround that I can redirect the top keyword to my website? Tri Nguyen @mankinchi would you recommend using Cypress to test API? symphony @symphony2014 Why not use unit test or postman ? @mankinchi I guess Cypress more suitable for E2E test. 3 replies Wim Vandenhaute @wvdhaute Hello, out of curiosity, what is the reason for https://docs.cypress.io/api/commands/fixture.html#this-context ? The requirement to use function callbacks here? 2 replies Patrick Schaub @pschaub hello there :) in our company i have weird issues with cypress. sometimes it flaky and i get "DOM detached" on our vue application. is there any way to slowdown the requests on a cypress test to better see what happens? or any idea how to detect what exactly is triggering this? and does anybody have a good idea how to wait for hydration of a vue app? 5 replies Kirill Popolov @ezhikov Hello. I'm using WSL and want to test project inside WSL, but I don't want to setup X server, since result is ugly and buggy. So, I'm using pnpx cypress open to run Cypress, pointing it to WSL directory and getting EISDIR when file watcher is trying to watch /: Error: EISDIR: illegal operation on a directory, watch '/' at FSWatcher.start (internal/fs/watchers.js:165:26) at Object.watch (fs.js:1329:11) at createFsWatchInstance (C:\Users\kpopo\AppData\Local\Cypress\Cache\4.12.1\Cypress\resources\app\packages\server\node_modules\chokidar\lib\nodefs-handler.js:116:15) at setFsWatchListener (C:\Users\kpopo\AppData\Local\Cypress\Cache\4.12.1\Cypress\resources\app\packages\server\node_modules\chokidar\lib\nodefs-handler.js:163:15) at NodeFsHandler._watchWithNodeFs (C:\Users\kpopo\AppData\Local\Cypress\Cache\4.12.1\Cypress\resources\app\packages\server\node_modules\chokidar\lib\nodefs-handler.js:325:14) at NodeFsHandler._handleDir (C:\Users\kpopo\AppData\Local\Cypress\Cache\4.12.1\Cypress\resources\app\packages\server\node_modules\chokidar\lib\nodefs-handler.js:548:19) at C:\Users\kpopo\AppData\Local\Cypress\Cache\4.12.1\Cypress\resources\app\packages\server\node_modules\chokidar\index.js:435:21 at async Promise.all (index 0) { errno: -4068, syscall: 'watch', code: 'EISDIR', path: '/', filename: '/' } Any ideas how to proceed from here or debug this? Patrick Schaub @pschaub 2 replies agrmayank03 @agrmayank03 Unable to close PopUp Alert or unable to click ok button in any alert popup in cypress iframepage.switch('#_bmain').xpath("user name").type('') after login this, a popup alert message with OK button is coming which is not closing automatically and i am unable to close it with any manual code.. (we can't inspect the coming popup) Example , i used below codes: cy.get('button').contains('OK').click() if (arguments && arguments[0] === 'onbeforeunload') { return; } return original.apply(this, arguments); }; }) iframepage.switch('#_bmain').xpath("user name").type('') after login this, a popup alert message with OK button is coming which is not closing automatically and i am unable to close it with any manual code.. (we can't inspect the coming popup) Example , i used below codes: cy.get('button').contains('OK').click() if (arguments && arguments[0] === 'onbeforeunload') { return; } return original.apply(this, arguments); }; }) Gerard de Brieder @smeevil Hi, is anyone here using cypress-autorecord? I can record requests fine, but when replaying them i run in all kinds of async issues. Did anyone else notice this ? agrmayank03 @agrmayank03 Victor Aprea @vicatcu can someone explain to me this source of flake: "is not visible because its ancestor has position: fixed CSS property and it is overflowed by other elements." Nikita Voloboev @nikitavoloboev Cypress.Commands.add('hasValidationError', { prevSubject: 'element' }, (subject, msg) => { cy.wrap(subject).closest('.field').find('.label.red').should('have.text', msg); }); if I have smth like this cy.get('[data-test-process-popover]').wrap() will the above be similar im not sure how the .wrap gets used Sergey Khristenko @sergeyKhristenko Hi! Is there any spec-level timeout in cypress? Something like if test is running longer than 'n' mins then stop it and fail? Gleb Bahmutov @bahmutov Hey there, I'm probably just dum but I've been trying to out how to do something for a little while with no luck. Basically I have a platform I'm working in where we have 3 apps that share a "reset password" page. I'm trying to write tests for that reset password page using cypress, and one of the things I'm trying to test is that when the reset is complete, the user is automatically navigated back to the correct app. I'm getting some errors when I try to do that regarding "Blocked a frame with origin "http://localhost:8081" from accessing a cross-origin frame." Is there somewhere I need to add some config in cypress to allow my other pages to load? Thanks. Abhinaba Ghosh @abhinaba-ghosh Is there any option to log error messages nicely? I was using throw new Error, but it is not the case anymore. Is there any command available like: cy.error() or cy.log('', {error:true})? rhshah007 @rhshah007 Hi amazing people here! Does anyone know how to integrate cypress with bamboo or harness? Thanks! Hemant Choudhari @hemantc09 Hi there, I have impltemented the OKTA but somehow its keep giving me OKTA login screen even though I see it working 200 response. 1. Same OKTA login code works in electron 2. Same code doesnt work in chrome. I did some research and figured the "samesite " cookie related issue. I added a code cy.set('sameSite', value). //i tried all values. But still getting the error. Does any one face this issue?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23878732323646545, "perplexity": 6881.274016096096}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178368608.66/warc/CC-MAIN-20210304051942-20210304081942-00116.warc.gz"}
http://clay6.com/qa/9628/domain-of-y-log-1-x-is-	# Domain of $y=log(1+x)$ is ? $\begin{array}{1 1} (0, \infty ) \\ (-1, \infty ) \\ (1, \infty) \\ [-1, \infty) \end{array}$ Toolbox: • $logx$ is defined for x$> 0$ $1+x > 0$ $\Rightarrow x > -1$ Domain is $(-1,\infty)$ edited May 17, 2014	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9050383567810059, "perplexity": 3581.2682766614453}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125946256.50/warc/CC-MAIN-20180423223408-20180424003408-00451.warc.gz"}
http://mathhelpforum.com/calculus/149884-paramtrization-line-integral-print.html	# Paramtrization and Line Integral • July 1st 2010, 03:36 PM keysar7 Paramtrization and Line Integral a) Parametrize the curve $x^{\frac{2}{3}}+y^{\tfrac{2}{3}}=a^{\tfrac{2}{3}}\ \$ in the standard counterclockwise sense. b) Evaluate $\text{F(x) = (}\tfrac{-1}{\sqrt[{3}]{{y}}}\text{ ,}\tfrac{1}{\sqrt[{3}]{{x}}}\text{ )}$ over one complete transversal of the above curve. _____________________ a) $x=a\text{ }\cos ^{3}t$ $y=a\text{ }\sin ^{3}t$ $0\text{ }\leq t\leq \text{ }2\pi$ b) Since the field is not conservative, we have to find the line integral (i.e. the answer is not zero)... My final answer is $-6\pi a^{\tfrac{2}{3}}$ However, I think the negative sign is not correct because the force field is along the path of motion, meaning positive would make more sense... What do you think? • July 3rd 2010, 05:04 PM keysar7 I'm starting to doubt my answer. And nobody is offering any help... So here's another question. 1. Is there a way I could verify my parametrization? Is there a good online grapher that does both regular and parametric graphing? And 2. Even though I did the line integral by hand, is there an online integrator that could help in this case? • July 3rd 2010, 05:54 PM mr fantastic Quote: Originally Posted by keysar7 a) Parametrize the curve $x^{\frac{2}{3}}+y^{\tfrac{2}{3}}=a^{\tfrac{2}{3}}\ \$ in the standard counterclockwise sense. b) Evaluate $\text{F(x) = (}\tfrac{-1}{\sqrt[{3}]{{y}}}\text{ ,}\tfrac{1}{\sqrt[{3}]{{x}}}\text{ )}$ over one complete transversal of the above curve. _____________________ a) $x=a\text{ }\cos ^{3}t$ $y=a\text{ }\sin ^{3}t$ $0\text{ }\leq t\leq \text{ }2\pi$ b) Since the field is not conservative, we have to find the line integral (i.e. the answer is not zero)... My final answer is $-6\pi a^{\tfrac{2}{3}}$ However, I think the negative sign is not correct because the force field is along the path of motion, meaning positive would make more sense... What do you think? The magnitude of your answer is correct. I don't know why you get a negative because I get $3 a^{2/3} \int_{t = 0}^{t = 2 \pi} \cos^2 (t) + \sin^2 (t) \, dt = 3 a^{2/3} (2 \pi - 0) = +6 \pi a^{2/3}$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9801467657089233, "perplexity": 568.9054387610025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398460519.28/warc/CC-MAIN-20151124205420-00274-ip-10-71-132-137.ec2.internal.warc.gz"}
http://www.ck12.org/chemistry/Free-Energy/lesson/Free-Energy/r5/	<meta http-equiv="refresh" content="1; url=/nojavascript/"> Free Energy ( Read ) \| Chemistry \| CK-12 Foundation You are viewing an older version of this Concept. Go to the latest version. # Free Energy % Best Score Practice Free Energy Best Score % Free Energy 0 0 0 All aboard! The steam engine pictured above is slowly going out of style, but is still a picturesque part of the modern railroad. The water in a boiler is heated by a fire (usually fueled by coal) and turned to steam. This steam then pushes the pistons that drive the wheels of the train. It is the pressure created by the steam which allows work to be done in moving the train. ### Free Energy Many chemical reactions and physical processes release energy that can be used to do other things. When the fuel in a car is burned, some of the released energy is used to power the vehicle. Free energy is energy that is available to do work. Spontaneous reactions release free energy as they proceed. Recall that the determining factors for spontaneity of a reaction are the enthalpy and entropy changes that occur for the system. The free energy change of a reaction is a mathematical combination of the enthalpy change and the entropy change. $\Delta G^\circ=\Delta H^\circ - T \Delta S^\circ$ The symbol for free energy is $G$ , in honor of American scientist Josiah Gibbs (1839-1903), who made many contributions to thermodynamics. The change in Gibbs free energy is equal to the change in enthalpy minus the mathematical product of the change in entropy multiplied by the Kelvin temperature. Each thermodynamic quantity in the equation is for substances in their standard states. The usual units for $\Delta H$ is kJ/mol, while $\Delta S$ is often reported in J/K • mol. It is necessary to change the units for $\Delta S$ to kJ/K • mol, so that the calculation of $\Delta G$ is in kJ/mol. A spontaneous reaction is one that releases free energy, and so the sign of $\Delta G$ must be negative. Since both $\Delta H$ and $\Delta S$ can be either positive or negative, depending on the characteristics of the particular reaction, there are four different general outcomes for $\Delta G$ and these are outlined in the table below: $\Delta H$ $\Delta S$ $\Delta G$ − value (exothermic) + value (disordering) always negative + value (endothermic) + value (disordering) negative at higher temperatures − value (exothermic) − value (ordering) negative at lower temperatures + value (endothermic) − value (ordering) never negative Keep in mind that the temperature in the Gibbs free energy equation is the Kelvin temperature and so can only be positive. When $\Delta H$ is negative and $\Delta S$ is positive, the sign of $\Delta G$ will always be negative, and the reaction will be spontaneous at all temperatures. This corresponds to both driving forces being in favor of product formation. When $\Delta H$ is positive and $\Delta S$ is negative, the sign of $\Delta G$ will always be positive, and the reaction can never be spontaneous. This corresponds to both driving forces working against product formation. #### Summary • Free energy is defined. • Relationships between enthalpy, entropy, and free energy are described. #### Practice 2. What happens to the total energy when the ball rolls down the slide? 3. How does $H$ change in a spontaneous reaction? 4. How does $S$ change in a spontaneous reaction? #### Review 1. What do spontaneous reactions do? 2. What are the units for $\Delta H$ ? 3. What are the units for $\Delta S$ ?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 26, "texerror": 0, "math_score": 0.7732044458389282, "perplexity": 1004.0391446839785}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663467.44/warc/CC-MAIN-20140930004103-00380-ip-10-234-18-248.ec2.internal.warc.gz"}
https://www.lmfdb.org/ModularForm/GL2/Q/holomorphic/837/2/j/c/	# Properties Label 837.2.j.c Level $837$ Weight $2$ Character orbit 837.j Analytic conductor $6.683$ Analytic rank $0$ Dimension $2$ CM discriminant -3 Inner twists $4$ # Learn more ## Newspace parameters Level: $$N$$ $$=$$ $$837 = 3^{3} \cdot 31$$ Weight: $$k$$ $$=$$ $$2$$ Character orbit: $$[\chi]$$ $$=$$ 837.j (of order $$6$$, degree $$2$$, minimal) ## Newform invariants Self dual: no Analytic conductor: $$6.68347864918$$ Analytic rank: $$0$$ Dimension: $$2$$ Coefficient field: $$\Q(\sqrt{-3})$$ Defining polynomial: $$x^{2} - x + 1$$ Coefficient ring: $$\Z[a_1, \ldots, a_{13}]$$ Coefficient ring index: $$1$$ Twist minimal: yes Sato-Tate group: $\mathrm{U}(1)[D_{6}]$ ## $q$-expansion Coefficients of the $$q$$-expansion are expressed in terms of a primitive root of unity $$\zeta_{6}$$. We also show the integral $$q$$-expansion of the trace form. $$f(q)$$ $$=$$ $$q + 2 q^{4} + ( -5 + 5 \zeta_{6} ) q^{7} +O(q^{10})$$ $$q + 2 q^{4} + ( -5 + 5 \zeta_{6} ) q^{7} + ( 6 - 3 \zeta_{6} ) q^{13} + 4 q^{16} + ( -7 + 7 \zeta_{6} ) q^{19} + ( -5 + 5 \zeta_{6} ) q^{25} + ( -10 + 10 \zeta_{6} ) q^{28} + ( -1 + 6 \zeta_{6} ) q^{31} + ( 3 + 3 \zeta_{6} ) q^{37} + ( 1 + \zeta_{6} ) q^{43} -18 \zeta_{6} q^{49} + ( 12 - 6 \zeta_{6} ) q^{52} + ( 5 - 10 \zeta_{6} ) q^{61} + 8 q^{64} + 11 \zeta_{6} q^{67} + ( 16 - 8 \zeta_{6} ) q^{73} + ( -14 + 14 \zeta_{6} ) q^{76} + ( -7 - 7 \zeta_{6} ) q^{79} + ( -15 + 30 \zeta_{6} ) q^{91} + 14 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$2q + 4q^{4} - 5q^{7} + O(q^{10})$$ $$2q + 4q^{4} - 5q^{7} + 9q^{13} + 8q^{16} - 7q^{19} - 5q^{25} - 10q^{28} + 4q^{31} + 9q^{37} + 3q^{43} - 18q^{49} + 18q^{52} + 16q^{64} + 11q^{67} + 24q^{73} - 14q^{76} - 21q^{79} + 28q^{97} + O(q^{100})$$ ## Character values We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/837\mathbb{Z}\right)^\times$$. $$n$$ $$218$$ $$406$$ $$\chi(n)$$ $$-1$$ $$\zeta_{6}$$ ## Embeddings For each embedding $$\iota_m$$ of the coefficient field, the values $$\iota_m(a_n)$$ are shown below. For more information on an embedded modular form you can click on its label. Label $$\iota_m(\nu)$$ $$a_{2}$$ $$a_{3}$$ $$a_{4}$$ $$a_{5}$$ $$a_{6}$$ $$a_{7}$$ $$a_{8}$$ $$a_{9}$$ $$a_{10}$$ 26.1 0.5 + 0.866025i 0.5 − 0.866025i 0 0 2.00000 0 0 −2.50000 + 4.33013i 0 0 0 161.1 0 0 2.00000 0 0 −2.50000 4.33013i 0 0 0 $$n$$: e.g. 2-40 or 990-1000 Significant digits: Format: Complex embeddings Normalized embeddings Satake parameters Satake angles ## Inner twists Char Parity Ord Mult Type 1.a even 1 1 trivial 3.b odd 2 1 CM by $$\Q(\sqrt{-3})$$ 31.e odd 6 1 inner 93.g even 6 1 inner ## Twists By twisting character orbit Char Parity Ord Mult Type Twist Min Dim 1.a even 1 1 trivial 837.2.j.c 2 3.b odd 2 1 CM 837.2.j.c 2 31.e odd 6 1 inner 837.2.j.c 2 93.g even 6 1 inner 837.2.j.c 2 By twisted newform orbit Twist Min Dim Char Parity Ord Mult Type 837.2.j.c 2 1.a even 1 1 trivial 837.2.j.c 2 3.b odd 2 1 CM 837.2.j.c 2 31.e odd 6 1 inner 837.2.j.c 2 93.g even 6 1 inner ## Hecke kernels This newform subspace can be constructed as the intersection of the kernels of the following linear operators acting on $$S_{2}^{\mathrm{new}}(837, [\chi])$$: $$T_{2}$$ $$T_{5}$$ ## Hecke characteristic polynomials $p$ $F_p(T)$ $2$ $$T^{2}$$ $3$ $$T^{2}$$ $5$ $$T^{2}$$ $7$ $$25 + 5 T + T^{2}$$ $11$ $$T^{2}$$ $13$ $$27 - 9 T + T^{2}$$ $17$ $$T^{2}$$ $19$ $$49 + 7 T + T^{2}$$ $23$ $$T^{2}$$ $29$ $$T^{2}$$ $31$ $$31 - 4 T + T^{2}$$ $37$ $$27 - 9 T + T^{2}$$ $41$ $$T^{2}$$ $43$ $$3 - 3 T + T^{2}$$ $47$ $$T^{2}$$ $53$ $$T^{2}$$ $59$ $$T^{2}$$ $61$ $$75 + T^{2}$$ $67$ $$121 - 11 T + T^{2}$$ $71$ $$T^{2}$$ $73$ $$192 - 24 T + T^{2}$$ $79$ $$147 + 21 T + T^{2}$$ $83$ $$T^{2}$$ $89$ $$T^{2}$$ $97$ $$( -14 + T )^{2}$$ show more show less	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9839755296707153, "perplexity": 3763.658535399431}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988923.22/warc/CC-MAIN-20210508181551-20210508211551-00502.warc.gz"}
http://rmenez.es/	# Postgres 102 - Explains and Advanced Features In this tutorial, we’re going to cover some good-to-know Postgres features and tricks for query optimization. The only prerequisite is basic SQL and having Docker/Postgres installed. ## Setting up our environment First things first, let’s make some mock data for us to play around with. We’re going to make a table of domains (e.g. espn.com) and domain categories (e.g. sports publishers): And we’re going to insert some data: Sidenote generate_series is a wonderful little function that does exactly what you think it does. It’s fantastic for making mock data. Next, let’s make a table that connects the two together: Now it’s very easy to get a list of domains in any category: Now let’s make things a little more complicated. Let’s add parent categories so we can get a categories topology. Imagine a “Sports” category that can contain “Football” and “Basketball” categories. To do this, we need a table that defines the parent-child relationships for categories: Okay, so far so good. How can we get a list of domains in parent categories? One option is to do a simple join: However, what if we want the domains of a category and we don’t know if it’s a parent category or not? One possible solution is to both and union the results together: But A) this is super ugly and B) it stops working if our parent categories get parent categories. In other words, we are only solving a graph that’s two layers deep. A better solution is to use something called a “recursive common table expression”. But first, you should first understand a normal “common table expression” (CTE): The with syntax here is the CTE. It’s a useful tool to cache subqueries and often, I find them much cleaner than actual subqueries because you can give them names! A recursive CTE is slightly different because it allows a CTE to iterate on itself: Now our join will work no matter how many layers we have! However, it’s quite a bit of work to write this out every time. If we were using an ORM, we’d be reading a lot of documentation to get this syntax down. To avoid this, we can write a view: The database will pretend this is a table and even join other tables to it! However, be very careful with views because as you add filters and joins, the query planner may be very confused, as we’ll see later. If the data in your view doesn’t change very often, one common tool is a materialized view. Mviews, as they’re common called, allow you to cache the results of the view and only refresh them manually: Keep in mind though: refresh materialized view will block reads. If you add a unique index to your mview (as you should), you can use refresh materialized view concurrently, which will refresh your mview without blocking reads. ## Foreign data wrappers When you have a lot of data, it’s common to split your tables between multiple databases. To simulate this, let’s create another docker instance. This time, we’ll add a “link” so the second docker instance can network to the first. We’ll be using a Postgres extension called postgres_fdw that allows you to communicate to other Postgres instances. There’s a lot of cool Postgres extensions out there: they range from adding different data types to different foreign data wrappers even new storage engines and indices. There are also foreign data wrappers to MySQL, Redis, Dynamo, you name it. ## Optimizing queries Okay, now the fun stuff :). Let’s create a brand_domain_creative table. We use something more-or-less shaped like this table in Moat Pro and it tells us the estimated impressions (score) a creative had on a certain day on a certain domain. Neat! Next we’re going to fill it with ~60M rows of simulated data. This may take a short while. Now we can do queries like “what are the top 10 brands in January for domain 0?” Yikes! Never mind. That’s taking way too slow. Ctrl+C to interrupt the query and get out of there. To see what happened, we can use the explain query. It’ll output the database’s execution plan for running the query: You’ll notice that each step has a cost estimate. Postgres takes statistics about your tables to estimate how long each step would take so it can intelligently choose the optimal strategy. In this case, the statistics are a wee-bit off as it thinks the domain will have ~1500 rows in this date range when in actuality, it’s around 31k. We can tell it to re-analyze its contents via an analyze command: Now our explain looks something like this: Even with more accurate statistics, the database doesn’t have any other option. To execute this query, it needs to go through every single row and do a count. How can we give it a shortcut? An index of course! What is an index? Essentially, think of of it as a glossary for a very large book. If you want to find each page that has the word aardvark, it’s much faster to find the entry in the glossary than to read every page. By default, Postgres indices are b-trees under the hood because they’re very versatile. However, you can choose other index types if you know what you’re doing. Building this index took a long time because the computer had to go through every single data point. When you think about it, two and a half minutes to organize 60M data points sounds pretty great. Dang, computers are cool. Sidenote Why are they called B-trees? Rudolf Bayer and Ed McCreight invented it while working at Boeing, so it could stand for “Boeing”, “Bayer”, or even “balance” tree. McCreight says they couldn’t decide between the options. They couldn’t name it Boeing without lawyers being involved, so the company missed out on some great free advertising. Now let’s try this query again! That was significantly faster. And it’ll be faster if you run it again because of caching: Caching? How does caching work? Well, virtual memory plays the biggest role here, but Postgres has shared_buffers that cache recent information including: • Table data • Indexes • Query execution plans Keeping shared_buffers consistent all of these while writes are coming in is some serious voodoo magic, so if you see a Postgres contributor, buy them a beer. Let’s see how our query was faster via an explain analyze. explain analyze is like an explain but it also runs the query to give you more information. verbose and buffers give you debug information about each step. Let’s interpret this explain from inside out. • “Bitmap index scan”: our index is large enough to take up several blocks. Because of the way B-Trees work, we can make a map that can tell us which blocks contain indices that match our conditions. The resulting array of booleans is our bitmap. We then use this bitmap to read the relevant index blocks and collect all the indices that match our conditions. This took 1.27s. • “Bitmap heap scan”: Armed with our indices, we create a bitmap of heap blocks to read and then we read them. This took almost no time at 0.16s and resulted in 31k rows. • “Sort”: Looks like Postgres is sorting the rows with quicksort to make it easier to… • “GroupAggregate”: Group the rows together by brand_id and sum the scores (334 resulting rows). • “Sort”: Sort our grouped rows based on sum(score) DESC using top-N heapsort • “Limit”: limit our results from 100 to 10. Sidenote Quicksort is in-place, so it makes sense they chose that for 31k rows. Top-N heapsort is a sort where you only keep the Top-N, which is significantly less complex. It only makes sense if you do a limit after your sort. Can we do better? Sure! Seems like the slow part is getting stuff from the index. We have to read 118k buffers here and only 31k buffers to actually get the data (gee, I’m starting to suspect our buffers are exactly 10k rows each). Why does does index need to read so many blocks? Well, it’s because of the shape of our index. Our index looks like this: (start_date, domain_id, brand_id, creative_id). This means if you ordered our index in a list, it would look like this: So in every 1M index entries, only 1k of them are relevant to our query at hand. Thus, we can assume that we have to read a lot of different index blocks to collect our heap. What happens if we make a new index organized by (domain_id, start_date)? Then our index blocks are significantly closer together and our b-tree doesn’t have to make keys for creative_id/brand_id. Great Neptune’s trident, that was fast! Let’s see how things changed: As expected, we got our rows out significantly faster (144ms). Interestingly, the DB switched from a GroupAggregate to a HashAggregate even though the only step that should have been affected was the index scan. Databases are mysterious beasts. In this case, it bought us 2ms. Huzzah! Sidenote Another common reason for slow Bitmap Index Scans is a lack of vaccuuming. By default, Postgres keeps old versions of rows arounds for MVCC (Multi-version consistency control) and they can remain in your index as well. vaccuum frequently, kids. ## Performance tuning Let’s try another query: what are brands that have appeared on the most domains? Yikes. This is going to be slow again. Our indices can only eliminate half of our dataset. What can we do? One solution is to have a (start_date, brand, domain) index. Maybe this way, Postgres doesn’t need the actual rows to perform the query: Programmer uses index! It’s not very effective! Whoa, wtf? Why is it doing a sequential scan on the rows? Even an analyze doesn’t change this. If it used the index, it would go through 31 (days) * 334 (brand) * 1000 (domain) = 10.354M index entries. That’s 60 times fewer than going through 600M rows! Well, the difference is that index disk access is random whereas the sequential scan is, well, sequential. The optimizer gives random reads an estimated random_page_cost cost of “4” by default. And keep in mind that reading one index block involves reading a number of other index blocks because that’s how b-trees work. But wait! My computer has an SSD! Shouldn’t they be weighed the same? Well, you can tune that in your Postgres config by changing random_page_cost to 1 :). Or, you can do it temporarily in your session: Wtf Rodrigo? You lied! It’s still doing a sequential scan! Well, as a hack, if you set seq_page_cost to 9999, you can see what its index plan would look like: Huh, so the database doesn’t have a method to do an index scan and do a GroupAggregate at the same time! So it’s forced to to index scan for 31M entries! Maybe there’s a good reason for that - database programming is hard because there’s a ton of corner cases. If you want to research it, pull requests are welcome ;). ## Pre-aggregation First, let’s set our seq_page_cost back to normal: So how can we make the above query faster? Well, if it’s dedicated to doing a sequential scan, we can simply give it less rows! In this query, we don’t need the creative column. So what if we removed it and rolled up all the creative scores into brands? The contents of this table are ~3x smaller! So it makes sense that our query time went down by that much. And what happens if we add an index? Well, now we get out 10M row method :). But here’s one more optimization we can do! We reduced brand_domain_creative to brand_domain and in our business logic, we frequently do month long queries. What happens if we rollup if start_date to the nearest month? Now, this query turns into: Woosh! The moral of the story here is, you can learn to be a database whisperer, but normally the simplest approach (pre-compute as much as you can) is the right answer. However, every neat trick in CS comes at a cost and pre-aggregation is no exception. Specifically: • Disk space • Compute time • Out of sync tables One last thing: what if you have a query where you want to see the brands with the most domains from ‘2017-01-25’ to ‘2017-02-28? In this case, the optimal query involves getting the daily rows from brand_domain and the monthly rows from monthly_brand: Pretty freakin’ fast. In Moat Pro, we have every cut imaginable, from brand to monthly_creative_hostname to alltime_tag_brand_creative. We have a query engine that choose the right cuts and aggregates their results together. # An Introduction to Linear Regression In this post, we will be using a lot of Python. All of the code can be found here. We’ll be using data from R2D3, which contains real estate information about New York City and San Francisco real estate. ## Regression One of the most important fields within data science, regression is about describing data. Simply put, we will try to draw the best line possible through our data. First, an example. Let’s plot some New York City apartments’ prices by square foot: As you can see, there’s a bit of bunching up in the lower left corner because we have a bunch of outliers. Let’s say any apartment over 2M or 2000 square feet is an outlier (although, I think this is our dataset showing it’s age…). Okay, so we can notice a couple things about this data: • There’s a minimum number of square feet and price. No one has an apartment smaller than 250 square feet and no one has a price lower than 300K. This makes sense. • The data seems to go in a up-right direction, so we more or less draw a line naively if we tried. • As we go along the axes, the data spreads. There must be other variables at work. ### Drawing our line Let’s try to draw the best straight line we can though the data. This is called linear regression. So our line is going to have the familiar-looking formula: \begin{align} h_\theta(x) = \theta_0 + \theta_1 x \end{align} Whereh_\theta(x)$is our hypthesis$h$of the price given a square foot of$x$. Our goal is to find our$\thetas, which define the slope and y-intercept of our line. So how do we define the best line? Through an cost function, which defines how off a line is! The line with the least cost is the best line. Okay, so how do we choose an cost function? Well, there’s a lot of different cost functions out there, but least squares error is perhaps the most common: \begin{align} J(\theta) = {1 \over 2} \sum_{i=0}^n (h_\theta(x_i) - y)^2 \end{align} Essentially, for each data point(x_i, y_i)$, we’re simply taking the difference between$y_{i}$and$h_\theta(x_i)$and squaring it. Then we’re summing them all together and halving it. Makes sense. ### Gradient Descent Okay, so now the hard part. We have data and a cost function, so now we need a process for reducing cost. To do this, we’ll use gradient descent. Gradient descent works by constantly updating any$\theta_j$in the direction that will dimension$J(\theta). Or: \begin{align} \theta_j := \theta_j - \alpha {\delta \over \delta \theta_j} J(\theta) \end{align} Where\alpha$is essentially “how far” down the slope you want to go at every step. Thus, with a little bit of math, we can find the derivative of our$\theta_j$with respect to$J(\theta)for an individual data point: \begin{align} {\delta \over \delta \theta_j} J(\theta) &= {\delta \over \delta \theta_j} {1 \over 2} (h_\theta(x) - y)^2 \cr &= 2 \cdot {1 \over 2} \cdot (h_\theta(x) - y) \cdot {\delta \over \delta \theta_j} (h_\theta(x) - y) \cr &= (h_\theta(x) - y) \cdot {\delta \over \delta \theta_j} (h_\theta(x) - y) \end{align} Now things begin to diverge for our\thetas: \begin{align} {\delta \over \delta \theta_0} J(\theta) &= (h_\theta(x) - y) \cdot {\delta \over \delta \theta_0} (\theta_0 + \theta_1 x - y) \cr &= (h_\theta(x) - y) \end{align} \begin{align} {\delta \over \delta \theta_1} J(\theta) &= (h_\theta(x) - y) \cdot {\delta \over \delta \theta_1} (\theta_0 + \theta_1 x - y) \cr &= (h_\theta(x) - y) \cdot x \end{align} So now we can apply our derivatives to the original algorithm… \begin{align} \theta_0 := \theta_0 + \alpha (y - h_\theta(x)) \cr \theta_1 := \theta_1 + \alpha (y - h_\theta(x)) \cdot x \end{align} However, this only applies to one data point. How do we apply this to multiple data points? ### Batch Gradient Descent The idea behind batch gradient descent is simple: go through your batch and get all the derivatives of{\delta \over \delta \theta_0} J(\theta). Then take the average: \begin{align} \theta_0 := \theta_0 + \alpha \sum_{i=0}^m (y - h_\theta(x)) \cr \theta_1 := \theta_1 + \alpha \sum_{i=0}^m (y - h_\theta(x)) \cdot x \end{align} This means that you only change your theta at the end of the batch: This results in: Pretty good! The code completes in 316 iterations, an error of 65662214541.7 and estimates\theta_0$to be 80241.5458922 and$\theta_1to be 1144.09527519. ### Stochastic Gradient Descent Another way to train our data is to apply our changes to each data point individually. This is stochastic gradient descent: \begin{align} \theta_0 := \theta_0 + \alpha (y - h_\theta(x)) \cr \theta_1 := \theta_1 + \alpha (y - h_\theta(x)) \cdot x \end{align} It has one big benefit: we don’t have to go through the entire batch. This is hugely important for problems with large, large datasets. You’ll see it used frequently in deep learning. It’s worth noting that this took longer than batch descent since our dataset is so small. Also, we had to loosen up the right answer since we oscillated around the error a lot more. We would oscillate a lot less if it weren’t for the randomness! There are in-betweens like mini-batch gradient descent, where you randomly turn your large dataset into small batches. This is hugely useful if you’re doing regression across multiple machines! ### Multivariate Linear Regression Okay, now things start to get fun. At the moment, we’re dealing with one input dimension (AKA “Simple” Linear Regression), which is great for getting started, but most datasets have more than one dimension. We can generalize our algorithm using linear algebra. First, let’s say that we haven$dimensions. Thus, when we treat every input$x$as a vector, we get: $$\overrightarrow{x}^{(i)} = \begin{bmatrix} x^{(i)}_1 \cr x^{(i)}_2 \cr \vdots \cr x^{(i)}_n \cr \end{bmatrix}$$ We can generalize our$m$number of training vectors to be: $$X = \begin{bmatrix} — (\overrightarrow{x}^{(1)})^T — \cr — (\overrightarrow{x}^{(2)})^T — \cr \vdots \cr — (\overrightarrow{x}^{(m)})^T — \cr \end{bmatrix}$$ And our answers,$y$, can be a vector as well: $$\overrightarrow{y} = \begin{bmatrix} y^{(1)} \cr y^{(2)} \cr \vdots \cr y^{(m)} \cr \end{bmatrix}$$ And our parameters as well: $$\overrightarrow{\theta} = \begin{bmatrix} \theta_{1} \cr \theta_{2} \cr \vdots \cr \theta_{n} \cr \end{bmatrix}$$ We’re losing our “error” parameter of$\theta. If you really want it, you can simply add a “1” column to each datapoint and that’ll accomplish the same thing and allow us to simplify our math and code a bit. So our hypothesis for an individual data point looks like: \begin{align} h_\theta(\overrightarrow{x}^{(i)}) = (\overrightarrow{x}^{(i)})^T \cdot \overrightarrow{\theta} \end{align} So going back to our cost function, which we can put in matrix form: \begin{align} J(\theta) &= {1 \over 2} \sum_{i=0}^n (h_\theta(\overrightarrow{x}^{(i)}) - y^{(i)})^2 \cr &= {1 \over 2} (h_\theta(X) - \overrightarrow{y})^T(h_\theta(X) - \overrightarrow{y}) \cr &= {1 \over 2} (X \cdot \overrightarrow{\theta} - \overrightarrow{y})^T(X \cdot \overrightarrow{\theta} - \overrightarrow{y}) \end{align} So if we wanted to find the derivative ofJ(\theta)$now (aka$\nabla_{\theta}J(\theta)), we’d have to do some funky math. If you want to read how it can be derived, I recommend reading page 11 of Andrew Ng’s lecture notes on Linear Regression. Skipping to the answer, we get: \begin{align} \nabla_{\theta}J(\theta) &= X^T(X \cdot \theta - \overrightarrow{y}) \end{align} And thus, we can create steps for our\overrightarrow{\theta}: \begin{align} \overrightarrow{\theta} := \overrightarrow{\theta} + \alpha X^T(\overrightarrow{y} - (X \cdot \theta)) \end{align} This kind of looks like our step for\theta_1not too long ago! \begin{align} \theta_1 := \theta_1 + \alpha (y - h_\theta(x)) x \end{align} ### Programming this in numpy We get a slightly different answer here than in our old batch gradient descent code because our y-intercept has a different learning rate. If we gave it enough repititions, it would eventually get near the same area. Of course, there are plenty of high level ML libraries to explore that do this stuff for you! However, it’s fun to understand what’s happening under the hood. ### Things to worry about Multivariable linear regression with gradient descent can have a lot of complications. For example, local minima: As you can see, gradient descent might accidentally think the minimum is in the saddle there. There’s a ton of interesting papers about this. Training multiple times with different starting parameters is one way around this. Overfitting is also an issue: You can avoid this by splitting your data into a large “training” set and a large “testing” set. That’s standard procedure in most data science problems. ### One last method: using the derivative As many of you know, if you set the derivative of a curve to 0, it’ll either be a local maxima or a local minima. Since our error function does not have an upper limit, we know that the point where the derivative is 0 is a local minima. So we can make our derivative\nabla_{\theta}J(\theta)zero: \begin{align} \nabla_{\theta}J(\theta) &= X^T(X\theta - \overrightarrow{y}) \cr 0 &= X^T(X\theta - \overrightarrow{y}) \cr X^TX\theta &= X^T\overrightarrow{y} \cr \theta &= (X^TX)^{-1}X^T\overrightarrow{y} \end{align} And we can throw it in our code: And it totally works! You may ask “but why did we learn all about the gradient descent stuff then”? Well, you’ll need it for things that aren’t as straight forward as linear regression like deep neural networks. ### To learn more: Andrew Ng’s notes on Linear Regression. ML @ Berkeley’s Machine Learning Crash Course. # How to Docker For Great Good ## What is Docker? Docker is a container system. It allows you to run code in a predefined environment that will Run Anywhere™. So how is it different from a virtual machine? To start a VM, you allocate resources (X bytes of memory, Y CPU cores, etc) and these allocations are absolute. That is, if the VM only needs half its allocated memory or just a few CPU cycles, you can’t remove/add it dynamically. That creates a lot of waste! It means that your services always use their maximum number of resources. In addition, you have the overhead of emulating their operating system and their hardware. For the most part, as developers, we really want only a few things: • Make sure processes can’t affect the host operating system. We want our containers to be a jail. • Make sure processes can’t affect one another. So give me isolated memory addresses and file systems. • Give me hard memory/CPU limits, so only use what you need until a certain limit to make sure it doesn’t affect other processes. That’s containers in a nut shell. Essentially Docker provides this by using: • cgroups: A Linux kernel feature that isolates and limits the resource usage (CPU, memory, disk I/O, network, etc.) of a collection of processes. • apparmor: A Linux security module that allows you to restrict per-program network access, raw socket access or file path access. • aufs (Another Union File System): Imagine a file system that works off of diffs. So every single change is just a diff layered on top of an existing file system. It allows you to “fork” other containers very easily. • Many more cool Linux modules and features This is why Docker originally could only run on Ubuntu. Only recently can you run it on OSX/Windows without VirtualBox! Downsides: • Difficult to get it working natively on host OSs • Security issues • Limited OS choice. (All official Docker images are using Ubuntu distro. Soon they’ll use Alpine Linux) ## Actually using Docker Okay, so first you need to install Docker. This installs the Docker daemon which controls all of the containers running on your computer. Assuming your Docker daemon is running, you can now pull the base Ubuntu image: Images are snapshots of a filesystem. You can push/pull images from a central repository. Docker, being a private company, made the default repo for pulling its own servers. You’ll learn how to push/pull from private container repos later. Now, we can use the base Ubuntu image to run a command: That was really fast (slightly longer than a second for me)! So what happened? • The Docker CLI parsed our command a realized that we wanted to run “echo ‘hello’” on the Ubuntu image. It passes that information to the Docker daemon. • The Docker daemon started a process with all of the voodoo magic that isolates it. • It made sure that the process had access to a file system that we pulled (the Ubuntu image). • That process ran our echo 'hello' command We can run any other bash command! For example, we could use ls to explore the filesystem. Neat, right? So it feels like an actual Linux virtual machine! What if we want to actually use bash within the container? We can use the ‘-i’ (interactive, keeps STDIN open) and ‘-t’ (pseudo-tty) options: ## Pulling a prebuilt image and advanced options Now we can have some fun. First, let’s pull the official Docker image for Redis: Now we can run Redis: You can see our currently running containers: And you can stop a running container: It worth mentioning that docker keeps old containers around! For example: This means two things: 1. Docker takes up more and more space. Use docker rm(docker ps -a -q). 2. If you assign a name to docker containers during run, you might see a name conflict. So use --rm ## Making our own Docker container Okay, now things can start to get fun. Let’s say we want to make a Docker container that runs a little flask app. First, let’s make a directory called test-app and make ourselves a little app: Next, let’s make a Dockerfile. Dockerfiles are files that define a container. They use some set commands defined by Docker: It’s worth mentioning that we’re using the offical “Python” image as our base. This installs pip and other goodies for us. So now we can build our actual Docker image: You’ll notice that after each command, it makes an intermediate container. Remember: Docker uses AUFS. As you customize your container instances’ file paths, your changes will be layers on top of this base image. Also, we ran with a -t option. This “tags” our container so we can reference it more easily. We can see it here: Now we can run it: To make a change, simply run docker build again! But that’s an annoying dev cycle… Okay, let’s say we want our Docker container to link to our host file system: Ka-pow! Volumes are layer on top of a container, which means that we overwrite the previous version of app.py. Now let’s try to make our Flask app talk to Redis. First let’s run a redis container: Cool, now let’s change app.py to talk to redis. First add the pip install for python-redis in our Dockerfile: Then we build it again: Then we run our Docker container while linking to the existing redis container: Now we can change our app.py to talk to redis: ## docker-compose Some people realized that all of this Docker stuff could be made simpler so they made a Python library to do that called “fig”. It was so successful that it became part of docker as “Docker Compose”. Essentially, it allows you to run several Docker containers at once: Now we can run docker-compose up and everything will be running. ## Docker in production Docker containers are powerful for development, but they’re a really powerful idea for deployment as well for a couple reasons: 1. Allows you to make micro-services super easily 2. Very easy clustering (docker-swarm, ECS, Kubernetes) 3. Easy ops: blue-green deployment and rollbacks are easy 4. Autoscaling There’s still no “set” way of doing things, so here’s an example of a task definition in ECS: “””json { “family”: “logstash-production”, “networkMode”: “bridge”, “containerDefinitions”: [ { “name”: “logstash”, “image”: “317260457025.dkr.ecr.us-east-1.amazonaws.com/search/logstash:1.0.1”, “cpu”: 512, “memory”: 1000, “essential”: true, “command”: [“-f”, “/src/logstash.production.conf”], “logConfiguration”: { “logDriver”: “awslogs”, “options”: { “awslogs-group”: “logstash-production”, “awslogs-region”: “us-east-1” } } } ], “placementConstraints”: [], “volumes”: [] } “”” And the work flow is simply: • Build your image: docker build -t $ECR_URL/<my_role_name>:VERSION . • Push your image to ECR: docker push$ECR_URL/<my_role_name>:VERSION • Update your task definition: aws ecs register-task-definition --cli-input-json file://production.json • Tell your AWS cluster to use the new task definition (either in the UI or the CLI). It comes with a couple headaches: • Making security definitions and IAM roles • Making your actual cluster instances (different IAM role for this!) • Why on earth aren’t there CNAMEs for ECR urls? Odds are, you know about Python lists and dicts. But there’s a couple other really useful ones out there. ### Tuples Most of you have heard of this. Tuples are immutable collections - once you make them, you can’t change them. Why are tuples useful? Two reasons: 1. Immutability is good sometimes 2. It saves space. ### Sets Sets are kind of like dictionaries without values. They work the same way under the hood (with a hashmap) but keys don’t store anything. It’s very useful to keep track of unique things that happen. You can also use frozenset, which is immutable like a tuple. ### collections The collections library has a bunch of useful ones: • namedtuple() - make a tuple with predefined named fields. Great for things like SQLAlchemy rows. • deque - a simple Python queue • Counter - counts things. Kind of like a set for counting. • OrderedDict - dict that remembers order • defaultdict - you can define a default thing to get in your dictionary ### Generators They’re pretty great: Generators start again at the previous place when their called again. If the generator function actually returns, it raises a StopIteration and the generator is done. They’re good because they don’t require much memory. That’s why they recommend you use xrange instead of range. This is cool: This is cooler: This is coolest: ## Comprehensions List/dict/tuple/set comprehensions are amazing. Want to make a simple list? Easy. And you can add filters: And do double loops! Neat-o gang. It saves a lot of LOC. I use it frequently in API calls to generate JSON blobs. See? Now they don’t look so scary. ## Common Python gotchas Credit for most of this section goes to the Python Guide. ### Mutable default arguments This is a classic Python interview question by pedantic people. What do you think will happen when I run this? Huh? Not what you expected right? Remember that functions are made before the code gets run. So the same list stays. Instead of that, you should always do: Don’t use mutable objects as default values (dicts, lists, etc). You can use strings and ints because they aren’t mutable. ### Closures are weird Here, we make lambdas in the comprehension: You’d expect the result to be 0,2,4,6,8 but you actually get 8,8,8,8,8! Why? Because the closure is generated at run time and we leave our loop with i as 8. After all, you’d expect this: To print 2, correct? Instead of this, use default values: ### Classes inheritance is weird This one comes from Martin Chikillian. Sure. K. Wat? When you reference an object’s attribute, it’ll first try to get it from its own definition. After that, it’ll go up and get it from its parents. This is called “Method Resolution Order (MRO)”. ### Local/global variables are weird The moment you assign something, it creates it in the local scope. So a += 1 turns into a = a + 1 and it doesn’t know what the second a is. To do this properly: ### is vs == Remember: is will only be true if two things are the same object. == will call the object’s __eq__ method, which you can override: There are a ton of other magic functions like __le__, __lte__, __add__ that affect other operators like <, <=, +. ## iPython is great It remembers your history, does tab completion, give information about objects, has magic pasting. It even has magic functions like %timeit: Or %run, which runs external scripts. ## Context Managers Context managers are cool if you need to make sure something gets cleaned up: You can do other cool things with contextlib: ## List slicing and dicing Python’s slice notation is the bomb. Get the last element by using -1: mylist[-1]. You can also get slices this way: mylist[0:5] or mylist[:5] or mylist[5:]. You can even define the “jumps”: myrange(10)[::2] gets even numbers. A good trick to reverse lists is to do myrange(10)[::-1] (although you should probably use reversed() instead!). ## args and kwargs and splat * is called the “splat” operator. Use it for making functions that take multiple things: Or use it for the opposite: ## itertools.chain I love itertools. Very handy library. Combine iterables: Use group by: Combinations and permutations (great for tests): ## zip Handy for combining lists for iterating: ## Decorators are great Wrap your functions! Here’s a decorator that makes sure a view is only useable if the user is logged in: ## Best Python -m tools: A lot of handy tools out there. -m runs the main function of a module. Here’s a good list. Some highlights: ### SimpleHTTPServer Handy for making a quick HTTPServer: python -m SimpleHTTPServer 8000 ### json.tool Handy for pretty printing: echo '{"greeting": "hello", "name": "world"}' \| python -m json.tool ## Gzip python -m gzip [file] # compress python -m gzip -d [file] # decompress ### antigravity python -m antigravity ### this python -m this # Hello World I’ve started and abandoned many blogs in the past. Over time, most of them fizzeled out because I thought that I didn’t have anything worth writing. If it wasn’t original, I reasoned, I wouldn’t be worth my time to write and worth the time of others to read. Turns out, that’s a crappy approach to writing because you never get better that way. Quantity generate quality in the long run. So, I’ve created this blog with a completely different goal in mind: write as often as possible, even if I’m writing about something pretty stupid. I think there’ll be other benefits: 1. Hopefully, I’ll learn to become more succinct in real life. I ramble a lot when speaking and it doesn’t make me the best communicator. 2. In learning to write more clearly, maybe I’ll learn to think more clearly. It’s possible that good communication is just a symptom of a well-organized mind. 3. Having a written record of things my thoughts and opinions sound like it’ll be nice in a few years [1]. 4. Writing teaches empathy. The best writers make sure there is no ambiguity by placing themselves in the position of the reader. Understanding others is a skill that makes you more successful in, I believe, almost every field imaginable. Let’s see how far this goes! [1] As a kid, I used to hate being photographed. It seemed forced to me. However, as I’ve grown older, I often wish I had more pictures.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5540421009063721, "perplexity": 2424.45159058557}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376828056.99/warc/CC-MAIN-20181217020710-20181217042710-00349.warc.gz"}
http://michaelnielsen.org/polymath1/index.php?title=Higher-dimensional_Fujimura&diff=next&oldid=1268	# Difference between revisions of "Higher-dimensional Fujimura" Let $\overline{c}^\mu_{n,4}$ be the largest subset of the tetrahedral grid: $\{ (a,b,c,d) \in {\Bbb Z}_+^4: a+b+c+d=n \}$ which contains no tetrahedrons $(a+r,b,c,d), (a,b+r,c,d), (a,b,c+r,d), (a,b,c,d+r)$ with $r \gt 0$; call such sets tetrahedron-free. These are the currently known values of the sequence: n 0 1 2 3 4 5 6 7 $\overline{c}^\mu_{n,4}$ 1 3 7 14 24 37 55 78 ## n=0 $\overline{c}^\mu_{0,4} = 1$: There are no tetrahedrons, so no removals are needed. ## n=1 $\overline{c}^\mu_{1,4} = 3$: Removing any one point on the grid will leave the set tetrahedron-free. ## n=2 $\overline{c}^\mu_{2,4} = 7$: Suppose the set can be tetrahedron-free in two removals. One of (2,0,0,0), (0,2,0,0), (0,0,2,0), and (0,0,0,2) must be removed. Removing any one of the four leaves three tetrahedrons to remove. However, no point coincides with all three tetrahedrons, therefore there must be more than two removals. Three removals (for example (0,0,0,2), (1,1,0,0) and (0,0,2,0)) leaves the set tetrahedron-free with a set size of 7. ## General n A lower bound of 2(n-1)(n-2) can be obtained by keeping all points with exactly one coordinate equal to zero. You get a non-constructive quadratic lower bound for the quadruple problem by taking a random subset of size $cn^2$. If c is not too large the linearity of expectation shows that the expected number of tetrahedrons in such a set is less than one, and so there must be a set of that size with no tetrahedrons. However, $c = (24^{1/4})/6 + o(1/n)$, which is lower than the previous lower bound. With coordinates (a,b,c,d), consider the value a+2b+3c. This forms an arithmetic progression of length 4 for any of the tetrahedrons we are looking for. So we can take subsets of the form a+2b+3c=k, where k comes from a set with no such arithmetic progressions. [This paper, Corollary 1] gives a complicated formula for a lower bound on the proportion of retained points: $C\frac{(log N)^{1/4}}{2^\sqrt{8 log N}}$, for some absolute constant C. An upper bound can be found by counting tetrahedrons. For a given n the tetrahedral grid has n(n+1)(n+2)(n+3)/24 tetrahedrons. Each point on the grid is part of n tetrahedrons, so (n+1)(n+2)(n+3)/24 points must be removed to remove all tetrahedrons. This gives an upper bound of (n+1)(n+2)(n+3)/8 remaining points.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9697526097297668, "perplexity": 499.68479736690887}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540510336.29/warc/CC-MAIN-20191208122818-20191208150818-00269.warc.gz"}
http://mathoverflow.net/questions/88408/is-a-reduced-torsion-free-module-of-finite-rank-over-an-henselian-ring-free/88411	# Is a reduced, torsion-free module of finite rank over an Henselian ring free? Let $R$ be an Henselian discrete valuation ring with field of fractions $K$. Let $M$ be a torsion-free $R$-module of finite rank (i.e. $dim_K(M\otimes_RK)<+\infty$). Let $D$ be the maximal divisible $R$-submodule of $M$, then $M$ is said to be reduced if $D=0$. If I am not wrong if $M$ is reduced, of finite rank and torsion free, then $M$ is free when $R$ is complete. Is the same true if $R$ is only Henselian? What if $R$ is any discrete valuation ring? - in fact when $R$ is complete, $M$ must even be finitely generated. – Konstantin Ardakov Feb 14 '12 at 8:36 Sorry, when I say that I want to prove that $M$ is free I mean "free and finitely generated". Is that what you mean? – Federigo Feb 14 '12 at 8:52 No. "Free" means a direct sum of (possibly infinitely many) copies of $R$. I meant that if your ring $R$ is complete, then not only is it true that any $M$ satisfying your conditions is free, but in fact it must also be finitely generated and free, i.e. a direct sum of finitely many copies of $R$. Given $M$ is free (this is not totally trivial), that $M$ is finitely generated follows trivially from the assumption that your $M$ has finite rank. Anyway, a-fortiori gave you exactly the counterexample you need below. – Konstantin Ardakov Feb 14 '12 at 9:10 Yes yes...that's what I meant!!! So I understood clearly from the beginning and that's what my question was asking even if not specified, thank you! The book in the library has been taken by someone else ... I have to wait ... – Federigo Feb 14 '12 at 9:44 Theorem 19 in Kaplansky's Infinite Abelian Groups gives an example of a torsion-free, reduced, indecomposable rank 2 module for any incomplete discrete valuation ring. In short, the construction is as follows: choose $\lambda\in\hat R\setminus R$. This induces a homomorphism $\tilde\lambda\colon K\to\hat R/R$. The short exact sequence $0\to R\to\hat R\to\hat R/R\to 0$ induces an injection $\mathrm{Hom}(K,\hat R/R)\to\mathrm{Ext}^1(K,R)$. The image of $\tilde\lambda$ under this injection corresponds to the desired rank 2 module $M$ sitting in a non-split extension $0\to R\to M\to K\to 0$. Any divisible element would induce a splitting, so $M$ is reduced. Since there is no surjection $R^2\to K$, the module $M$ cannot be free. - Do you mean example of a torsion-free, reduced, indecomposable rank 2 module which is "not free"? Anyway... thank you, I'll check on this book. That's probably the reference I needed. – Federigo Feb 14 '12 at 8:37 Again, when I say that I want to prove that $M$ is free I mean "free and finitely generated". Sorry, but I think you understood. Ok, let me go to the library... – Federigo Feb 14 '12 at 8:46 Indeomposable of rank 2...yeah... I understand :-) – Federigo Feb 14 '12 at 10:06 Let $A$ be a local ring. Let $M$ be a finitely generated flat $A$-module. Then $M$ is free; see Theorem 1.2.16 in http://ukcatalogue.oup.com/product/9780198502845.do I am not assuming $M$ to be finitely generated, but only of finite rank. – Federigo Feb 14 '12 at 7:57 When I say that I want to prove that $M$ is free I mean "free and finitely generated". Sorry. – Federigo Feb 14 '12 at 8:45	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9238749742507935, "perplexity": 319.4013125059409}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-52/segments/1419447554236.61/warc/CC-MAIN-20141224185914-00095-ip-10-231-17-201.ec2.internal.warc.gz"}
https://robotics.stackexchange.com/questions/8973/how-to-estimate-the-position-of-multiple-static-ground-targets-captured-from-a-d	How to estimate the position of multiple static ground targets captured from a down facing camera? An aerial vehicle captures images of the ground using its down facing camera. From the images, multiple targets are converted from their pixel position to the camera reference frame using the pinhole camera model. Since the targets are static and there is information of the vehicle attitude and orientation, each sample is then converted to the world referencial frame. Note that all targets are on a flat, level plane. The vehicle keeps "scanning" for the targets and converting them to the world referencial frame. Due to the quality of the camera and detection algorithm, as well as errors on the altitude information, the position of the "scanned" targets is not constant (not accurate). A good representation might be a gaussian distribution around the target true position, however it will also be influenced by the movement of the aerial vehicle. What's the best approach to estimate the position of the targets from multiple readings? This basically resumes to a problem of noise removal (as well as outlier removal) and estimation, so I would like to know what algorithms and strategies could solve the problem. In the end I expect to implement and test a collection of different approachs to understand their performance on this specific problem. Furthermore, this system is implemented using ROS, so if you know of packages that already do what I'm searching for I would be glad to hear. You can also cite papers on the topic that you think might be of my interest. • I voted to close this because it's an unbounded design problem (you don't have a problem, you're just looking for advice). That said, the key phrase that I think will get you started is called structure from motion. Basically, the pixel location only corresponds to an angle based on the camera transform. You need to know angle and depth to get a real x/y coordinate. Jan 22 '16 at 22:25 • The problem I need resolved is one of noise removal and estimation of multiple signals at the same time. I'm searching for help on resolving that issue, don't get why you call it an unbounded design problem. And what you proposed is actually the part that I already solved since I wrote that I already converted the position of the target in order to the world referencial frame. Jan 23 '16 at 12:23 • Can you please revise your question to include how you are currently getting measurements? The way that I had read your question, I thought you had an aerial vehicle with known X/Y/Z/$\theta$ and a camera, and with nothing else and only 1 frame you were trying to determine the X/Y/Z of ground targets, which isn't possible unless you have more information. What method are you using to determine ground coordinates? What kind of noise or measurement error are you seeing? Jan 24 '16 at 0:10	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.17847982048988342, "perplexity": 494.50878650382805}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585181.6/warc/CC-MAIN-20211017175237-20211017205237-00083.warc.gz"}
https://economics.stackexchange.com/questions/8833/what-is-the-purpose-of-the-local-non-satiation-assumption-in-the-first-welfare-t	# What is the purpose of the local non-satiation assumption in the first welfare theorem? The profit maximization assumption implies $$\text{if } x_i \succ x_i^* \text{ then } p_ix_i > p_i w_i$$ Okay so this just says if the agent is utility maximizing / rational, then if he doesn't choose a bundle strictly preferable to his bundle then it must not be affordable. Why is the local non-satiation assumption needed to then say $$\text{if } x_i \succeq x_i^* \text{ then } p_ix_i \geq p_i w_i$$ Why isn't this just automatic from the profit maximization assumption? If we know $x_i \succ x_i^* \implies p_ix_i > p_i w_i$, isn't it obvious that $x_i = x_i^* \implies p_ix_i = p_i w_i$ and so $$\text{if } x_i \succeq x_i^* \text{ then } p_ix_i \geq p_i w_i$$ The assumptions are different. First one states that if a bundle is better than the optimal one the consumer cannot afford it. The second one states that if a bundle is as good (not necessarily better) than the optimal one it has to cost as least as much, not less. Consider a space with just one type of good, $x$, and a utility function $U(x) = 0$. Let the endowment of the consumer be $w = 1$. While $$\text{if } x_i \succ x_i^* \text{ then } p_ix_i > p_i w_i$$ is still true, $$\text{if } x_i \succeq x_i^* \text{ then } p_ix_i \geq p_i w_i$$ isn't, because $x^* = 0$ is both optimal and feasible, thus $$x^* \succeq x^* \text{ AND } p x^* < p w.$$ More complicated examples (multiple goods, global non-satiation fulfilled) may also be constructed. • The math isn't helping me understand this. How would local satiation prevent a market from reaching a pareto optimal state? – B T Mar 27 '16 at 3:28 • @BT You have posted your own question about that, haven't you? – Giskard Mar 27 '16 at 5:50 • Well, I posted a question about the conditions under which the equilibrium is guaranteed to be pareto optimal. The answer involves local satiation as a condition, but the question didn't explicitly ask why it was a condition, and this one does. – B T Mar 27 '16 at 6:04 • I think the problem is this example doesn't explain what local nonsatiation is or why its needed. Rather, it instead provides an example for why utility maximizing doesn't imply the second claim is necessarily true. I would have preferred something explaining exactly what local nonsatiation provides that resolves the situation...which is what the title asks. But it is nonetheless a very clever example – Stan Shunpike Mar 27 '16 at 6:54 • @StanShunpike It is unfortunate that - if I understand you correctly now - the title and the body of the question are very different. It is also unfortunate that you did not comment when I answered the question 5 months ago... – Giskard Mar 27 '16 at 7:49 Ok I think I might understand now why local nonsatiation is important for tending toward a pareto optimal market allocation. Consider the following picture, where all the circles represent possible allocations, and their position on the graph represents the utility received by each person in a simple two-person market: In this case, X, Y, Z, and D all give person 1 the same utility. In such a situation, X, Y, and Z are all possible equilibria given complete markets and price taking behavior even though they're not pareto-optimal. In a situation with local nonsatiation, this situation couldn't exist, and thus a pareto optimal equilibrium is ensured. Weak pareto optimality doesn't require local non-satiation.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8095216751098633, "perplexity": 675.5881205709848}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574039.24/warc/CC-MAIN-20190920134548-20190920160548-00054.warc.gz"}
https://codegolf.stackexchange.com/questions/82938/golf-all-the-16-logic-gates-with-2-inputs-and-1-output/83093	# Golf all the 16 logic gates with 2 inputs and 1 output! For example, the gate A and B is a logic gate with 2 inputs and 1 output. There are exactly 16 of them, because: • each logic gate takes two inputs, which can be truthy or falsey, giving us 4 possible inputs • of the 4 possible inputs, each can have an output of truthy and falsey • therefore, there are 2^4 possible logic gates, which is 16. Your task is to write 16 programs/functions which implement all of them separately. They are valid as long as they output truthy/falsey values, meaning that you can implement A or B in Python as lambda a,b:a+b, even if 2 is produced for A=True and B=True. Score is total bytes used for each function/program. ## List of logic gates 1. 0,0,0,0 (false) 2. 0,0,0,1 (and) 3. 0,0,1,0 (A and not B) 4. 0,0,1,1 (A) 5. 0,1,0,0 (not A and B) 6. 0,1,0,1 (B) 7. 0,1,1,0 (xor) 8. 0,1,1,1 (or) 9. 1,0,0,0 (nor) 10. 1,0,0,1 (xnor) 11. 1,0,1,0 (not B) 12. 1,0,1,1 (B implies A) 13. 1,1,0,0 (not A) 14. 1,1,0,1 (A implies B) 15. 1,1,1,0 (nand) 16. 1,1,1,1 (true) Where the first number is the output for A=false, B=false, the second number is the output for A=false, B=true, the third number is the output for A=true, B=false, the fourth number is the output for A=true, B=true. var QUESTION_ID=82938,OVERRIDE_USER=48934;function answersUrl(e){return"https://api.stackexchange.com/2.2/questions/"+QUESTION_ID+"/answers?page="+e+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+ANSWER_FILTER}function commentUrl(e,s){return"https://api.stackexchange.com/2.2/answers/"+s.join(";")+"/comments?page="+e+"&pagesize=100&order=desc&sort=creation&site=codegolf&filter="+COMMENT_FILTER}function getAnswers(){jQuery.ajax({url:answersUrl(answer_page++),method:"get",dataType:"jsonp",crossDomain:!0,success:function(e){answers.push.apply(answers,e.items),answers_hash=[],answer_ids=[],e.items.forEach(function(e){e.comments=[];var s=+e.share_link.match(/\d+/);answer_ids.push(s),answers_hash[s]=e}),e.has_more\|\|(more_answers=!1),comment_page=1,getComments()}})}function getComments(){jQuery.ajax({url:commentUrl(comment_page++,answer_ids),method:"get",dataType:"jsonp",crossDomain:!0,success:function(e){e.items.forEach(function(e){e.owner.user_id===OVERRIDE_USER&&answers_hash[e.post_id].comments.push(e)}),e.has_more?getComments():more_answers?getAnswers():process()}})}function getAuthorName(e){return e.owner.display_name}function process(){var e=[];answers.forEach(function(s){var r=s.body;s.comments.forEach(function(e){OVERRIDE_REG.test(e.body)&&(r="<h1>"+e.body.replace(OVERRIDE_REG,"")+"</h1>")});var a=r.match(SCORE_REG);a&&e.push({user:getAuthorName(s),size:+a[2],language:a[1],link:s.share_link})}),e.sort(function(e,s){var r=e.size,a=s.size;return r-a});var s={},r=1,a=null,n=1;e.forEach(function(e){e.size!=a&&(n=r),a=e.size,++r;var t=jQuery("#answer-template").html();t=t.replace("{{PLACE}}",n+".").replace("{{NAME}}",e.user).replace("{{LANGUAGE}}",e.language).replace("{{SIZE}}",e.size).replace("{{LINK}}",e.link),t=jQuery(t),jQuery("#answers").append(t);var o=e.language;/<a/.test(o)&&(o=jQuery(o).text()),s[o]=s[o]\|\|{lang:e.language,user:e.user,size:e.size,link:e.link}});var t=[];for(var o in s)s.hasOwnProperty(o)&&t.push(s[o]);t.sort(function(e,s){return e.lang>s.lang?1:e.lang<s.lang?-1:0});for(var c=0;c<t.length;++c){var i=jQuery("#language-template").html(),o=t[c];i=i.replace("{{LANGUAGE}}",o.lang).replace("{{NAME}}",o.user).replace("{{SIZE}}",o.size).replace("{{LINK}}",o.link),i=jQuery(i),jQuery("#languages").append(i)}}var ANSWER_FILTER="!t)IWYnsLAZle2tQ3KqrVveCRJfxcRLe",COMMENT_FILTER="!)Q2B_A2kjfAiU78X(md6BoYk",answers=[],answers_hash,answer_ids,answer_page=1,more_answers=!0,comment_page;getAnswers();var SCORE_REG=/<h\d>\s([^\n,][^\s,]),.?(\d+(?:\.\d+)?)(?=[^\n\d<>](?:<(?:s>[^\n<>]<\/s>\|[^\n<>]+>)[^\n\d<>])<\/h\d>)/,OVERRIDE_REG=/^Override\sheader:\s/i; body{text-align:left!important}#answer-list,#language-list{padding:10px;width:290px;float:left}table thead{font-weight:700}table td{padding:5px} <script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script> <link rel="stylesheet" type="text/css" href="//cdn.sstatic.net/codegolf/all.css?v=83c949450c8b"> <div id="answer-list"> <h2>Leaderboard</h2> <table class="answer-list"> <thead> <tr><td></td><td>Author</td><td>Language</td><td>Size</td></tr></thead> <tbody id="answers"> </tbody> </table> </div><div id="language-list"> <h2>Winners by Language</h2> <table class="language-list"> <thead> <tr><td>Language</td><td>User</td><td>Score</td></tr></thead> <tbody id="languages"> </tbody> </table> </div><table style="display: none"> <tbody id="answer-template"> <tr><td>{{PLACE}}</td><td>{{NAME}}</td><td>{{LANGUAGE}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr></tbody> </table> <table style="display: none"> <tbody id="language-template"> <tr><td>{{LANGUAGE}}</td><td>{{NAME}}</td><td>{{SIZE}}</td><td><a href="{{LINK}}">Link</a></td></tr></tbody> </table> • Your functions/programs may share code. What does this mean? Also, may the programs be in different languages? – Lynn Jun 14 '16 at 23:36 • I find the explanation confusing: "of the 4 possible inputs each can have and output of truthy and falsy". Doesn't this imply 8 (42) states? – DavidC Jun 14 '16 at 23:50 • The names you're missing are the AND-NOT gates (A AND NOT B and B AND NOT A). – Mego Jun 15 '16 at 1:33 • So it happened again. There are 18 answer, mostly simple and correct, then out of nowhere the question became "unclear what you're asking". I you don't like a challenge, go on, take another, do not close it! – edc65 Jun 15 '16 at 17:25 • @dorukayhan See: vacuous truth – Sp3000 Jun 15 '16 at 21:19 # Dominoes, 122,000 bytes or 72 tiles The byte count is the size of the saved file which is 0.122 MB. Domino computing was the inspiration. I have tested all of these up to symmetry (and beyond!) via a virtual-reality Steam game called Tabletop Simulator. ## Details • I/O • Start - This is included for clarity (not counted towards total) and is what 'calls' or 'executes' the function. Should be 'pressed' after input is given [Yellow]. • Input A - This is included for clarity (not counted towards total) and is 'pressed' to indicated a 1 and unpressed otherwise [Green]. • Input B - This is included for clarity (not counted towards total) and is 'pressed' to indicated a 1 and unpressed otherwise [Blue]. • Output - This is counted towards total. It is the domino that declares the result of the logic gate [Black]. • T/F • A fallen output domino represents a result of True or 1 • A standing output domino represents a result of False or 0 • Pressing • To give input or start the chain, spawn the metal marble • Set the lift strength to 100% • Lift the marble above the desired domino • Drop the marble ## Gates • false, 1 • and, 6 4 • A and not B, 4 3 • A, 1 • not A and B, 4 3 • B, 1 • xor, 15 11 • or, 1 • nor, 3 2 • xnor, 17 13 • not B, 2 • B implies A, 7 6 • not A, 2 • A implies B, 7 6 • nand, 16 15 • true, 1 ## TL;DR I had been waiting/wanting a domino-friendly challenge and when I saw this, I couldn't pass it up. The only problem was that apparently no one owns dominoes any more! So eventually I gave in and bought a Double Twelve. This set has 91 tiles, which gave me the idea of have a 'function call'/start domino instead of the normal (long) 'time delay' method. Credit for the 90 degree turn belongs to dominoesdouble07's channel. After building these with physical dominoes, it was ruled on meta that valid solutions should be digital. So I recreated these gates in Tabletop Simulator. Sadly, TS and reality don't agree on domino physics. This required me adding 11 dominoes but I also saved 8. Overall, virtual dominoes are about x150 more effective in terms of building and testing (Ctrl+Z). Update • -9 [17-03-13] Shortened xor xnor nand • +11 [17-03-03] Added digital xnor and xor • -8 [17-03-03] Digitized all the gates (except xor and xnor). Blocking on Tabletop only requires 1 domino, instead of 2. • [16-09-23] Shrunk images • -11 [16-09-18] Nearly cut xor in half again. Thanks to @DJMcMayhem for xnor and Joe for xor. • -31 [16-08-31] Updated some pics and shaved some tiles and cut xor in half • +1 We need more domino golfing on PPCG – Beta Decay Aug 29 '16 at 10:53 • Related. – Martin Ender Aug 29 '16 at 11:58 • Wow. This is one of the most original answers I have ever seen on this site. – James Aug 31 '16 at 19:24 • It looks like you could take one domino off if you squish the xnor together and have 4 across the top, rather than 5. Then again, I haven't tested it at all. – James Sep 3 '16 at 15:44 • Thanks for taking the time to make this a valid answer. However, the link to the source file is a bit hard to find. Normally, the link in the header leads to the language itself. So I'd link that one to the steam game and then put the link to the actual "source file" in a separate, clearly labelled link somewhere in the body of the answer. – Martin Ender Mar 9 '17 at 13:19 ## Hexagony, 89 bytes Thanks to FryAmTheEggman for some necessary inspiration for the XOR solution. 0000 !@ 0001 ?.\|@! 0010 #?#!)@ 0011 ?!@ 0100 +?\|@!? 0101 ??!@ 0110 ?<@!!<_\~( 0111 ?<<@! 1000 )\!#?@{ 1001 (~?/@#! 1010 ??\|@!) 1011 \#??!1@ 1100 ?(~!@ 1101 ?.\|@!) 1110 ?$@#)!< 1111 1!@ All programs use 0 for false and 1 for true. Try it online! This is not a test suite, you'll have to copy in the different programs and inputs yourself. The above solution is within 2-bytes of optimality (unless we relax the truthy/falsy interpretation, I guess). I've let a brute force search run for close to two days over all programs that fit into side-length 2, i.e. up to 7 bytes (not quite all programs - I made a few assumptions on what every valid program needs and what no valid program could have). The search found solutions for 15 of the 16 possible gates - and often a lot more than just one. You can find a list of all the alternative solutions in this pastebin where I've also grouped them by equivalent behaviour. The ones I'm showing above I've selected because they are either the simplest or the most interesting solution, and I'll add explanations for them tomorrow. As for the 16th gate: XOR is the only gate that can apparently not be implemented in 7 bytes. A brute force search over larger programs is unfortunately not feasible with the code I currently have. So XOR had to be written by hand. The shortest I've found so far is the above 10-byte program, which is based on a failed (but very close) attempt by FryAmTheEggman. It's possible that an 8-byte or 9-byte solution exists, but other than that, all the solutions should indeed be optimal. ## Explanations Warning: wall of text. On the off-chance anyone's interested how these highly compressed Hexagony programs actually work, I've included explanations for each of them below. I've tried to choose the simplest solution for each gate in cases where more than one optimal program exists, in order to keep the explanations reasonably short. However, some of them still boggle the mind, so I thought they deserve a bit more elaboration. ### 0000: False I don't think we'll need a diagram for this one: ! @ . . . . . Since the entire memory grid is initialised to zeros, ! simply prints a zero and @ terminates the program. This is also the only 2-byte solution. ### 0001: And ? . \| @ ! . . This basically implements short-circuiting. The grey diagram below shows the beginning of the program, where the first input is read with ? and the instruction pointer (IP) wraps around to the the left corner where the \| mirror reflects it. Now the corner acts as a conditional, such there are two different execution paths depending on the value of the first input. The red diagram shows the control flow for A = 0 and the green diagram for A = 1: As you can see, when the A is 0, then we simply print it and terminate (remember that all . are no-ops). But when A is 1, then the IP traverses the first row again, reading B and printing that instead. In total there are sixteen 5-byte solutions for this gate. Fourteen of those are essentially the same as the above, either using > instead of \| or replacing the . with a command that's effectively a no-op, or putting ? in the second position: ?.\|@! .?\|@! ?=\|@! =?\|@! ?_\|@! _?\|@! ?0\|@! ?.>@! .?>@! ?=>@! =?>@! ?_>@! _?>@! ?0>@! And then there are two other solutions (which are equivalent to each other). These also implement the same short-circuiting logic, but the execution paths are a bit crazier (and left as an exercise to the reader): ?<!@\| ?<!@< ### 0010: A and not B # ? # ! ) @ . This also implements a form of short-circuiting, but due to the use of # the control flow is much trickier. # is a conditional IP switch. Hexagony actually comes with six IPs labelled 0 to 5, which start in the six corners of the grid, pointing along their clockwise edge (and the program always begins with IP 0). When a # is encountered, the current value is taken modulo 6, and control flow continues with the corresponding IP. I'm not sure what fit of madness made me add this feature, but it certainly allows for some surprising programs (like this one). We will distinguish three cases. When A = 0, the program is fairly simple, because the value is always 0 when # is encountered such that no IP-switching takes place: # does nothing, ? reads A (i.e. also does nothing), # still does nothing, ! prints the 0, ) increments it (this is important, otherwise the IP would not jump to the third line), @ terminates the program. Simple enough. Now let's consider the case (A, B) = (1, 0): The red path still corresponds to IP 0, and I've added the green path for IP 1. We see that after ? reads A (1 this time), the # switches to the IP that starts in the top right corner. That means ? can read B (0). Now ) increments that to 1, such that the # in the top left corner does nothing and we remain with IP 1. The ! prints the 1 and the IP wraps around the left diagonal. # still does nothing and @ terminates the program. Finally, the really weird case where both inputs are 1: This time, the second input is also 1 and ) increments it to 2. That means the # in the top left corner causes another IP switch to IP 2, indicate in blue. On that path, we first increment it further to 3 (although that's irrelevant) and then pass the ? a third time. Since we've now hit EOF (i.e. the input is exhausted), ? returns 0, ! prints that, and @ terminates the program. Notably, this is the only 6-byte solution for this gate. ### 0011: A ? ! @ . . . . This is simple enough that we won't need a diagram: ? reads A, ! prints it, @ terminates. This is the only 3-byte solution for this gate. (In principle, it would also be possible to do ,;@, but the search didn't include ;, because I don't think it can ever save bytes over ! for this task.) ### 0100: B and not A + ? \| @ ! ? . This one is a lot simpler than its "brother" 0010. The control flow is actually the same as we've seen above for 0001 (And). If A = 0, then the IP traverses the lower line, reading B and printing that before terminating. If A = 1 then the IP traverses the first line again, also reading B, but the + adds two unused memory edges so all it does is reset the current value to 0, so that ! always prints 0. There are quite a lot of 6-byte alternatives to this (42 in total). First, there's a ton of solutions equivalent to the above. We can again choose freely between \| and >, and + can be replaced with any other command that gives us an empty edge: "?\|@!? &?\|@!? '?\|@!? ?\|@!? +?\|@!? -?\|@!? ^?\|@!? {?\|@!? }?\|@!? "?>@!? &?>@!? '?>@!? ?>@!? +?>@!? -?>@!? ^?>@!? {?>@!? }?>@!? In addition, we can also use ] instead of ?. ] moves to the next IP (i.e. selects IP 1), so that this branch instead reuses the ? in the top right corner. That gives another 18 solutions: "?\|@!] &?\|@!] '?\|@!] ?\|@!] +?\|@!] -?\|@!] ^?\|@!] {?\|@!] }?\|@!] "?>@!] &?>@!] '?>@!] ?>@!] +?>@!] -?>@!] ^?>@!] {?>@!] }?>@!] And then there's six other solutions that all work differently with varying levels of craziness: /[<@!? ?(#!@] ?(#>@! ?/@#/! [<<@!? [@$\!? ### 0101: B ? ? ! @ . . . Woohoo, another simple one: read A, read B, print B, terminate. There are actually alternatives to this though. Since A is only a single character, we can also read it with ,: ,?!@ And there's also the option of using a single ? and using a mirror to run through it twice: ?\|@! ?>@! ### 0110: Xor ? < @ ! ! < _ \ ~ ( . . . . . . . . . Like I said above, this was the only gate that wouldn't fit in side-length 2, so this a handwritten solution by FryAmTheEggman and myself, and there's a good chance that it isn't optimal. There are two cases to distinguish. If A = 0 the control flow is fairly simple (because in that case we only need to print B): We start on the red path. ? reads A, < is a branch which deflects the zero left. The IP wraps to the bottom, then _ is another mirror, and when the IP hits the corner, it wraps to the top left corner and continues on the blue path. ? reads B, ! prints it. Now ( decrements it. This is important because it ensures that the value is non-positive (it's either 0 or -1 now). That makes IP wrap to the to right corner, where @ terminates the program. When A = 1 things get a bit trickier. In that case we want to print not B, which in itself isn't too difficult, but the execution path is a bit trippy. This time, the < deflects the IP right and then next < just acts as a mirror. So the IP traverses the same path in reverse, reading B when it encounters ? again. The IP wraps around to the right corner and continues on the green path. It next encounters (~ which is "decrement, multiply by -1", which swaps 0 and 1 and therefore computes not B. \ is just a mirror and ! prints the desired result. Then ? tries to return another number but returns zero. The IP now continues in the bottom left corner on the blue path. ( decrements, < reflects, ( decrements again, so that the current value is negative when the IP hits the corner. It moves across the bottom right diagonal and then finally hits @ to terminate the program. ### 0111: Or ? < < @ ! . . More short-circuiting. The A = 0 case (the red path) is a bit confusing here. The IP gets deflected left, wraps to the bottom left corner, gets immediately reflected by the < and returns to the ? to read B. It then wraps to the rigt corner, prints B with ! and terminates. The A = 1 case (the green path) is a bit simpler. The < branch deflects the IP right, so we simply print the !, wrap back to the top left, and terminate at @. There is only one other 5-byte solution: \>?@! It works essentially the same, but the actual execution paths are quite different and it uses a corner for branching instead of a <. ### 1000: Nor ) \ ! # ? @ { This might be my favourite program found in this search. The coolest thing is that this implementation of nor actually works for up to 5 inputs. I'll have to get into the details of the memory model a bit to explain this one. So as a quick refresher, Hexagony's memory model is a separate hexagonal grid, where each edge holds an integer value (initially all zero). There's a memory pointer (MP) which indicates an edge and a direction along that edge (such that there's two neighboring edges in front of and behind the current edge, with meaningful left and right neighbours). Here is a diagram of the edges we'll be using, with the MP starting out as shown in red: Let's first consider the case where both inputs are 0: We start on the grey path, which simply increments edge A to 1 so that the # switches to IP 1 which is the blue path, starting in the top right corner. \ does nothing there and ? reads an input. We wrap to the top left corner where ) increments that input. Now as long as the input is zero, this will result in a 1, so that # doesn't do anything. Then { moves the MP to the left, i.e. on the first iteration from A to B. Since this edge still has its initial zero the IP wraps back to the top right corner and on a new memory edge. So this loop will continue as long as ? reads zeros, moving the MP around the hexagon from B to C to D and so on. It doesn't matter whether ? returns a zero because it was an input or because it was EOF. After six iterations through this loop, { returns to A. This time, the edge already holds the value 1 from the very first iteration, so the IP wraps to the left corner and continues on the green path instead. ! simply prints that 1 and @ terminates the program. Now what if any of the inputs is 1? Then ? reads that 1 at some point and ) increments it to 2. That means # will now switch IPs again and we'll continue in the right corner on the red path. ? reads another input (if there is one), which doesn't really matter and { moves one edge further. This has to be an unused edge, hence this works for up to 5 inputs. The IP wraps to the top right where it's immediately reflected and wraps to the left corner. ! prints the 0 on the unused edge and # switches back to IP 0. That IP was still waiting around on the #, going southwest (grey path), so it immediately hits the @ and terminates the program. In total there are seven 7-byte solutions for this gate. 5 of them work the same as this and simply use other commands to move to an unused edge (and may walk around a different hexagon or in a different direction): )\!#?@" )\!#?@' )\!#?@^ )\!#?@{ )\!#?@} And there is one other class of solutions which only works with two inputs, but whose execution paths are actually even messier: ?]!\|<)@ ?]!\|<1@ ### 1001: Equality ( ~ ? / @ # ! This also makes very clever use of conditional IP selection. We need to distinguish again between A = 0 and A = 1. In the first case we want to print not B, in the second we want to print B. For A = 0 we also distinguish the two cases for B. Let's start with A = B = 0: We start on the grey path. (~ can be ignored, the IP wraps to the left corner (still on the grey path) and reads A with ?. ( decrements that, so we get -1 and IP wrap to the bottom left corner. Now like I said earlier, # takes the value modulo 6 before choosing he IP, so a value of -1 actually gets out IP 5, which starts in the left corner on the red path. ? reads B, ( decrements that as well so that we remain on IP 5 when we hit # again. ~ negates the -1 so that the IP wraps to the bottom right corner, prints the 1 and terminates. Now if B is 1 instead, the current value will be 0 when we hit # the second time, so we switch back to IP 0 (now on the green path). That hits ? a third time, yielding 0, ! prints it and @ terminates. Finally, the case where A = 1. This time the current value is already zero when we hit # for the first time, so this never switches to IP 5 in the first place. We simply continue immediately on the green path. ? now doesn't just give a zero but returns B instead. ! prints it and @ terminates again. In total there are three 7-byte solutions for this gate. The other two work very differently (even from each other), and make even weirder use of #. In particular they read one or more values with , (reading a character code instead of an integer) and then use that value modulo 6 to pick an IP. It's pretty nuts. ),)#?@! ?~#,~!@ ### 1010: Not B ? ? \| @ ! ) . This one is fairly simple. The execution path is the horizontal branch we already know from and earlier. ?? reads A and then immediately B. After reflecting at \| and branching, for B = 0 we will execute the bottom branch, where ) increments the value to 1 which is then printed by !. On the top branch (if B = 1) the ? simply reset the edge to 0 which is then also printed by !. There are eight 6-byte programs for this gate. Four of them are pretty much the same, using either > instead of \| or 1 instead of ) (or both): ??>@!) ??>@!1 ??\|@!) ??\|@!1 Two use a single ? which is used twice due to a mirror. The negation then happens as we did for xor with either (~ or ~). ?>!)~@ ?>!~(@ And finally, two solutions use a conditional IP switch, because why use the simple way if the convoluted one also works: ??#)!@ ??#1!@ ### 1011: B implies A \ # ? ? ! 1 @ This uses some rather elaborate IP switching. I'll start with the A = 1 case this time, because it's simpler: We start on the grey path, which reads A with ? and then hits the #. Since A is 1 this switches to IP 1 (green path). The ! immediately prints that, the IP wraps to the top left, reads B (unnecessarily) and terminates. When A = 0 things get a bit more interesting. First let's consider A = B = 0: This time, the # does nothing and we remain on IP 0 (red path from that point onward). ? reads B and 1 turns it into a 1. After wrapping to the top left corner, we hit # again, so we end up on the green path after all, and print 1 as before, before terminating. Finally, here is (A, B) = (0, 1), the false case: Note that I've removed the initial grey path for clarity, but the program begins the same way, and we end up on the red path as before. So this time the second ? returns 1. Now we encounter the 1. At this point it's important to understand what digits actually do in Hexagony (so far we've only used them on zeros): when a digit is encountered, the current value is multiplied by 10 and then the digit is added. This is normally used to write decimal numbers verbatim into the source code, but it means that B = 1 is actually mapped to the value 11. So when we hit #, this is taken modulo 6 to give 5 and hence we switch to IP 5 (instead of 1 as before) and continue on the blue path. Hitting ? a third time returns a zero, so ! prints that, and after another two ?, the IP wraps to the bottom right where the program terminates. There are four 7-byte solutions to this and they all work differently: #)/!?@$<!?_@#1 \#??!1@ \|/)#?@! ### 1100: Not A ? ( ~ ! @ . . Just a simple linear one: read A with ?, negate with (~, print with !, terminate with @. There's one alternative solution, and that's negating with ~) instead: ?~)!@ ### 1101: A implies B ? . \| @ ! ) . This is a lot simpler than the opposite implication we just talked about. It's again one of those horizontal branch programs, like the one for and. If A is 0, it simply gets incremented to 1 on the bottom branch and printed. Otherwise, the top branch is executed again where ? reads B and then ! prints that instead. There's a ton of alternatives here (66 solutions in total), mostly due to free choice of effective no-ops. For a start we can vary the above solution in all the same ways we could for and and we can also choose between ) and 1: ?.\|@!) .?\|@!) ?=\|@!) =?\|@!) ?_\|@!) _?\|@!) ?0\|@!) ?.\|@!1 .?\|@!1 ?=\|@!1 =?\|@!1 ?_\|@!1 _?\|@!1 ?0\|@!1 ?.>@!) .?>@!) ?=>@!) =?>@!) ?_>@!) _?>@!) ?0>@!) ?.>@!1 .?>@!1 ?=>@!1 =?>@!1 ?_>@!1 _?>@!1 ?0>@!1 And then there's a different version using conditional IP selection, where the first command can be chosen almost arbitrarily, and there is also a choice between ) and 1 for some of those options: "?#1!@ &?#1!@ '?#1!@ )?#1!@ ?#1!@ +?#1!@ -?#1!@ .?#1!@ 0?#1!@ 1?#1!@ 2?#1!@ 3?#1!@ 4?#1!@ 5?#1!@ 6?#1!@ 7?#1!@ 8?#1!@ 9?#1!@ =?#1!@ ^?#1!@ _?#1!@ {?#1!@ }?#1!@ "?#)!@ &?#)!@ '?#)!@ ?#)!@ +?#)!@ -?#)!@ 0?#)!@ 2?#)!@ 4?#)!@ 6?#)!@ 8?#)!@ ^?#)!@ _?#)!@ {?#)!@ }?#)!@ ### 1110: Nand ?$ @ # ) ! < The last complicated one. If you're still reading, you've almost made it. :) Let's look at A = 0 first: ? reads A and then we hit $. This is a jump command (like Befunge's #) which skips the next instruction so that we don't terminate on the @. Instead the IP continues at #. However since A is 0, this doesn't do anything. ) increments it to 1 so that the IP continues on the bottom path where the 1 is printed. The < deflects the IP to the right where it wraps to the left corner and the program terminates. Next, when the input is (A, B) = (1, 0) we get this situation: It's essentially the same as before except that at the # we switch to IP 1 (green path), but since B is 0 we switch back to IP 0 when we hit # a second time (now blue path), where it prints 1 as before. Finally, the A = B = 1 case: This time, when we # the second time, the current value is still 1 so that we don't change the IP again. The < reflects it and the third time we hit ? we get a zero. Hence the IP wraps to the bottom left where ! prints the zero and the program ends. There are nine 7-byte solutions in total for this. The first alternative simply uses 1 instead of ): ?$@#1!< Then there's two solutions that will do your head in with the amount of IP switching that's going on: )?#_[!@ 1?#_[!@ These actually blew my mind: the interesting part is that IP switching can be used as a deferred conditional. The language's IP-switching rules are such that the current IP makes another step before the switch happens. If that step happens to go through a corner, then the current value decides on which branch the IP will continue if we ever switch back to it. Exactly this happens when the input is A = B = 1. Although this is all consistent with how I designed the language, I was never aware of this implication of the spec, so it's nice when my language teaches me some new tricks :D. Then there's a third solution whose amount of IP switching is even worse (although it doesn't make use of that deferred conditional effect): >?1]#!@ And then there's another one: ?$@#)!< And then there's these four equivalent solutions, which do use some non-conditional IP switching and instead implement all the logic via branches and corners: ]<?<@!) ]<?<@!1 ]\|?<@!) ]\|?<@!1 ### 1111: True 1 ! @ . . . . You've earned yourself something simple for the end: set edge to 1, print with !, terminate with @. :) Of course, there's one alternative: )!@ As usual, all control flow diagrams created with Timwi's HexagonyColorer and the memory diagram with his EsotericIDE. • Aaaaaand the tl;dr award goes to... (kidding obviously, great answer and very well written out, +1) – Bassdrop Cumberwubwubwub Jul 22 '16 at 15:15 • This is the reason you are not active on chat anymore?? – Optimizer Jul 30 '16 at 6:32 • Sort of late, but could you add a link to your brute force code? – nedla2004 Feb 3 '17 at 21:48 • @nedla2004 I usually don't keep them around, but it's always a modified version of this script. – Martin Ender Feb 3 '17 at 22:19 # APL, 2220 18 bytes The true and false entries are complete programs, and the other 14 are functions. (Thanks to Adám.) 0000 false 0 (complete program) 0001 p and q ∧ 0010 p and not q > 0011 p ⊣ 0100 not p and q < 0101 q ⊢ 0110 xor ≠ 0111 p or q ∨ 1000 not p and not q ⍱ 1001 eq = 1010 not q ~⊢ 1011 p or not q ≥ 1100 not p ~⊣ 1101 not p or q ≤ 1110 not p or not q ⍲ 1111 true 1 (complete program) Try it here. • +1 Nice use of atops! You can save two bytes by making 0000 and 1111 into trad-fns 0 and 1. – Adám Jun 15 '16 at 8:11 • There is a consensus to allow tfns, but not to count the first line. This corresponds to not counting the filename in languages that use files as program containers with program name = filename. – Adám Jun 15 '16 at 10:24 • – Adám Jun 15 '16 at 10:32 • Jelly: 19 bytes. This: 18 bytes. Doesn't this mean that you outgolfed Dennis? +1 for that. – NoOneIsHere Jun 16 '16 at 17:21 # Chess/mediocre chess player in endgame, 70 pieces Inspired by that domino answer, I decided another game should have this honor. Note that I took a few rules for how the pieces move. Because I don't feel like studying the optimal moves for every situation, the rules for whites move is simple: Stay out of check, capture the highest ranking piece he can that turn, while losing as little material as possible, and stop a pawn from promoting, in that order of priority. If there are two spaces he can move to, with equal favourability, he can move to either (hence in these, if he can move to more than one square, they are the same colour). Note that white will capture with something even if it gets captured, if the piece it is attacking is higher value than the one lost. Values are here:pawn<knight=bishop<rook<queen The input is whether a rook is present or not. Note that rooks are only labelled with names A and B when it matters: if the gate behaves the same when the rooks are switched, they are not labelled. The output is the colour of the square white king ends on: White=1, black=0 Before the images, I want to apologise for poor images. I'm not much good at holding a camera steady. False, 4: AND, 4: A and not B, 5 (I think I can get this down to three, but do not have board right now): A, 4: Not A and B,5 (I think I can get this down to three, but do not have board right now): B, 4: Xor,5 (I know a way to make it 4, but I don't have the board right now): Or, 4: Nor, 4: Xnor, 5 (I know a way to make it 4, but I don't have the board right now): Not B, 4: B implies A, 5 (I think I can get this down to three, but do not have board right now): Not A, 4: A implies B, 5 (I think I can get this down to three, but do not have board right now): Nand, 4: True, 4: • Wow, I had no idea that programming in chess was possible... Could you post a video/simulation of a few of these in action? – Beta Decay Sep 5 '16 at 9:50 • hmmm, I currently don't have access to the chess board. I would probably say that the A implies B/B implies a/etc are hardest to understand due to the effect of pawns on the kings movement. I should probably add better explanation for those two – Destructible Lemon Sep 5 '16 at 9:58 • Glad to inspire :D If I am understanding correctly, the board and piece locations are equivalent to a program. The rooks are the input, so I can place them on any square as long as it is the right color? – NonlinearFruit Sep 6 '16 at 1:44 • No, the input of the rooks is whether they are present or absent from the board. They are labelled a and b when they are not symmetrical gates (when it matters the different a and b). Also I realised how I could golf off 2 pieces, but I don't have the board right now. Paintbrush must be utilised :) – Destructible Lemon Sep 6 '16 at 2:18 • On your "And" case, if you remove the right rook, what's stopping the king from moving down (to white)? – Nathan Merrill Oct 18 '16 at 15:01 # Jelly, 19 bytes 0 0 0 0 ¤ 1 byte Empty niladic chain. Returns default argument 0. 0 0 0 1 & 1 byte Bitwise AND. 0 0 1 0 > 1 byte Greater than. 0 0 1 1 0 bytes Empty link. Returns left argument. 0 1 0 0 < 1 byte Less than. 0 1 0 1 ị 1 byte At-index (x,y -> [y][x]). Returns right argument. 0 1 1 0 ^ 1 byte Bitwise XOR. 0 1 1 1 \| 1 byte Bitwise OR. 1 0 0 0 \|¬ 2 byte Logical NOT of bitwise OR. 1 0 0 1 = 1 byte Equals. 1 0 1 0 ¬} 2 bytes Logical NOT of right argument. 1 0 1 1 * 1 byte Exponentiation. 1 1 0 0 ¬ 1 byte Logical NOT of left argument. 1 1 0 1 >¬ 2 bytes Logical NOT of greater than. 1 1 1 0 &¬ 2 bytes Logical NOT of bitwise AND. 1 1 1 1 ! 1 byte Factorial. Try it online! • I love the use of Factorial to convert either 0 or 1 to 1. – Neil Jun 15 '16 at 8:33 • Is Jelly UTF-8? If yes then ¤ and ¬ are 2 bytes, not 1. – Vi. Sep 29 '16 at 20:10 • @Vi. Jelly supports UTF-8, but it also supports a custom code page that encodes each of the 256 characters it understands as a single byte each. The bytes link in the header points to it. – Dennis Sep 29 '16 at 20:12 • 0 0 1 0 > 1 byte Greater than. wouldn't this fail if the second input was negative? – MD XF Jun 17 '17 at 21:28 • @MFXF We can choose which truthy and which falsy value we support. – Dennis Jun 17 '17 at 21:31 # NAND logic gates — 31 gates As the creator of the original series of NAND gate questions, I couldn't pass up the opportunity to use these gates to solve another logic gate problem. In each of these diagrams, the top input is A while the bottom input is B. • @xnor might be flattered to know that his logic gate is the one that requires the most NAND gates to make D: – Joe Z. Jun 16 '16 at 20:21 • Could you at least use Logisim to format your code? – mbomb007 Jun 16 '16 at 20:24 • @mbomb007 I'll edit that in later. I'm not so experienced with Logisim, so it might take a while. – Joe Z. Jun 16 '16 at 20:25 • But I like handwriting better. – Leaky Nun Jun 16 '16 at 20:31 • Alternatively you could switch to nor gate and format it using redstone... – jimmy23013 Jun 22 '16 at 5:38 # Bitwise Cyclic Tag, 118 bits = 14.75 bytes Bitwise Cyclic Tag is perhaps the simplest Turing-complete language ever devised. There is a program tape and a data tape, both consisting of a list of bits. The program tape is interpreted cyclically until the data tape is empty, as follows: • 0: delete the first bit from the data tape. • 1x: if the first bit of the data tape is 1, append the bit x to the data tape. We initialize the data tape with a 1 followed by the two input bits (the 1 is necessary because there is no way to create a 1 if the data tape consists entirely of 0s), and we use the final deleted data bit as the gate’s output. • 0,0,0,0 (false): 001 • 0,0,0,1 (and): 1001001 • 0,0,1,0 (A and not B): 0110100 • 0,0,1,1 (A): 1001 • 0,1,0,0 (not A and B): 0100 • 0,1,0,1 (B): 0 • 0,1,1,0 (xor): 0110110010 • 0,1,1,1 (or): 0110 • 1,0,0,0 (nor): 1101001000 • 1,0,0,1 (xnor): 110101001100 • 1,0,1,0 (not B): 1100100 • 1,0,1,1 (B implies A): 110101101000 • 1,1,0,0 (not A): 11010000 • 1,1,0,1 (A implies B): 11010011001 • 1,1,1,0 (nand): 10110100100010 • 1,1,1,1 (true): 1100 • Congratulations! – Leaky Nun Aug 5 '16 at 4:12 • Is the trailing 1 on false required? – CalculatorFeline Jun 18 '17 at 15:48 • @CalculatorFeline Yes, we need to append a 0 to the tape so it can be deleted last. – Anders Kaseorg Jun 18 '17 at 18:51 • Ah. Forgot about that+wrapping. Clever! – CalculatorFeline Jun 18 '17 at 21:34 ## Python 2, 137 bytes [].sort min int.__rshift__ round range {}.get cmp max lambda a,b:a<1>b lambda a,b:a==b lambda a,b:b<1 pow {0:1,1:0}.get {0:1}.get lambda a,b:a+b<2 slice Takes inputs like min(True,False) (or as min(1,0)). Takes heavy advantage of outputs only needing to have the right Truthy-Falsey value. Whenever possible, uses a built-in to avoid a costly lambda. I used code to search for built-ins that work. My favorite one is {0:1}.get, which I thought of by hand. The dictionary {0:1} maps the key 0 to the value 1. Its get method takes a key and a default, outputting the value matching the key, or the default if there's no such key. So, the only way to output a 0 is as {0:1}.get(1,0), with missing key 1 and default 0. One can get other variants with different dictionaries, but only this one was the shortest. built_in_names = list(__builtins__) object_names = ["int","(0)","(1)"] + \ ["True","False","0L","1L","0j","1j"] + \ ["str", "''", "'0'","'1'","'a'"] + \ ["list", "[]", "[0]", "[1]","['']","[[]]","[{}]"] + \ ["set","set()","{0}","{1}","{''}"] + \ ["dict","{}","{0:0}","{0:1}","{1:0}","{1:1}","{0:0,1:0}", "{0:0,1:1}","{0:1,1:0}","{0:1,1:1}"] + \ ["id"] object_method_names = [object_name+"."+method_name for object_name in object_names for method_name in dir(eval(object_name))] additional_func_names = [ "lambda a,b:0", "lambda a,b:1", "lambda a,b:a", "lambda a,b:b", "lambda a,b:b<1", "lambda a,b:a<1", "lambda a,b:a+b", "lambda a,b:ab", "lambda a,b:a==b", "lambda a,b:a-b", "lambda a,b:a<=b", "lambda a,b:a>=b", "lambda a,b:a>b", "lambda a,b:a<b", "lambda a,b:a<1>b", "lambda a,b:a+b<2"] func_names = built_in_names + object_method_names + additional_func_names t=True f=False cases = [(f,f),(f,t),(t,f),(t,t)] def signature(func): table = [bool(func(x,y)) for x,y in cases] table_string = ''.join([str(int(val)) for val in table]) return table_string d={} for func_name in func_names: try: func = eval(func_name) result = signature(func) if result not in d or len(func_name)<len(d[result]): d[result]=func_name except: pass total_length = sum(len(func) for sig,func in d.items()) print total_length print for sig in sorted(d): print d[sig] • Can't you use methods of built-ins like int's __lt__ or __eq__? These will further decrease byte count: int.__gt__ instead of lambda a,b:b<1, int.__eq__ instead of lambda a,b:a==b and so on – Gábor Fekete Jul 29 '16 at 11:05 • @GáborFekete Those don't exist in Python 2 because ints offload comparisons to cmp. I haven't tried this for Python 3. – xnor Jul 29 '16 at 11:11 • Oh right now I see! – Gábor Fekete Jul 29 '16 at 11:24 • Save 4 bytes by using the function not for 0001, False - ideone – Jonathan Allan Sep 4 '16 at 1:52 • @JonathanAllan That's clever, but I think that not doesn't meet the requirements of a function because you can't do f=not;f(3,4). The string not happens to work because the supposed function arguments look like a tuple, just as 3+ would work as 3+(4) even though 3+ as not a function that can take 4 as an input. – xnor Sep 4 '16 at 22:35 # Go (game), 33 stones, 73 intersections If domino and chess are acceptable, then this. It can't be too golfy on a full 19x19 Go board. So I used small rectangular boards. The input is whether the stones marked 1 and 2 are present. The output is whether black wins. It uses area scoring, 0.5 komi, situational superko, no suicide. All black to play. Some are given multiple solutions. White wins (2, 1x5): ➊━━━➋ 1 and 2 (3, 2x3): ➊◯➋ ┗┷┛ 1 and not 2 (2, 1x5): ╺➊━➁╸ 1 (2, 1x5): ╺➊➁━╸ ╺➊━━➁ ➀━➁━╸ Not 1 and 2 (2, 1x5): ╺➋━➀╸ 2 (2, 1x5): ╺➋➀━╸ 1 xor 2 (2, 2x3): ➀┯➁ ┗┷┛ 1 or 2 (2, 1x5): ╺➊━➋╸ ➀━━━➁ 1 nor 2 (2, 1x4): ➊━━➋ ╺➀➁╸ 1 = 2 (2, 1x7): ╺━➀━➁━╸ Not 2 (2, 1x3): ➀➁╸ 1 or not 2 (2, 1x4): ➀➁━╸ ➀━➁╸ ╺➊➁╸ ➋➊━╸ ➋━➊╸ Not 1 (2, 1x3) ➁➀╸ Not 1 or 2 (2, 1x4): ➁➀━╸ 1 nand 2 (2, 1x3): ➊━➋ Black wins (2, 1x3): ➊➋╸ ➀━➁ ➊━➁ This page helped me a bit: http://www.mathpuzzle.com/go.html Maybe someone could find a 2 stone solution for 1 and 2 on a 1x9 board... • What are your rules for suicide? Disallowed? And what happens when one side fills the entire board? Is that considered suicide? – Martin Ender Sep 23 '16 at 14:25 • @MartinEnder Disallowed. And yes, that's considered suicide. – jimmy23013 Sep 23 '16 at 16:43 • The 1x7 solution seemed wrong. I'm trying to fix it... – jimmy23013 Oct 4 '16 at 0:36 # Javascript ES6, 124 bytes a=>0 Math.min parseInt a=>a a=>b=>a<b a=>b=>b a=>b=>a^b Math.max a=>b=>~a&~b a=>b=>a==b a=>b=>~b Math.pow a=>~a a=>b=>a<=b a=>b=>~a\|~b a=>1 I seriously hate lambdas right now. • If I'm allowed to write some programs and some functions... I think you could change a=>b=>0 to a=>0 and say the grammar calling it is (a=>0)(a,b), only for those 4 entries. – jimmy23013 Jun 15 '16 at 11:33 • Oh yeah, thanks! – Mama Fun Roll Jun 15 '16 at 14:00 • Math.min instead of a=>b=>a&b. Math.max instead of a=>b=>a\|b. Math.pow instead of a=>b=>a>=b. – Conor O'Brien Jun 16 '16 at 0:37 • Also, since NaN is falsey, you can do parseInt instead of a=>b=>a>b. – Conor O'Brien Jun 16 '16 at 21:11 • @algmyr !NaN => true, !!NaN => false – Mama Fun Roll Jul 29 '16 at 14:14 # Retina, 62 39 bytes 23 bytes thanks to @MartinEnder! 0000 false 1 byte : 2 0001 p and q 2 bytes: 11 0010 p and not q 2 bytes: 10 0011 p 2 bytes: ^1 0100 not p and q 2 bytes: 01 0101 q 2 bytes: 1$ 0110 xor 5 bytes: 01\|10 0111 p or q 1 byte : 1 1000 not p and not q 2 bytes: 00 1001 xnor 5 bytes: (.)\1 1010 not q 2 bytes: 0$1011 p or not q 5 bytes: ^1\|0$ 1100 not p 2 bytes: ^0 1101 not p or q 5 bytes: ^0\|1$1110 not p or not q 1 byte : 0 1111 true 0 bytes: Takes input as PQ. Outputs an integer between 0 to 3. 0 is falsey, others are truthy. ## Explanation They are all just regexes. For example, 01\|10 just matches 01 or 10. In 0000, 2 will never be in the input, so it never matches. In 1111, it matches the empty string, which there are 4. • ^1\|0$ should only match 1 character strings. What's going on here? – CalculatorFeline Mar 2 '17 at 15:44 • @CalculatorFeline It matches [1 at beginning of input] OR [0 at end of input]. Took me a minute to get it too... – ETHproductions Aug 18 '17 at 3:46 • Precedence, guys.... – Leaky Nun Aug 18 '17 at 4:07 • I guess ^1\|0$ is harder to read than 1.\|.0. Seems to make reading harder in all – l4m2 Dec 7 '17 at 5:25 ## Stack Cats, 67 + 64 = 131 bytes Note that the +64 is from applying the -nm flags to each program. -n indicates numeric I/O, and -m mirrors the source code across the last character - not all submissions need these flags technically, but for consistency and simplicity I'm scoring them all the same way. -2 -2 -3 -3 !I 0 0 0 0 <I!+ -4 -4 -4 1 \|!TI 0 0 0 1 [>I=I_ -4 -4 3 -2 I_ 0 0 1 0 :I=I: -2 -2 3 3 TI 0 0 1 1 [<!>X -2 1 -2 -2 _TI 0 1 0 0 \|!TI: -2 1 -3 1 !-\|_I 0 1 0 1 <!I!>X -2 3 3 -2 ^TI 0 1 1 0 ^:]<_I -2 3 3 3 -_TI 0 1 1 1 I<-I! 2 -3 -3 -3 -\|_I 1 0 0 0 ^{!:}I_ 2 -3 -3 2 _\|I 1 0 0 1 _\|[<I!: 1 -2 1 -2 :]I: 1 0 1 0 _!:\|]X 1 -2 1 1 I\<X 1 0 1 1 >I>!I 2 2 -3 -3 -I 1 1 0 0 I^:! 2 2 -3 2 _I_ 1 1 0 1 \|I\|^:! 1 2 2 -1 \|!:^I 1 1 1 0 -I<I 1 1 1 1 <X 1 1 1 1 +I+ () in Stack Cats checks whether an element is positive or nonpositive (i.e. 0 or negative), so we're using that for truthy/falsy respectively. The second column is just for interest, and lists the best gates with 0/1s as outputs (with total score 90). Input is delimiter-separated bits via STDIN. Try it online! Stack Cats is a reversible esoteric language, where programs have reflective symmetry. Given a snippet f (e.g. >[[(!-)/), the mirror image (e.g. \(-!)]]<) computes the inverse f^-1. As such, even length programs do nothing (or get stuck in an infinite loop), and the only non-trivial programs have odd length, computing f g f^-1 where g is the centre operator. Since half the source code is always redundant, it can be left out, and running the code with the -m flag indicates that the source code should be mirrored over the last character to retrieve the actual source code. For example, the program <X is actually <X>, which is symmetrical. Golfing in Stack Cats is highly unintuitive, so the above programs had to be found by brute force. Most of them are surprisingly complex, but I'll explain a few and add to this answer when I have time. For now, some explanations and alternative solutions for the 0/1 versions can be found on the Github repository here. • Note that the +64 is from applying the -nm flags to each program. 3 16 = 48 or 2 * 16 = 32, either way 64 is way hai – cat Jun 15 '16 at 22:32 • @cat The flags cost 4 per program, as you have to count the space as well. – FryAmTheEggman Jun 16 '16 at 0:55 • @cat relevant meta post: meta.codegolf.stackexchange.com/questions/273/… – Martin Ender Jun 16 '16 at 5:23 • It's been over a year. Do you have time yet? – CalculatorFeline Jun 18 '17 at 15:52 ## Haskell, 7876 75 bytes 1. _#_=2<1 2. && 3. > 4. pure 5. < 6. _#b=b 7. /= 8. \|\| 9. (not.).max 10. == 11. _#b=not b 12. >= 13. a#_=not a 14. <= 15. (not.).min 16. _#_=1<2 Edit: -1 byte thanks to @cole. • I was just about to comment "dude, _#_ isn't a standard operator!" And then I realised... Well done. – MathematicalOrchid Jun 16 '16 at 14:09 • 4 could be pure – cole Jul 28 '19 at 0:32 • @cole: Thanks. Wow, pure was introduced into Prelude back in 2015, so it was available at the time of this challenge. – nimi Jul 28 '19 at 1:16 # Minecraft, 89 blocks In all of the following photos, blue blocks are for Input A and orange blocks are for Input B ## 16. TRUE gate - 1 blocks ## 15. NAND gate - 1x2x3 = 6 blocks ## 14. A=>B - 1x2x3 = 6 blocks ## 13. NOT A - 2 blocks ## 12. B=>A - 1x2x3 = 6 blocks ## 11. NOT B - 2 blocks ## 10. XNOR - 1x3x4 = 12 blocks ## 9. NOR - 1x2x3 = 6 blocks ## 8. OR - 1 blocks ## 7. XOR - 1x3x4 = 12 blocks ## 6. B - 1 blocks ## 5. !A&B - 1x2x5 = 10 blocks ## 4. A - 1 blocks ## 3. A&!B - 1x2x5 = 10 blocks ## 2. AND - 2x2x3 = 12 blocks ## 1. FALSE- 1 blocks • In the second to last image (AND) you could save 6 blocks by putting the torches on top to the back of the blocks, i.e. opposite to the levers. Swap the torch in the middle for a piece of dust and remove the dust at the top, bringing it down to 1x2x3=6 blocks. – Luca H Nov 23 '17 at 11:12 # Brachylog, 36 34 bytes 0000 false \ Backtrack (always false) 0001 p and q 1. Unify input and output with 1 0010 p and not q >. Input > Output 0011 p 1 Unify input with 1 0100 not p and q <. Input < Output 0101 q ,1. Unify output with 1 0110 xor '. Input and output cannot unify 0111 p or q 1;1. Unify input with 1 or unify output with 1 1000 not p and not q 0. Unify input and output with 0 1001 eq . Unify input with output 1010 not q ,0. Unify output with 0 1011 p or not q >=. Input >= Output 1100 not p 0 Unify input with 0 1101 not p or q <=. Input <= Output 1110 not p or not q 0;0. Unify input with 0 or unify output with 0 1111 true Empty program (always true) This expects 0 as falsy value and 1 as truthy value. Returns true or false. p is Input and q is Output. • How do you input the output? – Leaky Nun Jun 15 '16 at 6:59 • @LeakyNun Just like the input. The main predicate you query has two arguments, called Input and Output by convention, but you can set values to both, or return values from both. – Fatalize Jun 15 '16 at 7:01 • This is the right tool for the job :P – Conor O'Brien Jun 15 '16 at 21:03 # Prolog, 147 145 bytes Gained 2 bytes thanks to @SQB a(a,a). % 0000 false b(1,1). % 0001 P and Q c(1,0). % 0010 P and not Q d(1,_). % 0011 P e(0,1). % 0100 not P and Q f(_,1). % 0101 Q g(P,Q):-P\=Q. % 0110 P xor Q h(1,_). % 0111 P or Q h(0,1). i(0,0). % 1000 not P and not Q j(P,P). % 1001 P == Q k(_,0). % 1010 not Q m(P,Q):-P>=Q. % 1011 P or not Q n(0,_). % 1100 not P r(P,Q):-P=<Q. % 1101 not P or Q s(0,_). % 1110 not P or not Q s(1,0). t(_,_). % 1111 true Query x(P,Q). with x being the appropriate letter and P and Q set to either 0 or 1. Returns true or false. SWISH example including tests - enter runTest. to run. • Does it support a(2,2). for false? – jimmy23013 Jun 15 '16 at 7:54 • @jimmy23013 I guess it could if I assume that 2 is falsy. Not sure if that's acceptable. – Fatalize Jun 15 '16 at 7:55 • @jimmy23013 Actually, a(a,a). (or any other letter) works too and a is not an acceptable input for truthness, so that's good. Thanks for the suggestion. – Fatalize Jun 15 '16 at 8:03 # NTFJ, 86 bytes 0000 false ~ 0001 p and q \|:\| 0010 p and not q :\|\|:\| 0011 p$ 0100 not p and q #{:\|\|:\| 0101 q #{$0110 xor :#{:#{:\|\|#}:\|\|\| 0111 p or q :\|#{:\|\| 1000 not p and not q :\|#{:\|\|:\| 1001 eq :#{:#{:\|\|#}:\|\|\|:\| 1010 not q #{$:\| 1011 p or not q #{:\|\| 1100 not p $:\| 1101 not p or q :\|\| 1110 not p or not q \| 1111 true # Try it here! But read below first. Input is implicit on stack. Result is let on stack. Add 16 bytes (one * to the end of each) if you want 0x00 or 0x01 to output representing 0 and 1. Add an additional 160 bytes if you want a 0 or a 1 printed. (Put ~~##~~~#{@ before each .) NTFJ's only binary operator is NAND, so each of these is written in NAND form. Let's go through each of them. ## 0: false ~ ~ represents a false bit. Simple enough. Since input is implicit at the bottom of the stack, this is left at the top of it. ## 1: p and q \|:\| NTFJ operates on a stack. : is the command for duplicate. Observe that p and qnot (p nand q) and that not q = q nand q. Command \| Stack \| p q \| \| (p nand q) : \| (p nand q) (p nand q) \| \| (p nand q) nand (p nand q) \| => not (p nand q) \| => p and q (Note, then, :\|can be said to be negation and \|:\| can be said to be conjunction) ## 2: p and not q :\|\|:\| Observe that this just a negation, :\| and a conjunction \|:\|. Command \| Stack \| p q :\| \| p (not q) \|:\| \| p and (not q) ## 3: p $ $ pops an item from the stack. So... yeah. ## 4: not p and q #{:\|\|:\| This is the same thing as 2, except with #{ at the beginning. # pushes 1 (the true bit) and { rotates the stack left once. Simple enough. ## 5: q #{$ Rotate left once, drop. ## 6: xor :#{:#{:\|\|#}:\|\|\| Observe: p xor q = (p and (not q)) or ((not p) and q) ; by experimentation (trust me) = (not ((not p) nand q)) or (not (p nand (not q))) ; by definition of nand = not (((not p) nand q) and (p nand (not q))) ; by De Morgan's laws = ((not p) nand q) nand (p nand (not q)) ; by definition of nand However, there is no way to duplicate the stack entirely. So, we're going to have to bring each of p, q to the top and duplicate it. Command \| Stack \| p q : \| p q q #{ \| q q p : \| q q p p #{ \| q p p q :\| \| q p p (not q) \| \| q p (p nand (not q)) #} \| (p nand (not q)) q p :\| \| (p nand (not q)) q (not p) \| \| (p nand (not q)) (q nand (not p)) \| \| (p nand (not q)) nand (q nand (not p)) And thus, we have our xor. ## 7: p or q :\|#{:\|\| Negate top, bring bottom to top, negate that, and nand them together. Basically, p or q = (not p) nand (not q). ## 8: not p and not q :\|#{:\|\|:\| This is simply the negation of 7. Easy. ## 9: eq :#{:#{:\|\|#}:\|\|\|:\| This is just xnor, or not xor. Simple again. #{$:\| Negation of 5. ## 11: p or not q #{:\|\| Negate p, nand. (not p) nand q = not ((not p) and q) = p or (not q) (by De Morgan's laws). ## 12: not p $:\| Drop, stop, and negate. ## 13: not p or q :\|\| De Morgan's laws to save the day, again! Same process as 11, just negating q instead of p. ## 14: not p or not q \| This is just a mimic nand. ## 15: true # # is the true bit. • just why... >_> – Rɪᴋᴇʀ Jun 15 '16 at 21:36 • idk exactly how this works but it seems pretty cool +1 – Downgoat Jun 15 '16 at 21:37 • Why isn't 5 just an empty program, and 10 just :\|? – Joffan Jul 29 '16 at 14:09 ## Mathematica, 67 bytes 0>1& And #&&!#2& #& !#&&#2& #2& Xor Or Nor Xnor !#2& #\|\|!#2& !#& !#\|\|#2& Nand 1>0& Each of these evaluates to a function, so you can use them like #&&!#2&[True, False] Xor[True, False] Ah, if only integers were truthy/falsy in Mathematica, those four longer ones could have been shortened considerably. • If integers aren't truthy/falsey, what happens when you put them in an if statement? – Conor O'Brien Jun 22 '16 at 16:33 • @CᴏɴᴏʀO'Bʀɪᴇɴ it remains unevaluated. – Martin Ender Jun 22 '16 at 16:39 # MATL, 34 23 bytes I hope I got the order all right! Zero is falsey, non-zero is truthy. Each function takes two implicit inputs (although it may ignore some inputs). The first input is A, and the second is B. You can input 0/1 for true/false, or T/F. Here is a TryItOnline example for test case 3. Saved 4 bytes by using for and, and another 4 by using >/< instead of ~wY&/w~Y& after I saw Dennis' answer! 1. 0,0,0,0 0 (ignores input, just returns a zero) 2. 0,0,0,1 * (and) 3. 0,0,1,0 < (not-A and B) 4. 0,0,1,1 D (A) 5. 0,1,0,0 > (not-B and A) 6. 0,1,0,1 xD (discard A, display B) 7. 0,1,1,0 Y~ (xor) 8. 0,1,1,1 + (or) 9. 1,0,0,0 +~ (not-or) 10. 1,0,0,1 = (A=B) 11. 1,0,1,0 x~ (not-B) 12. 1,0,1,1 <~ (not-B or A) 13. 1,1,0,0 ~ (not-A) 14. 1,1,0,1 ~+ (not-A or B) 15. 1,1,1,0 ~ (not(A and B)) 16. 1,1,1,1 1 (just returns 1) • Number six thinks it's funny. – Conor O'Brien Jun 15 '16 at 3:06 • @CᴏɴᴏʀO'Bʀɪᴇɴ Number 6 is the best, I like number 12 too! xD! – David Jun 15 '16 at 3:19 • Don't you have the "unequal" function? – Leaky Nun Jun 15 '16 at 5:27 • No (I don't think so at least) – David Jun 15 '16 at 5:31 • @David I think number 7 can be replaced by - – Luis Mendo Jun 15 '16 at 9:30 # dc, 37 bytes dc ("desk calculator") is a standard unix command, a stack-based postfix calculator. It lacks bit operations, and comparison operators can only be used to execute macros (which is not worth the bytes). Integer division makes up for some of that. These scripts expect 0 and 1 values on the stack, and leave the result on the stack. 0,0,0,0 (false) 0 0,0,0,1 (and) ab 0,0,1,0 -1+2/ (a-b+1)/2 0,0,1,1 (A) r reverse a, b: a now on top 0,1,0,0 -1-2/ (a-b-1)/2 0,1,0,1 (B) (0 bytes) do nothing: b on top 0,1,1,0 (xor) - a-b 0,1,1,1 (or) + a+b 1,0,0,0 (nor) +v1- sqrt(a+b) -1 1,0,0,1 (xnor) +1- a+b-1 1,0,1,0 (not B) 1- b-1 1,0,1,1 (if B then A) -1+ a-b+1 1,1,0,0 (not A) r1- a-1 1,1,0,1 (if A then B) -1- a-b-1 1,1,1,0 (nand) 1- ab - 1 1,1,1,1 (true) 1 ## Labyrinth, 85 bytes Thanks to Sp3000 for saving 2 bytes. !@ ??&!@ ??~&!@ ?!@ ?~?&!@ ??!@ ??$!@ ??\|!@ ??\|#$!@ ??$#$!@ ?#?$!@ ?#?$\|!@ ?#$!@ ?#$?\|!@ ??&#$!@ 1!@ All of these are full programs, reading two integers 0 or 1 from STDIN (using any non-digit separator), and printing the result as 0 or 1 to STDOUT. Try it online! (Not a test suite, so you'll have to try different programs and inputs manually.) As for explanations, these are all rather straightforward. All programs are linear, and the commands in use do the following: ? Read integer from STDIN and push. ! Pop integer and write to STDOUT. @ Terminate program. & Bitwise AND of top two stack items. \| Bitwise OR of top two stack items.$ Bitwise XOR of top two stack items. ~ Bitwise NOT of top stack item. # Push stack depth (which is always 1 when I use it in the above programs). 1 On an empty stack, this pushes 1. Note that I'm using # is always used to combine it with \$, i.e. to compute XOR 1, or in other words for logical negation. Only in a few cases was I able to use ~ instead, because the subsequent & discards all the unwanted bits from the resulting -1 or -2. # IA-32 machine code, 63 bytes Hexdump of the code, with the disassembly: 0000 33 c0 xor eax, eax; c3 ret; 0001 91 xchg eax, ecx; 23 c2 and eax, edx; c3 ret; 0010 3b d1 cmp edx, ecx; d6 _emit 0xd6; c3 ret; 0011 91 xchg eax, ecx; c3 ret; 0100 3b ca cmp ecx, edx; d6 _emit 0xd6; c3 ret; 0101 92 xchg eax, edx; c3 ret; 0110 91 xchg eax, ecx; 33 c2 xor eax, edx; c3 ret; 0111 8d 04 11 lea eax, [ecx + edx]; c3 ret; 1000 91 xchg eax, ecx; // code provided by l4m2 09 d0 or eax, edx; 48 dec eax; c3 ret; 1001 3b ca cmp ecx, edx; 0f 94 c0 sete al; c3 ret; 1010 92 xchg eax, edx; 48 dec eax; c3 ret; 1011 39 d1 cmp ecx, edx; // code provided by l4m2 d6 _emit 0xd6; 40 inc aex; c3 ret; 1100 91 xchg eax, ecx; 48 dec eax; c3 ret; 1101 3b d1 cmp edx, ecx; // code inspired by l4m2 d6 _emit 0xd6; 40 inc aex; c3 ret; 1110 8d 44 11 fe lea eax, [ecx+edx-2] // code provided by l4m2 c3 ret; 1111 91 xchg eax, ecx; 40 inc eax; c3 ret; The code is longer than it could be, because it uses a standard coding convention: input in ecx and edx, and output in al. This may be expressed in C as unsigned char __fastcall func(int, int); It seems that MS Visual Studio doesn't understand the undocumented SALC opcode, so I had to use its code, instead of name. Thanks you l4m2 for improving some of the code samples! • 1110 8D4411FE LEA EAX, [ECX+EDX-2] – l4m2 Dec 18 '17 at 9:13 # C 34 bytes #define g(n,a,b)((n-1)>>3-b-2a)&1 Where n is the function number to use, but I think it would be refused so I propose this other one: # C 244 bytes (using memory) typedef int z[2][2]; z a={0,0,0,0}; z b={0,0,0,1}; z c={0,0,1,0}; z d={0,0,1,1}; z e={0,1,0,0}; z f={0,1,0,1}; z g={0,1,1,0}; z h={0,1,1,1}; z i={1,0,0,0}; z j={1,0,0,1}; z k={1,0,1,0}; z l={1,0,1,1}; z m={1,1,0,0}; z n={1,1,0,1}; z o={1,1,1,0}; z p={1,1,1,1}; it uses double indexed array. n[0][1] is (A implies B)(0,1) # Forth 138 bytes I just learned Forth. I suppose that's Ansi Forth compatible as it run also on gforth. : z create dup , 1+ does> @ -rot 3 swap - swap 2* - rshift 1 and ; 0 z a z b z c z d z e z f z g z h z i z j z k z l z m z n z o z p drop Function z create a new function with the name provided then put the logic gate number from the top of stack to the new function address. It leaves the next (n+1) logic gate function in the stack for the next declaration. you can test it : And A B 0 0 b . cr 0 1 b . cr 1 0 b . cr 1 1 b . cr ( "." print top of stack "cr" is cariage return ) • You only have to provide snippets of code for each function. – CalculatorFeline Jun 18 '17 at 15:57 # C, 268 bytes #define c(a,b)0 // 0000 #define d(a,b)a&b // 0001 #define e(a,b)a>b // 0010 #define f(a,b)a // 0011 #define g(a,b)a<b // 0100 #define h(a,b)b // 0101 #define i(a,b)a^b // 0110 #define j(a,b)a\|b // 0111 #define k(a,b)!b>a // 1000 #define l(a,b)a==b // 1001 #define m(a,b)!b // 1010 #define n(a,b)!b\|a // 1011 #define o(a,b)!a // 1100 #define p(a,b)!a\|b // 1101 #define q(a,b)!b\|!a // 1110 #define r(a,b)1 // 1111 Macros seem shorter than functions. ## Brian & Chuck, 183 bytes Thanks to Sp3000 for saving 4 bytes. Some of the programs contain an unprintable character. In particular, every \x01 should be replaced with the <SOH> (0x01) control character: 0000 ? #>. 0001 ,-?,-?>?\x01 #}>. 0010 ,-?,?>?\x01 #}>. 0011 ,?\x01+? #>. 0100 ,?,-?>?\x01 #}>. 0101 ,,?\x01+? #>. 0110 ,?>},?>?_\x01 #}+{>?_}>. 0111 ,\x01?,?>? #{>. 1000 ,?,?>?\x01 #}>. 1001 ,-?>},?>?_\x01 #}+{>>?_}>. 1010 ,,-?\x01+? #>. 1011 ,\x01?,-?>? #{>. 1100 ,-?\x01+? #>. 1101 ,\x01-?,?>? #{>. 1110 ,\x01-?,-?>? #{>. 1111 ? #>+. Input and output use byte values, so input should be two 0x00 or 0x01 bytes (without separator) and output will be one such byte. This is actually also the most sensible definition of truthy/falsy for B&C because the only control flow command ? regards zeros as falsy and everything else truthy. ### Explanations First a quick B&C primer: • Every program consists of two Brainfuck-like instances, each written on its own line. We call the first one Brian and the second one Chuck. Execution begins on Brian. • Each program's tape is the other program's source code, and each program's instruction pointer is the other program's tape head. • Only Brian can use the , (input byte) command and only Chuck can use the . (output byte) command. • Brainfuck's [] loop does not exist. Instead, the only control flow you have is ? which switches control to the other instance iff the current value under the tape head is nonzero. • In addition to > and <, there's { and } which are essentially equivalent to the Brainfuck snippets [<] and [>], that is, they move the tape head to the next zero position in that direction. The main difference is that { can also be stopped at the left end of the tape, regardless of what value it has. • For convenience, any _s in the source code are replaced with null-bytes (as these are very useful in nontrivial programs in order to catch { and }). Note that in all programs, Chuck's tape begins with a #. This could really be anything. ? works such that the tape head moves one cell before starting execution (so that the condition itself isn't executed if it happens to be a valid command). So we can't ever use the first cell of Chuck for code. There are five classes of programs, which I'll explain in detail later. For now I'm listing them here in order of increasing complexity. ### 0000, 1111: Constant functions ? #>. ? #>+. These are very simple. We switch to Chuck unconditionally. Chuck moves the tape head to the unused cell to the right and either prints it directly, or increments it first to print 1. ### 0011, 0101, 1010, 1100: Functions depending on only one input ,?\x01+? #>. ,,?\x01+? #>. ,,-?\x01+? #>. ,-?\x01+? #>. Depending on whether we start with , or ,, we're working with A or B. Let's look at the first example 0011 (i.e. A). After reading the value, we use ? as a conditional on that value. If A = 1, then this switches to Chuck, who moves the tape head to the right and prints the literally embedded 1-byte. Otherwise, control remains on Brian. Here, the 1-byte is a no-op. Then we increment the input well with + to make sure it's non-zero and then switch to Chuck with ?. This time, > moves to an unused cell to the right which is then printed as 0. In order to negated one of the values we simply decrement it with -. This turns 1 into 0 and 0 into -1, which is non-zero and hence truthy as far as ? is concerned. ### 0001, 0010, 0100, 1000: Binary functions with one truthy result ,-?,-?>?\x01 #}>. ,-?,?>?\x01 #}>. ,?,-?>?\x01 #}>. ,?,?>?\x01 #}>. This is an extension of the previous idea in order to work with two inputs. Let's look at the example of 1000 (NOR). We (potentially) read both inputs with ,?. If either of those is 1, the ? switches to Chuck. He moves the tape head to the end with } (onto the empty cell after Brian's code), moves another cell with > (still zero) and prints it with .. However, if both inputs are zero, then control is still with Brian. > then moves the tape head onto the } such that this command isn't executed when we switch to Chuck with ?. Now all that Chuck does is >. which only moves onto the 1-cell and prints that. We can easily obtain the other three functions by negating one or both of the inputs as required. ### 0111, 1011, 1101, 1110: Binary functions with three truthy results ,\x01?,?>? #{>. ,\x01?,-?>? #{>. ,\x01-?,?>? #{>. ,\x01-?,-?>? #{>. A minor modification of the previous idea in order to negated the result (i.e. print 0 when we've passed through all of Brian and 1 otherwise). Let's look at 0111 (OR) as an example. Note that the embedded 1-byte is a no-op, so this still starts with ,?,?. If either input is 1 we switch to Chuck, who moves the tape head back to the start with {. >. moves the tape head onto that 1-byte and prints it. If both inputs are zero then we remain with Brian, move the tape head onto { to skip it and then switch to Chuck. When he executes >. this time he moves onto the empty cell after Brian's code and prints the 0. Again, we easily obtain the other functions by negating one or both inputs. ### 0110, 1001: Binary functions with two truthy results ,?>},?>?_\x01 #}+{>?_}>. ,-?>},?>?_\x01 #}+{>>?_}>. This one is a bit trickier. The previous functions were reasonably simple because they can be short-circuited - the value of the first input can decide the output, and if it doesn't then we look at the other input. For these two functions, we always need to look at both inputs. The basic idea is to use the first input to decide whether the second input choose between 0 and 1 or between 1 and 0. Let's take 0110 (XOR) as an example: Consider A = 0. In this case we want to output B as is. , reads A, ? does nothing. > moves onto the next (nonzero) cell so that } brings us to the _ on Chuck. Here, we read B with , and use ? again. If B was 0 as well, we're still on Brian. > skips the } on Chuck and ? switches so that the >. prints the 0 embedded in Brian's source code. If B was 1 on the other hand, Chuck does execute the } which moves into the _ in Brian's code already, so the >. then prints the 1-byte instead. If A = 1, then we do switch to Chuck right away, who will execute }+{>?. What this does is move to the _ in Brian's source code, turns it into a 1 as well with +, then moves back to the start { and skips Brian's ? by moving one cell to the right with > before handing control back to him. This time, after Brian read's B, if B = 0, and Chuck uses >. the cell next to Brian's ? will be 1 instead of 0. Also, when B = 1, Chuck's } skips right over what to used to be a gap and moves all the way to the end of the tape, so that >. prints a zero instead. This way we're printing not B. In order to implement equivalence, we simply negated A before using it as a condition. Note that due to this we also need to add another > to Chuck to skip that - as well when moving back to the start. # ClojureScript, 88 84 76 74 bytes nil and false are falsy, all other values are truthy. Booleans coerce to 0/1 for arithmetic and inequalities. Functions can take the wrong number of arguments. 0000 nil? ; previously: (fn[]nil) 0001 and 0010 < 0011 true? ; previously: (fn[x]x) 0100 > 0101 (fn[x y]y) 0110 not= 0111 or 1000 #(= 0(+ % %2)) 1001 = 1010 #(not %2) 1011 <= 1100 not 1101 >= 1110 #(= 0(* % %2)) 1111 / ; previously: (fn[]4), inc • Isn't 0 falsy? – Leaky Nun Jun 15 '16 at 5:41 • Not in ClojureScript. – MattPutnam Jun 15 '16 at 13:57 • @LeakyNun Not in most LISPs or functional programming languages, which Clojure definitely is – cat Jun 28 '16 at 22:50 • @cat Yes in most functional programming languages! Python, for example, evaluates not not(0) to False, which is the falsey value. – Erik the Outgolfer Jul 17 '16 at 16:55 • @EʀɪᴋᴛʜᴇGᴏʟғᴇʀ Er... Python is neither purely functional nor the type of functional language I'm talking about. Python is imperative, mostly, and with some smaller (poorly executed) functional aspects. Erlang, Haskell (I think), Common LISP, Clojure, Racket, Scheme, Factor, Standard ML, Objective CAML, etc 0 is just another value and is as a result truthy, and the symbol for false (#f, f, false, etc) is false. All other values are truthy in most functional languages. – cat Jul 17 '16 at 17:02 # Brainfuck, 184178 174 bytes Input/output uses U+0000 and U+0001. 0000 . 0001 ,[,[->+<]]>. 0010 ,[,-[+>+<]]>. 0011 ,. 0100 ,-[,[->+<]]>. 0101 ,,. 0110 ,>,[-<->]<[>>+<]>. 0111 ,-[,-[+>-<]]>+. 1000 ,-[,-[+>+<]]>. 1001 ,>,[-<->]<[>>-<]>+. 1010 ,,-[+>+<]>. 1011 ,-[,[->-<]]>+. 1100 ,-[+>+<]>. 1101 ,[,-[+>-<]]>+. 1110 ,[,[->-<]]>+. 1111 +. • Your reading a conditional second input looks expensive. E.g. for 0001 couldn't you just do ,[,>]<. (given an interpreter which allows you to go left of the starting cell)? – Martin Ender Jul 28 '16 at 7:15 • @MartinEnder I figured that I wouldn't just copy Dennis' answer here. – Leaky Nun Jul 28 '16 at 7:21 # Brain-Flak, 418, 316 bytes Try it online! Let the inputs be the top two numbers on the stack at the start of the program (zero for false one for true) and the output be top of the stack at the end of the program (zero for false else for true). ### false, 4 bytes (Courtesy of Leaky Nun) (<>) ### and, 36 bytes (({}{}[(())()])){{}{}(((<{}>)))}{}{} ### A and not B, 40 bytes ((({}){}{}[(())()])){{}{}(((<{}>)))}{}{} ### A, 6 bytes ({}<>) ### not A and B, 38 bytes ((({}){}{}[(())])){{}{}(((<{}>)))}{}{} ### B, 2 bytes {} ### xor, 34 bytes (({}{}[(())])){{}{}(((<{}>)))}{}{} ### or, 6 bytes ({}{}) ### nor, 34 bytes (({}{}<(())>)){{}{}(((<{}>)))}{}{} ### xnor, 10 bytes ({}{}[()]) ### not B, 34 bytes {}(({}<(())>)){{}{}(((<{}>)))}{}{} ### B implies A, 14 bytes (({}){}{}[()]) ### not A, 34 bytes (({}<{}(())>)){{}{}(((<{}>)))}{}{} ### A implies B, 16 bytes (({}){}{}[()()]) ### nand, 12 bytes ({}{}[()()]) ### true, 6 bytes <>(()) ## Explanation Since most of these are very similar I am not going to explain exactly how each of them works. I try my best to make it clear however how all of the sixteen work. Firstly are the gates that return three of the same value (i.e. 2, 3, 5, 8, 9, 12, 14, and 15). These all follow the same pattern. First you convert the input into a two bit number with a as the twos place and B as the ones. This is done with this snippet (({}){}{}). You then subtract the value of the two bit input you want to isolate ({}[value]). (In the actual code the subtraction and the conversion are done in one step to save bytes). This can be combined with a not if needed: (({}<(())>)){{}{}(((<{}>)))}{}{}. Next up: and, nor, or, xor, and xnor. These work similarly to the ones above. In fact some of these are included above, however this method is shorter. The trick I used here is that these each correspond to a sum of A B. e.g. xor evaluates to true if A+B = 1 and false otherwise. First you add A B and subtract the relevant amount. Expressed as ({}{}[0,1,2 or 3]). Then if necessary conduct a not Next up: A, B, not A and not B. These are pretty much self explanatory. We start by removing the unnecessary value and then we either negate or finish. Lastly are the two simpletons: true and false. For these we push the correct value to the off stack. The <> nilad returns zero so we can save two bytes by using the switch as the zero value. Not the most efficient solution out there (perhaps the most efficient in Brain-Flak), but I had a good deal of fun writing these and I implore you to attempt to shorten these. • (<>) is enough for false; also, (<{}{}>) is 8 bytes – Leaky Nun Jul 28 '16 at 1:20 • Wow I had a much stricter definition of the challenge. Thank you. I will reduce this greatly – Post Rock Garf Hunter Jul 28 '16 at 1:35 • What do you mean? – Leaky Nun Jul 28 '16 at 1:35 • I thought that I had to remove the existing inputs and place the result in its place. (<>) will leave the inputs and put the zero on the other stack. – Post Rock Garf Hunter Jul 28 '16 at 1:36 • Isn't <> enough for false due to implicit zeroes? Also, I think a can be the empty program. true can be <>[][] (doesn't save bytes, but looks cool :P). – CalculatorFeline Jun 18 '17 at 16:04 ## ProgFk, 18.5 17.5 bytes As ProgFk's instructions are specified in nibbles, the below code is given in hexadecimal, one logic gate per line and with spaces in between the bytes. 3 E1 DE 2D <empty> DE 1 1 E3 E2 E2 D E3 D 1D DE 2 D DE 1D E1 D 4 ### Explanation ProgFk is a tape-based esolang (similar to Brainfuck) where each cell is a bit and instructions are given as nibbles (4 bytes). Instructions operate on the cell pointed to by the instruction pointer. Input is given in the first and second cells (with A and B being the first and second cells respectively), and the instruction pointer starts at the first cell. Output is stored in the first cell. Each instruction used is explained below. 1 Increment the instruction pointer. 2 Decrement the instruction pointer. 3 Set the current bit to 0. 4 Set the current bit to 1. D Perform a NOT on the current bit. E The next instruction is an extended instruction. Extended instructions: 1 Set the current bit to the current bit AND the next bit. 2 Set the current bit to the current bit OR the next bit. 3 Set the current bit to the current bit XOR the next bit. 6 Swap the current bit and the next bit. Saved a byte thanks to @LeakyNun! ## Actually, 24 bytes These programs take input as A\nB (with \n representing a newline), which leaves B on top of the stack, with A below. False is represented by 0, and True is represented by any positive integer. é0 (false: clear stack, push 0) * (and: multiply) < (A and not B: less-than) > (B and not A: greater-than)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4577958881855011, "perplexity": 3314.8943403012254}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875141806.26/warc/CC-MAIN-20200217085334-20200217115334-00459.warc.gz"}
https://aakinshin.net/posts/non-normal-median-distribution/	# Non-normal median sampling distribution Let’s consider the classic sample median. If a sample is sorted and the number of sample elements is odd, the median is the middle element. In the case of an even number of sample elements, the median is an arithmetic average of the two middle elements. Now let’s say we randomly take many samples from the same distribution and calculate the median for each of them. Next, we build a sampling distribution based on these median values. There is a well-known fact that this distribution is asymptotically normal with mean $$M$$ and variance $$1/(4nf^2(M))$$, where $$n$$ is the number of elements in samples, $$f$$ is the probability density function of the original distribution, and $$M$$ is the true median of the original distribution. Unfortunately, if we try to build such sampling distributions in practice, we may see that they are not always normal. There are some corner cases that prevent us from using the normal model in general. If you implement general routines that analyze the median behavior, you should keep such cases in mind. In this post, we briefly talk about some of these cases. ### Regular case We start with a regular case when the median sampling distribution actually behaves like a normal one. Let’s consider the standard exponential distribution ($$\lambda = 1$$): Its median of this distribution is well-known: $M = \frac{\ln 2}{\lambda}$ The corresponding PDF is also known: $f(x) = \lambda e^{-\lambda x}$ Thus, the mean of the sampling distribution is $$\mu = M = \ln 2 \approx 0.693$$. If we set $$n = 50$$, the variance is $$\sigma^2 = 1/(4nf^2(m)) = 0.02$$. Now let’s generate $$10\,000$$ samples of size $$50$$, get the sample median for each of them, and build the kernel density estimation of the sampling distribution using the Sheather & Jones method: As we can see, the actual sampling distribution is pretty close to the theoretical one. So far, the normality assumption works as expected. ### Small samples Now let’s reduce the sample size to $$n=5$$ and repeat the experiment. The theoretical model has the same mean, but the variance is $$\sigma^2 = 0.2$$. Here are the simulation results: Now the theoretical model is not so close to the empirical one. The median sampling distribution is only asymptotically normal. Thus, we shouldn’t expect the predicted normality on small samples. The “proper” sample size heavily depends on the underlying distributions. In some cases, you may need several hundreds of elements in each sample to achieve the expected normality. ### Zero PDF Now let’s talk about corner cases. The variance of the sampling distribution should be asymptotically equal $$1/(4nf^2(M))$$. But what if $$f(M) = 0$$? Let’s consider a perfect bimodal distribution formed by two uniform distributions $$\mathcal{U}(-2, -1)$$ and $$\mathcal{U}(1, 2)$$: Here is the corresponding empirical sampling distribution: As we can see, it’s trimodal. Doesn’t look like a normal one, does it? Unfortunately, when $$f(M) = 0$$, we can’t rely on the normal model anymore. ### Infinite PDF Another corner case is $$f(M) = \infty$$. Let’s consider the rectified Gaussian distribution which could be obtained from the normal distribution by replacing all the negative values with zeros: This distribution is a mixture of a discrete one (the Dirac delta function $$\delta(0)$$) and a continuous one (the “right part” of the normal distribution) with equal weights. Such cases often arise in real life when we have common “border” values across sampling data. Here is the corresponding sampling distribution: It definitely doesn’t look like a normal one. ### Conclusion Asymptotical models could be useful in statistical analysis when we are sure that external conditions allow getting a picture that is close enough to the theoretical one. Without careful analysis of these conditions, we couldn’t apply the asymptotical model in the general case. As we can see, a mindless usage of the normal model for the median sampling distribution could bring a lot of trouble in corner cases.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.96141117811203, "perplexity": 257.6055628045804}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030335514.65/warc/CC-MAIN-20221001003954-20221001033954-00524.warc.gz"}
https://tug.org/pipermail/tex-live/2014-December/036170.html	# [tex-live] Errors building latest 2014 tex --ini latex.ltx Joseph Wright joseph.wright at morningstar2.co.uk Mon Dec 8 23:23:53 CET 2014 ```On 08/12/2014 18:22, Juan Falgueras wrote: > > The problem is not me making the default fmts I use a lot of fmt for further faster texing… That is something I have been doing for many years (since 1989, to be precise). The problem is when I active the 2014 version. With the 2012 nor before, I have ever seen any trouble > > I am sending you the Terminal output of simply: > > tex --ini latex.ltx > > that ends with: > > … > (/usr/local/texlive/2014/texmf-dist/tex/generic/hyph-utf8/patterns/tex/hyph-ka. > tex > ! Undefined control sequence. > \utfthreeuniglyph ... \expandafter {\the \numexpr > 4096(#1-224)+64(`#2-128)... > l.36 .^^e1^^83^^90 > ^^e1^^83^^954^^e1^^83^^a0^^e1^^83^^ac^^e1^^83^^a7^^e1^^83^^90 > > ? x > No pages of output. > Transcript written on latex.log. > > > > > Thanks for any hint here. I am really stuck with this error. e-TeX is assumed nowadays by everything other than 'pure' plain TeX. AS such, the \numexpr primitive is used by some of the hyphenation patterns built into the LaTeX format by babel. You have two broad options - Enable the e-TeX extensions, e.g. etex --ini latex.ltx - Use a custom version of either the entire hyphenation control file or the specifc files using the extensions to avoid using e-TeX. The LaTeX team announced some years ago that e-Tex would be assumed and while latex.ltx doesn't currently require the extensions other team packages do, quite apart from third-party code. I'd therefore strongly recommend the first approach: enable e-TeX. -- Joseph Wright ```	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9615399241447449, "perplexity": 22751.337018967577}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247481249.5/warc/CC-MAIN-20190216230700-20190217012700-00478.warc.gz"}
https://firefox-source-docs.mozilla.org/devtools/tests/performance-tests-damp.html	# Performance Tests: DAMP¶ DAMP (DevTools At Maximum Performance) is our test suite to track performance. ## How to run it locally?¶ ./mach talos-test --suite damp Note that the first run is slower as it pulls a large tarball with various website copies. This will run all DAMP tests, you can filter by test name with: ./mach talos-test --suite damp --subtests console This command will run all tests which contains “console” in their name. Note that in continuous integration, DAMP tests are split in smaller tests suites: damp-inspector, damp-other and damp-webconsole. Actually --suite damp is only used locally because it contains all possible tests and makes it easier to use. But if needed you can substitute damp with any of the other test suites if you want to only run tests associated to a given test suite. You can find the mapping between tests and test suites in damp-tests.js. ### Command line options¶ #### Running tests only once¶ ./mach talos-test --suite damp --cycles 1 --tppagecycles 1 --cycles will limit the number of Firefox restart to only one, while --tppagecycles will limit the number of test re-run in each firefox start to one. This is often helpful when debugging one particular subtest. #### Taking screenshots¶ DEBUG_DEVTOOLS_SCREENSHOTS=1 ./mach talos-test --suite damp When passing DEBUG_DEVTOOLS_SCREENSHOTS env variable, screenshots will be taken after each subtest was run. The screenshot will be opened in new tabs and their title includes the subtest label. Firefox won’t automatically close so that you can view the screenshots. #### Recording a profile¶ ./mach talos-test --suite damp --gecko-profile --gecko-profile-entries 100000000 This will automatically record the tests and open the profile. You may use the following command in order to focus on just one subtest run: ./mach talos-test --suite damp --subtests custom.webconsole --cycles 1 --tppagecycles 1 --gecko-profile --gecko-profile-entries 100000000 ## How to run it on try?¶ ./mach try fuzzy --query "'test-linux1804-64-shippable-qr/ 'damp" --rebuild 6 • Linux appears to build and run quickly, and offers quite stable results over the other OSes. The vast majority of performance issues for DevTools are OS agnostic, so it doesn’t really matter which one you run them on. • “damp” is the talos bucket in which we run DAMP. • And 6 is the number of times we run DAMP tests. That’s to do averages between all the 6 runs and helps filtering out the noise. ## How to get performance profiles on try?¶ Once you have a successful try job for damp: • select this job in treeherder • click on the ... menu in the bottom left • select “Create Gecko Profile” This should start a new damp job called damp-p. Once damp-p is finished: • select the damp-p job • click on Job Details tab • click on open in Firefox Profiler ## What does it do?¶ DAMP measures three important operations: • Open a toolbox • Close the toolbox It measures the time it takes to do each of these operations for the following panels: inspector, console, netmonitor debugger, memory, performance. It runs all these three tests two times. Each time against a different web page: • “simple”: an empty webpage. This test highlights the performance of all tools against the simplest possible page. • “complicated”: a copy of bild.de website. This is supposed to represent a typical website to debug via DevTools. Then, there are a couple of extra tests: • “cold”: we run the three operations (open toolbox, page reload and close toolbox) first with the inspector. This is run first after Firefox’s startup, before any other test. This test allows to measure a “cold startup”. When a user first interacts with DevTools, many resources are loaded and cached, so that all next interactions will be significantly faster. • and many other smaller tests, focused on one particular feature or possible slowness for each panel. ## How to see the results from try?¶ First, open TreeHerder. A link is displayed in your console when executing ./mach try. You should also receive a mail with a link to it. Look for “T-e10s(+6)”, click on “+6”, then click on “damp”: On the bottom panel that just opened, click on “Compare result against another revision”. You are now on PerfHerder, click on “Compare”, Next to “Talos” select menu, in the filter textbox, type “damp”. Under “damp opt e10s” item, mouse over the “linux64” line, click on “subtests” link. And here you get the results for each DAMP test: On this page, you can filter by test name with the filter box on top of the result table. This table has the following columns: • Base: Average time it took to run the test on the base build (by default, the last 2 days of DAMP runs on mozilla-central revisions) • New: Average time it took to run the test on the new build, the one with your patches. Both “Base” and “New” have a “± x.xx%” suffix which tells you the variance of the timings. i.e. the average difference in percent between the median timing and both the slowest and the fastest. • Delta: Difference in percent between the base and new runs. The color of this can be red, orange or green: • Red means “certainly regressing” • Orange means “possibly regressing” • Green means “certainly improving” • No colored background means “nothing to conclude” The difference between certainly and possibly is explained by the next column. • Confidence: If there is a significant difference between the two runs, tells if the results is trustworthy. • “low” either means there isn’t a significant difference between the two runs, or the difference is smaller than the typical variance of the given test. If the test is known to have an execution time varying by 2% between two runs of the same build, and you get a 1% difference between your base and new builds, the confidence will be low. You really can’t make any conclusion. • “med” means medium confidence and the delta is around the size of the variance. It may highlight a regression, but it can still be justified by the test noise. • “high” means that this is a high confidence difference. The delta is significantly higher than the typical test variance. A regression is most likely detected. There is also “Show only important changes” checkbox, which helps seeing if there is any significant regression. It will only display regressions and improvements with a medium or high confidence. ## How to contribute to DAMP?¶ DAMP is based on top of a more generic test suite called Talos. Talos is a Mozilla test suite to follow all Firefox components performance. It is written in Python and here are the sources in mozilla-central. Compared to the other test suites, it isn’t run on the cloud, but on dedicated hardware. This is to ensure performance numbers are stable over time and between two runs. Talos runs various types of tests. More specifically, DAMP is a Page loader test. The source code for DAMP is also in mozilla-central. See Writing new performance test for more information about the implementation of DAMP tests. ## How to use PerfHerder charts¶ On PerfHerder charts, each circle is a push on mozilla-central. When you see a spike or a drop, you can try to identify the patch that relates to it by clicking the circles. It will show a black popup. Then click on the changeset hash like “cb717386aec8” and you will get a mercurial changelog. Then it is up to you to read the changelog and see which changeset may have hit the performance. For example, open this page. This is tracking inspector opening performance against the “Simple” page. See the regression on Dec 31th? Now, click on the first yellow circle of this spike. You will get a black popup like this one: Click on the changelog link to see which changesets were added during this run. Here, you will see that the regression comes from these patches: • Bug 1245921 - Turn toolbox toolbar into a React component • Bug 1245921 - Monkey patch ReactDOM event system for XUL	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3234735131263733, "perplexity": 3646.6611180359155}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662531779.10/warc/CC-MAIN-20220520093441-20220520123441-00775.warc.gz"}
http://www.avlandesign.com/inf-density.htm	Density Density, or volumic mass, is a measure of mass per unit volume. The average density of an object equals its total mass divided by its total volume. An object made from a comparatively dense material (such as iron) will have more mass than an equal-sized object made from some less dense substance (such as aluminium). A tables of densities of some materials: ## Notation, units, and properties The standard symbol used for density is ρ, the Greek letter rho. So we have where m is the object's total mass ([M]; kg) V is the object's total volume ([L³]; m³) The SI unit of density is the kilogram per cubic metre (kg/m³), but grams per cubic centimeter (g/cm³) and kilograms per litre (kg/L) are also commonly used. Liquid water has a density of about 1000 kg/m³ (or 1 kg/L or 1 g/cm³), solid iron has a density of about 8000 kg/m³, and air at room temperature and atmospheric pressure has a density of about 1.2 kg/m³. The density of an object or substance depends on its temperature, with higher temperature usually (but not always) resulting in lower density. This temperature-density relationship is captured by the substance's volumetric thermal expansion coefficient β. The density of a gas (and to a much lesser extent also that of a solid or liquid) further depends on the pressure, with higher pressure resulting in higher density. The density of a gas is very dependent on the gas laws. The density of an object does not have to be uniform, for instance if the object is composed of different materials, or if its pressure or temperature is not the same everywhere. The density of a moving gas may vary if its velocities yield a Mach number higher than about 0.3. In this case, one defines the density at a specific point by taking a tiny sphere around that point and dividing the mass contained within that sphere by the sphere's volume. Density of water (at 1 atm) Density of air (at 1 atm) Temp (°C) Density (kg/m3) 100 958.4 80 971.8 60 983.2 40 992.2 30 995.6502 25 997.0479 22 997.7735 20 998.2071 15 999.1026 10 999.7026 4 999.9720 0 999.8395 Temp (°C) Density (kg/m3) –25 1.423 –20 1.395 –15 1.368 –10 1.342 –5 1.316 0 1.293 5 1.269 10 1.247 15 1.225 20 1.204 25 1.184 30 1.164 35 1.146 density of air at room temperature (20°C): 1.204 kg/m3 Other units In Imperial units or U.S. customary units, the units of density include pounds per cubic foot (lb/ft³), pounds per cubic yard (lb/yd³), pounds per cubic inch (lb/in³), ounces per cubic inch (oz/in³), pounds per gallon (for U.S. or imperial gallons) (lb/gal), pounds per U.S. bushel (lb/bu), in some engineering calculations slugs per cubic foot, and other less common units. The maximum density of pure water at a pressure of one standard atmosphere is 999.861 kg/m³; this occurs at a temperature of about 3.98°C (277.13 K). From 1901 to 1964, a litre was defined as exactly the volume of 1 kg of water at maximum density, and the maximum density of pure water was 1.000 000 kg/L (now 0.999 972 kg/L). However, while that definition of the litre was in effect, just as it is now, the maximum density of pure water was 0.999 972 kg/dm³. During that period students had to learn the esoteric fact that a cubic centimeter and a milliliter were slightly different volumes, with 1 mL = 1.000 028 cm³. (often stated as 1.000 027 cm³ in earlier literature). Specific gravity Another form of measurement closely associated with density is specific gravity. The specific gravity of a material is the density of that material compared to the density of some standard. For solids and liquids, the most common standard is water, whose density is 1.00 gram per cubic centimeter. The specific gravity of iron, then, is its density (7.87 grams per cubic centimeter) divided by the density of water (1.00 gram per cubic centimeter). You can see that the numerical value for the specific gravity of a solid or liquid is always the same as that of its density. The reason is that the divisor in every case is 1 gram per cubic centimeter, the density of water. For iron, the specific gravity is 7.87. The only difference between density and specific gravity for solids and liquids is that specific gravity has no label. In dividing 7.87 grams per cubic centimeter by 1.00 gram per cubic centimeter, the labels divide out (cancel), leaving only the number. The specific gravity of gases is somewhat more difficult since the most common standards are air (density = 1.293 grams per cubic centimeter) or hydrogen (density = 0.0899 gram per cubic centimeter). The specific gravity of oxygen using air as a standard, then, is its density (1.429 grams per cubic centimeter) divided by the density of air (1.293 grams per cubic centimeter), or 1.105. Using hydrogen as a standard, the specific gravity of oxygen is 1.429 grams per cubic centimeter ÷ 0.0899 gram per cubic centimeter, or 15.9.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8634520769119263, "perplexity": 771.5462938223783}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860115836.8/warc/CC-MAIN-20160428161515-00017-ip-10-239-7-51.ec2.internal.warc.gz"}
https://gitlab.isc.org/sebschrader/kea/-/blame/4ae9b5ea7462f0d2a7c87c8b3466ca100a310c74/src/lib/dhcp/iface_mgr.h	iface_mgr.h 24 KB Tomek Mrugalski committed Jun 30, 2011 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 // Copyright (C) 2011 Internet Systems Consortium, Inc. ("ISC") // // Permission to use, copy, modify, and/or distribute this software for any // purpose with or without fee is hereby granted, provided that the above // copyright notice and this permission notice appear in all copies. // // THE SOFTWARE IS PROVIDED "AS IS" AND ISC DISCLAIMS ALL WARRANTIES WITH // REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY // AND FITNESS. IN NO EVENT SHALL ISC BE LIABLE FOR ANY SPECIAL, DIRECT, // INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM // LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE // OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR // PERFORMANCE OF THIS SOFTWARE. #ifndef IFACE_MGR_H #define IFACE_MGR_H #include Tomek Mrugalski committed Oct 14, 2011 19 #include Tomek Mrugalski committed Oct 14, 2011 20 #include Tomek Mrugalski committed Oct 14, 2011 21 #include Tomek Mrugalski committed Nov 08, 2011 22 #include Tomek Mrugalski committed Dec 07, 2011 23 24 #include #include Tomek Mrugalski committed Nov 08, 2011 25 26 #include #include Tomek Mrugalski committed Jun 30, 2011 27 28 29 namespace isc { Tomek Mrugalski committed Oct 14, 2011 30 31 32 33 34 35 36 37 38 39 namespace dhcp { /// @brief handles network interfaces, transmission and reception /// /// IfaceMgr is an interface manager class that detects available network /// interfaces, configured addresses, link-local addresses, and provides /// API for using sockets. /// class IfaceMgr : public boost::noncopyable { public: /// type that defines list of addresses Tomek Mrugalski committed Nov 10, 2011 40 typedef std::vector AddressCollection; Tomek Mrugalski committed Oct 14, 2011 41 Tomek Mrugalski committed May 30, 2012 42 43 44 /// defines callback used when commands are received over control session typedef void (SessionCallback) (void); Tomek Mrugalski committed Oct 14, 2011 45 46 47 /// maximum MAC address length (Infiniband uses 20 bytes) static const unsigned int MAX_MAC_LEN = 20; Tomek Mrugalski committed Mar 13, 2012 48 49 50 51 52 53 54 55 56 /// @brief Packet reception buffer size /// /// RFC3315 states that server responses may be /// fragmented if they are over MTU. There is no /// text whether client's packets may be larger /// than 1500. For now, we can assume that /// we don't support packets larger than 1500. static const uint32_t RCVBUFSIZE = 1500; Tomek Mrugalski committed Nov 09, 2011 57 58 59 60 61 62 /// Holds information about socket. struct SocketInfo { uint16_t sockfd_; /// socket descriptor isc::asiolink::IOAddress addr_; /// bound address uint16_t port_; /// socket port uint16_t family_; /// IPv4 or IPv6 Tomek Mrugalski committed Dec 05, 2011 63 64 65 66 67 68 /// @brief SocketInfo constructor. /// /// @param sockfd socket descriptor /// @param addr an address the socket is bound to /// @param port a port the socket is bound to Tomek Mrugalski committed Nov 09, 2011 69 70 71 72 73 74 75 76 SocketInfo(uint16_t sockfd, const isc::asiolink::IOAddress& addr, uint16_t port) :sockfd_(sockfd), addr_(addr), port_(port), family_(addr.getFamily()) { } }; /// type that holds a list of socket informations typedef std::list SocketCollection; Tomek Mrugalski committed Oct 14, 2011 77 /// @brief represents a single network interface Tomek Mrugalski committed Oct 14, 2011 78 /// Tomek Mrugalski committed Oct 14, 2011 79 80 81 /// Iface structure represents network interface with all useful /// information, like name, interface index, MAC address and /// list of assigned addresses Tomek Mrugalski committed Dec 05, 2011 82 83 class Iface { public: Tomek Mrugalski committed Nov 09, 2011 84 85 86 87 88 89 /// @brief Iface constructor. /// /// Creates Iface object that represents network interface. /// /// @param name name of the interface /// @param ifindex interface index (unique integer identifier) Tomek Mrugalski committed Oct 14, 2011 90 91 Iface(const std::string& name, int ifindex); Marcin Siodelski committed Aug 03, 2012 92 93 94 /// @brief Closes all open sockets on interface void closeSockets(); Tomek Mrugalski committed Nov 09, 2011 95 96 97 /// @brief Returns full interface name as "ifname/ifindex" string. /// /// @return string with interface name Tomek Mrugalski committed Oct 14, 2011 98 99 std::string getFullName() const; Tomek Mrugalski committed Nov 09, 2011 100 101 102 /// @brief Returns link-layer address a plain text. /// /// @return MAC address as a plain text (string) Tomek Mrugalski committed Oct 14, 2011 103 std::string getPlainMac() const; Tomek Mrugalski committed Jun 30, 2011 104 Tomek Mrugalski committed Mar 16, 2012 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 /// @brief Sets MAC address of the interface. /// /// @param mac pointer to MAC address buffer /// @param macLen length of mac address void setMac(const uint8_t mac, size_t macLen); /// @brief Returns MAC length. /// /// @return length of MAC address size_t getMacLen() const { return mac_len_; } /// @brief Returns pointer to MAC address. /// /// Note: Returned pointer is only valid as long as the interface object /// that returned it. const uint8_t* getMac() const { return mac_; } Tomek Mrugalski committed Dec 16, 2011 122 123 124 125 126 127 /// @brief Sets flag__ fields based on bitmask value returned by OS /// /// Note: Implementation of this method is OS-dependent as bits have /// different meaning on each OS. /// /// @param flags bitmask value returned by OS in interface detection Tomek Mrugalski committed Nov 30, 2011 128 129 void setFlags(uint32_t flags); Tomek Mrugalski committed Nov 09, 2011 130 131 132 /// @brief Returns interface index. /// /// @return interface index Tomek Mrugalski committed Nov 08, 2011 133 134 uint16_t getIndex() const { return ifindex_; } Tomek Mrugalski committed Nov 09, 2011 135 136 137 138 139 /// @brief Returns interface name. /// /// @return interface name std::string getName() const { return name_; }; Tomek Mrugalski committed Mar 16, 2012 140 141 142 143 144 145 146 147 148 149 /// @brief Sets up hardware type of the interface. /// /// @param type hardware type void setHWType(uint16_t type ) { hardware_type_ = type; } /// @brief Returns hardware type of the interface. /// /// @return hardware type uint16_t getHWType() const { return hardware_type_; } Tomek Mrugalski committed Nov 09, 2011 150 151 152 153 154 155 156 157 158 159 /// @brief Returns all interfaces available on an interface. /// /// Care should be taken to not use this collection after Iface object /// ceases to exist. That is easy in most cases as Iface objects are /// created by IfaceMgr that is a singleton an is expected to be /// available at all time. We may revisit this if we ever decide to /// implement dynamic interface detection, but such fancy feature would /// mostly be useful for clients with wifi/vpn/virtual interfaces. /// /// @return collection of addresses Tomek Mrugalski committed Nov 08, 2011 160 161 const AddressCollection& getAddresses() const { return addrs_; } Tomek Mrugalski committed Nov 09, 2011 162 163 164 165 166 167 /// @brief Adds an address to an interface. /// /// This only adds an address to collection, it does not physically /// configure address on actual network interface. /// /// @param addr address to be added Tomek Mrugalski committed Nov 08, 2011 168 169 170 171 void addAddress(const isc::asiolink::IOAddress& addr) { addrs_.push_back(addr); } Tomek Mrugalski committed Nov 09, 2011 172 173 174 175 176 177 178 179 180 /// @brief Deletes an address from an interface. /// /// This only deletes address from collection, it does not physically /// remove address configuration from actual network interface. /// /// @param addr address to be removed. /// /// @return true if removal was successful (address was in collection), /// false otherwise Tomek Mrugalski committed Nov 08, 2011 181 182 bool delAddress(const isc::asiolink::IOAddress& addr); Tomek Mrugalski committed Nov 09, 2011 183 184 /// @brief Adds socket descriptor to an interface. /// Tomek Mrugalski committed Feb 03, 2012 185 /// @param sock SocketInfo structure that describes socket. Tomek Mrugalski committed Nov 09, 2011 186 187 188 189 190 191 192 193 void addSocket(const SocketInfo& sock) { sockets_.push_back(sock); } /// @brief Closes socket. /// /// Closes socket and removes corresponding SocketInfo structure /// from an interface. /// Tomek Mrugalski committed Feb 03, 2012 194 /// @param sockfd socket descriptor to be closed/removed. Tomek Mrugalski committed Nov 09, 2011 195 196 197 /// @return true if there was such socket, false otherwise bool delSocket(uint16_t sockfd); Marcin Siodelski committed Aug 03, 2012 198 199 200 201 202 203 204 205 206 207 208 209 210 211 /// @brief Returns collection of all sockets added to interface. /// /// When new socket is created with @ref IfaceMgr::openSocket /// it is added to sockets collection on particular interface. /// If socket is opened by other means (e.g. function that does /// not use @ref IfaceMgr::openSocket) it will not be available /// in this collection. Note that functions like /// @ref IfaceMgr::openSocketFromIface use /// @ref IfaceMgr::openSocket internally. /// /// @return collection of sockets added to interface const SocketCollection& getSockets() const { return sockets_; } protected: Tomek Mrugalski committed Nov 09, 2011 212 213 214 /// socket used to sending data SocketCollection sockets_; Tomek Mrugalski committed Oct 14, 2011 215 216 217 218 219 /// network interface name std::string name_; /// interface index (a value that uniquely indentifies an interface) int ifindex_; Tomek Mrugalski committed Oct 14, 2011 220 221 /// list of assigned addresses Tomek Mrugalski committed Nov 08, 2011 222 AddressCollection addrs_; Tomek Mrugalski committed Oct 14, 2011 223 224 225 226 227 /// link-layer address uint8_t mac_[MAX_MAC_LEN]; /// length of link-layer address (usually 6) Tomek Mrugalski committed Mar 16, 2012 228 229 230 231 size_t mac_len_; /// hardware type uint16_t hardware_type_; Tomek Mrugalski committed Oct 14, 2011 232 Tomek Mrugalski committed Mar 16, 2012 233 public: Tomek Mrugalski committed Mar 16, 2012 234 235 236 /// @todo: Make those fields protected once we start supporting more /// than just Linux Tomek Mrugalski committed Nov 30, 2011 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 /// specifies if selected interface is loopback bool flag_loopback_; /// specifies if selected interface is up bool flag_up_; /// flag specifies if selected interface is running /// (e.g. cable plugged in, wifi associated) bool flag_running_; /// flag specifies if selected interface is multicast capable bool flag_multicast_; /// flag specifies if selected interface is broadcast capable bool flag_broadcast_; /// interface flags (this value is as is returned by OS, /// it may mean different things on different OSes) uint32_t flags_; Tomek Mrugalski committed Jun 30, 2011 256 }; Tomek Mrugalski committed Oct 14, 2011 257 Tomek Mrugalski committed Oct 14, 2011 258 259 260 261 262 // TODO performance improvement: we may change this into // 2 maps (ifindex-indexed and name-indexed) and // also hide it (make it public make tests easier for now) /// type that holds a list of interfaces Tomek Mrugalski committed Nov 08, 2011 263 typedef std::list IfaceCollection; Tomek Mrugalski committed Oct 14, 2011 264 265 266 267 268 269 270 271 272 273 274 275 276 277 /// IfaceMgr is a singleton class. This method returns reference /// to its sole instance. /// /// @return the only existing instance of interface manager static IfaceMgr& instance(); /// @brief Returns interface with specified interface index /// /// @param ifindex index of searched interface /// /// @return interface with requested index (or NULL if no such /// interface is present) /// Tomek Mrugalski committed Dec 14, 2011 278 Iface getIface(int ifindex); Tomek Mrugalski committed Oct 14, 2011 279 280 281 282 283 284 285 286 287 288 289 /// @brief Returns interface with specified interface name /// /// @param ifname name of searched interface /// /// @return interface with requested name (or NULL if no such /// interface is present) /// Iface* getIface(const std::string& ifname); Tomek Mrugalski committed Feb 17, 2012 290 291 /// @brief Returns container with all interfaces. /// Tomek Mrugalski committed Mar 08, 2012 292 293 294 295 /// This reference is only valid as long as IfaceMgr is valid. However, /// since IfaceMgr is a singleton and is expected to be destroyed after /// main() function completes, you should not worry much about this. /// Tomek Mrugalski committed Feb 17, 2012 296 297 298 /// @return container with all interfaces. const IfaceCollection& getIfaces() { return ifaces_; } Tomek Mrugalski committed Nov 09, 2011 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 /// @brief Return most suitable socket for transmitting specified IPv6 packet. /// /// This method takes Pkt6 (see overloaded implementation that takes /// Pkt4) and chooses appropriate socket to send it. This method /// may throw BadValue if specified packet does not have outbound /// interface specified, no such interface exists, or specified /// interface does not have any appropriate sockets open. /// /// @param pkt a packet to be transmitted /// /// @return a socket descriptor uint16_t getSocket(const isc::dhcp::Pkt6& pkt); /// @brief Return most suitable socket for transmitting specified IPv6 packet. /// /// This method takes Pkt4 (see overloaded implementation that takes /// Pkt6) and chooses appropriate socket to send it. This method /// may throw BadValue if specified packet does not have outbound /// interface specified, no such interface exists, or specified /// interface does not have any appropriate sockets open. /// /// @param pkt a packet to be transmitted /// /// @return a socket descriptor uint16_t getSocket(const isc::dhcp::Pkt4& pkt); Tomek Mrugalski committed Oct 14, 2011 325 326 327 328 329 330 /// debugging method that prints out all available interfaces /// /// @param out specifies stream to print list of interfaces to void printIfaces(std::ostream& out = std::cout); Tomek Mrugalski committed Dec 05, 2011 331 /// @brief Sends an IPv6 packet. Tomek Mrugalski committed Oct 14, 2011 332 /// Tomek Mrugalski committed Dec 05, 2011 333 /// Sends an IPv6 packet. All parameters for actual transmission are specified in Tomek Mrugalski committed Oct 14, 2011 334 335 /// Pkt6 structure itself. That includes destination address, src/dst port /// and interface over which data will be sent. Tomek Mrugalski committed Oct 14, 2011 336 337 338 339 /// /// @param pkt packet to be sent /// /// @return true if sending was successful Tomek Mrugalski committed Feb 17, 2012 340 bool send(const Pkt6Ptr& pkt); Tomek Mrugalski committed Oct 14, 2011 341 Tomek Mrugalski committed Dec 05, 2011 342 343 344 345 346 347 348 349 350 /// @brief Sends an IPv4 packet. /// /// Sends an IPv4 packet. All parameters for actual transmission are specified /// in Pkt4 structure itself. That includes destination address, src/dst /// port and interface over which data will be sent. /// /// @param pkt a packet to be sent /// /// @return true if sending was successful Tomek Mrugalski committed Feb 17, 2012 351 bool send(const Pkt4Ptr& pkt); Tomek Mrugalski committed Nov 08, 2011 352 Tomek Mrugalski committed Dec 05, 2011 353 /// @brief Tries to receive IPv6 packet over open IPv6 sockets. Tomek Mrugalski committed Oct 14, 2011 354 /// Tomek Mrugalski committed Dec 05, 2011 355 /// Attempts to receive a single IPv6 packet of any of the open IPv6 sockets. Tomek Mrugalski committed Oct 14, 2011 356 357 358 /// If reception is successful and all information about its sender /// are obtained, Pkt6 object is created and returned. /// Tomek Mrugalski committed Oct 14, 2011 359 360 361 /// TODO Start using select() and add timeout to be able /// to not wait infinitely, but rather do something useful /// (e.g. remove expired leases) Tomek Mrugalski committed Oct 14, 2011 362 /// Tomek Mrugalski committed Oct 14, 2011 363 /// @return Pkt6 object representing received packet (or NULL) Tomek Mrugalski committed Mar 07, 2012 364 Pkt6Ptr receive6(); Tomek Mrugalski committed Nov 08, 2011 365 Tomek Mrugalski committed Dec 05, 2011 366 367 368 369 370 371 /// @brief Tries to receive IPv4 packet over open IPv4 sockets. /// /// Attempts to receive a single IPv4 packet of any of the open IPv4 sockets. /// If reception is successful and all information about its sender /// are obtained, Pkt4 object is created and returned. /// Tomek Mrugalski committed May 30, 2012 372 /// @param timeout specifies timeout (in seconds) Tomek Mrugalski committed Dec 05, 2011 373 374 /// /// @return Pkt4 object representing received packet (or NULL) Tomek Mrugalski committed Jun 11, 2012 375 Pkt4Ptr receive4(uint32_t timeout); Tomek Mrugalski committed Nov 08, 2011 376 Tomek Mrugalski committed Nov 08, 2011 377 378 379 380 381 382 383 384 385 /// Opens UDP/IP socket and binds it to address, interface and port. /// /// Specific type of socket (UDP/IPv4 or UDP/IPv6) depends on passed addr /// family. /// /// @param ifname name of the interface /// @param addr address to be bound. /// @param port UDP port. /// Tomek Mrugalski committed Dec 05, 2011 386 387 388 /// Method will throw if socket creation, socket binding or multicast /// join fails. /// Tomek Mrugalski committed Nov 08, 2011 389 /// @return socket descriptor, if socket creation, binding and multicast Tomek Mrugalski committed Dec 05, 2011 390 /// group join were all successful. Tomek Mrugalski committed Dec 07, 2011 391 int openSocket(const std::string& ifname, Marcin Siodelski committed Jun 14, 2012 392 393 const isc::asiolink::IOAddress& addr, const uint16_t port); Tomek Mrugalski committed Nov 08, 2011 394 Marcin Siodelski committed Jun 14, 2012 395 396 /// @brief Opens UDP/IP socket and binds it to interface specified. /// Stephen Morris committed Jun 25, 2012 397 398 399 400 /// This method differs from \ref openSocket in that it does not require /// the specification of a local address to which socket will be bound. /// Instead, the method searches through the addresses on the specified /// interface and selects one that matches the address family. Marcin Siodelski committed Jun 14, 2012 401 402 403 /// /// @param ifname name of the interface /// @param port UDP port Marcin Siodelski committed Jun 15, 2012 404 /// @param family address family (AF_INET or AF_INET6) Marcin Siodelski committed Jun 14, 2012 405 406 /// @return socket descriptor, if socket creation, binding and multicast /// group join were all successful. Marcin Siodelski committed Jun 15, 2012 407 /// @throw isc::Unexpected if failed to create and bind socket. Marcin Siodelski committed Jul 06, 2012 408 409 /// @throw isc::BadValue if there is no address on specified interface /// that belongs to given family. Marcin Siodelski committed Jun 14, 2012 410 411 int openSocketFromIface(const std::string& ifname, const uint16_t port, Marcin Siodelski committed Jun 13, 2012 412 413 const uint8_t family); Marcin Siodelski committed Jun 14, 2012 414 415 /// @brief Opens UDP/IP socket and binds to address specified /// Stephen Morris committed Jun 25, 2012 416 417 /// This methods differs from \ref openSocket in that it does not require /// the specification of the interface to which the socket will be bound. Marcin Siodelski committed Jun 14, 2012 418 419 420 421 422 /// /// @param addr address to be bound /// @param port UDP port /// @return socket descriptor, if socket creation, binding and multicast /// group join were all successful. Marcin Siodelski committed Jun 15, 2012 423 /// @throw isc::Unexpected if failed to create and bind socket Marcin Siodelski committed Jul 06, 2012 424 425 /// @throw isc::BadValue if specified address is not available on /// any interface Marcin Siodelski committed Jun 14, 2012 426 427 428 429 430 int openSocketFromAddress(const isc::asiolink::IOAddress& addr, const uint16_t port); /// @brief Opens UDP/IP socket to be used to connect to remote address /// Stephen Morris committed Jun 25, 2012 431 432 433 434 /// This method identifies the local address to be used to connect to the /// remote address specified as argument. Once the local address is /// identified, \ref openSocket is called to open a socket and bind it to /// the interface, address and port. Marcin Siodelski committed Jun 14, 2012 435 436 437 438 439 /// /// @param remote_addr remote address to connect to /// @param port UDP port /// @return socket descriptor, if socket creation, binding and multicast /// group join were all successful. Marcin Siodelski committed Jun 15, 2012 440 /// @throw isc::Unexpected if failed to create and bind socket Marcin Siodelski committed Jun 14, 2012 441 442 int openSocketFromRemoteAddress(const isc::asiolink::IOAddress& remote_addr, const uint16_t port); Marcin Siodelski committed Jun 13, 2012 443 Tomek Mrugalski committed Nov 08, 2011 444 Tomek Mrugalski committed Dec 05, 2011 445 446 447 448 449 /// Opens IPv6 sockets on detected interfaces. /// /// Will throw exception if socket creation fails. /// /// @param port specifies port number (usually DHCP6_SERVER_PORT) Tomek Mrugalski committed Dec 07, 2011 450 451 /// /// @return true if any sockets were open Tomek Mrugalski committed Mar 08, 2012 452 bool openSockets6(const uint16_t port = DHCP6_SERVER_PORT); Tomek Mrugalski committed Dec 05, 2011 453 454 455 456 457 /// @brief Closes all open sockets. /// Is used in destructor, but also from Dhcpv4_srv and Dhcpv6_srv classes. void closeSockets(); Tomek Mrugalski committed Dec 07, 2011 458 459 460 /// Opens IPv4 sockets on detected interfaces. /// Will throw exception if socket creation fails. /// Tomek Mrugalski committed Dec 20, 2011 461 /// @param port specifies port number (usually DHCP4_SERVER_PORT) Tomek Mrugalski committed Dec 07, 2011 462 463 /// /// @return true if any sockets were open Tomek Mrugalski committed Mar 08, 2012 464 bool openSockets4(const uint16_t port = DHCP4_SERVER_PORT); Tomek Mrugalski committed Dec 07, 2011 465 Tomek Mrugalski committed Nov 30, 2011 466 467 468 469 470 /// @brief returns number of detected interfaces /// /// @return number of detected interfaces uint16_t countIfaces() { return ifaces_.size(); } Tomek Mrugalski committed May 30, 2012 471 472 473 474 475 476 477 478 479 480 481 482 /// @brief Sets session socket and a callback /// /// Specifies session socket and a callback that will be called /// when data will be received over that socket. /// /// @param socketfd socket descriptor /// @param callback callback function void set_session_socket(int socketfd, SessionCallback callback) { session_socket_ = socketfd; session_callback_ = callback; } Tomek Mrugalski committed Jun 11, 2012 483 /// A value of socket descriptor representing "not specified" state. Tomek Mrugalski committed Jun 12, 2012 484 static const int INVALID_SOCKET = -1; Tomek Mrugalski committed Jun 11, 2012 485 Tomek Mrugalski committed Oct 14, 2011 486 487 488 489 490 491 // don't use private, we need derived classes in tests protected: /// @brief Protected constructor. /// /// Protected constructor. This is a singleton class. We don't want Tomek Mrugalski committed Dec 05, 2011 492 /// anyone to create instances of IfaceMgr. Use instance() method instead. Tomek Mrugalski committed Oct 14, 2011 493 494 IfaceMgr(); Tomek Mrugalski committed Dec 07, 2011 495 virtual ~IfaceMgr(); Tomek Mrugalski committed Oct 14, 2011 496 Tomek Mrugalski committed Dec 05, 2011 497 498 499 500 501 502 503 504 505 506 507 /// @brief Opens IPv4 socket. /// /// Please do not use this method directly. Use openSocket instead. /// /// This method may throw exception if socket creation fails. /// /// @param iface reference to interface structure. /// @param addr an address the created socket should be bound to /// @param port a port that created socket should be bound to /// /// @return socket descriptor Tomek Mrugalski committed Feb 17, 2012 508 int openSocket4(Iface& iface, const isc::asiolink::IOAddress& addr, uint16_t port); Tomek Mrugalski committed Nov 08, 2011 509 Tomek Mrugalski committed Dec 05, 2011 510 511 512 513 514 515 516 517 518 519 520 /// @brief Opens IPv6 socket. /// /// Please do not use this method directly. Use openSocket instead. /// /// This method may throw exception if socket creation fails. /// /// @param iface reference to interface structure. /// @param addr an address the created socket should be bound to /// @param port a port that created socket should be bound to /// /// @return socket descriptor Tomek Mrugalski committed Feb 17, 2012 521 int openSocket6(Iface& iface, const isc::asiolink::IOAddress& addr, uint16_t port); Tomek Mrugalski committed Nov 08, 2011 522 Tomek Mrugalski committed Dec 05, 2011 523 524 525 /// @brief Adds an interface to list of known interfaces. /// /// @param iface reference to Iface object. Tomek Mrugalski committed Nov 08, 2011 526 527 528 529 void addInterface(const Iface& iface) { ifaces_.push_back(iface); } Tomek Mrugalski committed Oct 14, 2011 530 531 532 533 534 535 536 537 /// @brief Detects network interfaces. /// /// This method will eventually detect available interfaces. For now /// it offers stub implementation. First interface name and link-local /// IPv6 address is read from intefaces.txt file. void detectIfaces(); Tomek Mrugalski committed Nov 30, 2011 538 539 540 541 542 543 544 545 546 /// @brief Stub implementation of network interface detection. /// /// This implementations reads a single line from interfaces.txt file /// and pretends to detect such interface. First interface name and /// link-local IPv6 address or IPv4 address is read from the /// intefaces.txt file. void stubDetectIfaces(); Tomek Mrugalski committed Oct 14, 2011 547 548 549 550 // TODO: having 2 maps (ifindex->iface and ifname->iface would) // probably be better for performance reasons /// List of available interfaces Tomek Mrugalski committed Nov 08, 2011 551 IfaceCollection ifaces_; Tomek Mrugalski committed Oct 14, 2011 552 553 554 555 556 557 558 /// a pointer to a sole instance of this class (a singleton) static IfaceMgr * instance_; // TODO: Also keep this interface on Iface once interface detection // is implemented. We may need it e.g. to close all sockets on // specific interface Tomek Mrugalski committed Nov 09, 2011 559 560 561 //int recvsock_; // TODO: should be fd_set eventually, but we have only //int sendsock_; // 2 sockets for now. Will do for until next release Tomek Mrugalski committed Oct 14, 2011 562 563 564 565 // we can't use the same socket, as receiving socket // is bound to multicast address. And we all know what happens // to people who try to use multicast as source address. Tomek Mrugalski committed Oct 14, 2011 566 /// length of the control_buf_ array Tomek Mrugalski committed Mar 07, 2012 567 size_t control_buf_len_; Tomek Mrugalski committed Oct 14, 2011 568 Tomek Mrugalski committed Oct 14, 2011 569 570 571 /// control-buffer, used in transmission and reception boost::scoped_array control_buf_; Tomek Mrugalski committed Mar 07, 2012 572 573 574 575 576 577 578 /// @brief A wrapper for OS-specific operations before sending IPv4 packet /// /// @param m message header (will be later used for sendmsg() call) /// @param control_buf buffer to be used during transmission /// @param control_buf_len buffer length /// @param pkt packet to be sent void os_send4(struct msghdr& m, boost::scoped_array& control_buf, Stephen Morris committed Mar 09, 2012 579 size_t control_buf_len, const Pkt4Ptr& pkt); Tomek Mrugalski committed Mar 07, 2012 580 581 582 583 584 585 586 587 588 /// @brief OS-specific operations during IPv4 packet reception /// /// @param m message header (was used during recvmsg() call) /// @param pkt packet received (some fields will be set here) /// /// @return true if successful, false otherwise bool os_receive4(struct msghdr& m, Pkt4Ptr& pkt); Tomek Mrugalski committed May 30, 2012 589 590 591 592 593 /// socket descriptor of the session socket int session_socket_; /// a callback that will be called when data arrives over session_socket_ SessionCallback session_callback_; Tomek Mrugalski committed Oct 14, 2011 594 595 private: Stephen Morris committed Mar 09, 2012 596 /// @brief Creates a single instance of this class (a singleton implementation) Tomek Mrugalski committed Oct 14, 2011 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 static void instanceCreate(); /// @brief Joins IPv6 multicast group on a socket. /// /// Socket must be created and bound to an address. Note that this /// address is different than the multicast address. For example DHCPv6 /// server should bind its socket to link-local address (fe80::1234...) /// and later join ff02::1:2 multicast group. /// /// @param sock socket fd (socket must be bound) /// @param ifname interface name (for link-scoped multicast groups) /// @param mcast multicast address to join (e.g. "ff02::1:2") /// /// @return true if multicast join was successful /// bool Tomek Mrugalski committed Dec 23, 2011 614 615 joinMulticast(int sock, const std::string& ifname, const std::string& mcast); Tomek Mrugalski committed Nov 08, 2011 616 Marcin Siodelski committed Jun 14, 2012 617 618 619 620 621 /// @brief Identifies local network address to be used to /// connect to remote address. /// /// This method identifies local network address that can be used /// to connect to remote address specified. Marcin Siodelski committed Jun 15, 2012 622 /// It first creates socket and makes attempt to connect Marcin Siodelski committed Jun 14, 2012 623 624 625 626 627 628 629 /// to remote location via this socket. If connection /// is established successfully, the local address to which /// socket is bound is returned. /// /// @param remote_addr remote address to connect to /// @param port port to be used /// @return local address to be used to connect to remote address Marcin Siodelski committed Jun 15, 2012 630 /// @throw isc::Unexpected if unable to indentify local address Marcin Siodelski committed Jun 14, 2012 631 632 633 isc::asiolink::IOAddress getLocalAddress(const isc::asiolink::IOAddress& remote_addr, const uint16_t port); Tomek Mrugalski committed Oct 14, 2011 634 635 636 }; }; // namespace isc::dhcp Tomek Mrugalski committed Oct 14, 2011 637 }; // namespace isc Tomek Mrugalski committed Jun 30, 2011 638 639 #endif	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5618460774421692, "perplexity": 19770.21974815628}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030334855.91/warc/CC-MAIN-20220926082131-20220926112131-00350.warc.gz"}
https://rivet.hepforge.org/analyses/OPAL_2004_I648738.html	rivet is hosted by Hepforge, IPPP Durham ## Rivet analyses reference ### OPAL_2004_I648738 Quark and gluon jet fragmentation functions Experiment: OPAL (LEP) Inspire ID: 648738 Status: VALIDATED Authors: • Daniel Reichelt [d.reichelt@cern.ch] References: • Eur.Phys.J. C37 (2004) no.1, 25-47 • hep-ex/0404026 Beams: e+ e- Beam energies: (6.4, 6.4); (13.4, 13.4); (24.0, 24.0); (45.6, 45.6); (46.5, 46.5); (48.5, 48.5); (98.5, 98.5) GeV Run details: • For quark fragmentation $e^+e^-\to q\bar{q}$ events are required, while for gluon fragmentation the fictonal $e^+e^-\to gg$ process is required. Measurement of the fragmentation functions for quarks and gluons at LEP. Useful for studying the properties of gluon jets and the differences between quark and gluon jets. For the study of gluon jets the fictional $e^+e^-\to g g$ process must be used. The data in histograms labelled "hemisphere fragmentation" are measured from jets defined by hemispheres, with an energy scale defined by $E=\sqrt{s}/2$, while data in histograms named "durham fragmentation" are measured from jets defined by the durham algorithm with $Q_\mathrm{jet}=E_\mathrm{jet}\sin(\theta/2)$ as the energy scale. The rivet analysis defines the jet flavour from the initial quarks, as the data are corrected for impurities, and defines all jets as hemispheres with energy scale $E=\sqrt{s}/2$. Source code: OPAL_2004_I648738.cc 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 // -- C++ -- #include "Rivet/Analysis.hh" #include "Rivet/Projections/FinalState.hh" #include "Rivet/Projections/ChargedFinalState.hh" namespace Rivet { class OPAL_2004_I648738 : public Analysis { public: /// Constructor OPAL_2004_I648738() : Analysis("OPAL_2004_I648738"), _sumW(3,0.) { } /// @name Analysis methods //@{ void init() { declare(FinalState(), "FS"); declare(ChargedFinalState(), "CFS"); unsigned int ih=0; if (inRange(0.5sqrtS()/GeV, 4.0, 9.0)) { ih = 1; } else if (inRange(0.5sqrtS()/GeV, 9.0, 19.0)) { ih = 2; } else if (inRange(0.5sqrtS()/GeV, 19.0, 30.0)) { ih = 3; } else if (inRange(0.5sqrtS()/GeV, 45.5, 45.7)) { ih = 5; } else if (inRange(0.5sqrtS()/GeV, 30.0, 70.0)) { ih = 4; } else if (inRange(0.5sqrtS()/GeV, 91.5, 104.5)) { ih = 6; } assert(ih>0); // book the histograms _histo_xE.push_back(bookHisto1D(ih+5,1,1)); _histo_xE.push_back(bookHisto1D(ih+5,1,2)); if(ih<5) _histo_xE.push_back(bookHisto1D(ih+5,1,3)); } /// Perform the per-event analysis void analyze(const Event& event) { const double weight = event.weight(); // find the initial quarks/gluons ParticleVector initial; for (const GenParticle* p : Rivet::particles(event.genEvent())) { const GenVertex* pv = p->production_vertex(); const PdgId pid = abs(p->pdg_id()); if(!( (pid>=1&&pid<=5) \|\| pid ==21) ) continue; bool passed = false; for (const GenParticle* pp : particles_in(pv)) { const PdgId ppid = abs(pp->pdg_id()); passed = (ppid == PID::ELECTRON \|\| ppid == PID::HIGGS \|\| ppid == PID::ZBOSON \|\| ppid == PID::GAMMA); if(passed) break; } if(passed) initial.push_back(Particle(p)); } if(initial.size()!=2) { vetoEvent; } // type of event unsigned int itype=2; if(initial[0].pdgId()==-initial[1].pdgId()) { PdgId pid = abs(initial[0].pdgId()); if(pid>=1&&pid<=4) itype=0; else itype=1; } assert(itype<_histo_xE.size()); // fill histograms _sumW[itype] += 2.weight; const Particles& chps = applyProjection(event, "CFS").particles(); foreach(const Particle& p, chps) { double xE = 2.*p.E()/sqrtS(); _histo_xE[itype]->fill(xE, weight); } } /// Normalise histograms etc., after the run void finalize() { for(unsigned int ix=0;ix<_histo_xE.size();++ix) { if(_sumW[ix]>0.) scale(_histo_xE[ix],1./_sumW[ix]); } } //@} private: vector _sumW; /// @name Histograms //@{ vector _histo_xE; //@} }; // The hook for the plugin system DECLARE_RIVET_PLUGIN(OPAL_2004_I648738); }	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5387488007545471, "perplexity": 6265.40166288923}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583509336.11/warc/CC-MAIN-20181015163653-20181015185153-00402.warc.gz"}
https://viper.unige.ch/_bib/viper_report/VG:SMM1998	## Content-based query of image databases, inspirations from text retrieval: inverted files, frequency-based weights and relevance feedback ### Bibtex entry : @techreport { VG:SMM1998, author = { David McG. Squire and Wolfgang M{\"u}ller and Henning M{\"u}ller and Jilali Raki }, title = { Content-based query of image databases, inspirations from text retrieval: inverted files, frequency-based weights and relevance feedback }, institution = { Computer Vision Group, Computing Centre, University of Geneva }, year = { 1998 }, number = { 98.04 }, address = { rue G\'en\'eral Dufour, 24, CH-1211 Gen\eve, Switzerland }, month = { November }, url = { http://vision.unige.ch/publications/postscript/98/VGTR98.04_SquireMuellerMuellerRaki.ps.gz }, abstract = { In this paper we report the application of techniques inspired by text retrieval research to the content-based query of image databases. In particular, we show how the use of an inverted file data structure permits the use of a feature space of $\mathcal{O}(104)$ dimensions, by restricting search to the subspace spanned by the features present in the query. A suitably sparse set of colour and texture features is proposed. A scheme based on the frequency of occurrence of features in both individual images and in the whole collection provides a means of weighting possibly incommensurate features in a compatible manner, and naturally extends to incorporate relevance feedback queries. The use of relevance feedback is shown consistently to improve system performance, as measured by precision and recall. }, url1 = { http://vision.unige.ch/publications/postscript/98/VGTR98.04_SquireMuellerMuellerRaki.pdf }, vgclass = { report }, vgproject = { viper }, }` -- Keywords: machine learning, information geometry, data mining, Big Data, affective information retrieval (recherche d'information), information visualisation, content-based image and video retrieval (CBIR, CBR, CBVR, CBMR, CBMIR), information mining, classification, multimedia and multimodal information management, semantic web, knowledge base (RDF, OWL, XML, metadata, auto-annotation, description), multimodal information fusion	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.1945406049489975, "perplexity": 9300.658680655355}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500837.65/warc/CC-MAIN-20230208155417-20230208185417-00266.warc.gz"}
https://arxiv.org/abs/1004.3789	astro-ph.GA (what is this?) # Title: The Dual Origin of Stellar Halos II: Chemical Abundances as Tracers of Formation History Abstract: Fully cosmological, high resolution N-Body + SPH simulations are used to investigate the chemical abundance trends of stars in simulated stellar halos as a function of their origin. These simulations employ a physically motivated supernova feedback recipe, as well as metal enrichment, metal cooling and metal diffusion. As presented in an earlier paper, the simulated galaxies in this study are surrounded by stellar halos whose inner regions contain both stars accreted from satellite galaxies and stars formed in situ in the central regions of the main galaxies and later displaced by mergers into their inner halos. The abundance patterns ([Fe/H] and [O/Fe]) of halo stars located within 10 kpc of a solar-like observer are analyzed. We find that for galaxies which have not experienced a recent major merger, in situ stars at the high [Fe/H] end of the metallicity distribution function are more [alpha/Fe]-rich than accreted stars at similar [Fe/H]. This dichotomy in the [O/Fe] of halo stars at a given [Fe/H] results from the different potential wells within which in situ and accreted halo stars form. These results qualitatively match recent observations of local Milky Way halo stars. It may thus be possible for observers to uncover the relative contribution of different physical processes to the formation of stellar halos by observing such trends in the halo populations of the Milky Way, and other local L* galaxies. Comments: Version accepted for publication in ApJ Part 1. This version of the paper has been extended to include a detailed discussion of numerical issues Subjects: Astrophysics of Galaxies (astro-ph.GA); Cosmology and Nongalactic Astrophysics (astro-ph.CO) DOI: 10.1088/0004-637X/721/1/738 Cite as: arXiv:1004.3789 [astro-ph.GA] (or arXiv:1004.3789v2 [astro-ph.GA] for this version)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.940886378288269, "perplexity": 3030.741132280671}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948563083.64/warc/CC-MAIN-20171215021156-20171215041156-00286.warc.gz"}
https://natron.readthedocs.io/en/v2.3.15/plugins/fr.inria.built-in.Roto.html	# Roto node¶ This documentation is for version 1.0 of Roto (fr.inria.built-in.Roto). ## Description¶ Create masks and shapes ## Inputs¶ Input Description Optional Bg Yes Bg2 Yes Bg3 Yes Bg4 Yes ## Controls¶ Parameter / script name Type Default Function Opacity / opacity Double 1 Controls the opacity of the selected shape(s). Color / color Color r: 1 g: 1 b: 1 The color of the shape. This parameter is used when the output components are set to RGBA. Life Time / lifeTime Choice All Controls the life-time of the shape/stroke All: All frames Single: Only for the specified frame From start: From the start of the sequence up to the specified frame To end: From the specified frame to the end of the sequence Custom: Use the Activated parameter animation to control the life-time of the shape/stroke using keyframes Activated / activated Boolean On Controls whether the selected shape(s) should be rendered or not.Note that you can animate this parameter so you can activate/deactivate the shape throughout the time. Feather / feather Double 1.5 Controls the distance of feather (in pixels) to add around the selected shape(s) Feather fall-off / featherFallOff Double 1 Controls the rate at which the feather is applied on the selected shape(s). Source / sourceType Choice background Source color used for painting the stroke when the Reveal/Clone tools are used. foreground: The painted result at this point in the hierarchy. background: The original image unpainted connected to bg. background 2: The original image unpainted connected to bg1. background 3: The original image unpainted connected to bg2. background 4: The original image unpainted connected to bg3. background 5: The original image unpainted connected to bg4. background 6: The original image unpainted connected to bg5. background 7: The original image unpainted connected to bg6. background 8: The original image unpainted connected to bg7. background 9: The original image unpainted connected to bg8. background 10: The original image unpainted connected to bg9. Translate / cloneTranslate Double x: 0 y: 0 Rotate / cloneRotate Double 0 Scale / cloneScale Double x: 1 y: 1 Uniform / cloneUniform Boolean On Skew X / cloneSkewx Double 0 Skew Y / cloneSkewy Double 0 Skew Order / cloneSkewOrder Choice XY XY YX Center / cloneCenter Double x: 0.5 y: 0.5 Reset Center / resetCloneCenter Button Reset the clone transform center Reset Transform / resetCloneTransform Button Reset the clone transform to an identity Filter / cloneFilter Choice Cubic Filtering algorithm - some filters may produce values outside of the initial range () or modify the values even if there is no movement (+). Impulse: (nearest neighbor / box) Use original values. Bilinear: (tent / triangle) Bilinear interpolation between original values. Cubic: (cubic spline) Some smoothing. Keys: (Catmull-Rom / Hermite spline) Some smoothing, plus minor sharpening (). Simon: Some smoothing, plus medium sharpening (). Rifman: Some smoothing, plus significant sharpening (). Mitchell: Some smoothing, plus blurring to hide pixelation (*)(+). Parzen: (cubic B-spline) Greatest smoothing of all filters (+). Notch: Flat smoothing (which tends to hide moire’ patterns) (+). Black Outside / blackOutside Boolean On Fill the area outside the source image with black Clone time offset / timeOffset Integer 0 When the Clone tool is used, this determines depending on the time offset mode the source frame to clone. When in absolute mode, this is the frame number of the source, when in relative mode, this is an offset relative to the current frame. Mode / timeOffsetMode Choice Relative Time offset mode: when in absolute mode, this is the frame number of the source, when in relative mode, this is an offset relative to the current frame. Relative Absolute Brush Size / brushSize Double 25 This is the diameter of the brush in pixels. Shift + drag on the viewer to modify this value Brush Spacing / brushSpacing Double 0.1 Spacing between stamps of the paint brush Brush Hardness / brushHardness Double 0.2 Fall off of the brush effect from the center to the edge Brush effect / brushEffect Double 15 The strength of the effect Opacity / pressureOpacity Boolean On Alters the opacity of the paint brush proportionate to changes in pen pressure Size / pressureSize Boolean Off Alters the size of the paint brush proportionate to changes in pen pressure Hardness / pressureHardness Boolean Off Alters the hardness of the paint brush proportionate to changes in pen pressure Build-up / buildUp Boolean Off When checked, the paint stroke builds up when painted over itself Visible portion / strokeVisiblePortion Double start: 0 end: 1 Defines the range of the stroke that should be visible: 0 is the start of the stroke and 1 the end. Translate / translate Double x: 0 y: 0 Rotate / rotate Double 0 Scale / scale Double x: 1 y: 1 Uniform / uniform Boolean On Skew X / skewx Double 0 Skew Y / skewy Double 0 Skew Order / skewOrder Choice XY XY YX Center / center Double x: 0.5 y: 0.5 Reset Center / resetTransformCenter Button Reset the transform center Interactive / RotoTransformInteractive Boolean On When check, modifying the transform will directly render the shape in the viewer. When unchecked, modifications are applied when releasing the mouse button. Extra Matrix / extraMatrix Double x: 1 y: 0 z: 0 w: 0 : 1 : 0 : 0 : 0 : 1 This matrix gets concatenated to the transform resulting from the parameter above. Reset Transform / resetTransform Button Reset the transform to an identity	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2239260971546173, "perplexity": 11418.393621213252}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487635920.39/warc/CC-MAIN-20210618073932-20210618103932-00578.warc.gz"}
https://www.rdocumentation.org/packages/forecast/versions/3.03/topics/auto.arima	# auto.arima 0th Percentile ##### Fit best ARIMA model to univariate time series Returns best ARIMA model according to either AIC, AICc or BIC value. The function conducts a search over possible model within the order constraints provided. Keywords ts ##### Usage auto.arima(x, d=NA, D=NA, max.p=5, max.q=5, max.P=2, max.Q=2, max.order=5, start.p=2, start.q=2, start.P=1, start.Q=1, stationary=FALSE, ic=c("aic","aicc", "bic"), stepwise=TRUE, trace=FALSE, approximation=(length(x)>100 \| frequency(x)>12), xreg=NULL, allowdrift=TRUE, lambda=NULL) ##### Arguments x a univariate time series d Order of first-differencing. If missing, will choose a value based on KPSS test. D Order of seasonal-differencing. If missing, will choose a value based on CH test. max.p Maximum value of p max.q Maximum value of q max.P Maximum value of P max.Q Maximum value of Q max.order Maximum value of p+q+P+Q if model selection is not stepwise. start.p Starting value of p in stepwise procedure. start.q Starting value of q in stepwise procedure. start.P Starting value of P in stepwise procedure. start.Q Starting value of Q in stepwise procedure. stationary If TRUE, restricts search to stationary models. ic Information criterion to be used in model selection. stepwise If TRUE, will do stepwise selection (faster). Otherwise, it searches over all models. Non-stepwise selection can be very slow, especially for seasonal models. trace If TRUE, the list of ARIMA models considered will be reported. approximation If TRUE, estimation is via conditional sums of squares andthe information criteria used for model selection are approximated. The final model is still computed using maximum likelihood estimation. Approximation should be used for long time se xreg Optionally, a vector or matrix of external regressors, which must have the same number of rows as x. test Type of unit root test to use. See ndiffs for details. seasonal.test This determines which seasonal unit root test is used. See nsdiffs for details. allowdrift If TRUE, models with drift terms are considered. lambda Box-Cox transformation parameter. Ignored if NULL. Otherwise, data transformed before model is estimated. ##### Details Non-stepwise selection can be slow, especially for seasonal data. Stepwise algorithm outlined in Hyndman and Khandakar (2008) except that the default method for selecting seasonal differences is now the OCSB test rather than the Canova-Hansen test. ##### Value • Same as for arima ##### References Hyndman, R.J. and Khandakar, Y. (2008) "Automatic time series forecasting: The forecast package for R", Journal of Statistical Software, 26(3). Arima • best.arima • auto.arima ##### Examples fit <- auto.arima(WWWusage) plot(forecast(fit,h=20)) Documentation reproduced from package forecast, version 3.03, License: GPL (>= 2) ### Community examples Looks like there are no examples yet.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2260860651731491, "perplexity": 10760.119181051832}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655883439.15/warc/CC-MAIN-20200703215640-20200704005640-00391.warc.gz"}
http://www.ck12.org/book/Basic-Geometry/r1/section/12.4/	<meta http-equiv="refresh" content="1; url=/nojavascript/"> You are reading an older version of this FlexBook® textbook: CK-12 Geometry - Basic Go to the latest version. # 12.4: Rotations Difficulty Level: At Grade Created by: CK-12 ## Learning Objectives • Find the image of a figure in a rotation in a coordinate plane. ## Review Queue 1. Reflect $\triangle XYZ$ with vertices $X(9, 2), Y(2, 4)$ and $Z(7, 8)$ over the $y-$axis. What are the vertices of $\triangle Xâ€™Yâ€™Zâ€™$? 2. Reflect $\triangle Xâ€™Yâ€™Zâ€™$ over the $x-$axis. What are the vertices of $\triangle Xâ€Yâ€Zâ€$? 3. How do the coordinates of $\triangle Xâ€Yâ€Zâ€$ relate to $\triangle XYZ$? Know What? The international symbol for recycling is to the right. It is three arrows rotated around a point. Let’s assume that the arrow on the top is the preimage and the other two are its images. Find the center of rotation and the angle of rotation for each image. ## Defining Rotations Rotation: A transformation where a figure is turned around a fixed point to create an image. The lines drawn from the preimage to the center of rotation, and from the center of rotation to the image form the angle of rotation. In this section, we will only do counterclockwise rotations. Example 1: A rotation of $80^\circ$ clockwise is the same as what counterclockwise rotation? Solution: There are $360^\circ$ around a point. So, an $80^\circ$ rotation clockwise is the same as a $360^\circ-80^\circ=280^\circ$ rotation counterclockwise. Example 2: A rotation of $160^\circ$ counterclockwise is the same as what clockwise rotation? Solution: $360^\circ-160^\circ=200^\circ$ clockwise rotation. Investigation 12-1: Drawing a Rotation of $100^\circ$ Tools Needed: pencil, paper, protractor, ruler 1. Draw $\triangle ABC$ and a point $R$. 2. Draw $\overline{RB}$. 3. Place the center of a protractor on $R$ and the $0^\circ$ line on $\overline{RB}$. Mark a $100^\circ$ angle. 4. Mark $Bâ€™$ on the $100^\circ$ line so $RB = RBâ€™$. 5. Repeat steps 2-4 with $A$ and $C$. 6. Make $\triangle Aâ€™Bâ€™Câ€™$. Use this process to rotate any figure. Example 3: Rotate rectangle $RECT$ $80^\circ$ counterclockwise around $P$. Solution: Use Investigation 12-1. In step 3, change the angle to $80^\circ$. Each angle of rotation is $80^\circ$. $m \angle RPRâ€™ &= 80^\circ\\m \angle EPEâ€™ &= 80^\circ\\m \angle CPCâ€™ &= 80^\circ\\m \angle TPTâ€™ &= 80^\circ$ $180^\circ$ Rotation To rotate a figure $180^\circ$, in the $x-y$ plane, we use the origin as the center of the rotation. A $180^\circ$ angle is called a straight angle. So, an image rotated over the origin $180^\circ$ will be on the same line and the same distance away from the origin as the preimage, but on the other side. Example 4: Rotate $\triangle ABC$, with vertices $A(7, 4), B(6, 1)$, and $C(3, 1)$, $180^\circ$. Find the coordinates of $\triangle Aâ€™Bâ€™Câ€™$. Solution: You can either use Investigation 12-1 or the hint given above to find $\triangle Aâ€™Bâ€™Câ€™$. First, graph the triangle. If $A$ is (7, 4), that means it is 7 units to the right of the origin and 4 units up. $Aâ€™$ would then be 7 units to the left of the origin and 4 units down. $A(7,4) & \rightarrow Aâ€™(-7,-4)\\B(6,1) & \rightarrow Bâ€™(-6,-1)\\C(3,1) & \rightarrow Câ€™(-3,-1)$ Rotation of $180^\circ$: $(x,y) \rightarrow (-x,-y)$ Recall from the second section that a rotation is an isometry. This means that $\triangle ABC \cong \triangle Aâ€™Bâ€™Câ€™$. You can use the distance formula to show this. $90^\circ$ Rotation Similar to the $180^\circ$ rotation, the image of a $90^\circ$ will be the same distance away from the origin as its preimage, but rotated $90^\circ$. Example 5: Rotate $\overline{ST} \ 90^\circ$. Solution: When rotating something $90^\circ$, use Investigation 12-1 to see if there is a pattern. Rotation of $90^\circ$: $(x,y) \rightarrow (-y,x)$ Rotation of $270^\circ$ A rotation of $270^\circ$ counterclockwise would be the same as a rotation of $90^\circ$ plus a rotation of $180^\circ$. So, if the values of a $90^\circ$ rotation are $(-y, x)$, then a $270^\circ$ rotation would be the opposite sign of each, or $(y, -x)$. Rotation of $270^\circ$: $(x,y) \rightarrow (y,-x)$ Example 6: Find the coordinates of $ABCD$ after a $270^\circ$ rotation. Solution: Using the rule, we have: $(x,y) & \rightarrow (y,-x)\\ A(-4,5) & \rightarrow Aâ€™(5,4)\\B(1,2) & \rightarrow Bâ€™(2,-1)\\C(-6,-2) & \rightarrow Câ€™(-2,6)\\D(-8,3) & \rightarrow Dâ€™(3,8)$ While we can rotate any image any amount of degrees, only $90^\circ, 180^\circ$ and $270^\circ$ have special rules. To rotate a figure by an angle measure other than these three, you must use Investigation 12-1. Example 7: Algebra Connection The rotation of a quadrilateral is shown below. What is the measure of $x$ and $y$? Solution: Because a rotation is an isometry, we can set up two equations to solve for $x$ and $y$. $2y &= 80^\circ && 2x-3=15\\ y &= 40^\circ && \quad \ \ 2x=18\\& && \qquad \ x = 9$ Know What? Revisited The center of rotation is shown in the picture to the right. If we draw rays to the same place in each arrow, the two images are a $120^\circ$ rotation in either direction. ## Review Questions • Questions 1-10 are similar to Examples 1 and 2. • Questions 11-16 are similar to Investigation 12-1 and Example 3. • Questions 17-25 are similar to Examples 4-6. • Questions 26-28 are similar to Example 7. • Questions 29-34 are similar to Examples 4-6. • Questions 34-37 are a review. • Question 38 is similar to Example 4. In the questions below, every rotation is counterclockwise, unless otherwise stated. 1. If you rotated the letter $p \ 180^\circ$ counterclockwise, what letter would you have? 2. If you rotated the letter $p \ 180^\circ$ clockwise, what letter would you have? 3. A $90^\circ$ clockwise rotation is the same as what counterclockwise rotation? 4. A $270^\circ$ clockwise rotation is the same as what counterclockwise rotation? 5. A $210^\circ$ counterclockwise rotation is the same as what clockwise rotation? 6. A $120^\circ$ counterclockwise rotation is the same as what clockwise rotation? 7. A $340^\circ$ counterclockwise rotation is the same as what clockwise rotation? 8. Rotating a figure $360^\circ$ is the same as what other rotation? 9. Does it matter if you rotate a figure $180^\circ$ clockwise or counterclockwise? Why or why not? 10. When drawing a rotated figure and using your protractor, would it be easier to rotate the figure $300^\circ$ counterclockwise or $60^\circ$ clockwise? Explain your reasoning. Using Investigation 12-1, rotate each figure around point $P$ the given angle measure. 1. $50^\circ$ 2. $120^\circ$ 3. $200^\circ$ 4. $330^\circ$ 5. $75^\circ$ 6. $170^\circ$ Rotate each figure in the coordinate plane the given angle measure. The center of rotation is the origin. 1. $180^\circ$ 2. $90^\circ$ 3. $180^\circ$ 4. $270^\circ$ 5. $90^\circ$ 6. $270^\circ$ 7. $180^\circ$ 8. $270^\circ$ 9. $90^\circ$ Algebra Connection Find the measure of $x$ in the rotations below. The blue figure is the preimage. Find the angle of rotation for the graphs below. The center of rotation is the origin and the blue figure is the preimage. Your answer will be $90^\circ, 270^\circ$, or $180^\circ$. Two Reflections The vertices of $\triangle GHI$ are $G(-2, 2), H(8, 2)$, and $I(6, 8)$. Use this information to answer questions 24-27. 1. Plot $\triangle GHI$ on the coordinate plane. 2. Reflect $\triangle GHI$ over the $x-$axis. Find the coordinates of $\triangle Gâ€™Hâ€™Iâ€™$. 3. Reflect $\triangle Gâ€™Hâ€™Iâ€™$ over the $y-$axis. Find the coordinates of $\triangle Gâ€Hâ€Iâ€$. 4. What one transformation would be the same as this double reflection? ## Review Queue Answers 1. $X'(-9, 2), Y'(-2, 4), Z'(-7, 8)$ 2. $X''(-9, -2), Y''(-2, -4), Z''(-7, -8)$ 3. $\triangle X''Y''Z''$ is the double negative of $\triangle XYZ; (x, y) \rightarrow (-x, -y)$ 8 , 9 , 10 Feb 22, 2012 ## Last Modified: Dec 11, 2014 Files can only be attached to the latest version of None # Reviews Please wait... Please wait... Image Detail Sizes: Medium \| Original CK.MAT.ENG.SE.1.Geometry-Basic.12.4	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 126, "texerror": 0, "math_score": 0.7735068798065186, "perplexity": 600.4025091198165}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430455180384.30/warc/CC-MAIN-20150501043940-00074-ip-10-235-10-82.ec2.internal.warc.gz"}
https://deepai.org/publication/implicit-bias-of-linear-equivariant-networks	DeepAI # Implicit Bias of Linear Equivariant Networks Group equivariant convolutional neural networks (G-CNNs) are generalizations of convolutional neural networks (CNNs) which excel in a wide range of scientific and technical applications by explicitly encoding group symmetries, such as rotations and permutations, in their architectures. Although the success of G-CNNs is driven by the explicit symmetry bias of their convolutional architecture, a recent line of work has proposed that the implicit bias of training algorithms on a particular parameterization (or architecture) is key to understanding generalization for overparameterized neural nets. In this context, we show that L-layer full-width linear G-CNNs trained via gradient descent in a binary classification task converge to solutions with low-rank Fourier matrix coefficients, regularized by the 2/L-Schatten matrix norm. Our work strictly generalizes previous analysis on the implicit bias of linear CNNs to linear G-CNNs over all finite groups, including the challenging setting of non-commutative symmetry groups (such as permutations). We validate our theorems via experiments on a variety of groups and empirically explore more realistic nonlinear networks, which locally capture similar regularization patterns. Finally, we provide intuitive interpretations of our Fourier space implicit regularization results in real space via uncertainty principles. • 7 publications • 2 publications • 1 publication • 5 publications 12/27/2020 ### Universal Approximation Theorem for Equivariant Maps by Group CNNs Group symmetry is inherent in a wide variety of data distributions. Data... 12/12/2022 ### Implicit Neural Convolutional Kernels for Steerable CNNs Steerable convolutional neural networks (CNNs) provide a general framewo... 10/19/2021 ### Learning Equivariances and Partial Equivariances from Data Group equivariant Convolutional Neural Networks (G-CNNs) constrain featu... 10/22/2019 ### Explicitly Bayesian Regularizations in Deep Learning Generalization is essential for deep learning. In contrast to previous w... 06/09/2022 ### A General Framework For Proving The Equivariant Strong Lottery Ticket Hypothesis The Strong Lottery Ticket Hypothesis (SLTH) stipulates the existence of ... 06/16/2020 ### Robust Recovery via Implicit Bias of Discrepant Learning Rates for Double Over-parameterization Recent advances have shown that implicit bias of gradient descent on ove... 02/24/2021 ### Inductive Bias of Multi-Channel Linear Convolutional Networks with Bounded Weight Norm We study the function space characterization of the inductive bias resul...	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.833702027797699, "perplexity": 1703.8355043245992}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500126.0/warc/CC-MAIN-20230204110651-20230204140651-00755.warc.gz"}
http://www.lastfm.fr/user/gendervariant/library/music/The+Supremes/_/Come+See+About+Me?setlang=fr	# Bibliothèque Musique » The Supremes » 128 écoutes \| Se rendre sur la page du titre Titres (128) Titre Album Durée Date Come See About Me 2:39 27 jan. 2012, 17h41m Come See About Me 2:39 27 jan. 2012, 6h23m Come See About Me 2:39 26 jan. 2012, 23h55m Come See About Me 2:39 2 déc. 2011, 22h22m Come See About Me 2:39 2 déc. 2011, 22h19m Come See About Me 2:39 2 déc. 2011, 22h16m Come See About Me 2:39 2 déc. 2011, 22h14m Come See About Me 2:39 2 déc. 2011, 22h11m Come See About Me 2:39 2 déc. 2011, 22h08m Come See About Me 2:39 2 déc. 2011, 22h06m Come See About Me 2:39 2 déc. 2011, 22h03m Come See About Me 2:39 2 déc. 2011, 22h00m Come See About Me 2:39 2 déc. 2011, 21h58m Come See About Me 2:39 2 déc. 2011, 21h55m Come See About Me 2:39 2 déc. 2011, 21h52m Come See About Me 2:39 2 déc. 2011, 21h51m Come See About Me 2:39 2 déc. 2011, 21h48m Come See About Me 2:39 2 déc. 2011, 21h46m Come See About Me 2:39 2 déc. 2011, 21h43m Come See About Me 2:39 2 déc. 2011, 21h40m Come See About Me 2:39 2 déc. 2011, 21h38m Come See About Me 2:39 2 déc. 2011, 21h35m Come See About Me 2:39 2 déc. 2011, 21h32m Come See About Me 2:39 2 déc. 2011, 21h30m Come See About Me 2:39 2 déc. 2011, 21h27m Come See About Me 2:39 2 déc. 2011, 21h25m Come See About Me 2:39 2 déc. 2011, 21h22m Come See About Me 2:39 2 déc. 2011, 21h19m Come See About Me 2:39 2 déc. 2011, 21h17m Come See About Me 2:39 2 déc. 2011, 21h14m Come See About Me 2:39 2 déc. 2011, 21h11m Come See About Me 2:39 2 déc. 2011, 21h09m Come See About Me 2:39 2 déc. 2011, 21h06m Come See About Me 2:39 2 déc. 2011, 21h03m Come See About Me 2:39 2 déc. 2011, 21h01m Come See About Me 2:39 2 déc. 2011, 20h58m Come See About Me 2:39 2 déc. 2011, 20h55m Come See About Me 2:39 2 déc. 2011, 20h53m Come See About Me 2:39 2 déc. 2011, 20h50m Come See About Me 2:39 2 déc. 2011, 20h47m Come See About Me 2:39 2 déc. 2011, 20h45m Come See About Me 2:39 2 déc. 2011, 20h42m Come See About Me 2:39 2 déc. 2011, 20h39m Come See About Me 2:39 2 déc. 2011, 20h37m Come See About Me 2:39 2 déc. 2011, 20h34m Come See About Me 2:39 2 déc. 2011, 20h31m Come See About Me 2:39 2 déc. 2011, 20h29m Come See About Me 2:39 2 déc. 2011, 20h26m Come See About Me 2:39 2 déc. 2011, 20h23m Come See About Me 2:39 2 déc. 2011, 20h21m Come See About Me 2:39 2 déc. 2011, 20h18m Come See About Me 2:39 2 déc. 2011, 20h16m Come See About Me 2:39 2 déc. 2011, 20h13m Come See About Me 2:39 2 déc. 2011, 20h10m Come See About Me 2:39 2 déc. 2011, 20h08m Come See About Me 2:39 2 déc. 2011, 20h05m Come See About Me 2:39 2 déc. 2011, 20h02m Come See About Me 2:39 2 déc. 2011, 20h00m Come See About Me 2:39 2 déc. 2011, 19h57m Come See About Me 2:39 2 déc. 2011, 19h54m Come See About Me 2:39 2 déc. 2011, 19h52m Come See About Me 2:39 2 déc. 2011, 19h49m Come See About Me 2:39 2 déc. 2011, 19h46m Come See About Me 2:39 2 déc. 2011, 19h44m Come See About Me 2:39 2 déc. 2011, 19h41m Come See About Me 2:39 2 déc. 2011, 19h38m Come See About Me 2:39 2 déc. 2011, 19h36m Come See About Me 2:39 2 déc. 2011, 19h33m Come See About Me 2:39 2 déc. 2011, 19h30m Come See About Me 2:39 2 déc. 2011, 19h28m Come See About Me 2:39 2 déc. 2011, 19h25m Come See About Me 2:39 2 déc. 2011, 19h22m Come See About Me 2:39 2 déc. 2011, 19h20m Come See About Me 2:39 2 déc. 2011, 19h17m Come See About Me 2:39 2 déc. 2011, 19h14m Come See About Me 2:39 2 déc. 2011, 19h12m Come See About Me 2:39 2 déc. 2011, 19h09m Come See About Me 2:39 2 déc. 2011, 19h07m Come See About Me 2:39 2 déc. 2011, 19h04m Come See About Me 2:39 2 déc. 2011, 19h01m Come See About Me 2:39 2 déc. 2011, 18h59m Come See About Me 2:39 2 déc. 2011, 18h56m Come See About Me 2:39 2 déc. 2011, 18h53m Come See About Me 2:39 2 déc. 2011, 18h51m Come See About Me 2:39 2 déc. 2011, 18h48m Come See About Me 2:39 2 déc. 2011, 18h45m Come See About Me 2:39 2 déc. 2011, 18h43m Come See About Me 2:39 2 déc. 2011, 18h40m Come See About Me 2:39 2 déc. 2011, 18h37m Come See About Me 2:39 2 déc. 2011, 18h35m Come See About Me 2:39 2 déc. 2011, 18h32m Come See About Me 2:39 2 déc. 2011, 18h29m Come See About Me 2:39 2 déc. 2011, 18h27m Come See About Me 2:39 2 déc. 2011, 18h24m Come See About Me 2:39 2 déc. 2011, 18h21m Come See About Me 2:39 2 déc. 2011, 18h19m Come See About Me 2:39 2 déc. 2011, 18h16m Come See About Me 2:39 2 déc. 2011, 18h13m Come See About Me 2:39 2 déc. 2011, 18h11m Come See About Me 2:39 2 déc. 2011, 18h08m Come See About Me 2:39 2 déc. 2011, 18h05m Come See About Me 2:39 2 déc. 2011, 18h03m Come See About Me 2:39 2 déc. 2011, 18h01m Come See About Me 2:39 2 déc. 2011, 17h59m Come See About Me 2:39 2 déc. 2011, 17h56m Come See About Me 2:39 2 déc. 2011, 17h53m Come See About Me 2:39 2 déc. 2011, 17h51m Come See About Me 2:39 2 déc. 2011, 17h48m Come See About Me 2:39 2 déc. 2011, 17h45m Come See About Me 2:39 2 déc. 2011, 17h43m Come See About Me 2:39 2 déc. 2011, 17h40m Come See About Me 2:39 2 déc. 2011, 17h37m Come See About Me 2:39 2 déc. 2011, 17h35m Come See About Me 2:39 2 déc. 2011, 17h32m Come See About Me 2:39 2 déc. 2011, 17h29m Come See About Me 2:39 2 déc. 2011, 17h27m Come See About Me 2:39 2 déc. 2011, 17h24m Come See About Me 2:39 2 déc. 2011, 17h21m Come See About Me 2:39 2 déc. 2011, 17h19m Come See About Me 2:39 2 déc. 2011, 17h16m Come See About Me 2:39 2 déc. 2011, 17h13m Come See About Me 2:39 2 déc. 2011, 17h11m Come See About Me 2:39 2 déc. 2011, 17h09m Come See About Me 2:39 2 déc. 2011, 17h06m Come See About Me 2:39 2 déc. 2011, 17h05m Come See About Me 2:39 2 déc. 2011, 17h04m Come See About Me 2:39 2 déc. 2011, 17h02m Come See About Me 2:39 2 déc. 2011, 17h01m	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 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https://www.jipb.net/EN/abstract/abstract22368.shtml	J Integr Plant Biol. ›› 2007, Vol. 49 ›› Issue (8): 1142-1153. • Invited Expert Reviews • ### The Pleiomorphic Plant MTOC: An Evolutionary Perspective Roy C. Brown and Betty E. Lemmon • Published:2007-08-04 Abstract: γ-Tubulin is an essential component of the microtubule organizing center (MTOC) responsible for nucleating microtubules in both plants and animals. Whereas γ-tubulin is tightly associated with centrosomes that are inheritable organelles in cells of animals and most algae, it appears at different times and places to organize the myriad specialized microtubule systems that characterize plant cells. We have traced the distribution of γ-tubulin through the cell cycle in representative land plants (embryophytes) and herein present data that have led to a concept of the pleiomorphic and migratory MTOC. The many forms of the plant MTOC at spindle organization constitute pleiomorphism, and stage-specific “migration” is suggested by the consistent pattern of redistribution of γ-tubulin during mitosis. Mitotic spindles may be organized at centriolar centrosomes (only in final divisions of spermatogenesis), polar organizers (POs), plastid MTOCs, or nuclear envelope MTOCs (NE-MTOCs). In all cases, with the possible exception of centrosomes in spermatogenesis, the γ-tubulin migrates to broad polar regions and along the spindle fibers, even when it is initially a discrete polar entity. At anaphase it moves poleward, and subsequently migrates from polar regions (distal nuclear surfaces) into the interzone (proximal nuclear surfaces) where interzonal microtubule arrays and phragmoplasts are organized. Following cytokinesis, γ-tubulin becomes associated with nuclear envelopes and organizes radial microtubule systems (RMSs). These may exist only briefly, before establishment of hoop-like cortical arrays in vegetative tissues, or they may be characteristic of interphase in syncytial systems where they serve to organize the common cytoplasm into nuclear cytoplasmic domains (NCDs). Editorial Office, Journal of Integrative Plant Biology, Institute of Botany, CAS No. 20 Nanxincun, Xiangshan, Beijing 100093, China Tel: +86 10 6283 6133 Fax: +86 10 8259 2636 E-mail: jipb@ibcas.ac.cn	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.446804016828537, "perplexity": 19401.89646047537}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882571758.42/warc/CC-MAIN-20220812200804-20220812230804-00564.warc.gz"}
http://mathhelpforum.com/pre-calculus/50481-rocket-launched.html	1. Rocket Launched A small rocket is launched from a height of 72 feet. The height of therocket in feet, h, is represented by the equation h(t) = –16t2 + 64t + 72, where t = time, in seconds. Graph this equation. Use your graph to determine the number of seconds that the rocket will remain at or above 100 feet from the ground. 2. Originally Posted by magentarita A small rocket is launched from a height of 72 feet. The height of therocket in feet, h, is represented by the equation h(t) = –16t2 + 64t + 72, where t = time, in seconds. Graph this equation. Use your graph to determine the number of seconds that the rocket will remain at or above 100 feet from the ground. You have to draw 2 graphs: 1. $\displaystyle h(t) = -16t^2+64t+72$ and 2. $\displaystyle y = 100$ The period of time you are looking for is represented by the distance between the 2 intersections of these 2 graphs. Attached Thumbnails 3. Excellent.... Originally Posted by earboth You have to draw 2 graphs: 1. $\displaystyle h(t) = -16t^2+64t+72$ and 2. $\displaystyle y = 100$ The period of time you are looking for is represented by the distance between the 2 intersections of these 2 graphs.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8499666452407837, "perplexity": 628.3488955891232}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125936969.10/warc/CC-MAIN-20180419130550-20180419150550-00111.warc.gz"}
https://www.physicsforums.com/threads/gravitation-by-mtw-p-49-lambda-or-tau.416014/	# GRAVITATION by MTW: p.49, lambda or tau? 1. Jul 14, 2010 ### Living_Dog At the very bottom of the page they have that the straight line, using the definition of a vector as the derivative of the worldline is given as: $$P(0) + \lambda(\frac{dP}{d\tau})_o$$ But since the worldline, $$P(\tau)$$ is paramtrized by $$\tau$$ and not $$\lambda$$, then shouldn't the equation be: $$P(0) + \tau(\frac{dP}{d\tau})_o$$ ? 2. Jul 14, 2010 ### yossell I'm not sure what you think the trouble is. It seems fine to me. At that point, the world line isn't straight, and they just seem to be looking for the vector equation of the straight line which is tangent to that point. The equation is just the vector pointing to the point, plus k x tangent vector, with k an arbitrary real. There's no reason why this k should be intimately connected with t is there 3. Jul 14, 2010 ### Altabeh Just a little typo. Your correction is completely apposite. AB 4. Jul 15, 2010 ### yossell Altabeth if you get a chance, could you explain that to me. For the equation of the straight line that is a tangent to the curve, why does tau have to appear as the parameter in the vector equation? I can't see any connection. 5. Jul 15, 2010 ### Altabeh The parameter of curve is apparently $$\tau$$ and when you differentiate the straight line $$P(0) + \tau(\frac{dP}{d\tau})_o$$ with respect to $$\tau$$ then you get the tangent to curve at $$\tau=0$$ which is $$(dP(\tau)/d\tau)_0.$$ I f we take $$\lambda$$ to be related to $$\tau$$ linearly, $$\lamda=a\tau+b$$ with both $$a,b$$ being constants (a=/=0) then it doesn't let the differentiation produce the tangent through including an extra factor $$a$$ multiplied by the true tangent above. P.s. when you talk of straight line you're no longer allowed to asign a "vector equation" to this line. "tau" is just a parameter of curve and has the same role as $$t$$ in the Newtonian equation $$x=vt+x_0.$$ AB Last edited: Jul 15, 2010 6. Jul 15, 2010 ### yossell Thanks Altabeth, But in MTW they only say `the straight line' of the four velocity. For this, I'm struggling to see a connection between the parameter used on the curve and the parameter on the new straight line. It's surely irrelevant what it is, and provided to differentiate the function with respect the variable, whether it's tau or lambda, you get the right result. And from MTW P(0) and dP/d\tau are vectors, this is a vector equation, and they're calling it a straight line. 7. Jul 15, 2010 ### Altabeh Gotta be more careful here: They are saying that $$P(0)+\lambda (dP/d\tau)_0$$ is a straight line. You think incorrectly that $$P(0)$$ and $$dP/d\tau$$ are vectors whereas $$P(\tau)$$ and $$dP/d\tau$$ are respectively the straight world line of a free particle (a non-vector quantity) and the tangent on this world line so that both of $$P(0)$$ and $$dP/d\tau$$ due to being computed at some point ($$\tau=0$$) are to be considered as constants only. This means when taking the derivative of$$P(0)+\lambda (dP/d\tau)_0$$ with respect to the variable of world line, i.e. $$\tau$$, you get $$\frac{d\lambda}{d\tau} (\frac{dP}{d\tau})_0$$ which was expected to be the tangent to the world line, $$(\frac{dP}{d\tau})_0$$ $$\frac{d\lambda}{d\tau} =1$$ or $$\lambda=\tau.$$ I hope this helps. AB Similar Discussions: GRAVITATION by MTW: p.49, lambda or tau?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8222038745880127, "perplexity": 481.11085102210154}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187824068.35/warc/CC-MAIN-20171020101632-20171020121632-00092.warc.gz"}
http://apesoftware.com/calibration-control/help/uncertainty-budget.aspx	# Measurement Uncertainty Budget ## Perform uncertainty analysis of a measurement The Measurement Uncertainty Budget in Calibration Control is a simplified budget where Ape Software assumes no responsibility or liability for any unintentional errors. It is the User’s responsibility to ensure calculations and data entry are accurate and to confirm the suitability for any particular purpose. This budget is useful in situations where (a) each Component of Uncertainty is independent of the others, (b) the major Components are estimated with a high degree of accuracy, and (c) measurement results are measured directly or calculated with a linear formula using only multiplication or division (e.g., $W=V×I$ ). Note that each Measurement Uncertainty Budget is conducted for a single Nominal measurement for a unique piece of Equipment. ### Uncertainty Budget Dialog • Date: Date the Uncertainty Budget calculations were performed. • Equipment ID: The unique designation of Equipment a given study focuses on. • Nominal: Target value for the overall Uncertainty Budget analysis. • Unit of Measure: Measurement unit (e.g., inches, degrees, etc.) of the Nominal value for the Uncertainty Budget analysis. • Significant Digits: Number places to the right of the decimal. • Description: Description or title of the Uncertainty Budget analysis. • Notes: Any notes relevant to the Uncertainty Budget analysis. • Standards: Calibration standards/masters used in the study. • Combined [Standard] Uncertainty (${u}_{c}$): Summation in quadrature (i.e., root sum of the squares) of all the Sources of Uncertainty in the grid. ${u}_{c}=\sqrt{\sum _{k=1}^{n}{{u}_{k}}^{2}}$ • Coverage Factor (e.g., $k=2$ ): Used in the calculation of the Expanded Uncertainty and has a default value of $k=2$ . The Coverage Factor is a confidence level of the interval accounts for the variation in the estimate of the residual standard deviation, and is based on the assumption that the random errors have a normal distribution. • Expanded Uncertainty ($U$): The Expanded Uncertainty ($U$) assures a high level of confidence by re-scaling the Combined Uncertainty (${u}_{c}$) expressed with a different confidence level, e.g., 95 percent. The re-scaling is accomplished by multiplying by the coverage factor (i.e., $U=k×{u}_{c}$ ). In many cases, the coverage factor may be 2, which is typically used to approximate a 95% level of confidence. • Expanded Uncertainty Rounded (${U}_{\mathrm{ce}}$): The expanded uncertainty (${U}_{c}$) rounded to two significant digits. ### Uncertainty Detail Dialog Use the Detail dialog to describe each source of uncertainty (i.e., Component of Uncertainty) to be included in the overall Measurement Uncertainty Budget. • Source Name: Descriptive name for the Source of the Component of Uncertainty, which will be combined with other Components to create a single Uncertainty Budget. • Value ($a$): Numeric value related to the Unit of Measure. • Unit of Measure: Units measured in such as inches, Fahrenheit, mph, etc. • Type A/B: Method used to estimate uncertainty either Type A, if estimated statistically, or Type B, if inferred through non statistical methods such as historical measurements, manufacturer specifications, calibration certificates, published data, mathematical formulas, or general experience. • [Probability] Distribution: The Probability Distribution selected dictates the Divisor (next field). For example, a Normal 1s distribution has a Divisor of 1 where a Normal 2s distribution has a divisor of 2. The following values for each Probably Distribution are defaulted into the Divisor field, which can be overridden. No Divisor Normal 1s = 1 Normal 2s = 2 Normal 3s = 3 Normal @ 99% = 2.58 Rectangle = $\sqrt{3}$ = 1.7321 Triangle = $\sqrt{6}$ = 2.4495 U-Shaped = $\sqrt{2}$ = 1.4142 Rectangle = $\sqrt{\mathrm{12}}$ = 3.4641 • Divisor ($d$): The numeric value related to the Probability Distribution chosen. This value is automatically set when choosing the Probability Distribution (previous field) but can be edited independently after choosing the Distribution. • Degrees of Freedom ($v$): For Type A uncertainties, use the d.f. for the corresponding standard deviations. For Type B sources refer to calibration certificates or published reports. In some instances, where the standard deviation must be estimated from scientific judgment or partial data, an infinite d.f. is normally assumed. • Sensitivity Coefficient ($c$): Used to describe how the Component of Uncertainty contributes to the Combined Uncertainty when a simple functional relationship does not exist between the input quantities and the measurement result. For example, the unit of measure for the study may be in length units where an Uncertainty Component may be expressed in temperature or angular units. Use this field to change the weighting of the Component from the default of 1 (one). • Standard Uncertainty ($u$): Calculated by dividing the Value ($v$) by the Divisor ($d$) and then multiplying by the Sensitivity Coefficient ($c$): $u=\frac{a}{d}×c$ • Assumptions Explanation: Use this field to Explain any Assumptions made for the current Uncertainty Component. Here are a few online resources to get started with learning about Measurement Uncertainty. Here are a few spreadsheet examples of Measurement Uncertainty Budgets: ### References Last updated: 6 Feb 2017 Compatibility: Calibration Control version 8.3 to current Email: * Name: * Company: * Day Phone:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 24, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8982025384902954, "perplexity": 1997.4386420184524}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189495.77/warc/CC-MAIN-20170322212949-00494-ip-10-233-31-227.ec2.internal.warc.gz"}
http://bioinf.dimi.uniud.it/publication/structural-operational-semantics-for-continuous/	Structural operational semantics for continuous state probabilistic processes Abstract We consider the problem of modeling syntax and semantics of probabilistic processes with continuous states (e.g. with continuous data). Syntax and semantics of these systems can be defined as algebras and coalgebras of suitable endofunctors over Meas, the category of measurable spaces. In order to give a more concrete representation for these coalgebras, we present an SOS-like rule format which induces an abstract GSOS over Meas; this format is proved to yield a fully abstract universal semantics, for which behavioural equivalence is a congruence. To this end, we solve several problems. In particular, the format has to specify how to compose the semantics of processes (which basically are continuous state Markov processes). This is achieved by defining a language of measure terms, i.e., expressions specifically designed for describing probabilistic measures. Thus, the transition relation associates processes with measure terms. As an example application, we model a CCS-like calculus of processes placed in an Euclidean space. The approach we follow in this case can be readily adapted to other quantitative aspects, e.g. Quality of Service, physical and chemical parameters in biological systems, etc. © 2012 IFIP International Federation for Information Processing. Type Publication Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) Date	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8403084874153137, "perplexity": 722.6990712606246}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547584334618.80/warc/CC-MAIN-20190123151455-20190123173455-00384.warc.gz"}
https://www.varsitytutors.com/hotmath/hotmath_help/topics/solving-systems-of-linear-equations-using-elimination.html	# Solving Systems of Linear Equations Using Elimination ### Systems of Linear equations: A system of linear equations is just a set of two or more linear equations. In two variables $\left(x\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{and}\text{\hspace{0.17em}}\text{\hspace{0.17em}}y\right)$ , the graph of a system of two equations is a pair of lines in the plane. There are three possibilities: • The lines intersect at zero points. (The lines are parallel.) • The lines intersect at exactly one point. (Most cases.) • The lines intersect at infinitely many points. (The two equations represent the same line.) How to Solve a System of Linear Equations Using The Elimination Method (aka The Addition Method, aka The Linear Combination Method) • Step $1$ : Add (or subtract) a multiple of one equation to (or from) the other equation, in such a way that either the $x$ -terms or the $y$ -terms cancel out. • Step $2$ : Then solve for $x$ (or $y$ , whichever's left) and substitute back to get the other coordinate. Now, how do we know that a linear equation obtained by the addition of the first equation with a scalar multiplication of the second is equivalent to the first? Let us take an example. Consider the system $\begin{array}{l}3x+2y=3\\ x-y=-4\end{array}$ . Consider the equation obtained by multiplying the second equation by a constant $m$ and then adding the resultant equation with the first one. That is, $\left(3x+2y\right)+m\left(x-y\right)=\left(3\right)+m\left(-4\right)$ . What we need to prove is that this equation is equivalent to the equation $3x+2y=3$ . We have $x-y=-4⇒m\left(x-y\right)=-4m$ . Since $m\left(x-y\right)=-4m$ , subtract $m\left(x-y\right)$ from the left side and $-4m$ from the right side of the equation $\left(3x+2y\right)+m\left(x-y\right)=\left(3\right)-4m$ which will retain the balance. $\left(3x+2y\right)+m\left(x-y\right)-m\left(x-y\right)=\left(3\right)-4m-\left(-4m\right)$ Cancelling common terms we get, $3x+2y=3$ which is equivalent to the first equation. Therefore, the systems of equations $\begin{array}{l}3x+2y=3\\ x-y=-4\end{array}$ and $\begin{array}{l}\left(3x+2y\right)+m\left(x-y\right)=3+m\left(-4\right)\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x-y=-4\end{array}$ are equivalent. In general, for any system of equations $K=L$ and $P=Q$ , it ca be shown that $K+mP=L+mQ$ is equivalent to $K=L$ . Example: Solve the system $\left\{\begin{array}{l}4x+3y=-2\\ 8x-2y=12\end{array}$ Multiply the first equation by $-2$ and add the result to the second equation. $\begin{array}{l}-8x-6y=4\\ \underset{_}{\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}8x-2y=12}\\ \text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}-8y=16\end{array}$ Solve for $y$ . $y=-2$ Substitute for $y$ in either of the original equations and solve for $x$ . $\begin{array}{l}4x+3\left(-2\right)=-2\\ 4x-6=-2\\ 4x=4\\ x=1\end{array}$ The solution is $\left(1,-2\right)$ .	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 33, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9664043188095093, "perplexity": 161.97499915492628}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583659677.17/warc/CC-MAIN-20190118025529-20190118051529-00052.warc.gz"}
https://arxiv.org/abs/1210.7253	math.CO (what is this?) # Title: Bipartition of graphs based on the normalized cut and spectral methods Abstract: In the first part of this paper, we survey results that are associated with three types of Laplacian matrices:difference, normalized, and signless. We derive eigenvalue and eigenvector formulaes for paths and cycles using circulant matrices and present an alternative proof for finding eigenvalues of the adjacency matrix of paths and cycles using Chebyshev polynomials. Even though each results is separately well known, we unite them, and provide uniform proofs in a simple manner. The main objective of this study is to solve the problem of finding graphs, on which spectral clustering methods and normalized cuts produce different partitions. First, we derive a formula for a minimum normalized cut for graph classes such as paths, cycles, complete graphs, double-trees, cycle cross paths, and some complex graphs like lollipop graph $LP_{n,m}$, roach type graph $R_{n,k}$, and weighted path $P_{n,k}$. Next, we provide characteristic polynomials of the normalized Laplacian matrices ${\mathcal L}(P_{n,k})$ and ${\mathcal L}(R_{n,k})$. Then, we present counter example graphs based on $R_{n,k}$, on which spectral methods and normalized cuts produce different clusters. Subjects: Combinatorics (math.CO); Discrete Mathematics (cs.DM) Cite as: arXiv:1210.7253 [math.CO] (or arXiv:1210.7253v2 [math.CO] for this version) ## Submission history From: Yoshihiro Mizoguchi [view email] [v1] Fri, 26 Oct 2012 21:17:48 GMT (195kb,D) [v2] Sun, 4 Nov 2012 05:30:10 GMT (195kb,D)	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6151922941207886, "perplexity": 1234.1208775434736}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891812841.74/warc/CC-MAIN-20180219211247-20180219231247-00597.warc.gz"}
http://mathhelpforum.com/calculus/98030-derivative-problem.html	1. ## Derivative problem This is a problem for finding the $f'(x)$ of $x^3$ from a definition for a derivative which is derived from the definition for $m_{tan}$: $f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$ So, after plugging in the function $f'(x)=\lim_{h\to0}\frac{(x+h)^3-x^3}{h}$ and doing some mad Algebra, I get to this point $ =\lim_{h\to0}\frac{x^3+h^3+3h^2x+3x^2h}{h} $ and don't know where to go. Can anyone help? I think that maybe I missed or am blocking this bit of Algebra. A link to a relevant online Algebra reference text would also be appreciated. 2. Originally Posted by mathbit This is a problem for finding the $f'(x)$ of $x^3$ from a definition for a derivative which is derived from the definition for $m_{tan}$: $f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$ So, after plugging in the function $f'(x)=\lim_{h\to0}\frac{(x+h)^3-x^3}{h}$ and doing some mad Algebra, I get to this point $ =\lim_{h\to0}\frac{x^3+h^3+3h^2x+3x^2h}{h} $ and don't know where to go. Can anyone help? I think that maybe I missed or am blocking this bit of Algebra. A link to a relevant online Algebra reference text would also be appreciated. You're missing a term. It should be (in red) $ =\lim_{h\to0}\frac{x^3+h^3+3h^2x+3x^2h - \color{red}{x^3}}{h} $ 3. Doh!	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9363426566123962, "perplexity": 319.53393333675785}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721142.99/warc/CC-MAIN-20161020183841-00239-ip-10-171-6-4.ec2.internal.warc.gz"}
https://med.libretexts.org/Bookshelves/Nutrition/Book%3A_An_Introduction_to_Nutrition_(Zimmerman)/08%3A_Nutrients_Important_As_Antioxidants/8.3%3A_Antioxidant_Micronutrients	# 8.3: Antioxidant Micronutrients Skills to Develop • List the antioxidant nutrients. • Give examples of the best food sources of antioxidant nutrients. • Name some phytochemicals and their health benefits as backed by scientific evidence. The market is flooded with advertisements for “super antioxidant” supplements teeming with molecules that block free radical production, stimulate the immune system, prevent cancer, and reduce the signs of aging. Based on the antioxidant-supplement industry’s success, the general public appears to believe these health claims. However, these claims are not backed by scientific evidence; rather, there is some evidence suggesting supplements can actually cause harm. While scientists have found evidence supporting the consumption of antioxidant-rich foods as a method of reducing the risk of chronic disease, there is no “miracle cure;” no pill or supplement alone can provide the same benefits as a healthy diet. Remember, it is the combination of antioxidants and other nutrients in healthy foods that is beneficial. In this section, we will review how particular antioxidants function in the body, learn how they work together to protect the body against free radicals, and explore the best nutrient-rich dietary sources of antioxidants. Antioxidant Vitamins One dietary source of antioxidants is vitamins. In our discussion of antioxidant vitamins, we will focus on vitamins E, C, and A. ### Vitamin E Functions and Health Benefits Vitamin E is actually eight chemically similar substances, of which alpha-tocopherol appears to be the most potent antioxidant. Alpha-tocopherol and vitamin E’s other constituents are fat-soluble and primarily responsible for protecting cell membranes against lipid destruction caused by free radicals. After alpha-tocopherol interacts with a free radical it is no longer capable of acting as an antioxidant unless it is enzymatically regenerated. Vitamin C helps to regenerate some of the alpha-tocopherol, but the remainder is eliminated from the body. Therefore, to maintain vitamin E levels, you ingest it as part of your diet. In addition to its antioxidant functions, vitamin E, mainly as alpha-tocopherol, can change the functions of proteins in cells, plays a role in the operations of the immune system, enhances the dilation of blood vessels, and inhibits blood clot formation. Despite vitamin E’s numerous beneficial functions when taken in recommended amounts, large studies do not support the idea that taking higher doses of this vitamin will increase its power to prevent or reduce disease risk.Goodman, M., Bostlick RM, Kucuk O, Jones DP. 2011. Clinical trials of antioxidants as cancer prevention agents: past, present, and future. Free Radic Biol Med. 51(5): 1068–84., McGinley C, Shafat A. Donnelly AE. 2009. Does antioxidant vitamin supplementation protect against muscle damage. Sports Med. 39(12): 1011–32. #### Cardiovascular Disease Recall that low-density lipoproteins (LDLs) transport cholesterol and other lipids from the liver to the rest of the body. LDLs are often referred to as “bad cholesterol,” as an elevation in their levels in the blood is a risk factor for cardiovascular disease. Oxidation of the lipids and proteins in LDLs causes them to stick to the walls of arteries and this contributes to the development of fatty streaks and, eventually, plaque, which hardens the arteries. Hardening of the arteries, called atherosclerosis can lead to a heart attack. Vitamin E reduces the oxidation of LDLs, and it was therefore hypothesized that vitamin E supplements would protect against atherosclerosis. However, large clinical trials have not consistently found evidence to support this hypothesis. In fact, in the “Women’s Angiographic Vitamin and Estrogen Study,” postmenopausal women who took 400 international units (264 milligrams) of vitamin E and 500 milligrams of vitamin C twice per day had higher death rates from all causes.Waters, D.D. et al. “Effects of Hormone Replacement Therapy and Antioxidant Vitamin Supplements on Coronary Atherosclerosis in Postmenopausal Women: A Randomized Controlled Trial.” JAMA 288, no. 19 (2002): 2432–40. doi: 10.1001/jama.288.19.2432 Other studies have not confirmed the association between increased vitamin E intake from supplements and increased mortality. There is more consistent evidence from observational studies that a higher intake of vitamin E from foods is linked to a decreased risk of dying from a heart attack. ### Cancer The large clinical trials that evaluated whether there was a link between vitamin E and cardiovascular disease risk also looked at cancer risk. These trials, called the HOPE-TOO Trial and Women’s Health Study, did not find that vitamin E at doses of 400 international units (264 milligrams) per day or 600 international units (396 milligrams) every other day reduced the risk of developing any form of cancer.HOPE and HOPE-TOO Trial Investigators. “Effects of Long-Term Vitamin E Supplementation on Cardiovascular Events and Cancer.” JAMA 293 (2005):1338–47. http://jama.ama-assn.org/content/293/11/1338.long., Lee, I-M., et al. “Vitamin E in the Primary Prevention of Cardiovascular Disease and Cancer: The Women’s Health Study.” JAMA 294 (2005): 56–65. http://jama.ama-assn.org/content/294/1/56.long. #### Eye Conditions Oxidative stress plays a role in age-related loss of vision, called macular degeneration. Age-related macular degeneration (AMD) primarily occurs in people over age fifty and is the progressive loss of central vision resulting from damage to the center of the retina, referred to as the macula. There are two forms of AMD, dry and wet, with wet being the more severe form. In the dry form, deposits form in the macula; the deposits may or may not directly impair vision, at least in the early stages of the disease. In the wet form, abnormal blood vessel growth in the macula causes vision loss. Clinical trials evaluating the effects of vitamin E supplements on AMD and cataracts (clouding of the lens of an eye) did not consistently observe a decreased risk for either. However, scientists do believe vitamin E in combination with other antioxidants such as zinc and copper may slow the progression of macular degeneration in people with early-stage disease. #### Dementia The brain’s high glucose consumption makes it more vulnerable than other organs to oxidative stress. Oxidative stress has been implicated as a major contributing factor to dementia and Alzheimer’s disease. Some studies suggest vitamin E supplements delay the progression of Alzheimer’s disease and cognitive decline, but again, not all of the studies confirm the relationship. A recent study with over five thousand participants published in the July 2010 issue of the Archives of Neurology demonstrated that people with the highest intakes of dietary vitamin E were 25 percent less likely to develop dementia than those with the lowest intakes of vitamin E.Devore, E. E. et al. “Dietary Antioxidants and Long-Term Risk of Dementia.” Arch Neurol 67, no.7 (2010): 819–25. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2923546/?tool=pubmed. More studies are needed to better assess the dose and dietary requirements of vitamin E and, for that matter, whether other antioxidants lower the risk of dementia, a disease that not only devestates the mind, but also puts a substantial burden on loved ones, caretakers, and society in general. ### Dietary Reference Intakes for Vitamin E The Recommended Dietary Allowances (RDAs) and Tolerable Upper Intake Levels (ULs) for different age groups for vitamin E are given in Table $$\PageIndex{1}$$. The RDAs are based on scientific evidence that these levels of vitamin E in the diet prevent conditions associated with vitamin E deficiency, which are rare (signs and symptoms of such conditions are not always evident) but are primarily the result of nerve degeneration. People with malabsorption disorders, such as Crohn’s disease or cystic fibrosis, and babies born prematurely, are at higher risk for vitamin E deficiency. Fat in the diet is required for vitamin E absorption as it is packaged into lipid-rich chylomicrons in intestinal cells and transported to the liver. The liver stores some of the vitamin E or packages it into lipoproteins, which deliver it to cells. Table $$\PageIndex{1}$$: Dietary Reference Intakes for Vitamin E Age Group RDA Males and Females mg/day UL Infants (0–6 months) 4* Infants (7–12 months) 5* Children (1–3 years) 6 200 Children (4–8 years) 7 300 Children (9–13 years) 11 600 Adults (> 19 years) 15 1,000 Vitamin E supplements often contain more than 400 international units, which is almost twenty times the RDA. The UL for vitamin E is set at 1,500 international units for adults. There is some evidence that taking vitamin E supplements at high doses has negative effects on health. As mentioned, vitamin E inhibits blood clotting and a few clinical trials have found that people taking vitamin E supplements have an increased risk of stroke. In contrast to vitamin E from supplements, there is no evidence that consuming foods containing vitamin E compromises health. #### Dietary Sources of Vitamin E Vitamin E is found in many foods, especially those higher in fat, such as nuts and oils. Some spices, such as paprika and red chili pepper, and herbs, such as oregano, basil, cumin, and thyme, also contain vitamin E. (Keep in mind spices and herbs are commonly used in small amounts in cooking and therefore are a lesser source of dietary vitamin E.) See Table $$\PageIndex{2}$$ for a list of foods and their vitamin E contents. To increase your dietary intake of vitamin E from plant-based foods try a spinach salad with tomatoes and sunflower seeds, and add a dressing made with sunflower oil, oregano, and basil. Table $$\PageIndex{2}$$: Vitamin E Content of Various Foods Food Vitamin E (mg) Percent Daily Value Wheat-germ oil (1 Tbsp.) 20.3 100 Sunflower seeds (1 oz.) 7.4 37 Almonds (1 oz.) 6.8 34 Sunflower oil (1 Tbsp.) 5.6 28 Safflower oil (1 Tbsp.) 4.6 23 Hazelnuts (1 oz.) 4.3 22 Peanut butter (2 Tbsp.) 2.9 15 Peanuts (1 oz.) 2.2 11 Corn oil (1 Tbsp.) 1.9 10 Kiwi (1 medium) 1.1 6 Tomato (1 medium) 0.7 4 Spinach (1 c. raw) 0.6 3 ### Vitamin C Functions and Health Benefits Vitamin C, also commonly called ascorbic acid, is a water-soluble micronutrient essential in the diet for humans, although most other mammals can readily synthesize it. Vitamin C’s ability to easily donate electrons makes it a highly effective antioxidant. It is effective in scavenging reactive oxygen species, reactive nitrogen species, and many other free radicals. It protects lipids both by disabling free radicals and by aiding in the regeneration of vitamin E. In addition to its role as an antioxidant, vitamin C is a required part of several enzymes involved in the synthesis of collagen, signaling molecules in the brain, some hormones, and amino acids. Vitamin C levels in the body are affected by the amount in the diet, which influences how much is absorbed and how much the kidney allows to be excreted, such that the higher the intake, the more vitamin C is excreted. Vitamin C is not stored in any significant amount in the body, but once it has reduced a free radical, it is very effectively regenerated and therefore it can exist in the body as a functioning antioxidant for many weeks. #### Cardiovascular Disease Vitamin C’s ability to prevent disease has been debated for many years. Overall, higher dietary intakes of vitamin C (via food intake, not supplements), are linked to decreased disease risk. A review of multiple studies published in the April 2009 issue of the Archives of Internal Medicine concludes there is moderate scientific evidence supporting the idea that higher dietary vitamin C intakes are correlated with reduced cardiovascular disease risk, but there is insufficient evidence to conclude that taking vitamin C supplements influences cardiovascular disease risk.Mente, A., et al. “A Systematic Review of the Evidence Supporting a Causal Link between Dietary Factors and Coronary Heart Disease.” Arch Intern Med 169, no.7 (2009): 659–69. http://archinte.ama-assn.org/cgi/content/full/169/7/659. Vitamin C levels in the body have been shown to correlate well with fruit and vegetable intake, and higher plasma vitamin C levels are linked to reduced risk of some chronic diseases. In a study involving over twenty thousand participants, people with the highest levels of circulating vitamin C had a 42 percent decreased risk for having a stroke.Myint, P.K. et al. “Plasma Vitamin C Concentrations Predict Risk of Incident Stroke Over 10 Y[ears] in 20,649 Participants of the European Prospective Investigation into Cancer, Norfolk Prospective Population Study.” Am J Clin Nutr 87, no.1 (2008): 64–69. http://www.ajcn.org/content/87/1/64.long. #### Cancer There is some evidence that a higher vitamin C intake is linked to a reduced risk of cancers of the mouth, throat, esophagus, stomach, colon, and lung, but not all studies confirm this is true. As with the studies on cardiovascular disease, the reduced risk of cancer is the result of eating foods rich in vitamin C, such as fruits and vegetables, not from taking vitamin C supplements. In these studies, the specific protective effects of vitamin C cannot be separated from the many other beneficial chemicals in fruits and vegetables. #### Immunity Vitamin C does have several roles in the immune system, and many people increase vitamin C intake either from diet or supplements when they have a cold. Many others take vitamin C supplements routinely to prevent colds. Contrary to this popular practice, however, there is no good evidence that vitamin C prevents a cold. A review of more than fifty years of studies published in 2004 in the Cochrane Database of Systematic Reviews concludes that taking vitamin C routinely does not prevent colds in most people, but it does slightly reduce cold severity and duration. Moreover, taking megadoses (up to 4 grams per day) at the onset of a cold provides no benefits.Douglas, R.M. et al. “Vitamin C for Preventing and Treating the Common Cold.” Cochrane Database of Systematic Reviews 4 (2004): CD000980. http://www.ncbi.nlm.nih.gov/pubmed/15495002?dopt=Abstract. Gout is a disease caused by elevated circulating levels of uric acid and is characterized by recurrent attacks of tender, hot, and painful joints. There is some evidence that a higher intake of vitamin C reduces the risk of gout. #### Dietary Reference Intakes for Vitamin C The classic condition associated with vitamin C deficiency is scurvy. The signs and symptoms of scurvy include skin disorders, bleeding gums, painful joints, weakness, depression, and increased susceptibility to infections. Scurvy is prevented by having an Adequate Intake of fruits and vegetables rich in vitamin C. The RDAs and ULs for different age groups for vitamin C are listed in Table $$\PageIndex{4}$$. They are considered adequate to prevent scurvy. Vitamin C’s effectiveness as a free radical scavenger motivated the Institute of Medicine (IOM) to increase the RDA for smokers by 35 milligrams, as tobacco smoke is an environmental and behavioral contributor to free radicals in the body. Table $$\PageIndex{4}$$: Dietary Reference Intakes for Vitamin C Age Group RDA Males and Females mg/day UL Infants (0–6 months) 40* Infants (7–12 months) 50* Children (1–3 years) 15 400 Children (4–8 years) 25 650 Children (9–13 years) 45 1200 Adolescents (14–18 years) 75 (males), 65 (females) 1800 Adults (> 19 years) 90 (males), 75 (females) 2000 High doses of vitamin C have been reported to cause numerous problems, but the only consistently shown side effects are gastrointestinal upset and diarrhea. To prevent these discomforts the IOM has set a UL for adults at 2,000 milligrams per day (greater than twenty times the RDA). At very high doses in combination with iron, vitamin C has sometimes been found to increase oxidative stress, reaffirming that getting your antioxidants from foods is better than getting them from supplements, as that helps regulate your intake levels. There is some evidence that taking vitamin C supplements at high doses increases the likelihood of developing kidney stones, however, this effect is most often observed in people that already have multiple risk factors for kidney stones. #### Dietary Sources of Vitamin C Citrus fruits are great sources of vitamin C and so are many vegetables. In fact, British sailors in the past were often referred to as “limeys” as they carried sacks of limes onto ships to prevent scurvy. Vitamin C is not found in significant amounts in animal-based foods. Because vitamin C is water soluble, it leaches away from foods considerably during cooking, freezing, thawing, and canning. Up to 50 percent of vitamin C can be boiled away. Therefore, to maximize vitamin C intake from foods, you should eat fruits and vegetables raw or lightly steamed. For the vitamin C content of various foods, see Table $$\PageIndex{5}$$. Table $$\PageIndex{5}$$: Vitamin C Content of Various Foods Food Serving Vitamin C (mg) Orange juice 6 oz. 62–93 Grapefruit juice 6 oz. 62–70 Orange 1 medium 70 Grapefruit ½ medium 38 Strawberries 1 c. 85 Tomato 1 medium 16 Sweet red pepper ½ c. raw 95 Broccoli ½ c. cooked 51 Asparagus 1 c. cooked 20 Romaine lettuce 2 c. 27 Kale 1 c. boiled 53 Cauliflower 1 c. boiled 55 Potato 1 medium, baked 17 ### Vitamin A Functions and Health Benefits Vitamin A is a generic term for a group of similar compounds called retinoids. Retinol is the form of vitamin A found in animal-derived foods, and it is converted in the body to the biologically active forms of vitamin A: retinal and retinoic acid (thus retinol is sometimes referred to as “preformed vitamin A”). About 10 percent of plant-derived carotenoids, including beta-carotene, can be converted in the body to retinoids and are another source of functional vitamin A. The retinoids are aptly named as their most notable function is in the retina of the eye where they aid in vision, particularly in seeing under low-light conditions. This is why night blindness is the most definitive sign of vitamin A deficiency. Like vitamin E, vitamin A is fat-soluble and is packaged into chylomicrons in small intestine mucosal cells, and then transported to the liver. The liver stores and exports vitamin A as needed; it is released into the blood bound to a retinol-binding protein, which transports it to cells. Vitamin A has several important functions in the body, including maintaining vision and a healthy immune system. Many of vitamin A’s functions in the body are similar to the functions of hormones (for example, vitamin A can interact with DNA, causing a change in protein function). Vitamin A assists in maintaining healthy skin and the linings and coverings of tissues; it also regulates growth and development. As an antioxidant, vitamin A protects cellular membranes, helps in maintaining glutathione levels, and influences the amount and activity of enzymes that detoxify free radicals. #### Vision Retinol that is circulating in the blood is taken up by cells in the retina, where it is converted to retinal and is used as part of the pigment rhodopsin, which is involved in the eye’s ability to see under low light conditions. A deficiency in vitamin A thus results in less rhodopsin and a decrease in the detection of low-level light, a condition referred to as nightblindness. Insufficient intake of dietary vitamin A over time can also cause complete vision loss. In fact, vitamin A deficiency is the number one cause of preventable blindness worldwide. Vitamin A not only supports the vision function of eyes but also maintains the coverings and linings of the eyes. Vitamin A deficiency can lead to the dysfunction of the linings and coverings of the eye, causing dryness of the eyes, a condition called xerophthalmia. This condition can progress, causing ulceration of the cornea and eventually blindness. #### Immunity The common occurrence of advanced xerophthalmia in children who died from infectious diseases led scientists to hypothesize that supplementing vitamin A in the diet for children with xerophthalmia might reduce disease-related mortality. In Asia in the late 1980s, targeted populations of children were administered vitamin A supplements, and the death rates from measles and diarrhea declined by up to 50 percent. Vitamin A supplementation in these deficient populations did not reduce the number of children who contracted these diseases, but it did decrease the severity of the diseases so that they were no longer fatal. Soon after the results of these studies were communicated to the rest of the world, the World Health Organization (WHO) and the United Nations Children’s Fund (UNICEF) commenced worldwide campaigns against vitamin A deficiency. UNICEF estimates that the distribution of over half a billion vitamin A capsules prevents 350,000 childhood deaths annually.Sommer, A. “Vitamin A Deficiency and Clinical Disease: An Historical Overview.” J Nutr 138 (2008):1835–39. http://jn.nutrition.org/content/138/10/1835.long. In the twenty-first century, science has demonstrated that vitamin A greatly affects the immune system. What we are still lacking are clinical trials investigating the proper doses of vitamin A required to help ward off infectious disease and how large of an effect vitamin A supplementation has on populations that are not deficient in this vitamin. This brings up one of our common themes in this text—micronutrient deficiencies may contribute to the development, progression, and severity of a disease, but this does not mean that an increased intake of these micronutrients will solely prevent or cure disease. The effect, as usual, is cumulative and depends on the diet as a whole, among other things. #### Growth and Development Vitamin A acts similarly to some hormones in that it is able to change the amount of proteins in cells by interacting with DNA. This is the primary way that vitamin A affects growth and development. Vitamin A deficiency in children is linked to growth retardation; however, vitamin A deficiency is often accompanied by protein malnutrition and iron deficiency, thereby confounding the investigation of vitamin A’s specific effects on growth and development. In the fetal stages of life, vitamin A is important for limb, heart, eye, and ear development and in both deficiency and excess, vitamin A causes birth defects. Furthermore, both males and females require vitamin A in the diet to effectively reproduce. #### Cancer Vitamin A’s role in regulating cell growth and death, especially in tissues that line and cover organs, suggests it may be effective in treating certain cancers of the lung, neck, and liver. It has been shown in some observational studies that vitamin A-deficient populations have a higher risk for some cancers. However, vitamin A supplements have actually been found to increase the risk of lung cancer in people who are at high risk for the disease (i.e., smokers, exsmokers, workers exposed to asbestos). The Beta-Carotene and Retinol Efficacy Trial (CARET) involving over eighteen thousand participants who were at high risk for lung cancer found that people who took supplements containing very high doses of vitamin A (25,000 international units) and beta-carotene had a 28 percent higher incidence of lung cancer midway through the study, which was consequently stopped.Goodman, G.E. et al. “The Beta-Carotene and Retinol Efficacy Trial: Incidence of Lung Cancer and Cardiovascular Disease Mortality During 6-year Follow-up after Stopping Beta-Carotene and Retinol Supplements.” J Natl Cancer Inst 96, no. 23 (2004): 1743–50. http://jnci.oxfordjournals.org/content/96/23/1743.long. Vitamin A supplementation is a relatively common practice in treating some types of cancer patients and is thought to improve the effectiveness of some anticancer drugs, but many oncologists (physicians who treat cancer patients) do not recommend this practice as vitamin A may actually inhibit the actions of some anticancer drugs. #### Vitamin A Toxicity Vitamin A toxicity, or hypervitaminosis A, is rare. Typically it requires you to ingest ten times the RDA of preformed vitamin A in the form of supplements (it would be hard to consume such high levels from a regular diet) for a substantial amount of time, although some people may be more susceptible to vitamin A toxicity at lower doses. The signs and symptoms of vitamin A toxicity include dry, itchy skin, loss of appetite, swelling of the brain, and joint pain. In severe cases, vitamin A toxicity may cause liver damage and coma. Vitamin A is essential during pregnancy, but doses above 3,000 micrograms per day (10,000 international units) have been linked to an increased incidence of birth defects. Pregnant women should check the amount of vitamin A contained in any prenatal or pregnancy multivitamin she is taking to assure the amount is below the UL. ### Dietary Reference Intakes for Vitamin A There is more than one source of vitamin A in the diet. There is preformed vitamin A, which is abundant in many animal-derived foods, and there are carotenoids, which are found in high concentrations in vibrantly colored fruits and vegetables and some oils. Some carotenoids are converted to retinol in the body by intestinal cells and liver cells. However, only miniscule amounts of certain carotenoids are converted to retinol, meaning fruits and vegetables are not necessarily good sources of vitamin A. Beta-carotene dissolved in oil is more readily converted to retinol; one-half of a microgram of beta-carotene is converted to retinol. Overall, the carotenoids do not have the same biological potency of preformed vitamin A, but as you will soon find out, they have other attributes that influence health, most notably their antioxidant activity. The RDA for vitamin A includes all sources of vitamin A. The amount of vitamin A obtained from carotenoids—the retinol activity equivalent (RAE)—can be calculated. For example, 12 micrograms of fruit- or vegetable-based beta-carotene will yield 1 microgram of retinol, as mentioned. The RDA for vitamin A is considered sufficient to support growth and development, reproduction, vision, and immune system function while maintaining adequate stores (good for four months) in the liver. Table $$\PageIndex{6}$$: Dietary Reference Intakes for Vitamin A Age Group RDA Males and Females mcg/day UL Infants (0–6 months) 400* 600 Infants (7–12 months) 500* 600 Children (1–3 years) 300 600 Children (4–8 years) 400 900 Children (9–13 years) 600 1,700 Adolescents (14–18 years) Males: 900 2,800 Females: 700 Adults (> 19 years) Males: 900 3,000 Females: 700 ## Dietary Sources of Vitamin A Preformed vitamin A is found only in foods from animals, with the liver being the richest source because that’s where vitamin A is stored (Table $$\PageIndex{7}$$). The dietary sources of carotenoids will be given in the following text. Table $$\PageIndex{7}$$: Vitamin A Content of Various Foods Food Serving Vitamin A (IU) Percent Daily Value Beef liver 3 oz. 27,185 545 Chicken liver 3 oz. 12,325 245 Milk, skim 1 c. 500 10 Milk, whole 1 c. 249 5 Cheddar cheese 1 oz. 284 6 ## Phytochemicals Phytochemicals are chemicals in plants that may provide some health benefit. Carotenoids are one type of phytochemical. Phytochemicals also include indoles, lignans, phytoestrogens, stanols, saponins, terpenes, flavonoids, carotenoids, anthocyanidins, phenolic acids, and many more. They are found not only in fruits and vegetables, but also in grains, seeds, nuts, and legumes. Many phytochemicals act as antioxidants, but they have several other functions, such as mimicking hormones, altering absorption of cholesterol, inhibiting inflammatory responses, and blocking the actions of certain enzymes. Phytochemicals are present in small amounts in the food supply, and although thousands have been and are currently being scientifically studied, their health benefits remain largely unknown. Also largely unknown is their potential for toxicity, which could be substantial if taken in large amounts in the form of supplements. Moreover, phytochemicals often act in conjunction with each other and with micronutrients. Thus, supplementing with only a few may impair the functions of other phytochemicals or micronutrients. As with the antioxidant vitamins, it is the mixture and variety of phytochemicals in foods that are linked to health benefits. ## Carotenoids Function and Health Benefits Carotenoids are pigments synthesized by plants that give them their yellow, orange, and red color. Over six hundred carotenoids have been identified and, with just a few exceptions, all are found in the plant kingdom. There are two classes of carotenoids—the xanthophylls, which contain oxygen, and the carotenes, which do not. In plants, carotenoids absorb light for use in photosynthesis and act as antioxidants. Beta-carotene, alpha-carotene, gamma-carotene, and beta-cryptoxanthin are converted to some extent to retinol in the body. The other carotenoids, such as lycopene, are not. Many biological actions of carotenoids are attributed to their antioxidant activity, but they likely act by other mechanisms, too. ## Eye Conditions Lutein, found in green leafy vegetables, and zeaxanthin, found in peppers, corn, and saffron, act as antioxidants in the retina of the eye and protect it from ultraviolet light damage. Diets high in these carotenoids are associated with a decreased risk of AMD, and there is good evidence that supplements containing these carotenoids also provide vision benefits. A review published in the August 2010 issue of Current Medical Research and Opinion concludes that supplementation with lutein and zeaxanthin reduces the incidence of AMD and cataracts.Barker II, F. M. “Dietary Supplementation: Effects on Visual Performance and Occurrence of AMD and Cataracts.” Curr Med Res Opin 26, no. 8 (2010): 2011–23. http://informahealthcare.com/doi/abs...95.2010.494549. The data that supports that beta-carotene supplementation may delay the progression of AMD is more convincing when beta-carotene is taken in combination with other micronutrients. The Age-Related Eye Disease Study found that a supplement containing 500 milligrams of vitamin C, 400 international units of vitamin E, 15 milligrams of beta-carotene, 80 milligrams of zinc oxide, and 2 milligrams of copper as cupric oxide reduced the risk of progressing to advanced stages of AMD by 25 percent.Age-Related Eye Disease Study Research Group. “A Randomized, Placebo-Controlled, Clinical Trial of High-Dose Supplementation with Vitamins C and E, Beta-Carotene, and Zinc for Age-Related Macular Degeneration and Vision Loss.” Arch Ophthalmol 119, no. 10 (2001): 1417–36. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1462955/. This study did not find that the formulated supplement significantly prevented the onset of disease, only that it delayed its progression specifically in people with intermediate or advanced stage AMD. Studies are ongoing to determine if other antioxidant combinations actually protect against developing AMD at all. ## Cardiovascular Disease While some studies do associate a decreased risk for atherosclerosis with higher dietary intake of carotenoids, others do not. There is a large number of studies that show total carotenoid intake is associated with improvement in blood vessel function. A smaller number of studies show that intake of specific carotenoids, such as lycopene and alpha-carotene, are also associated with improved blood vessel function. The main problems associated with linking carotenoids to a decrease in cardiovascular disease risk, or any other disease for that matter, are that they are present in foods containing many other beneficial plant chemicals, and trials evaluating the effects of specific carotenoids in the form of supplements provide inconsistent and sometimes contradictory results. ## Cancer A higher intake of some carotenoids, but not others, is linked to decreased risks for some cancers. A review of two large studies (> 120,000 men and women) published in the October 2000 issue of The American Journal of Clinical Nutrition reports that there is no significant association between beta-carotene intake and lung cancer risk, but men and women with the highest intakes of total carotenoids had a more than 30 percent risk reduction for developing lung cancer.Michaud, D.S. et al. “Intake of Specific Carotenoids and Risk of Lung Cancer in 2 Prospective US Cohorts.” Am J Clin Nutr 72, no. 4 (2000): 990–97. http://www.ajcn.org/content/72/4/990.long. Other large studies conducted in Europe have confirmed the inverse relationship of total dietary carotenoid intake with lung cancer risk. There is some evidence that diets rich in lycopene, which is present in high concentrations in tomatoes, is linked to decreased prostate cancer risk, but it is not known if it is lycopene specifically or some other component in tomatoes that protects against prostate cancer. ## Carotenoid Bioavailability and Dietary Sources Carotenoids are not absorbed as well as vitamin A, but similar to vitamin A, they do require fat in the meal for absorption. In intestinal cells, carotenoids are packaged into the lipid-containing chylomicrons inside small intestine mucosal cells and then transported to the liver. In the liver, carotenoids are repackaged into lipoproteins, which transport them to cells. In contrast to most micronutrients, carotenoid availability is actually increased by the cooking process because cooking, along with chopping and homogenizing, releases carotenoids from the plant matrix. Thus, eating a can of tomatoes provides more lycopene than eating a raw tomato. However, overcooking transforms some of the carotenoids into inactive products, and in general it is best to chop and lightly steam vegetables containing carotenoids to maximize their availability from foods. Cooking carotenoid-containing foods in oil also enhances the bioavailability of carotenoids. In the United States, the most consumed carotenoids are alpha-carotene, beta-carotene, beta-cryptoxanthin, lycopene, lutein, and zeaxanthin. See Table $$\PageIndex{7}$$ for the carotenoid content of various foods. Table $$\PageIndex{7}$$: Alpha- and Beta-Carotene Content of Various Foods Food Serving Beta-carotene (mg) Alpha-carotene (mg) Pumpkin, canned 1c. 17.00 11.70 Carrot juice 1c. 22.00 10.20 Carrots, cooked 1c. 13.00 5.90 Carrots, raw 1 medium 5.10 2.10 Winter squash, baked 1c. 5.70 1.40 Collards, cooked 1c. 11.60 0.20 Tomato 1 medium 0.55 0.10 Tangerine 1 medium 0.13 0.09 Peas, cooked 1c. 1.20 0.09 Interactive $$\PageIndex{1}$$ Visit the USDA website and find out more about the carotenoid content of various foods: http://www.ars.usda.gov/Services/docs.htm?docid=20958 ### Three Other Phytochemicals and Their Potential Health Benefits Three classes of phytochemicals (other than carotenoids) are flavonoids, organosulfur compounds, and lignans. Their potential health benefits are discussed below. #### Flavonoids Flavonoids are a large class of chemicals including anthocyanidins (found in red, blue, and purple berries), flavanols (found in teas, chocolate, berries, apples, yellow onions, kale, and broccoli), and isoflavones (found in soy products). Flavonoids are very effective free radical scavengers, and there is some evidence that higher intakes of flavonoid-rich foods and/or beverages reduce the risk of cardiovascular disease, but this has not been consistently observed. Although flavonoids have been shown to reduce the incidence of some tumors in animals, similar studies in humans have been inconclusive. #### Organosulfur Compounds These compounds are predominantly found in garlic, but can also be found in onions and leeks. It’s suspected that the higher intake of garlic is the aspect of the Mediterranean diet that contributes to a decreased risk of cardiovascular disease. Animal and laboratory studies suggest the organosulfur compounds in garlic reduce cholesterol, are anti-inflammatory, stimulate the synthesis of glutathione, and cause death of cancer cells. There is some evidence in humans that garlic reduces cholesterol, but more recent studies did not confirm that the effect was signficant or sustained. A higher intake of garlic likely inhibits blood clot formation in humans. Observational studies suggest diets high in organosulfur compounds decrease the risk of gastric and colorectal cancer. For other cancers, the data is less consistent. #### Lignans Lignans are a group of chemical compounds obtained from many food sources, including grains, nuts, seeds, fruits, and vegetables, and especially flax seed. Some lignans are also called phytoestrogens as they can mimic or inhibit some of the actions of the hormone estrogen in the body. The antiestrogenic effect of some lignans suggests they may be helpful in treating hormone-dependent cancers, such as breast and ovarian cancers. However, studies are few and conflicting on whether eating foods high in lignans reduces breast or ovarian cancer. In regard to cardiovascular disease risk, diets rich in whole grains are protective, but it remains unclear whether it is the lignans in whole grains that are responsible for the reduced risk. Whole grains contain many other beneficial phytochemicals, micronutrients, and fiber. Interactive $$\PageIndex{2}$$ To discover more about phytochemicals, visit the website for the Micronutrient Information Center of the Linus Pauling Institute at Oregon State University: http://lpi.oregonstate.edu/infocenter/phytochemicals.html ## Other Dietary Sources of Beneficial Phytochemicals ### Herbs and Spices These are the aromatic parts of plants, such as the leaves, seeds, pods, and berries. They are an additional dietary source of phytochemicals, and many have exceptional antioxidant capacity. Throughout the ages, people have used spices and herbs not only for adding flavor to foods, but also as medicines. Curcumin, the principal component of tumeric, has been used for over two thousand years in India to treat a variety of ailments. As of 2011, over seventy clinical trials are investigating the health benefits of curcumin, which may include reducing cancer risk and delaying the progression of Alzheimer’s disease. You learned in the beginning of this chapter that nutmeg comes from the dried seed kernel of Myristica fragrans and has been used as an antimicrobial, antifungal, and anti-inflammatory agent, and as a pain reliever. In high doses nutmeg acts similar to a psychoactive drug in that it causes euphoria, delusions, and hallucinations. According to a study conducted on over 3,100 foods, beverages, spices, herbs, and supplements, the spices and herbs were the dietary sources most rich in antioxidants. Interactive $$\PageIndex{3}$$ Read the article, “The Total Antioxidant Content of More than 3,100 Foods, Beverages, Spices, Herbs, and Supplements Used Worldwide,” published in the January 2010 issue of the Nutrition Journal. It is a useful source to find dietary sources of antioxidants. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2841576/?tool=pubmed Tools for Change Add some spice, flavor, and decoration to your food along with beneficial antioxidants and phytochemicals. Embracing cuisine rich in spices and herbs further enhances the health benefits of eating a diet rich in fruit and vegetables. Think spices are too hot for your palate? As little as half a teaspoon of cinnamon has been shown in scientific studies to provide health benefits, such as improving glucose homeostasis in people with Type 2 diabetes. Over fifteen clinical trials are now evaluating the effectiveness of cinnamon as a adjunct treatment for Type 2 diabetes and/or cardiovascular disease. ### Tea Tea is an aromatic beverage made from the dried parts of plants steeped in hot water. Its health benefits have been known for years, and as with coffee the benefits are not just physiological, but also mental and social. In folklore, teas are considered curatives of stomachache, diarrhea, and even the plague. In The Book of Tea, Okakura Kakuzo asserts that consuming a cup of tea provides “the adoration of the beautiful among the sordid facts of everyday existence.”Okakura Kakuzo. The Book of Tea. (Berlin, Germany: Dover Publications, 1964). Teas can contain more than seven hundred different phytochemicals. Some of them may be beneficial and others may not be, as some reduce the dietary absorption of some micronutrients. The health claims of drinking tea—black, green, or red—number at least in the hundreds but remain mostly scientifically unsupported. There are a great number of studies showing that drinking tea is at least linked to a decreased risk of heart disease, cancer, and diabetes, but the exact phyotchemicals illiciting these health benefits are under intense scrutiny. Moreover, people who consume more tea are likely to drink fewer soft drinks and therefore, based on a “replacement theory,” have a reduced likelihood of having a chronic disease. ## Antioxidant Minerals In addition to the antioxidant vitamins and phytochemicals, several minerals have antioxidant function, including selenium, manganese, iron, copper, and zinc. #### Selenium Functions and Health Benefits Around twenty-five known proteins require selenium to function. Some are enzymes involved in detoxifying free radicals and include glutathione peroxidases and thioredoxin reductase. As an integral functioning part of these enzymes, selenium aids in the regeneration of glutathione and oxidized vitamin C. Selenium as part of glutathione peroxidase also protects lipids from free radicals, and, in doing so, spares vitamin E. This is just one example of how antioxidants work together to protect the body against free radical-induced damage. Other functions of selenium-containing proteins include protecting endothelial cells that line tissues, converting the inactive thyroid hormone to the active form in cells, and mediating inflammatory and immune system responses. Observational studies have demonstrated that selenium deficiency is linked to an increased risk of cancer. A review of forty-nine observational studies published in the May 2011 issue of the Cochrane Database of Systematic Reviews concludes that higher selenium exposure reduces overall cancer incidence by about 34 percent in men and 10 percent in women, but notes these studies had several limitations, including data quality, bias, and large differences among different studies.Dennert, G. et al. “Selenium for Preventing Cancer.” Cochrane Database of Systematic Reviews 5 (2011): CD005195. http://www.ncbi.nlm.nih.gov/pubmed/21563143. Additionally, this review states that there is no convincing evidence from six clinical trials that selenium supplements reduce cancer risk. Because of its role as a lipid protector, selenium has been suspected to prevent cardiovascular disease. In some observational studies, low levels of selenium are associated with a decreased risk of cardiovascular disease. However, other studies have not always confirmed this association and clinical trials are lacking. #### Dietary Reference Intakes for Selenium The IOM has set the RDAs for selenium based on the amount required to maximize the activity of glutathione peroxidases found in blood plasma. The RDAs for different age groups are listed in Table $$\PageIndex{8}$$. Table $$\PageIndex{8}$$: Dietary Reference Intakes for Selenium Age Group RDA Males and Females mcg/day UL Infants (0–6 months) 15* 45 Infants (7–12 months) 20* 65 Children (1–3 years) 20 90 Children (4–8 years) 30 150 Children (9–13 years) 40 280 Adults (> 19 years) 55 400 Selenium at doses several thousand times the RDA can cause acute toxicity, and when ingested in gram quantities can be fatal. Chronic exposure to foods grown in soils containing high levels of selenium (significantly above the UL) can cause brittle hair and nails, gastrointestinal discomfort, skin rashes, halitosis, fatigue, and irritability. The IOM has set the UL for selenium for adults at 400 micrograms per day. #### Dietary Sources of Selenium Organ meats, muscle meats, and seafood have the highest selenium content. Plants do not require selenium, so the selenium content in fruits and vegetables is usually low. Animals fed grains from selenium-rich soils do contain some selenium. Grains and some nuts contain selenium when grown in selenium-containing soils. See Table $$\PageIndex{9}$$ for the selenium content of various foods. Table $$\PageIndex{9}$$: Selenium Contents of Various Foods Food Serving mcg Brazil nuts 1 oz. 544.0 Shrimp 3 oz. 34.0 Crab meat 3 oz. 41.0 Ricotta cheese 1 c. 41.0 Salmon 3 oz. 40.0 Pork 3 oz. 35.0 Ground beef 3 oz. 18.0 Round steak 3 oz. 28.5 Beef liver 3 oz. 28.0 Chicken 3 oz. 13.0 Couscous 1 c. 43.0 Barley, cooked 1 c. 13.5 Milk, low-fat 1 c. 8.0 Walnuts, black 1 oz. 5.0 ### Manganese, Iron, Copper, and Zinc: Functions and Health Benefits As with selenium, manganese, iron, copper, and zinc are essential cofactors for enzymes involved in detoxifying free radicals. In the proper doses they allow for optimal detoxification of free radicals. In excess and when not bound to proteins, manganese, iron, and copper actually accelerate the production of free radicals. This is an attribute of all antioxidants in general, although the effect is greater for certain antioxidants. Antioxidants can become pro-oxidants when the conditions are altered. Recall that oxidative stress results from an imbalance in free radicals with their detoxifying and repair systems. Another factor that can cause oxidative stress is a high level of antioxidants, as some will revert to acting as pro-oxidants. ### Key Takeaways • Health claims of antioxidant supplements are not backed by scientific evidence and there is some evidence suggesting they cause harm. • Consuming antioxidant-rich foods is scientifically supported to reduce the risk of chronic diseases. • Antioxidants have specific functions, and they can act in concert with each other to protect against free radicals. • Some antioxidants are involved in the regeneration of other antioxidants. • Many phytochemicals act as antioxidants, but they perform several other functions as well. • Dietary antioxidants and phytochemicals in the proper doses are beneficial to health but can cause harm in excess. ### Discussion Starters 1. In regard to doses, discuss why it is better to obtain antioxidants from the diet and not from supplements. When might supplements be advantageous? 2. With more scientific evidence in hand, debate whether or not the supplement industry requires more regulation.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3482537567615509, "perplexity": 7542.3206441047505}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998879.63/warc/CC-MAIN-20190619003600-20190619025600-00284.warc.gz"}
https://math.stackexchange.com/questions/3088553/if-p-q-are-distinct-primes-and-a-is-not-divisible-by-p-or-q-then-gcd	# If $p,q$ are distinct primes and $a$ is not divisible by $p$ or $q$, then $\gcd(a, pq)=1$ [duplicate] If $$p,q$$ are distinct primes and $$a$$ is not divisible by $$p$$ or $$q$$, then $$\gcd(a, pq)=1$$. I want to show this using linear combinations, so that a linear combination of $$a$$, and $$py$$ will give $$1$$. So for some $$x,y,x',y'$$: $$ax+py = 1 = ax'+qy'$$, and $$a(x-x')+py-qy'=1-ax'-qy'$$. Not sure where to go from here. Hints appreciated. ## marked as duplicate by Bill Dubuque algebra-precalculus StackExchange.ready(function() { if (StackExchange.options.isMobile) return; $('.dupe-hammer-message-hover:not(.hover-bound)').each(function() { var$hover = $(this).addClass('hover-bound'),$msg = $hover.siblings('.dupe-hammer-message');$hover.hover( function() { $hover.showInfoMessage('', { messageElement:$msg.clone().show(), transient: false, position: { my: 'bottom left', at: 'top center', offsetTop: -7 }, dismissable: false, relativeToBody: true }); }, function() { StackExchange.helpers.removeMessages(); } ); }); }); Jan 26 at 18:31 $$ax+py = 1$$ and $$ax'+qy'=1$$. Rearranging, we have $$py = 1-ax$$ and $$qy'=1-ax'$$. Multiplying, we get $$pyqy'=(1-ax)(1-ax')=1-a (x+x')+a^2xx'.$$ Hence $$pq(yy')+a (x+x'-axx')=1.$$ If $$a$$ is not divisible by $$p$$ or $$q$$ then indeed there exist integers $$x$$, $$x'$$, $$y$$, and $$y'$$ such that $$ax+py=1\qquad\text{ and }\qquad ax'+qy'=1.$$ Now isolate $$py$$ from the first and $$qy'$$ from the second equation, and multiply the two results together. Can you finish from here?	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 27, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8256071209907532, "perplexity": 499.74145012384326}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027317130.77/warc/CC-MAIN-20190822130553-20190822152553-00158.warc.gz"}
https://www.zora.uzh.ch/id/eprint/118187/	# Population mixing and the risk of childhood leukaemia in Switzerland: a census-based cohort study Lupatsch, Judith E; Kuehni, Claudia E; Niggli, Felix; Ammann, Roland A; Egger, Matthias; Spycher, Ben D (2015). Population mixing and the risk of childhood leukaemia in Switzerland: a census-based cohort study. European Journal of Epidemiology, 30(12):1287-1298. ## Abstract Childhood leukaemia (CL) may have an infectious cause and population mixing may therefore increase the risk of CL. We aimed to determine whether CL was associated with population mixing in Switzerland. We followed children aged <16 years in the Swiss National Cohort 1990-2008 and linked CL cases from the Swiss Childhood Cancer Registry to the cohort. We calculated adjusted hazard ratios (HRs) for all CL, CL at age <5 years and acute lymphoblastic leukaemia (ALL) for three measures of population mixing (population growth, in-migration and diversity of origin), stratified by degree of urbanisation. Measures of population mixing were calculated for all municipalities for the 5-year period preceding the 1990 and 2000 censuses. Analyses were based on 2,128,012 children of whom 536 developed CL. HRs comparing highest with lowest quintile of population growth were 1.11 [95 % confidence interval (CI) 0.65-1.89] in rural and 0.59 (95 % CI 0.43-0.81) in urban municipalities (interaction: p = 0.271). Results were similar for ALL and for CL at age <5 years. For level of in-migration there was evidence of a negative association with ALL. HRs comparing highest with lowest quintile were 0.60 (95 % CI 0.41-0.87) in urban and 0.61 (95 % CI 0.30-1.21) in rural settings. There was little evidence of an association with diversity of origin. This nationwide cohort study of the association between CL and population growth, in-migration and diversity of origin provides little support for the population mixing hypothesis. ## Abstract Childhood leukaemia (CL) may have an infectious cause and population mixing may therefore increase the risk of CL. We aimed to determine whether CL was associated with population mixing in Switzerland. We followed children aged <16 years in the Swiss National Cohort 1990-2008 and linked CL cases from the Swiss Childhood Cancer Registry to the cohort. We calculated adjusted hazard ratios (HRs) for all CL, CL at age <5 years and acute lymphoblastic leukaemia (ALL) for three measures of population mixing (population growth, in-migration and diversity of origin), stratified by degree of urbanisation. Measures of population mixing were calculated for all municipalities for the 5-year period preceding the 1990 and 2000 censuses. Analyses were based on 2,128,012 children of whom 536 developed CL. HRs comparing highest with lowest quintile of population growth were 1.11 [95 % confidence interval (CI) 0.65-1.89] in rural and 0.59 (95 % CI 0.43-0.81) in urban municipalities (interaction: p = 0.271). Results were similar for ALL and for CL at age <5 years. For level of in-migration there was evidence of a negative association with ALL. HRs comparing highest with lowest quintile were 0.60 (95 % CI 0.41-0.87) in urban and 0.61 (95 % CI 0.30-1.21) in rural settings. There was little evidence of an association with diversity of origin. This nationwide cohort study of the association between CL and population growth, in-migration and diversity of origin provides little support for the population mixing hypothesis. ## Statistics ### Citations Dimensions.ai Metrics 9 citations in Web of Science® 11 citations in Scopus®	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8293522596359253, "perplexity": 9340.102342756738}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-45/segments/1603107894759.37/warc/CC-MAIN-20201027195832-20201027225832-00312.warc.gz"}
https://blog.henryong.com/2009/05/14/rich-text-fields-in-sharepoint-document-and-picture-libraries/?replytocom=3498	Did you know that if you have a multi-line text box/field in either a Document or Picture Library that your only formatting option is plain text? If you were using the same field in a List, then you get the options of configuring the output as Plain Text, Rich Text or Enhanced rich text. Multi-line text fields give you the ability to use plain, rich, or enhanced rich text... ... but Document and Picture Libraries don't give you this ability. I didn’t think that was right so I went digging through the object model to see if there was some magic property that I could change to make this happen. Using the trusty SharePoint Manager utility, lo and behold the Rich Text Property! There's a RichText property that is set to 'False' for multi-line text fields in Document and Picture Libraries. The only drawback I’ve experienced with this so far is that if you ever update the column in any way, for example changing the name of the column, this property will reset itself back to the default ‘False’.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8003659844398499, "perplexity": 1464.0648593251249}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948708.2/warc/CC-MAIN-20230327220742-20230328010742-00112.warc.gz"}
http://mathcountsnotes.blogspot.com/2014_08_10_archive.html	## Thursday, August 14, 2014 ### Dimensional Change Questions II Dimensional change questions II: Answer key below. If you've found you are not solid yet with these problems, 1a. There is a regular cylinder, which has a height equal to its radius. If the radius and height are both increased by 20%, by what % does the total volume of the cylinder increase? 1b. If the radius and height are both decreased by 20%, by what % does the total volume of the cylinder decrease? 1c. If the radius is increased by 50% and the height is decreased by 25%, what % of the volume of the original cylinder does the volume of the new cylinder represent? 1d. If the radius is increased by 25% and the height is decreased by 50%, what % of the volume of the original cylinder does the volume of the new cylinder represent? 1e. If the height is increased by 300%, what % does the radius need to be decreased by for the volume to remain the same? 2. If the side of a cube is increased by 30%, by what % does the total surface area of the cube increase? By what % does the volume increase? 3a. If the volume of a cube increases by 174.4%, by what % does the total surface area of the cube increase? 3b. By what % did the side length of the cube increase? Answer key to dimensional change questions II: 1a. There is a regular cylinder, which has a height equal to its radius. If the radius and height are both increased by 20%, by what % does the total volume of the cylinder increase? 72.8% 1b. If the radius and height are both decreased by 20%, by what % does the total volume of the cylinder decrease? 48.8% (Only 0.83 = 0.512 = 51.2% of the original percentage left and 100% - 51.2% = 48.8%.) 1c. If the radius is increased by 50% and the height is decreased by 25%, what % of the volume of the original cylinder does the volume of the new cylinder represent? 168.75% 1d. If the radius is increased by 25% and the height is decreased by 50%, what % of the volume of the original cylinder does the volume of the new cylinder represent? 78.125% 1e. If the height is increased by 300%, what % does the radius need to be decreased by for the volume to remain the same? 50% 2. If the side of a cube is increased by 30%, by what % does the total surface area of the cube increase? By what % does the volume increase? The surface area will increase 69% and the volume will increase 119.7% 3a. If the volume of a cube increases by 174.4%, by what % does the total surface area of the cube increase? 96% 3b. By what % did the side length of the cube increase? 40%	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8802445530891418, "perplexity": 336.83303002368604}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948511435.4/warc/CC-MAIN-20171210235516-20171211015516-00304.warc.gz"}
http://science.sciencemag.org/content/268/5211/722	Reports # Immune system impairment and hepatic fibrosis in mice lacking the dioxin-binding Ah receptor See allHide authors and affiliations Science 05 May 1995: Vol. 268, Issue 5211, pp. 722-726 DOI: 10.1126/science.7732381 ## Abstract The aryl hydrocarbon (Ah) receptor (AHR) mediates many carcinogenic and teratogenic effects of environmentally toxic chemicals such as dioxin. An AHR-deficient (Ahr-/-) mouse line was constructed by homologous recombination in embryonic stem cells. Almost half of the mice died shortly after birth, whereas survivors reached maturity and were fertile. The Ahr-/- mice showed decreased accumulation of lymphocytes in the spleen and lymph nodes, but not in the thymus. The livers of Ahr-/- mice were reduced in size by 50 percent and showed bile duct fibrosis Ahr-/- mice were also nonresponsive with regard to dioxin-mediated induction of genes encoding enzymes that catalyze the metabolism of foreign compounds. Thus, the AHR plays an important role in the development of the liver and the immune system.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8644214272499084, "perplexity": 23721.13679685802}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583515375.86/warc/CC-MAIN-20181022180558-20181022202058-00165.warc.gz"}
https://kyleparrish.com/blog/powershell-script-config-file/	# Creating a Config File for your PowerShell Scripts Creating a Config File for your PowerShell Scripts # Introduction Recently, I was working on a PowerShell scripts that I wanted to share with others on my team but did not want to commit it to our Git repository with the customizable variables declared in the code (Always best practice. Keep the sensitives out of repos!). Instead, I wanted to implement a way to have a config file where these configurable variables can be set and the main script would load them when launched. A quick “DuckDuckGo” search led to many others that have had the same goal but I didn’t find one that really worked like I had intended. Here are my steps that I used to accomplish what I had in mind. ## The config file I simply wanted a config file that mimicked what we typically see in a Docker .env file. Each line consists of a variable name and value (key-value pair) in the format <key>=<value>. Here is an example of what that file may look like. LISTENIP=0.0.0.0 LISTENPORT=8443 APPID=1cb8ea0e-fa15-47b2-9bd5-957117c01678 OU=OU=Users,DC=Corp,DC=com This aproach provides a very simple layout that is easily recognized and can be repeated without looking back and thinking “how did I set that up again?”. ## The PowerShell Code The code snippet to retieve the values and set the variables consists of the following: • Foreach loop to process each line of the file • Splits the pair at the first “=” character • Sets a variable based on the Name and Value parsed out of each line Foreach ($i in$(Get-Content script.conf)){ Set-Variable -Name $i.split("=")[0] -Value$i.split("=",2)[1] } The first line begins the loop with Foreach ($i in$(Get-Content script.conf)){ which pulls in the content of the config file and sets the current line to the value $i. For each line we use the split method to pull apart the key/value pair and will use that information to declare the variable.$i.split("=")[0] splits the line up into parts using the “=” as a delimiter and selects the first part in the list ([0]). Typically, each line will only contain one “=” sign but in some cases this may not be true. One example that I came across was when working with Active Directory DistinguishedNames such as “OU=Users,DC=contoso,DC=com”. This would allow the name to be parsed but would split the remaining content of the line into additional parts depending on the number of “=” it contained. “DISTINGUISHEDNAME=OU=Users,DC=contoso,DC=com” would become: DISTINGUISHEDNAME OU Users contoso com But, what we want are the two parts to be: DISTINGUISHEDNAME OU=Users=contoso=com This is why the value is determined via $i.split("=",2)[1]. The addition of the “2” after specifiying our delimeter is telling PowerShell to return a maximium of two substrings. So regardless of the amount of “=” signs in the string it will only split on the first one, returning a name (before the first “=") and a value (after the first “="). The [1] is used to select the second value in the list and set that as the value of the variable. ## Putting it to use Now that we have the structure in place, lets put it into practice and see what the it looks like all tied together. Our scenario will be I am writing a simple PowerShell script to call a webservice and it requires an API key and a special User-Agent in the HTTP header. Once the script is complete I want to share this with the community but I don’t want my API key and User-Agent values included in the script. ### Create the script This script makes a GET request against https://swapi.co, a popular Star Wars API, to find intersting details about a specified starship seen in the films. #### script.conf We will only be working with two values in the config file. The APIKEY and the USERAGENT. APIKEY=R2D2C3P0BB8 USERAGENT='Luke-SkyWalker' #### Get-DeathStar.ps1 The main script uses the snippet shown above to pull in the content of the script.conf file and sets the values accordingly. Foreach ($i in $(Get-Content script.conf)){ Set-Variable -Name$i.split("=")[0] -Value $i.split("=",2)[1] }$Headers = @{ 'APIKey' = $APIKEY 'User-Agent' =$USERAGENT 'Content-Type' = 'application/json' } $Url = 'https://swapi.co/api/starships/9/' Invoke-RestMethod -Method GET -Uri$Url -Headers \$Headers If we inspect the request with a tool such as Fiddler4 we can see our custom values being passed in the header. GET https://swapi.co/api/starships/9/ HTTP/1.1 Content-Type: application/json APIKey: R2D2C3P0BB8 User-Agent: 'Luke-SkyWalker' Host: swapi.co Connection: Keep-Alive ## Using with Git Now that we have the two components working together how do we address the concens with sharing via Git? First, we need to initialize the directory as a Git repository and set the origin. git init Then, we need to create a new file named .gitignore. This is where we place regex patterns of anything we do not want to be included when we push this git repo. Our .gitignore will include the following: *.conf This tells git to not include any files that have the .conf extension. To be sure that others who may use this repo understand how to setup the config file for their use, we can create a new file named script.cong.example that only contains that variable names that are expected. APIKEY= USERAGENT= The README.md could mention the need to copy the script.conf.example to a new file named script.conf. ## Before running script Be sure to copy the script.conf.example file to script.conf and add your custom values before running the get-deathstar.ps1 script. Now, with everything setup we can push our new repository to Github and it will not include our sensitive data.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.15373651683330536, "perplexity": 2000.7212311476844}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178363782.40/warc/CC-MAIN-20210302065019-20210302095019-00399.warc.gz"}
https://dsp.stackexchange.com/questions/25619/what-is-the-entropy-for-these-cases	# What is the entropy for these cases? This question stems from an article, where the abstract mentions the need for using symbols in information theory. Random chains of symbols (zeros and ones or characters) $s_1, s_2,\ldots,$ drawn from some finite alphabet appear in practically all sciences. Examples include spins in one-dimensional mag- nets, written texts, DNA sequences (here symbols are alphabets), geological records of the orientation of the magnetic field of the earth, and bits in the storage and transmission of digital data. The paper presents technique for finding the entropy of symbols. My Question is that if entropy of symbols is important then what about the entropy of real valued numbers? From the perspective of entropy, is there a proof or some information in text where it provides information that the entropy of random symbols is greater or lesser than the entropy of real numbers. Q1: In other words, what would be the entropy of random variables having binary values and entropy of real valued random variables? A fair coin takes 2 values -0/1 with equal probability and its entropy is 1 bit. So, is 1 bit the maximum entropy? Would entropy of binary random variables be less or more than entropy of real valued random variables and how to show? So, I would like to know if there is a proof or material from which it can be inferred if the entropy of characters is lesser/ greater or same with the entropy of real numbers. Q2: I want to know why symbols are used in coding and other applications such as storage from the viewpoint of entropy and information theory. • I'm wondering why you cut-and-paste the first part of your question from here without referring to it? – Peter K. Sep 3 '15 at 22:36 The entropy $H(X)$ of a continuous random variable $X$ is infinite. Proof is trivial (note that we can, without loss of generality, use the natural logarithm, since any other logarithm is the same but with a factor: $\log_b(x) = \frac 1{\ln(b)}\ln(x)$): \begin{array} \\H(X) &= E\{I(X)\}\\ &= \int\limits_{-\infty}^{\infty}{-\ln\left(P(X=x)\right) dx} \end{array} The point here is that for any really continuously distributed random variable, the probability that a specific real value gets "hit" is $P(X=x)\equiv 0 \,\forall x$, and hence, the information contained in that event happening would be infinite. You hence cannot directly compare discrete alphabets with dense intervals (such as the whole $\mathbb R$). Hence, people invented differential Entropy. For your real-valued (=1-dimensional) case, this is nothing but the obvious: $$h(x) = \int\limits_{-\infty}^{\infty} f(x)\log_b\left(f(x)\right)dx \text{,}$$ with $f$ being the continuous probability density function of $X$. Now, all you need to compare your discrete case with the continuous is model the discrete PDF for the alphabet $\mathbb X$ $$f_\text{discrete}(x) = \sum\limits_{x_i\in\mathbb X} \delta(x - x_i)P_\text{discrete}(x_i)$$ $\delta$ is the dirac function. Caveat not everything you know about the discrete entropy applies to differential entropy. Read the Wikipedia Article! • I think your answer is a bit imprecise; you're mixing the concepts "real-valued random variable" and "continuous random variable". The important concept here is whether the RV is discrete, and not the specific values it can take. For example, if a RV can take values $\lbrace \sqrt{2},\sqrt{3} \rbrace$, it is real-valued, but you can find its entropy. – MBaz Sep 8 '15 at 16:54 • @MBaz... yeah. Shouldn't have written that when I was so tired, will rephrase. Sep 8 '15 at 17:27 • @MBaz rereading everything, I'm not quite sure I get your point... I never claim the discrete variable can't take real values. Sep 8 '15 at 17:29 • @MBaz: nevermind. First sentence. Sep 8 '15 at 17:29 • @MarcusMüller: Thank you for your reply, I had to do a thorough reading before I could get back to you. So, I learned that the entropy or entropy rate of a random bit sequence = 1 and from your answer the entropy of continuous random variable is $\infty$. So, in communications do we prefer a finite number = 1 or an infinite entropy? If entropy = $\infty$, it means we are less certain about what the information will be next. Whereas if entropy =1, then there is no information conveyed. Sep 16 '15 at 21:36 • Based on MarcusMiller & your reply, we prefer binary encoding or digital transmission. But, the entropy or entropy rate of a random bit sequence = 1 & entropy of continuous random variable is $\infty$. If entropy = $\infty$, it means we are less certain about what the information will be next. Whereas if entropy =1, then there is no information conveyed. All this is confusing. What is the desired entropy preferred in communication--$\infty$ or 1 & what is this the reason for bit based communication/digital if entropy =1? Can you please shed some light + references if any? Sep 16 '15 at 21:38	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7912651300430298, "perplexity": 519.381544946595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304217.55/warc/CC-MAIN-20220123081226-20220123111226-00159.warc.gz"}
https://scienceon.kisti.re.kr/srch/selectPORSrchArticle.do?cn=JAKO200502637304625	$\require{mediawiki-texvc}$ • 검색어에 아래의 연산자를 사용하시면 더 정확한 검색결과를 얻을 수 있습니다. • 검색연산자 검색연산자 기능 검색시 예 () 우선순위가 가장 높은 연산자 예1) (나노 (기계 \| machine)) 공백 두 개의 검색어(식)을 모두 포함하고 있는 문서 검색 예1) (나노 기계) 예2) 나노 장영실 \| 두 개의 검색어(식) 중 하나 이상 포함하고 있는 문서 검색 예1) (줄기세포 \| 면역) 예2) 줄기세포 \| 장영실 ! NOT 이후에 있는 검색어가 포함된 문서는 제외 예1) (황금 !백금) 예2) !image * 검색어의 란에 0개 이상의 임의의 문자가 포함된 문서 검색 예) semi "" 따옴표 내의 구문과 완전히 일치하는 문서만 검색 예) "Transform and Quantization" 과학기술 지식인프라 ScienceON 안녕하세요! ScienceON 챗봇입니다. 궁금한 것은 저에게 물어봐주세요. Unified Parametric Approaches for Observer Design in Matrix Second-order Linear Systems 원문보기 Abstract This paper designs observers for matrix second-order linear systems on the basis of generalized eigenstructure assignment via unified parametric approach. It is shown that the problem is closely related with a type of so-called generalized matrix second-order Sylvester matrix equations. Through establishing two general parametric solutions to this type of matrix equations, two unified complete parametric methods for the proposed observer design problem are presented. Both methods give simple complete parametric expressions for the observer gain matrices. The first one mainly depends on a series of singular value decompositions, and is thus numerically simple and reliable; the second one utilizes the right factorization of the system, and allows eigenvalues of the error system to be set undetermined and sought via certain optimization procedures. A spring-mass system is utilized to show the effect of the proposed approaches. 참고문헌 (16) 1. M. J. Balas, 'Trends in large space structure control theory: fondest hopes,' IEEE Trans. on Automatic Control, vol. 27, no. 3, pp. 522-535, June 1982 2. A. Bhayah and C. Desoer, 'On the design of large flexible space structures (LFSS),' IEEE Trans. on Automatic Control, vol. 30, no. 11, pp. 1118-1120, November 1985 3. A. M. Diwekar and R. K. Yedavalli, 'Stability of matrix second-order systems: new conditions and perspectives,' IEEE Trans. on Automatic Control, vol. 44, no. 9, pp. 1773-1777, September 1999 4. S.-K. Kwak and R. K. Yedavalli, 'New approaches for observer design in linear matrix second order systems,' Proc. of the American Control Conference, pp. 2311-2315, 2000 5. G. R. Duan, L. S. Zhou, and Y. M. Xu, 'A parametric approach for observer-based control system design,' Proc. of the Asia-Pacific Conf. Measurement and Control, Guangzhou, PR China, pp. 259-300, 1991 6. G. R. Duan, 'On the solution to Sylvester matrix equation AV+BW=EVF,' IEEE Trans. on Automatic Control, vol. 41, no. 4, pp. 612-614, April 1996 7. T. G. J. Beelen and G. W. Veltkamp, 'Numerical computation of a coprime factorization of a transfer-function matrix,' Syst. Control Lett., vol. 9, no. 3, pp. 281-288, 1987 8. G. R. Duan and G. P. Liu, 'Complete parametric approach for eigenstructure assignment in a class of second-order linear systems,' Automatica, vol. 38, pp. 725-729, 2002 9. P. C. Hughes and R. E. Skelton, 'Controllability and observability of linear matrix second-order system,' Journal of Applied Mechanics, vol. 47, no. 2, pp. 415-421, June 1980 10. M. A. Demetriou, 'UIO for fault detection in vector second order systems,' Proc. of the American Control Conference, Arlington, VA, pp. 1121-1126, June 25-27, 2001 11. G. R. Duan, 'Solution of matrix equation AV+BW=EVF and eigenstructure assignment for descriptor systems,' Automatica, vol. 28, no. 3, pp. 639-643, 1992 12. B. N. Datta, and F. Rincon, 'Feedback stabilization of a second-order system: a nonmodal approach,' Linear Algebra Applications, vol. 188/189, pp. 135-161, 1993 13. N. K. Nichols and J. Kautsky, 'Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case,' SIAM Journal on Matrix Analysis and Applications, vol. 23, no. 1, pp. 77-102, 2001 14. A. M. Diwekar and R. K. Yedavalli, 'Smart structure control in matrix second-order form,' Smart Materials and Structures, vol. 5, pp.429- 436, 1996 15. A. J. Laub and W. F. Arnold, 'Controllability and observability criteria for multivariable linear second-order model,' IEEE Trans. on Automatic Control, vol. 29, no. 2, pp. 163-165, February 1984 16. K. B. Datta and S. Gangopadhyay, 'Reduction of transfer functions to coprime forms,' Control Theory Adv. Technol., vol. 7, pp. 321-334, 1991 이 논문을 인용한 문헌 (0) 1. 이 논문을 인용한 문헌 없음 원문보기 원문 PDF 다운로드 • ScienceON : 원문 URL 링크 원문 PDF 파일 및 링크정보가 존재하지 않을 경우 KISTI DDS 시스템에서 제공하는 원문복사서비스를 사용할 수 있습니다. (원문복사서비스 안내 바로 가기) 상세조회 0건 원문조회 0건 DOI 인용 스타일	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3387519121170044, "perplexity": 13736.096543070162}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038464045.54/warc/CC-MAIN-20210417192821-20210417222821-00042.warc.gz"}
https://reference.wolfram.com/language/ref/Re.html	# Re Re[z] gives the real part of the complex number z. # Details • Mathematical function, suitable for both symbolic and numerical manipulation. • Re[expr] is left unevaluated if expr is not a numeric quantity. • Re automatically threads over lists. • Re can be used with CenteredInterval objects. » # Examples open allclose all ## Basic Examples(4) Find the real part of a complex number: Find the real part of a complex number expressed in polar form: Plot over a subset of the complex plane: Use Re to specify regions of the complex plane: ## Scope(30) ### Numerical Evaluation(8) Evaluate numerically: Complex number input: Evaluate to high precision: Mixedprecision complex inputs: Evaluate efficiently at high precision: Re threads elementwise over lists and matrices: Re can deal with realvalued intervals: Re can be used with CenteredInterval objects: ### Specific Values(6) Values of Re at fixed points: Value at zero: Values at infinity: Exact inputs: Evaluate for complex exponentials: Evaluate symbolically: ### Visualization(5) Visualize on the real axis: Plot on the real axis: Visualize Re in the complex plane: Visualize Re in three dimensions: Use Re to specify regions of the complex plane: ### Function Properties(5) Re is defined for all real and complex inputs: The range of Re is the whole real line: This is true even in the complex plane: Re is an odd function: Re is not a differentiable function: The difference quotient does not have a limit in the complex plane: There is only a limit in certain directions, for example, the real direction: Obtain this result using ComplexExpand: ### Function Identities and Simplifications(6) Automatic simplification: Expand assuming real variables x and y: Simplify Re using appropriate assumptions: Express a complex number as a sum of its real and imaginary parts: Express in terms of real and imaginary parts: Find the real part of a Root expression: ## Applications(3) Flow around a cylinder as the real part of a complexvalued function: Construct a bivariate real harmonic function from a complex function: The real part satisfies Laplace's equation: Reconstruct an analytic function from its real part : Example reconstruction: Check the result: ## Properties & Relations(8) Use Simplify and FullSimplify to simplify expressions containing Re: Prove that the disk is in the right half-plane: ComplexExpand assumes variables to be real: Here z is not assumed real, and the result should be in terms of Re and Im: FunctionExpand does not assume variables to be real: ReImPlot plots the real and imaginary parts of a function: Use Re to describe regions in the complex plane: Reduce can solve equations and inequalities involving Re: With FindInstance you can get sample points of regions: Use Re in Assumptions: Integrate often generates conditions in terms of Re: ## Possible Issues(2) Re can stay unevaluated for numeric arguments: Re is a function of a complex variable and is therefore not differentiable: As a complex function, it is not possible to write Re[z] without involving Conjugate[z]: In particular, the limit that defines the derivative is direction dependent and therefore does not exist: Use ComplexExpand to get differentiable expressions for real-valued variables: ## Neat Examples(1) Use Re to plot a 3D projection of the Riemann surface of : Wolfram Research (1988), Re, Wolfram Language function, https://reference.wolfram.com/language/ref/Re.html (updated 13). #### Text Wolfram Research (1988), Re, Wolfram Language function, https://reference.wolfram.com/language/ref/Re.html (updated 13). #### CMS Wolfram Language. 1988. "Re." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 13. https://reference.wolfram.com/language/ref/Re.html. #### APA Wolfram Language. (1988). Re. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Re.html #### BibTeX @misc{reference.wolfram_2021_re, author="Wolfram Research", title="{Re}", year="13", howpublished="\url{https://reference.wolfram.com/language/ref/Re.html}", note=[Accessed: 21-May-2022 ]} #### BibLaTeX @online{reference.wolfram_2021_re, organization={Wolfram Research}, title={Re}, year={13}, url={https://reference.wolfram.com/language/ref/Re.html}, note=[Accessed: 21-May-2022 ]}	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8398078680038452, "perplexity": 5174.172404841572}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662543264.49/warc/CC-MAIN-20220522001016-20220522031016-00758.warc.gz"}
http://clay6.com/qa/3660/show-that-the-function-f-x-left-x-lambda-quad-x-1-lambda-x-2-1-quad-x-geq1-	Browse Questions # Show that the function $f(x)= \left\{ \begin{array}{1 1} x+\lambda, & \quad x< 1 \\ \lambda x^2+1, & \quad x\geq1 \end{array} \right.$ is continuous function, regardless of the choice of $\lambda \in R$ Toolbox: • For continuous function at $x = 1. LHL = RHL = f(1)$ LHL $\lim\limits_{x \to 1}\: x+\lambda=1+\lambda$ LHL $\lim\limits_{x \to 1}\: \lambda x^2+1=\lambda+1$ $f(1) = \lambda+1$ $\Rightarrow$ is continuous regardsless of choice of $\lambda$ edited Mar 26, 2013	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8477005958557129, "perplexity": 2232.175286445519}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917118707.23/warc/CC-MAIN-20170423031158-00593-ip-10-145-167-34.ec2.internal.warc.gz"}
https://pbelmans.ncag.info/blog/2010/12/27/an-h-tree-in-tikz/	Via Walking Randomly's post Fractals on Wolfram Alpha – an update I stumbled upon his previous post Plotting Fractals with Wolfram Alpha. And something struck me, I invented / discovered those H-trees when I was a little kid! I remember drawing them when I was in second grade (you're 7 years old then, at least in Belgium), enjoying the laborious yet beautiful nature of them. I also drew gigantic heaps of blocks in oblique projection, oh, how many sheets of grid paper (5 by 5 millimetre) I have filled that way... I guess I was the weird kid of our class. I wanted to board train nostalgia and draw them in TikZ. And this was even easier than I imaged, as there is a library for fractal decorations! If only TikZ did the dishes. Based on the code I found in $TEXMF/tex/generic/pgf/libraries/pgflibrarydecorations.fractals.code.tex I quickly hacked together the following code: This code must be either placed in $TEXMF/tex/generic/pgf/libraries/pgflibrarydecorations.fractals.code.tex or the file itself (or your personal contain-it-all package, just someplace where it can be found). Now you just draw a tikzpicture with a single recursively decorated line: which results in I hope I got the factor right, but I guess 1/(2sqrt(2)) is the one I needed. A complete minimal working example is given: which should result in (after pdfcrop) this output. LaTeX easily exceeds its total allocated memory, more iterations are impossible (unless you decrease the length of the line or the zooming factor, for some reason).	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.577083170413971, "perplexity": 2362.576931823529}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077843.17/warc/CC-MAIN-20210414155517-20210414185517-00168.warc.gz"}
https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/cut	# cut 0th Percentile ##### Convert Numeric to Factor cut divides the range of x into intervals and codes the values in x according to which interval they fall. The leftmost interval corresponds to level one, the next leftmost to level two and so on. Keywords category ##### Usage cut(x, …)# S3 method for default cut(x, breaks, labels = NULL, include.lowest = FALSE, right = TRUE, dig.lab = 3, ordered_result = FALSE, …) ##### Arguments x a numeric vector which is to be converted to a factor by cutting. breaks either a numeric vector of two or more unique cut points or a single number (greater than or equal to 2) giving the number of intervals into which x is to be cut. labels labels for the levels of the resulting category. By default, labels are constructed using "(a,b]" interval notation. If labels = FALSE, simple integer codes are returned instead of a factor. include.lowest logical, indicating if an ‘x[i]’ equal to the lowest (or highest, for right = FALSE) ‘breaks’ value should be included. right logical, indicating if the intervals should be closed on the right (and open on the left) or vice versa. dig.lab integer which is used when labels are not given. It determines the number of digits used in formatting the break numbers. ordered_result logical: should the result be an ordered factor? further arguments passed to or from other methods. ##### Details When breaks is specified as a single number, the range of the data is divided into breaks pieces of equal length, and then the outer limits are moved away by 0.1% of the range to ensure that the extreme values both fall within the break intervals. (If x is a constant vector, equal-length intervals are created, one of which includes the single value.) If a labels parameter is specified, its values are used to name the factor levels. If none is specified, the factor level labels are constructed as "(b1, b2]", "(b2, b3]" etc. for right = TRUE and as "[b1, b2)", … if right = FALSE. In this case, dig.lab indicates the minimum number of digits should be used in formatting the numbers b1, b2, …. A larger value (up to 12) will be used if needed to distinguish between any pair of endpoints: if this fails labels such as "Range3" will be used. Formatting is done by formatC. The default method will sort a numeric vector of breaks, but other methods are not required to and labels will correspond to the intervals after sorting. As from R 3.2.0, getOption("OutDec") is consulted when labels are constructed for labels = NULL. ##### Value A factor is returned, unless labels = FALSE which results in an integer vector of level codes. Values which fall outside the range of breaks are coded as NA, as are NaN and NA values. ##### Note Instead of table(cut(x, br)), hist(x, br, plot = FALSE) is more efficient and less memory hungry. Instead of cut(, labels = FALSE), findInterval() is more efficient. ##### References Becker, R. A., Chambers, J. M. and Wilks, A. R. (1988) The New S Language. Wadsworth & Brooks/Cole. split for splitting a variable according to a group factor; factor, tabulate, table, findInterval. quantile for ways of choosing breaks of roughly equal content (rather than length). .bincode for a bare-bones version. • cut • cut.default ##### Examples library(base) # NOT RUN { Z <- stats::rnorm(10000) table(cut(Z, breaks = -6:6)) sum(table(cut(Z, breaks = -6:6, labels = FALSE))) sum(graphics::hist(Z, breaks = -6:6, plot = FALSE)\$counts) cut(rep(1,5), 4) #-- dummy tx0 <- c(9, 4, 6, 5, 3, 10, 5, 3, 5) x <- rep(0:8, tx0) stopifnot(table(x) == tx0) table( cut(x, b = 8)) table( cut(x, breaks = 3(-2:5))) table( cut(x, breaks = 3(-2:5), right = FALSE)) ##--- some values OUTSIDE the breaks : table(cx <- cut(x, breaks = 2(0:4))) table(cxl <- cut(x, breaks = 2(0:4), right = FALSE)) which(is.na(cx)); x[is.na(cx)] #-- the first 9 values 0 which(is.na(cxl)); x[is.na(cxl)] #-- the last 5 values 8 ## Label construction: y <- stats::rnorm(100) table(cut(y, breaks = pi/3(-3:3))) table(cut(y, breaks = pi/3(-3:3), dig.lab = 4)) table(cut(y, breaks = 1(-3:3), dig.lab = 4)) # extra digits don't "harm" here table(cut(y, breaks = 1(-3:3), right = FALSE)) #- the same, since no exact INT! ## sometimes the default dig.lab is not enough to be avoid confusion: aaa <- c(1,2,3,4,5,2,3,4,5,6,7) cut(aaa, 3) cut(aaa, 3, dig.lab = 4, ordered = TRUE) ## one way to extract the breakpoints labs <- levels(cut(aaa, 3)) cbind(lower = as.numeric( sub("\\((.+),.", "\\1", labs) ), upper = as.numeric( sub("[^,],([^]])\\]", "\\1", labs) )) # } Documentation reproduced from package base, version 3.6.2, License: Part of R 3.6.2 ### Community examples mark@niemannross.com at Feb 6, 2019 base v3.5.2 [Example file for linkedin learning](https://linkedin-learning.pxf.io/rweekly_cut) r # Description: cut to set intervals numericVector <- runif(100, min = 1, max = 256 ) cut(numericVector, 3) cut(numericVector, 3, labels = c("low","med","high")) cut(numericVector, 3, labels = FALSE) cut(numericVector,breaks = c(1,100,200,256)) vezy.remi@gmail.com at Oct 14, 2016 base v3.3.1 ## Cut with custom labels Cut specifies labels formated with [formatC](https://www.rdocumentation.org/packages/base/versions/3.3.1/topics/formatC?) (eg. "[b1, b2)" ). It is not always convenient, so you can add the labels argument to give your own levels. Unfortunately, no exemples are provided in the base documentation. As Josh O'Brien says in his [answer](http://stackoverflow.com/a/13061832/6947799) on stackoverflow, 11 breaks delimit 10 levels which will require only 10 labels. Setting our own levels using the base exemple Z variable, with three cuts: - the minimum - the mean - the maximum The variable will be cut in two levels: - any value below or equal to the mean - any value above the mean See interactive R block: r Z <- stats::rnorm(10000) a= cut(Z, breaks = c(min(Z), mean(Z), max(Z)), labels= c("Mean_or_Below", "Above")) print(head(a)) we made a new factor a that is easier to use afterwards.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23912662267684937, "perplexity": 5500.579621912977}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141196324.38/warc/CC-MAIN-20201129034021-20201129064021-00645.warc.gz"}
http://scholarpedia.org/article/Rayleigh-Benard_Convection	# Rayleigh-Bénard convection (Redirected from Rayleigh-Benard Convection) Post-publication activity Curator: A. V. Getling Rayleigh - Bénard convection is a fluid flow (thermal convection) due to a non-uniform temperature distribution in a plane horizontal fluid layer heated from below. Such flows result from the development of the convective instability, if the static vertical temperature gradient (the gradient that would be present in a motionless fluid under the same conditions) is large enough. A horizontal layer of convecting fluid is the most comprehensively studied example of nonlinear systems exhibiting self-organization (pattern-forming systems). Rayleigh - Bénard convection, which shares a number of important properties with many other pattern-formation mechanisms, is considered the "granddaddy of canonical examples used to study pattern formation and behavior in spatially extended systems" (Newell et al 1993). Convective motion enhances dramatically the heat transfer through the layer compared to the molecular heat conduction. The moving fluid parcels, which are agents of heat exchange, normally have velocities and effective free paths much greater than the corresponding figures for molecules. Therefore, the heat flux through the layer of convecting fluid may be several orders of magnitude higher than the heat flux due to molecular thermal conductivity. ## History The role of non-uniform heating as the producer of most types of fluid motions in the Universe was first recognised in the mid-eighteenth century, nearly simultaneously by George Hadley and Mikhail Lomonosov. Well-directed studies of convection in horizontal fluid layers heated from below trace back to Bénard's experiments (Bénard 1900), in which the instability mechanism was, however, not purely thermal and was closely related to the thermocapillary effect. Lord Rayleigh (1916) was the first to consider a linear problem of the onset of thermal convection in a horizontal layer, and a more comprehensive analysis of this problem was given by Pellew and Southwell (1940). A highly extensive survey of the linear stability problems, including investigations of the effects of rotation and magnetic field on Rayleigh - Bénard convection, was presented in a classical monograph by Chandrasekhar (1961). Subsequent studies mainly dealt with nonlinear convection regimes and related pattern-formation processes. The volume of relevant publications has grown dramatically, and a number of monographs of a more or less wide scope summarize them [a concise review of many results that refer specifically to Rayleigh - Bénard convection and were obtained by the end of the 1990s can be found in Getling (1998)]. ## Linear analysis Figure 1: The neutral curve of the convective instability. In its classical formulation, the problem of convective instability of an infinite horizontal fluid layer heated from below is treated in the framework of the Boussinesq approximation: the fluid density $$\rho$$ is considered to be independent of the pressure (i.e., incompressibility is assumed) and to depend linearly on the temperature $$T:$$ $\tag{1}\rho -\rho _0=-\rho _0\alpha (T-T_0),$ where $$\rho _0$$ is the density value for some suitably chosen reference temperature $$T_0$$. The volumetric coefficient of thermal expansion $$\alpha$$ is considered to be small and the material parameters of the fluid (kinematic viscosity $$\nu$$, thermal diffusivity $$\chi$$, and the coefficient $$\alpha$$ itself) to vary little over the layer. Then the density variations can be neglected everywhere in the equations but in the buoyancy term, where it is multiplied by the gravitational acceleration $${\mathbf g}$$. The basic non-dimensional parameters controlling the regimes of convection are the Rayleigh and the Prandtl number, $\tag{2}R=\frac{\alpha g\Delta Th^3}{\nu \chi },\quad P=\frac \nu \chi,$ where $$h$$ is the layer thickness and $$\Delta T$$ is the temperature difference between the bottom and top boundaries of the layer (if their temperatures are fixed; otherwise, the definition of $$R$$ should be properly modified). Figure 2: Schematic of two types of convection cells: (a) rolls; (b) hexagonal convection cells of the $$l$$ and $$g$$ types. Assume that the equations of fluid motion, continuity, and heat transfer are linearised with respect to infinitesimal perturbations. Then, given $$R$$ and the horizontal wavevector of the perturbation, $$\mathbf k$$, the boundary-value problem of stability of the motionless state of the fluid yields growth rates $$\lambda_n$$ ($$n-1$$ being the number of nodes of the eigenfunction describing the vertical dependence of the vertical velocity component) that depend only on the wavenumber $$k=\|\mathbf k\|$$ but not on the direction of $$\mathbf k$$. The neutral curve $$R=R_1(k)$$ in the plane $$(k,R)$$, i.e., the locus of points where the perturbations have zero growth rate $$\lambda_1$$, is shown in Fig. 1. The region above this curve corresponds to growing perturbations, while they all decay in the region below the curve. The minimum value of $$R_1(k)$$ is termed the critical Rayleigh number $$R_\mathrm c$$, and the wavenumber at which this minimum is reached, $$k_\mathrm c$$, is known as the critical wavenumber. Thus, the layer is convectively unstable at $$R>R_\mathrm c$$, while it is stable at $$R<R_\mathrm c$$ and the case of $$R=R_\mathrm c$$ corresponds to neutral, or marginal, stability. If the Rayleigh number (in other words, the static temperature gradient properly non-dimensionalised) is increased from below $$R_\mathrm c$$, convection sets in first at $$R=R_\mathrm c$$ as a steady flow of infinitesimal amplitude with the wavenumber $$k=k_\mathrm c$$. The larger $$R$$, the wider the band of wavenumbers $$k$$ in which perturbations can grow. Nonlinear effects restrict their growth to a certain level. Within a fairly wide range of $$R$$, a well-defined characteristic wavenumber (which depends not only on the parameters of the regime but also on the prehistory of the flow) can be noted in convective flows. The selection of this wavenumber is a very subtle issue, which has been addressed in numerous studies (see, in particular, Chapter 6 in Getling 2008). Figure 3: Convection cells in experiments: (a) quasi-two-dimensional rolls observed by V.S. Berdnikov and V.A. Markov (bright specks are aluminum flakes used to visualise the flow), unpublished; (b) hexagonal cells in a fluid with a strong temperature dependence of viscosity (Richter 1978). The values of $$R_\mathrm c$$ and $$k_\mathrm c$$ are specified, to a first approximation, by the boundary conditions at the top and bottom layer surfaces. If the temperatures at these boundaries are fixed, the critical Rayleigh numbers are: • for two stress-free boundaries $\tag{3} R_c= \frac{27}{4}\pi ^4=657.511,\quad k_c=\frac{\pi}{\sqrt{2}}=2.221;$ • for two rigid boundaries $\tag{4} R_c =1707.762,\quad k_c=3.117;$ • and for one rigid and one stress-free boundary $\tag{5} R_c=1100.657,\quad k_c=2.682.$ Prior to Rayleigh's study, a necessary (but insufficient) condition of convective instability was found for compressible atmospheres (in the context of stability of the solar atmosphere) by K. Schwarzschild (1906) to be $-\frac{\mathrm dT}{\mathrm dz}\equiv\left \|\frac{\mathrm dT}{\mathrm dz}\right \|>\left \|\frac{\mathrm dT}{\mathrm dz}\right \|_s,$ where $$z$$ is the vertical coordinate (height) and the derivative on the right-hand side of the inequality refers to the isentropic stratification of the layer. This criterion came to be known as the Schwarzschild criterion. It has a clear physical meaning. Assume that the atmosphere is stratified adiabatically. If a fluid parcel that was initially in thermal and mechanical equilibrium with the ambient medium is displaced in a vertical direction from its initial position then, to a first approximation, its thermodynamic state experiences adiabatic changes and the parcel remains in equilibrium with the medium at any new height. If the temperature of the motionless medium varies with height more slowly and, accordingly, its density more rapidly than they would vary in the case of an adiabatic distribution, the parcel displaced upward proves to be heavier and the parcel displaced downward proves to be lighter than the medium. In both cases, the parcel will tend to return to its initial position. If, conversely, the temperature of the medium varies with height more rapidly and the density more slowly than in the adiabatic case, the density difference between the parcel and medium will produce a buoyancy force, which can result in the development of the convective instability. Dissipative factors, i.e., viscosity and thermal conduction, act so as to quench the convective instability. For this reason, the fact that the Schwarzschild criterion is satisfied is not sufficient for the development of convection. Since the driving force of convection in a compressible medium is directly related to the excess of the static temperature gradient (in its absolute magnitude) over the adiabatic gradient, precisely this excess appears, instead of the temperature gradient itself, in the equations of convection for a compressible medium. A perfectly regular, spatially periodic flow described by the linear theory and observed in weakly supercritical conditions (at $$R-R_\mathrm c \ll R_\mathrm c$$) is constituted of identical "building blocks" (convection cells) closely packing the layer, and linear theory does not reveal any differences in the conditions of development of cells of various planforms. Most frequently, the following idealised planforms are considered: • two-dimensional rolls (Fig. 2a); • square cells (superpositions of two sets of mutually perpendicular rolls); • hexagonal cells (superpositions of three sets of rolls rotated by an angle of $$2\pi/3$$ to one another); hexagons of the so-called $$l$$ and $$g$$ types, shown in Fig. 2b, differ in the direction of circulation. In experiments, nearly two-dimensional rolls (Fig. 3a) are typical of layers without any appreciable asymmetry of the physical conditions with respect to the horizontal midplane, under weakly or moderately supercritical conditions. If, however, such an up - down asymmetry is present (e.g., due to a temperature dependence of viscosity or other material properties of the fluid), three-dimensional cells arise (Fig. 3b). ## Supercritical regimes As the Rayleigh number is increased, various flow instabilities can develop. The growth of numerous instability modes is possible, depending on the Rayleigh number, Prandtl number, horizontal wavenumber of the originally developed flow, and many other factors. As a result, the patterns of supercritical convection are diverse and highly sensitive not only to the parameters of the regime, $$R$$ and $$P$$, but also to the geometry of the container, to the boundary conditions, and to the prehistory of the flow. A comprehensive study of the instabilities of the convective flows was undertaken by F.H. Busse and his colleagues [see, in particular, Busse (1978, 1985); a fairly complete survey of these studies carried out by 1998 was given by Getling (1998)]. In particular, if the original flow forms a roll pattern, the rolls can acquire a wavelike form (the zig-zag instability), a secondary flow in the form of narrower rolls normal to the original ones can develop (the cross-roll instability), the rolls can undergo a deformation with asymmetrically located left-side and right-side broadenings (the skewed-varicose instability), the rolls can undulate (the oscillatory instability), etc. There are also particular instability modes that can transform the original roll flow into a three-dimensional flow that resembles a cell pattern. At sufficiently high supercritical Rayleigh numbers, nonlinear effects can ultimately lead to the development of turbulence (Busse 1985; Koschmieder 1993; for a summary of some more recent results see Getling 1998). ## References • H. Bénard, Les tourbillons cellulaires dans une nappe liquide, Rev. Gén. Sciences Pure Appl., 11: 1261 - 1271, 11: 1309--1328, 1900. • F.H. Busse, Non-linear properties of thermal convection, Rep. Prog. Phys., 41: 1929 - 1967, 1978. • F.H. Busse, Transition to turbulence in Rayleigh - Bénard convection, In Hydrodynamic Instabilities and the Transition to Turbulence, eds. H.L. Swinney and J.P. Gollub (Topics in Appl. Phys., vol. 45), 2nd edition, Berlin, Springer, 1985, pp. 97 - 137. • S. Chandrasekhar, Hydrodynamic and Hydromagnetic Stability, Oxford University Press, Oxford, 1961; Dover Publications, Inc., New York, 1981. • A. V. Getling, Rayleigh - Bénard Convection: Structures and Dynamics, World Scientific, Singapore, 1998 [Russian version: Editorial URSS, Moscow, 1999]. • E. L. Koschmieder, Bénard Cells and Taylor Vortices, Cambridge Univ. Press, Cambridge, 1993. • A.C. Newell, T. Passot, and J. Lega, Order parameter equations for patterns, Ann. Rev. Fluid Mech., 25: 399 - 453, 1993. • A. Pellew and R. V. Southwell, On maintained convective motion in a fluid heated from below, Proc. Roy. Soc. A, 176: 312 - 343, 1940. • Lord Rayleigh, On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side, Phil. Mag., Ser.6, 32: 529 - 546, 1916. • F.M. Richter, Experiments on the stability of convection rolls in fluid whose viscosity depends on temperature, J. Fluid Mech., 89: 553 - 560, 1978. • K. Schwarzschild, Über das Gleichgewicht der Sonnenatmosphäre, Nachr. Kgl. Ges. Wiss. Göttingen, Math.-Phys. Klasse, Nr. 1: 41 - 53, 1906.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8957054615020752, "perplexity": 1134.4195746955106}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583771929.47/warc/CC-MAIN-20190121090642-20190121112642-00375.warc.gz"}
http://mathhelpforum.com/calculus/7738-convergence.html	# Math Help - convergence 1. ## convergence Prove that $\lim_{k\to\infty}\int_0^{k}\sin(x)\sin\left(x^2\ri ght)dx$ converges. 2. Originally Posted by putnam120 Prove that $\lim_{k\to\infty}\int_0^{k}\sin(x)\sin\left(x^2\ri ght)dx$ converges. Are you sure it converges? The standard sine curve, $\int_0^{\infty} \sin xdx$ diverges by oscillation. 3. yes i am sure that it converges. here is a hint $\lim_{k\to\infty}\int_0^k\frac{2x\sin(x)\sin\left( x^2\right)}{2x}dx$ and integration by parts and general applications of limits. 4. here is a solution that my friend gave me. using the hint we have $\frac{\cos(x^2)\sin(x)}{-2x}\big \|_0^{\infty} + \int_0^{\infty}\frac{2x\cos(x)\cos(x^2)}{4x^2}dx-\int_0^{\infty}\frac{\cos(x^2)\sin(x)}{4x^2}dx$ the first expression converges to $-\frac{1}{2}$. for the third expression we can change the lower limit to 1, since this will not effect the convergence. so we have $\int_1^{\infty}\frac{\cos(x^2)\cos(x)}{4x^2}dx\le\ int_1^{\infty}\frac{dx}{4x^2}$ which converges. To handle the second expression we apply integration by parts once again and get. $\frac{\sin(x^2)\cos(x)}{4x^2}\big \|_0^{\infty}-\int_1^{\infty}\frac{4x\sin(x)\sin(x^2)}{16x^4}dx-\int_1^{\infty}\frac{8x\sin(x^2)\cos(x)}{16x^4}dx$ to evaluate the first term we can either use l'hopitals rule or taylor series, your pick, either way you find that it does converge. For the last 2 we use fact that $\int_1^{\infty}\frac{A\sin(x)\cos(x^2)}{16x^4}dx\l e A\int_1^{\infty}\frac{dx}{16x^4}$ which converges. 5. The only mistake is that you cannot write, $\int_0^{\infty} \frac{2x \sin x\sin x^2}{2x} dx$ You need to change the lower bound because otherwise the functions do not agree everywhere. Now, I will check what you posted and see if it is correct (I still think that there is no convergence). 6. Originally Posted by ThePerfectHacker Are you sure it converges? The standard sine curve, $\int_0^{\infty} \sin xdx$ diverges by oscillation. Have you graphed the integrand? For large x the function creates "wave-packets" : oscillations within a sine envelope where, on the inside of the envelope, the wavelength is very small. For all intents the function "fills in" all the empty spaces of the sine envelope, creating a net zero area effect. I don't see why this integral shouldn't coverge, though obviously my argument above is hardly a proof. -Dan 7. @Hacker. yes i know. at that point i should have changed the lower limit to 1. and to topsquark: if you evaluate it you get $\lim_{k\to\infty}\int_0^{k}\sin(x)dx=\lim_{k\to\in fty}-\cos(x)\big\|_0^{k}$ which is just $\lim_{k\to\infty}-\cos(k)+\cos(0)$ and $\lim_{k\to\infty}\cos(k)$ does not exist because of oscillation. 8. Originally Posted by topsquark . I don't see why this integral shouldn't coverge, though obviously my argument above is hardly a proof. What is the limit of $\cos x$? When you approach by $x=2\pi,4\pi,6\pi...$ limit is 1. When you appraoch by $x=\pi,3\pi,5\pi,...$ limit is -1. 9. Originally Posted by putnam120 @Hacker. yes i know. at that point i should have changed the lower limit to 1. and to topsquark: if you evaluate it you get $\lim_{k\to\infty}\int_0^{k}\sin(x)dx=\lim_{k\to\in fty}-\cos(x)\big\|_0^{k}$ which is just $\lim_{k\to\infty}-\cos(k)+\cos(0)$ and $\lim_{k\to\infty}\cos(k)$ does not exist because of oscillation. Sorry. I didn't look at what I quoted. I was referring to the integrand in the original problem. $sin(x)sin(x^2)$ is the one that oscillates in what I called a "wave packet." -Dan Attached Thumbnails 10. Originally Posted by putnam120 $\int_1^{\infty}\frac{\cos(x^2)\cos(x)}{4x^2}dx\le\ int_1^{\infty}\frac{dx}{4x^2}$ which converges. Aha! I think I caught a mistake with my trained eye. If, the continous functions $0\leq f(x)\leq g(x)$ And, $\smallint g(x)$ converges then so does $\smallint f(x)$ (Of course I mean the improper intergral). But your inequality does not satisfy the one above, namely because it can be negative. However, I have a way to fix this error. Using the integral series test we need to test, $\sum_{k=1}^{\infty} \frac{\cos k^2 \cos k}{4k^2}$ and see whether it converges. It does since its absolutely convergent, since $\|\cos k^2 \cos k\|\leq 1$. 11. $-\int_1^{\infty}\frac{dx}{4x^2}\le\int_1^{\infty}\f rac{\cos(x^2)\cos(x)}{4x^2}dx\le\int_1^{\infty}\fr ac{dx}{4x^2}$ both of which converge to a real value. thus the middle term converges since it is bounded between two convergent series.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 28, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.989197313785553, "perplexity": 661.8214828385428}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375096301.47/warc/CC-MAIN-20150627031816-00012-ip-10-179-60-89.ec2.internal.warc.gz"}
http://news.sky-map.org/starview?object_type=1&object_id=1710&object_name=HR+7613&locale=EN	NEWS@SKY (Science&Space News) Home To Survive in the Universe .MYA{ color: yellow; text-decoration: none; :hover { color: red; text-decoration: none; } } Services Why to Inhabit Top Contributors Astro Photo The Collection Forum Blog New! FAQ Login # 22 Cyg Contents ### Images DSS Images Other Images ### Related articles Heavy Element Abundances in Late-B and Early-A Stars. I. Co-Added IUE Spectra of HgMn StarsVery heavy elements (Pt, Au, Hg, Tl, and Bi) are found to be enhanced inthe atmospheres of the chemically peculiar stars of the upper mainsequence by up to a million times the solar system levels. Suchenhancements are believed to result from atmospheric dynamics (i.e.,diffusion) rather than scenarios that dredge up nuclear-processedmaterial to the surface or transfer processed material between binarycompanions. However, the theoretical framework needs to be furtherconstrained by observations beyond the realm of the spectral types forwhich such abundance enhancements are observed at optical wavelengths.The International Ultraviolet Explorer (IUE) satellite collected spectraof bright stars for which chemical peculiarities have been derived fromground-based data. For several elements the abundance enhancements haveonly been recently measured using Hubble Space Telescope data and havetherefore not yet been exploited in the IUE data. We have initiated aprogram to analyze IUE high-dispersion spectra to more fullycharacterize the pattern of very heavy element enhancement for manymercury-manganese (HgMn) stars and to potentially extend the spectralclass (effective temperature) boundaries over which these abundanceanomalies are known to exist. The abundances of very heavy elements inchemically normal B and A-type stars provide a base level that may becompared with the solar system abundances. These early spectral typestars may therefore reveal clues for galactic chemical evolution studiessince they were formed at a later epoch than the Sun in the history ofthe Galaxy. This first paper presents the motivation for the analyses tofollow, outlines our spectral co-addition technique for IUE spectra, anddiscusses the choice of model atmospheres and the synthetic spectrumprocedures, while initiating the study by highlighting the abundance ofgold in several HgMn stars. Elemental abundance analyses with the EBASIM spectrograph of the 2.1-m CASLEO Observatory Telescope. I. The late B and early A stars vec xi Octantis, alpha Sextantis, and 68 TauriWe used data from the EBASIM spectrograph of the 2.1-m CASLEO telescopeto study three rather sharp-lined late B to early A stars xi Oct (B6IV), alpha Sex (B9.5 III), and 68 Tau (A2 IV). These measurements arecompared with those from the Anglo-Austrialian Telescope for the firststar and to those from the coudé spectrograph of the 1.22-mtelescope of the Dominion Astrophysical Observatory (DAO) for the othertwo stars. The equivalent width scales of the EBASIM and the DAO dataare similar. Thus for the latter two stars the DAO data is also used inthe analyses. Both xi Oct and alpha Sex generally have abundancesclose to those of the Sun in the range of values found for other normalstars with similar effective temperatures. The abundance pattern for 68Tau is that of a metallic-lined star as is well known.Tables 5 to 7 are only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/406/987 Rotational Velocities of B StarsWe measured the projected rotational velocities of 1092 northern B starslisted in the Bright Star Catalogue (BSC) and calibrated them againstthe 1975 Slettebak et al. system. We found that the published values ofB dwarfs in the BSC average 27% higher than those standards. Only 0.3%of the stars have rotational velocities in excess of two-thirds of thebreakup velocities, and the mean velocity is only 25% of breakup,implying that impending breakup is not a significant factor in reducingrotational velocities. For the B8-B9.5 III-V stars the bimodaldistribution in V can be explained by a set of slowly rotating Ap starsand a set of rapidly rotating normal stars. For the B0-B5 III-V starsthat include very few peculiar stars, the distributions in V are notbimodal. Are the low rotational velocities of B stars due to theoccurrence of frequent low-mass companions, planets, or disks? Therotational velocities of giants originating from late B dwarfs areconsistent with their conservation of angular momentum in shells.However, we are puzzled by why the giants that originate from the earlyB dwarfs, despite having 3 times greater radii, have nearly the samerotational velocities. We find that all B-type primaries in binarieswith periods less than 2.4 days have synchronized rotational and orbitalmotions; those with periods between 2.4 and 5.0 days are rotating withina factor 2 of synchronization or are nearly synchronized.'' Thecorresponding period ranges for A-type stars are 4.9 and 10.5 days, ortwice as large. We found that the rotational velocities of the primariesare synchronized earlier than their orbits are circularized. The maximumorbital period for circularized B binaries is 1.5 days and for Abinaries is 2.5 days. For stars of various ages from 107.5 to1010.2 yr the maximum circularized periods are a smoothexponential function of age. Rotational velocities of A-type stars in the northern hemisphere. II. Measurement of v sin iThis work is the second part of the set of measurements of v sin i forA-type stars, begun by Royer et al. (\cite{Ror_02a}). Spectra of 249 B8to F2-type stars brighter than V=7 have been collected at Observatoirede Haute-Provence (OHP). Fourier transforms of several line profiles inthe range 4200-4600 Å are used to derive v sin i from thefrequency of the first zero. Statistical analysis of the sampleindicates that measurement error mainly depends on v sin i and thisrelative error of the rotational velocity is found to be about 5% onaverage. The systematic shift with respect to standard values fromSlettebak et al. (\cite{Slk_75}), previously found in the first paper,is here confirmed. Comparisons with data from the literature agree withour findings: v sin i values from Slettebak et al. are underestimatedand the relation between both scales follows a linear law ensuremath vsin inew = 1.03 v sin iold+7.7. Finally, thesedata are combined with those from the previous paper (Royer et al.\cite{Ror_02a}), together with the catalogue of Abt & Morrell(\cite{AbtMol95}). The resulting sample includes some 2150 stars withhomogenized rotational velocities. Based on observations made atObservatoire de Haute Provence (CNRS), France. Tables \ref{results} and\ref{merging} are only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.125.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/393/897 Photometric Monitoring of Bright Be Stars. IV. 1996-1999We report long-term UBV observations of 15 bright, active Be stars,namely: X Persei, EW Canis Majoris, θ Coronae Borealis, 4 (V839)Herculis, 88 (V744) Herculis, 66 (V2048) Ophiuchi, NW Serpentis, CXDraconis, 12 (V395) Vulpeculae, 28 (V1624) Cygni, QR Vulpeculae, 59(V832) Cygni, EW Lacertae, ο Andromedae, and KX Andromedae. Theobservations were made in 1996-1999 through the Automatic PhotometricTelescope Service in Arizona and through the American Association ofVariable Star Observers (AAVSO) photoelectric photometry program andhave been added to a database extending back 20 years. We describe thestars' recent behavior and also comment on the long-term behavior ofsome of them. They vary photometrically on timescales ranging from abouta day to many years. Cyclicities in the light variations of S Doradus stars III. P CygniOn the basis of new photometric observations and archived data publishedsince 1907, we discuss the light variations of P Cygni. We conclude thatthere are alpha Cygni-type microvariations with a stable (pulsation)quasi-period of 17.3 days. There are also longer cycles of variationwith P ~ 100 d, so-called 100 d-type micro-variations, and with P ~1500-1600 d, a short S Dor-type phase. Catalogue of Apparent Diameters and Absolute Radii of Stars (CADARS) - Third edition - Comments and statisticsThe Catalogue, available at the Centre de Données Stellaires deStrasbourg, consists of 13 573 records concerning the results obtainedfrom different methods for 7778 stars, reported in the literature. Thefollowing data are listed for each star: identifications, apparentmagnitude, spectral type, apparent diameter in arcsec, absolute radiusin solar units, method of determination, reference, remarks. Commentsand statistics obtained from CADARS are given. The Catalogue isavailable in electronic form at the CDS via anonymous ftp tocdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcar?J/A+A/367/521 Research Note Hipparcos photometry: The least variable starsThe data known as the Hipparcos Photometry obtained with the Hipparcossatellite have been investigated to find those stars which are leastvariable. Such stars are excellent candidates to serve as standards forphotometric systems. Their spectral types suggest in which parts of theHR diagrams stars are most constant. In some cases these values stronglyindicate that previous ground based studies claiming photometricvariability are incorrect or that the level of stellar activity haschanged. Table 2 is only available in electronic form at the CDS viaanonymous ftp to cdsarc.u-strasbg.fr (130.79.128.5) or viahttp://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/367/297 Eclipsing Binaries as Astrophysical Laboratories: Internal Structure, Core Convection, and Evolution of the B-Star Components of V380 CygniNew photometric solutions have been carried out on the importanteccentric eclipsing system V380 Cygni (B1.5 II-III+B2 V) from UBVdifferential photoelectric photometry obtained by us. The photometricelements obtained from the analysis of the light curves have beencombined with the spectroscopic solution recently published by Popper& Guinan and have led to the physical properties of the systemcomponents. The effective temperature of the stars has been determinedby fitting IUE UV spectrophotometry to Kurucz model atmospheres andcompared with other determinations from broadband and intermediate-bandstandard photometry. The values of mass, absolute radius, and effectivetemperature for the primary and secondary stars are 11.1+/-0.5Msolar, 14.7+/-0.2 Rsolar, 21,350+/-400 K, and6.95+/-0.25 Msolar, 3.74+/-0.07 Rsolar,20,500+/-500 K, respectively. In addition, a redetermination of thesystem's apsidal motion rate has been done from the analysis of 12eclipse timings obtained from 1923 to 1995. The apsidal motion studyyields the internal mass distribution of the more luminous component.Using stellar structure and evolutionary models with modern inputphysics, tests on the extent of convection in the core of the moremassive B1.5 II-III star of the system have been carried out. Both theanalysis of the logg-logTeff diagram and the apsidal motionstudy indicate a star with a larger convective core, and thus morecentrally condensed, than currently assumed. This has been quantified inform of an overshooting parameter with a value ofαov~0.6+/-0.1. Finally, the tidal evolution of thesystem (synchronization and circularization times) has also beenstudied. A Second Catalog of Orbiting Astronomical Observatory 2 Filter Photometry: Ultraviolet Photometry of 614 StarsUltraviolet photometry from the Wisconsin Experiment Package on theOrbiting Astronomical Observatory 2 (OAO 2) is presented for 614 stars.Previously unpublished magnitudes from 12 filter bandpasses withwavelengths ranging from 1330 to 4250 Å have been placed on thewhite dwarf model atmosphere absolute flux scale. The fluxes wereconverted to magnitudes using V=0 for F(V)=3.46x10^-9 ergs cm^-2 s^-1Å^-1, or m_lambda=-2.5logF_lambda-21.15. This second catalogeffectively doubles the amount of OAO 2 photometry available in theliterature and includes many objects too bright to be observed withmodern space observatories. Elemental abundance analyses with DAO spectrograms - XIX. The superficially normal B stars zeta Draconis, epsilon Lyrae, 8 Cygni and 22 CygniElemental abundances of the superficially normal early and middle Bstars zeta Dra, epsilon Lyr, 8 Cyg and 22 Cyg are derived, consistentwith previous studies in this series, using spectrograms obtained withReticon and CCD detectors. Almost all of the derived metal abundancesare found to be solar within the errors of the analysis. However, theHe/H ratios are slightly greater than solar. Flux Distributions for 59 Stars in CygnusAbsolute flux distributions are given for 59 Cygnus stars in thespectral range of 320--720 nm with a step of 5 nm. Their rms errors areon the average 2--4%. The synthetic color indices calculated for theflux distributions are compared with the observed color indices in threephotometric systems. UBV photometry of Be stars at Hvar: 1972--1990A summary of results of the systematic UBV photoelectric monitoring ofbright northern Be stars carried out at the Hvar Observatory between1972 and 1990 is presented. Altogether, 76 Be stars of all luminosityclasses were observed and 13,848 UBV measurements secured.Simultaneously, 9,648 UBV measurements of 48 check stars (most of themof early spectral types) were obtained. A careful transformation of allobservations into the standard Johnson system allowed detection andmonitoring of even very mild long-term light and colour variations ofthese objects. Almost all early-type Be stars in the sample turned outto be variable. For several stars phase-locked light variations relatedto their binary nature were established. Sudden brightenings, on a timescale of a few days, were detected for o Cas and QR Vul. Tables 2 and 3are only available in electronic form at CDS via ftp tocdsarc.u-strasbg.fr (130.79.128.5) or via http://cdsweb.u-strasbg.fr/Abstract.html New Photometric Data for HD 142703 and HD 192640Not Available The ROSAT all-sky survey catalogue of optically bright OB-type stars.For the detailed statistical analysis of the X-ray emission of hot starswe selected all stars of spectral type O and B listed in the Yale BrightStar Catalogue and searched for them in the ROSAT All-Sky Survey. Inthis paper we describe the selection and preparation of the data andpresent a compilation of the derived X-ray data for a complete sample ofbright OB stars. Vitesses radiales. Catalogue WEB: Wilson Evans Batten. Subtittle: Radial velocities: The Wilson-Evans-Batten catalogue.We give a common version of the two catalogues of Mean Radial Velocitiesby Wilson (1963) and Evans (1978) to which we have added the catalogueof spectroscopic binary systems (Batten et al. 1989). For each star,when possible, we give: 1) an acronym to enter SIMBAD (Set ofIdentifications Measurements and Bibliography for Astronomical Data) ofthe CDS (Centre de Donnees Astronomiques de Strasbourg). 2) the numberHIC of the HIPPARCOS catalogue (Turon 1992). 3) the CCDM number(Catalogue des Composantes des etoiles Doubles et Multiples) byDommanget & Nys (1994). For the cluster stars, a precise study hasbeen done, on the identificator numbers. Numerous remarks point out theproblems we have had to deal with. Coronographic imaging of T Tauri: discovery of an optical jet in Burnham nebula.We present coronographic images of T Tauri and its surrounding nebula(Burnham nebula) obtained with the STScI coronograph at Calar Alto(Spain) and with the STScI-Torino coronograph at ESO-NTT in Hα6563, [SII] 6716-6731 and 6670/80 A satellite continuum filters. Takingadvantage of the subarcsec seeing conditions, we mapped thecircumstellar environment down to 2" from the star, corresponding to320A.U. at the T Tauri distance of 160pc. Both the Hα and [SII]images reveal a complex morphology, characterized by several clumps ofshock-excited gas superimposed on large scale continuum emission. Inparticular, we detected a jet-like feature departing from the immediatesurroundings of the star in a southly direction that leads to a regionof shock excited clumps. A curved filament departs from this region,crossing Burnham nebula up to the previously known Herbig-Haro object HHA (Schwartz 1990). The south-western part of Burnham nebula ischaracterized by a number of small, nearly circular clumps. A faint,isolated HH object is also present in the northern part of the nebula.Taking into account all the available data, we suggest that the opticaljet is emitted by T Tau S roughly along the plane of the sky. The jet atfirst moves into the neutral components originating the shock excitedknots and then impacts with the edges of the cavity associated to theoutflows. The jet wiggling due to the orbital motion of the emittingsource and/or to precession phenomena could explain the peculiarexcitation status of the Burnham nebula. Reliable photometric reductions to the standard UBV (or uvby) system and accurate UBV magnitudes of bright standard stars from the northern part of the international Be programA modified method of computer reduction of UBV (or uvby) photoelectricobservations to standard systems, which combines advantages of what hasso far been achieved in this area, is described in detail. A completereduction of over 46000 UBV observations obtained at Hvar Observatorybetween 1972 and 1991, and of nearly 5000 UBV observations secured atSkalnate Pleso Observatory between 1980 and 1987, was carried out usingthe new technique. It is argued that replacing the original Johnson'sUBV values for the non-variable stars that were observed by the meanvalues based on repeated observations over several years and applyingthe new reduction technique can ensure a stable reproduction of UBVmagnitudes, obviously quite close to the standard Johnson's ones, overmany years and from observatories situated at very different altitudesabove sea level within about 0.01mag in all three UBV magnitudes. A listof new accurate mean UBV values of 191 stars which were regularlyobserved at Hvar - and a part of them also at Skalnate Pleso - ascomparison, check and standard stars in the Be- and Ap-star observingprograms, is included for future use by photometric observers in theNorthern Hemisphere. For a number of these stars, we can guaranteesecular constancy within 0.mag01 during the past 5 to 15 years. Photoelectric monitoring of bright Be stars. II - 1989, 1990, 1991UBV photometry obtained with the 0.25-m Automatic Photometric Telescopeof 12 bright, active Be stars: Theta Coronae Borealis, 4 Herculis, 88Herculis, 66 Ophiuchi, MWC 601, CX Draconis, 12 Vulpeculae, 28 Cygni, QRVulpeculae, Omicron Andromedae, EW Lacertae, and KX Andromedae isreported and discussed. The nature and cause of the photometricvariations and their relationship to variations at other wavelengths areexplored. Atlas of extinction curves derived from ultraviolet spectra of the TD-1 satelliteThe collection of 166 extinction curves derived from the publishedlow-resolution spectra acquired with the aid of the spectrometer onboard the TD-1 satellite is presented. The observed variety ofextinction laws is apparently due to the varied physical parameters ofinterstellar clouds; for example, the bright stars, included in thesample of TD-1 material, are very likely to be obscured by single clouds(interstellar or circumstellar). The system of standards constructedwith the aid of a special procedure allowing the possible effects ofspectral mismatch to be avoided and making possible the derivation ofextinction curves even in cases of very small E(B-V)S, was applied. Thecurves are presented in the form of plots, normalized to E(B-V) = 1. The stellar temperature scale for stars of spectral types from O8 to F6 and the standard deviation of the MK spectral classificationEmpirical effective temperature of 211 early-type stars found in aprevious investigation (Kontizas and Theodossiou, 1980; Theodossiou,1985) are combined with the effective temperatures of 313 early-typestars from the literature. From these effective temperatures of a totalnumber of 524 early-type stars of spectral types from O8 to F6 a newstellar temperature scale is developed along with the standard deviationof the MK spectral classification. The frequency and formation mechanism of B2-B5 main-sequence binariesTwenty coude spectra were obtained for each of the 74 B2-B5 IV or Vstars, and the results of their radial velocities were combined withthose of a previous study of 42 similar stars, to examine the frequencyand the formation mechanism of these binaries. New improved orbitalelements are listed for nine known double-lined and 26 single-linedspectroscopic binaries. It is found that, systems with periods of 0.01yr to 100,000 yrs, have secondary frequencies that fit the Salpeter(1955) luminosity function (but not the van Rhijn function), indicatingthat these systems were formed primarily by capture. For systems withperiods shorter than 0.01 yr, the separations of components are only afew stellar radii, suggesting that these systems have undergone masstransfer; their secondary masses have no direct information concerningthe formation mechanism. Third preliminary catalogue of stars observed with the photoelectric astrolabe of the Beijing Astronomical Observatory.Not Available Empirical temperature calibrations for early-type starsThree temperature calibrations of suitable photometric quantities havebeen derived for O and B stars. A sample of 120 stars with reliableT(eff.) determinations has been used for establishing each calibration.The different calibrations have been critically discussed and compared.Temperature determinations for 1009 program stars have been obtainedwith an accuracy of the order of 10 percent. Stellar integrated fluxes in the wavelength range 380 NM - 900 NM derived from Johnson 13-colour photometryPetford et al. (1988) have reported measured integrated fluxes for 216stars with a wide spread of spectral type and luminosity, and mentionedthat a cubic-spline integration over the relevant Johnson 13-colormagnitudes, converted to fluxes using Johnson's calibration, is inexcellent agreement with those measurements. In this paper a list of thefluxes derived in this way, corrected for a small dependence on B-V, isgiven for all the 1215 stars in Johnson's 1975 catalog with completeentries. Photoelectric monitoring of bright Be starsThe paper describes and summarizes BV photometric observations of 34bright, active Be stars made at various times between 1981 and 1987 witha 0.4-m telescope at the University of Toronto. These observationsdemonstrate the photometric variability of Be stars on time scales ofhours to years. Photoelectric and visual photometry of P CygniA total of 225 V, BV, or UBV photoelectric observations of P Cyg weremade in 1985 and 1986, as part of a long-term UBV photometric campaignon bright Be stars. The star varied irregularly by up to 0.2 mag in V ontime scales ranging from a few days to a few months. The characteristictime scale was 35-40 days. The variations in (B-V) and (U-B) color wereconsiderably smaller than those in V, and were apparently not related tothem in any simple way. Also analyzed are the 10-day means of the visualobservations of P Cyg in the archives of the American Association ofVariable Star Observers. These indicate that there are no strictlyperiodic brightness variations of the star greater than 0.01 mag, butthey suggest that there may be variations of about 0.2 mag on a timescale of a decade or more. The relation between the brightnessvariations and the other properties of P Cyg is discussed briefly. Observations of interstellar diffuse absorption band at 4430 AObservations of the interstellar diffuse absorption band at 4430 A for800 O and B stars in Neckel's (1967) catalog are being carried out, and482 spectra obtained up to September 1983 have been reduced. It isconfirmed that the strength of the interstellar diffuse absorption bandat 4430 A does not simply relate to the abundance of interstellar grainson the line of sight. The relation between the color excess E(B-V) andthe equivalent width of the band to the direction of l = 130-140 deg andb = -5 to +5 deg shows that some parameter(s) other than E(B-V) is (are)needed to understand the cause of this band. Research Note - Absolute UBV Photometry at the Zacatecas ObservatoryAbstract image available at:http://adsabs.harvard.edu/cgi-bin/nph-bib_query?1985RMxAA..11...55S&db_key=AST A catalog of ultraviolet interstellar extinction excesses for 1415 starsUltraviolet interstellar extinction excesses are presented for 1415stars with spectral types B7 and earlier. The excesses with respect to Vare derived from Astronomical Netherlands Satellite (ANS) 5-channel UVphotometry at central wavelengths of approximately 1550, 1800, 2500, and3300 A. A measure of the excess extinction in the 2200-A extinction bumpis also given. The data are valuable for investigating the systematicsof peculiar interstellar extinction and for studying the character of UVinterstellar extinction in the general direction of stars for which theextinction-curve shape is unknown. Submit a new article	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8418213725090027, "perplexity": 7959.049382967656}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583656665.34/warc/CC-MAIN-20190116031807-20190116053807-00324.warc.gz"}
https://www.mapsofworld.com/where-is/ye.html	Maps of World Current, Credible, Consistent Search Select Country Flag World Map / Where Is / Where is Ye # Where is Ye Location Maps of Cities in Myanmar Last Updated : August 16, 2016	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8942996263504028, "perplexity": 24891.06326297462}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818688932.49/warc/CC-MAIN-20170922093346-20170922113346-00413.warc.gz"}
https://ask.sagemath.org/question/46779/matrix-projection-blues/	# Matrix projection blues edit Hi on OpenCourseware MIT site: Lecture 15: Projections onto subspaces [edited :the code on sagecell sagemath org was not the good one ! it was the first version I wrote. when I updated the code in the cell, that does not work, I had to open a new cell] code on sagecell sagemath org Q1: p is the b projected vector on vector a below all letters are matrices E=B-P with P=XA E=B-XA as E perpendicular to A => dot product(A,E)) = 0 means A.transpose()E=0 then A^T(B-XA)=0 so A^T(XA)=A^TB (and this is false !) but Gilbert Strang write XA^TA=A^TB (and this is good !) but we are not allowed to commute A^TXA by XA^TA if X is a matrix ! I know I made a mistake in my raisonning but I fail to find it ! Q2 : Why I must write X=A (A.transpose())/(( (A.transpose()) * A ).det()) instead of X=A * (A.transpose())/(( (A.transpose()) * A )) why I need to add .det() ? edit retag close merge delete I know the first question is basic math question not a sagemath question, sorry, tell me if I must post it on a math forum instead. now the code in the link is my last code. ( 2019-06-03 12:53:43 -0600 )edit Sort by » oldest newest most voted Q1. In his lecture, Prof. Strang begins with the simplest case: the orthogonal projection of a vector $\mathbf{b}$ onto a one dimensional subspace $S=\mathrm{span}\langle\mathbf{a}\rangle$, $\mathbf{a}$ being a non-null vector in $\mathbb{R}^n$. The projection vector $\mathbf{p}$ should be a multiple of $\mathbf{a}$, so Prof. Strang writes it as $\mathbf{p}=x\mathbf{a}$. Here $x$ is a scalar number, not a matrix, and $\mathbf{a}$ is a vector, identified with a $n\times 1$ matrix. He wants to deduce that $\mathbf{p}=P\mathbf{b}$, where $P$ is the projection matrix $P=\frac{1}{\mathbf{a}^T\mathbf{a}}\mathbf{a}\mathbf{a}^T,$ which is an $n\times n$ matrix. To this end, Prof. Strang writes the projection vector as $\mathbf{p}=\mathbf{a}\,x$. Now, you should see $\mathbf{p}$ and $\mathbf{a}$ as $n\times1$ matrices and $x$ as a one dimensional vector or a $1\times1$ matrix, so that $\mathbf{a}$ and $x$ can be multiplied. Thus, we have $x\,\mathbf{a}=\mathbf{a}\,x.$ This identity does not mean that $\mathbf{a}$ and $x$ are two matrices that commute. Just read the left and right sides as stated above. It is true that the notation may be a bit misleading. Perhaps it would be better to write $(x)$ instead of $x$ if $x$ should be seen as a $1\times 1$ matrix (parentheses are used to delimit matrices). For example, $4\begin{pmatrix} 1 \\ 2 \\ 3\end{pmatrix} =\begin{pmatrix} 4 \\ 8 \\ 12\end{pmatrix} =\begin{pmatrix} 1 \\ 2 \\ 3\end{pmatrix}(4).$ The advantage of expressing $\mathbf{p}$ as $\mathbf{a}x$ is that generalization is then possible. If $S$ is spanned by the linearly independent vectors $\mathbf{a}_1,\ldots,\mathbf{a}_k$, the orthogonal projection $\mathbf{p}$ of a vector $\mathbf{b}$ onto $S$ should be a linear combination of $\mathbf{a}_1,\ldots,\mathbf{a}_k$, that is, $\mathbf{p}=x_1\mathbf{a}_1+\cdots+x_k\mathbf{a}_k=AX$ with $A=\left(\mathbf{a}_1 \vert\ldots \vert\mathbf{a}_k\right)$ and $X=\begin{pmatrix}x_1 \\ \vdots \\ x_k\end{pmatrix}$ The reasoning in Prof. Strang’s lecture would then show that $\mathbf{p}=P\mathbf{b}$, where $P$ is now the projection matrix $P=A(A^TA)^{-1}A^T.$ Returning to your question, you write P=XA where, in fact, you should write $\mathbf{p}=x\mathbf{a}$ and consider $x$ being an scalar, not a matrix. Consequently, since $x$ is a scalar, from $\mathbf{a}^T(\mathbf{b}-\mathbf{p})=0$, one has $\mathbf{a}^T\mathbf{b}=\mathbf{a}^T\mathbf{p}=\mathbf{a}^T(x\mathbf{a})=x\mathbf{a}^T\mathbf{a}.$ Hence $x=\frac{\mathbf{a}^T\mathbf{b}}{\mathbf{a}^T\mathbf{a}}.$ Q2. In your code, A.transpose()A is a $1\times 1$ matrix. You cannot divide by a matrix. Thus you need to extract the unique element of this matrix, either with the .det() method or simply writing (A.transpose()*A)[0,0]. By the way, note that, in the video, the projection matrix is denoted by $P$, not $X$. In SageMath, I think that it is better to use vector instead of matrix to represent $\mathbf{a}$, $\mathbf{b}$ and $\mathbf{p}$, as shown here. more Thanks a lot, Juanjo I understand my mistakes now. I'm a bit ashamed of the confusion I made, sorry. ( 2019-06-04 01:36:19 -0600 )edit ( 2019-06-04 04:45:11 -0600 )edit	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8252337574958801, "perplexity": 454.7714736148357}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703547475.44/warc/CC-MAIN-20210124075754-20210124105754-00713.warc.gz"}
https://www.wilderssecurity.com/threads/suspicious-file.79959/	# suspicious file Discussion in 'Trojan Defence Suite' started by subzerox, May 13, 2005. Not open for further replies. 1. ### subzeroxRegistered Member Joined: May 5, 2005 Posts: 35 Hi, i had three files rated as suspicious and looks as follows: alarm: Suspicious filename Name: HTA file in suspicious location File: C:\system volume information\_restore{f82617b8-3574-4b04... This file or shall i say files, because this file displayed three times.These files has been deleted before because it showed this message before with a previous scan. I didn't know exactly what action to take but i have taken the chance to delete it and not knowing what other programs i would disturb eventualy but now these files show up again. I have no clue what these files mean or how i can find out , so if anybody can tell me where these files belongs to or how i can find out i would very much appreciate this because in my oppinion i have a possible infection at this point. 2. ### PilliRegistered Member Joined: Feb 13, 2002 Posts: 6,217 Location: Hampshire UK Hi subzerox, If you had a previous infection which you cleaned then these suspicious files are in your system restore file. To clear this go to system restore settings and disable it. reboot and make sure there are no restore points then re-enable system restore. HTH Pilli 3. ### subzeroxRegistered Member Joined: May 5, 2005 Posts: 35 well i'm not even sure it is a infection but it is rated as suspicious, i am going to do what you advised but is this a real infection? Joined: Apr 15, 2002 Posts: 11,271 Since it's in your sys restore....some of the more helpful info concerning the HTA is unavailable....so without that info it would be a Guess. For example: Suspicious Filename: HTA file in suspicious location File: c:\program files\microsoft money\system\lnpg.hta As noted in the below thread....it might have been placed there by your scanner because the "suspicious detection reports" were "too sensitive" ? 5. ### subzeroxRegistered Member Joined: May 5, 2005 Posts: 35 When i was going to disable system restore i had the following display from worm guard....... Is this a normal message display or do i have to worry? img214.echo.cx/my.php?image=screenhunter32hs.jpg #### Attached Files: • ###### WormGuard.gif File size: 45.6 KB Views: 152 Last edited by a moderator: May 13, 2005 6. ### subzeroxRegistered Member Joined: May 5, 2005 Posts: 35 Bubba i'm sorry if did something wrong when posting the link for the image but it was the first time ever doing something like that. I'm kind of curious is the editing done because this looks better and faster to reply to or is the other way of posting the image "illegal". 7. ### PilliRegistered Member Joined: Feb 13, 2002 Posts: 6,217 Location: Hampshire UK Rstrui should be on your WormGuard allowed list when running XP. Please add this line to your Allowed list. Note you will have to change your path if you have windows on a different drive - folder than C:\ c:\windows\system32\restore\rstrui.exe HTH Pilli Joined: Apr 15, 2002 Posts: 11,271 You did great It's a personal preference of mine to see the image as we follow along without leaving the confines of Wilders Not even close to being illegal....and if it had been....I would not have left the clickable hyper link It ain't much....but the below thread is an attempt to show to make an attachment in case you are unsure. This thread---> FAQ: Screen Shots and Image Posting 9. ### subzeroxRegistered Member Joined: May 5, 2005 Posts: 35 Thanks Pilli, that did it i have those files removed. @bubba i'm chilled	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8123645782470703, "perplexity": 5018.192958157657}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-47/segments/1510934805923.26/warc/CC-MAIN-20171120071401-20171120091401-00259.warc.gz"}
https://arxiv.org/list/math.FA/1904?skip=25&show=25	# Functional Analysis ## Authors and titles for math.FA in Apr 2019, skipping first 25 [ total of 171 entries: 1-25 \| 26-50 \| 51-75 \| 76-100 \| 101-125 \| ... \| 151-171 ] [ showing 25 entries per page: fewer \| more \| all ] [26] Title: Elliptic problems and holomorphic functions in Banach spaces Subjects: Functional Analysis (math.FA) [27] Title: Decompositions with atoms and molecules for variable exponent Triebel-Lizorkin-Morrey spaces Comments: 29 pages; this article is a result of splitting arXiv:1808.05304 in two parts; the first part is now arXiv:1808.05304v2, with 17 pages, while the second part has given rise to the present article Subjects: Functional Analysis (math.FA) [28] Title: (Non-)amenability of the Fourier algebra in the cb-multiplier norm Authors: Volker Runde Comments: Lemma 3.2 is wrong. A counterexample is given in the noted added in proof of [MR1391474; Lau, A. T.-M., Loy, R. J., and Willis, G. A., Amenability of Banach and C-algebras on locally compact groups. Studia Math. 119 (1996), no. 2, 161--178] Subjects: Functional Analysis (math.FA); Operator Algebras (math.OA) [29] Title: Generalizing Lieb's Concavity Theorem via Operator Interpolation Authors: De Huang Subjects: Functional Analysis (math.FA); Operator Algebras (math.OA) [30] Title: Riesz transforms for Dunkl transforms on $L^\infty$ and Dunkl-type $BMO$ space Authors: Wentao Teng Subjects: Functional Analysis (math.FA) [31] Title: Simultaneous approximation in Lebesgue and Sobolev norms via eigenspaces Subjects: Functional Analysis (math.FA) [32] Title: Local average sampling and reconstruction with fundamental splines of fractional order Subjects: Functional Analysis (math.FA) [33] Title: The Zak transform and representations induced from characters of an abelian subgroup Comments: Conference proceedings for SampTA 2019, 4 pages Subjects: Functional Analysis (math.FA); Classical Analysis and ODEs (math.CA); Representation Theory (math.RT) [34] Title: Tracial moment problems on hypercubes Authors: Cong Trinh Le Comments: 13 pages, equivalence of the solvability of two kinds of K-moment problems was established, main results improved Subjects: Functional Analysis (math.FA); Operator Algebras (math.OA) [35] Title: $L^0$--convex compactness and random normal structure in $L^0(\mathcal{F},B)$ Subjects: Functional Analysis (math.FA) [36] Title: Prescribing tangent hyperplanes to $C^{1,1}$ and $C^{1,ω}$ convex hypersurfaces in Hilbert and superreflexive Banach spaces Subjects: Functional Analysis (math.FA) [37] Title: Kantorovich problems and conditional measures depending on a parameter Subjects: Functional Analysis (math.FA) [38] Title: Boundary values of holomorphic semigroups and fractional integration Subjects: Functional Analysis (math.FA) [39] Title: Benedicks-Amrein-Berthier theorem for the Heisenberg motion group and quaternion Heisenberg group Comments: We have added a related topic, called Strong annihilating pair for the Weyl transform. Together with we have generalized Proposition 3.5. arXiv admin note: text overlap with arXiv:1810.06390 Subjects: Functional Analysis (math.FA) [40] Title: Convex Sobolev inequalities related to unbalanced optimal transport Subjects: Functional Analysis (math.FA); Analysis of PDEs (math.AP) [41] Title: Arov--Krein entropy functionals and indefinite interpolation problems Subjects: Functional Analysis (math.FA); Classical Analysis and ODEs (math.CA); Complex Variables (math.CV) [42] Title: On complex symmetric block Toeplitz operators Subjects: Functional Analysis (math.FA) [43] Title: A Kaczmarz algorithm for sequences of projections, infinite products, and applications to frames in IFS $L^{2}$ spaces Subjects: Functional Analysis (math.FA); Numerical Analysis (math.NA); Optimization and Control (math.OC); Probability (math.PR) [44] Title: On Riemann Integration in Metrizable Vector Spaces Subjects: Functional Analysis (math.FA) [45] Title: On upper bounds for regularity indices related to approximation theory Comments: Dedicated to Prof. Dr. Stephan Dahlke on the occasion of his 60th birthday; 25 pages, 3 figures Subjects: Functional Analysis (math.FA); Analysis of PDEs (math.AP) [46] Title: Plans on measures and AM-modulus Subjects: Functional Analysis (math.FA) [47] Title: A summability principle and applications Subjects: Functional Analysis (math.FA) [48] Title: On distributional adjugate and derivative of the inverse Subjects: Functional Analysis (math.FA); Analysis of PDEs (math.AP) [49] Title: Entropy numbers of finite dimensional mixed-norm balls and function space embeddings with small mixed smoothness Subjects: Functional Analysis (math.FA) [50] Title: Martingale Optimal Transport Duality	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6495900750160217, "perplexity": 6387.583330840938}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540517156.63/warc/CC-MAIN-20191209013904-20191209041904-00005.warc.gz"}
https://www.tensorflow.org/versions/r0.10/api_docs/python/nn/activation_functions_	# Activation Functions. The activation ops provide different types of nonlinearities for use in neural networks. These include smooth nonlinearities (sigmoid, tanh, elu, softplus, and softsign), continuous but not everywhere differentiable functions (relu, relu6, and relu_x), and random regularization (dropout). All activation ops apply componentwise, and produce a tensor of the same shape as the input tensor. ### tf.nn.relu(features, name=None) Computes rectified linear: max(features, 0). ##### Args: • features: A Tensor. Must be one of the following types: float32, float64, int32, int64, uint8, int16, int8, uint16, half. • name: A name for the operation (optional). ##### Returns: A Tensor. Has the same type as features. ### tf.nn.relu6(features, name=None) Computes Rectified Linear 6: min(max(features, 0), 6). ##### Args: • features: A Tensor with type float, double, int32, int64, uint8, int16, or int8. • name: A name for the operation (optional). ##### Returns: A Tensor with the same type as features. ### tf.nn.elu(features, name=None) Computes exponential linear: exp(features) - 1 if < 0, features otherwise. ##### Args: • features: A Tensor. Must be one of the following types: float32, float64. • name: A name for the operation (optional). ##### Returns: A Tensor. Has the same type as features. ### tf.nn.softplus(features, name=None) Computes softplus: log(exp(features) + 1). ##### Args: • features: A Tensor. Must be one of the following types: float32, float64, int32, int64, uint8, int16, int8, uint16, half. • name: A name for the operation (optional). ##### Returns: A Tensor. Has the same type as features. ### tf.nn.softsign(features, name=None) Computes softsign: features / (abs(features) + 1). ##### Args: • features: A Tensor. Must be one of the following types: float32, float64, int32, int64, uint8, int16, int8, uint16, half. • name: A name for the operation (optional). ##### Returns: A Tensor. Has the same type as features. ### tf.nn.dropout(x, keep_prob, noise_shape=None, seed=None, name=None) Computes dropout. With probability keep_prob, outputs the input element scaled up by 1 / keep_prob, otherwise outputs 0. The scaling is so that the expected sum is unchanged. By default, each element is kept or dropped independently. If noise_shape is specified, it must be broadcastable to the shape of x, and only dimensions with noise_shape[i] == shape(x)[i] will make independent decisions. For example, if shape(x) = [k, l, m, n] and noise_shape = [k, 1, 1, n], each batch and channel component will be kept independently and each row and column will be kept or not kept together. ##### Args: • x: A tensor. • keep_prob: A scalar Tensor with the same type as x. The probability that each element is kept. • noise_shape: A 1-D Tensor of type int32, representing the shape for randomly generated keep/drop flags. • seed: A Python integer. Used to create random seeds. See set_random_seed for behavior. • name: A name for this operation (optional). ##### Returns: A Tensor of the same shape of x. ##### Raises: • ValueError: If keep_prob is not in (0, 1]. ### tf.nn.bias_add(value, bias, data_format=None, name=None) Adds bias to value. This is (mostly) a special case of tf.add where bias is restricted to 1-D. Broadcasting is supported, so value may have any number of dimensions. Unlike tf.add, the type of bias is allowed to differ from value in the case where both types are quantized. ##### Args: • value: A Tensor with type float, double, int64, int32, uint8, int16, int8, complex64, or complex128. • bias: A 1-D Tensor with size matching the last dimension of value. Must be the same type as value unless value is a quantized type, in which case a different quantized type may be used. • data_format: A string. 'NHWC' and 'NCHW' are supported. • name: A name for the operation (optional). ##### Returns: A Tensor with the same type as value. ### tf.sigmoid(x, name=None) Computes sigmoid of x element-wise. Specifically, y = 1 / (1 + exp(-x)). ##### Args: • x: A Tensor with type float32, float64, int32, complex64, int64, or qint32. • name: A name for the operation (optional). ##### Returns: A Tensor with the same type as x if x.dtype != qint32 otherwise the return type is quint8. ### tf.tanh(x, name=None) Computes hyperbolic tangent of x element-wise. ##### Args: • x: A Tensor or SparseTensor with type float, double, int32, complex64, int64, or qint32. • name: A name for the operation (optional). ##### Returns: A Tensor or SparseTensor respectively with the same type as x if x.dtype != qint32 otherwise the return type is quint8.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.614166796207428, "perplexity": 12107.329965195164}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463607647.16/warc/CC-MAIN-20170523143045-20170523163045-00338.warc.gz"}
http://tex.stackexchange.com/questions/68482/marginpar-border-with-grey-background-and-round-black-edges	# \marginpar border with grey background and round black edges I often use \marginpar{} which is boring to me. Is there a way to add grey background and round black edges so it would look like this: - 1st solution, just using tikz Here's a solution that renews the \marginpar command and uses TikZ to provide very flexible decorations \documentclass{article} \usepackage{tikz} \usepackage{lipsum} \let\oldmarginpar\marginpar % renew the \marginpar command to draw % a node; it has a default setting which % can be overwritten \renewcommand{\marginpar}[2][rectangle,draw,fill=orange,rounded corners]{% \oldmarginpar{% \tikz \node at (0,0) [#1]{#2};}% } \begin{document} \marginpar{margin text here} \lipsum[1] \marginpar[fill=red,text=yellow,circle]{margin text here} \lipsum[2] \end{document} 2nd solution, using mdframed This one uses the mdframed package for the framing, and defines an environment rather than a command. I've copied some code from the tufte document class to define an environment mymarginpar \documentclass{article} \usepackage[xcolor]{mdframed} \usepackage{lipsum} %==================================== % shamelessly copied from tufte documentclass %==================================== \makeatletter % Margin float environment \newsavebox{\@my@margin@floatbox} \newenvironment{@my@margin@float}[1][-1.2ex]% {% \begin{lrbox}{\@my@margin@floatbox}% \begin{minipage}{\marginparwidth}% \hbox{}\vspace*{#1}% \noindent% } {\end{minipage}% \end{lrbox}% \marginpar{\usebox{\@my@margin@floatbox}}% } % marginpar environment \newenvironment{mymarginpar}[1][-1.2ex]% {\begin{@my@margin@float}[#1]% \begin{mdframed}[backgroundcolor=black!30,linecolor=red]% }% {\end{mdframed}\end{@my@margin@float}} \makeatother \begin{document} \begin{mymarginpar} margin text here \end{mymarginpar} \lipsum \end{document} If you want rounded corners, you can investigate the tikz-method of the mdframed, see the documentation for details. - Nice to see my package ;-) However I don't know whether a standard TikZ implementation is easier. – Marco Daniel Aug 23 '12 at 18:47 This example you provided returns an error: "! LaTeX Error: Command \marginpar already defined." – 71GA Aug 23 '12 at 18:58 @71GA not for me- are you sure you're using it as-is? Or have you tried to replace mymarginpar with marginpar? – cmhughes Aug 23 '12 at 19:01 I am sure tried it once more. It doesnt work. I literally copied your example. – 71GA Aug 23 '12 at 21:03 @71GA not sure what's going on, perhaps an update is in order. Meanwhile, I've added another solution that uses tikz, perhaps you'll prefer this anyway :) – cmhughes Aug 23 '12 at 22:14	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.911418080329895, "perplexity": 7198.096416796779}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1398223204388.12/warc/CC-MAIN-20140423032004-00356-ip-10-147-4-33.ec2.internal.warc.gz"}
https://planetmath.org/pi	# pi The symbol $\pi$ was first introduced by William Jones [7, 8] in 1706 to denote the ratio between the perimeter and the diameter on any given circle. In other words, dividing the perimeter of any circle by its diameter always gives the same answer, and this number is defined to be $\pi$. A 12-digit approximation of $\pi$ is given by $3.14159265358...$ Over human history there were many attempts to calculate this number precisely. One of the oldest approximations appears in the Rhind Papyrus (circa 1650 B.C.) where a geometrical construction is given where $(16/9)^{2}=3.1604\ldots$ is used as an approximation to $\pi$ although this was not explicitly mentioned. It wasn’t until the Greeks that there were systematical attempts to calculate $\pi$. Archimedes [1], in the third century B.C. used regular polygons inscribed and circumscribed to a circle to approximate $\pi$: the more sides a polygon has, the closer to the circle it becomes and therefore the ratio between the polygon’s area between the square of the radius yields approximations to $\pi$. Using this method he showed that $223/71<\pi<22/7$ $(3.140845\ldots<\pi<3.142857\ldots)$. Around the world there were also attempts to calculate $\pi$. Brahmagupta [1] gave the value of $\sqrt{10}=3.16227\ldots$ using a method similar to Archimedes’. Chinese mathematician Tsu Chung-Chih (ca. 500 A.D.) gave the approximation $355/113=3.141592920\ldots$. Later, during the renaissance, Leonardo de Pisa (Fibonacci) [1] used 96-sideed regular polygons to find the approximation $864/275=3.141818\ldots$ For centuries, variations on Archimedes’ method were the only tool known, but Viète [1] gave in 1593 the formula $\frac{2}{\pi}=\sqrt{\frac{1}{2}}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}% }}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}+\frac{1}{2}\sqrt{\frac{1}{2}}% }}\cdots$ which was the first analytical expression for $\pi$ involving infinite summations or products. Later with the advent of calculus many of these formulas were discovered. Some examples are Wallis’ [1] formula: $\frac{\pi}{2}=\frac{2}{1}\cdot\frac{2}{3}\cdot\frac{4}{3}\cdot\frac{4}{5}\cdot% \frac{6}{5}\cdots$ and Leibniz’s formula, $\frac{\pi}{4}=1-\frac{1}{3}+\frac{1}{5}-\frac{1}{7}+\frac{1}{9}-\frac{1}{11}+\cdots,$ obtained by developing $\arctan(\pi/4)$ using power series, and with some more advanced techniques, $\pi=\sqrt{6\zeta(2)},$ found by determining the value of the Riemann Zeta function at $s=2$ (http://planetmath.org/ValueOfTheRiemannZetaFunctionAtS2). The Leibniz expression provides an alternate way to define $\pi$ (namely 4 times the limit of the series) and it is one of the formal ways to define $\pi$ when studying analysis in order to avoid the geometrical definition. It is known that $\pi$ is not a rational number (quotient of two integers). Moreover, $\pi$ is not algebraic over the rationals (that is, it is a transcendental number). This means that no polynomial with rational coefficients can have $\pi$ as a root. Its irrationality implies that its decimal expansion (or any integer base for that matter) is not finite nor periodic. ## References Title pi Canonical name Pi Date of creation 2013-03-22 11:51:41 Last modified on 2013-03-22 11:51:41 Owner mathcam (2727) Last modified by mathcam (2727) Numerical id 27 Author mathcam (2727) Entry type Definition Classification msc 01A40 Classification msc 01A32 Classification msc 01A25 Classification msc 01A20 Classification msc 01A16 Classification msc 51-00 Classification msc 11-00 Classification msc 22A22 Classification msc 46L05 Classification msc 82-00 Classification msc 83-00 Classification msc 81-00 Related topic RegularPolygon Related topic Limit Related topic Diameter Related topic TranscedentalNumber Related topic AlgebraicNumber Related topic ExtensionMathbbRmathbbQIsNotFinite Related topic WallisFormulae	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 28, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9073799848556519, "perplexity": 1076.7156677534733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704843561.95/warc/CC-MAIN-20210128102756-20210128132756-00322.warc.gz"}
https://openintro-ims.netlify.app/intro-stat-inference.html	# 5 Introduction to statistical inference Statistical inference is primarily concerned with understanding and quantifying the uncertainty of parameter estimates. While the equations and details change depending on the setting, the foundations for inference are the same throughout all of statistics. We start with two case studies designed to motivate the process of making decisions about research claims. We formalize the process through the introduction of the hypothesis testing framework, which allows us to formally evaluate claims about the population. Finally we expand on the familiar idea of using a sample proportion to estimate a population proportion. That is, we create what is called a confidence interval, which is a range of plausible values where we may find the true population value. Throughout the book so far, you have worked with data in a variety of contexts. You have learned how to summarize and visualize the data as well as how to model multiple variables at the same time. Sometimes the dataset at hand represents the entire research question. But more often than not, the data have been collected to answer a research question about a larger group of which the data are a (hopefully) representative subset. You may agree that there is almost always variability in data – one dataset will not be identical to a second dataset even if they are both collected from the same population using the same methods. However, quantifying the variability in the data is neither obvious nor easy to do, i.e. answering the question “how different is one dataset from another?” is not trivial. Suppose your professor splits the students in your class into two groups: students who sit on the left side of the classroom and students who sit on the right side of the classroom. If $$\hat{p}_{L}$$ represents the proportion of students who sit on the left side of the classroom and own an Apple product and and $$\hat{p}_{R}$$ represents the proportion of students who sit on the right side of the classroom and own an Apple product, would you be surprised if $$\hat{p}_{L}$$ did not exactly equal $$\hat{p}_{R}$$? While the proportions $$\hat{p}_{L}$$ and $$\hat{p}_{R}$$ would probably be close to each other, it would be unusual for them to be exactly the same. We would probably observe a small difference due to chance. If we don’t think the side of the room a person sits on in class is related to whether the person owns an Apple product, what assumption are we making about the relationship between these two variables? (Reminder: for these Guided Practice questions, you can check your answer in the footnote.)105 Studying randomness of this form is a key focus of statistics. Throughout this chapter, and those that follow, we provide three different approaches for quantifying the variability inherent in data: randomization, bootstrapping, and mathematical models. Using the methods provided in this chapter, we will be able to draw conclusions beyond the dataset at hand to research questions about larger populations that the samples come from. ## 5.1 Randomization tests The first type of variability we will explore comes from experiments where the explanatory variable (or treatment) is randomly assigned to the observational units. As you learned in Chapter 1, a randomized experiment can be used to assess whether or not one variable (the explanatory variable) causes changes in a second variable (the response variable). Every dataset has some variability in it, so to decide whether the variability in the data is due to (1) the causal mechanism (the randomized explanatory variable in the experiment) or instead (2) natural variability inherent to the data, we set up a sham randomized experiment as a comparison. That is, we assume that each observational unit would have gotten the exact same response value regardless of the treatment level. By reassigning the treatments many many times, we can compare the actual experiment to the sham experiment. If the actual experiment has more extreme results than any of the sham experiments, we are led to believe that it is the explanatory variable which is causing the result and not just variability inherent to the data. Using a few different case studies, let’s look more carefully at this idea of a randomization test. ### 5.1.1 Gender discrimination case study We consider a study investigating gender discrimination in the 1970s, which is set in the context of personnel decisions within a bank.106 The research question we hope to answer is, “Are females discriminated against in promotion decisions made by male managers?” The data from this study can be found in the openintro package: gender_discrimination. #### Observed data The participants in this study were 48 male bank supervisors attending a management institute at the University of North Carolina in 1972.107 They were asked to assume the role of the personnel director of a bank and were given a personnel file to judge whether the person should be promoted to a branch manager position. The files given to the participants were identical, except that half of them indicated the candidate was male and the other half indicated the candidate was female. These files were randomly assigned to the subjects. Is this an observational study or an experiment? How does the type of study impact what can be inferred from the results?108 For each supervisor both the gender associated with the assigned file and the promotion decision were recorded. Using the results of the study summarized in Table 5.1, we would like to evaluate if females are unfairly discriminated against in promotion decisions. In this study, a smaller proportion of females are promoted than males (0.583 versus 0.875), but it is unclear whether the difference provides convincing evidence that females are unfairly discriminated against. Table 5.1: Summary results for the gender discrimination study. decision gender promoted not promoted Total male 21 3 24 female 14 10 24 Total 35 13 48 The data are visualized in Figure 5.1 as a set of cards. Note that each card denotes a personnel file (an observation from our dataset) and the colors indicate the decision: red for promoted and white for not promoted. Additionally, the observations are broken up into the male and female groups. Statisticians are sometimes called upon to evaluate the strength of evidence. When looking at the rates of promotion for males and females in this study, why might we be tempted to immediately conclude that females are being discriminated against? The large difference in promotion rates (58.3% for females versus 87.5% for males) suggest there might be discrimination against women in promotion decisions. However, we cannot yet be sure if the observed difference represents discrimination or is just due to random chance. Since we wouldn’t expect the sample proportions to be exactly equal, even if the truth was that the promotion decisions were independent of gender, we can’t rule out random chance as a possible explanation when simply comparing the sample proportions. The previous example is a reminder that the observed outcomes in the sample may not perfectly reflect the true relationships between variables in the underlying population. Table 5.1 shows there were 7 fewer promotions in the female group than in the male group, a difference in promotion rates of 29.2% $$\left( \frac{21}{24} - \frac{14}{24} = 0.292 \right).$$ This observed difference is what we call a point estimate of the true difference. The point estimate of the difference is large, but the sample size for the study is small, making it unclear if this observed difference represents discrimination or whether it is simply due to chance. Chance can be thought of as the claim due to natural variability; discrimination can be thought of as the claim the researchers set out to demonstrate. We label these two competing claims, $$H_0$$ and $$H_A:$$ • $$H_0:$$ Null hypothesis. The variables gender and decision are independent. They have no relationship, and the observed difference between the proportion of males and females who were promoted, 29.2%, was due to random chance. • $$H_A:$$ Alternative hypothesis. The variables gender and decision are not independent. The difference in promotion rates of 29.2% was not due to random chance, and equally qualified females are less likely to be promoted than males. Hypothesis testing These hypotheses are part of what is called a hypothesis test. A hypothesis test is a statistical technique used to evaluate competing claims using data. Often times, the null hypothesis takes a stance of no difference or no effect. If the null hypothesis and the data notably disagree, then we will reject the null hypothesis in favor of the alternative hypothesis. There are many nuances to hypothesis testing, so don’t worry if you aren’t a master of hypothesis testing at the end of this section. We’ll discuss these ideas and details many times in this chapter as well as in the chapters that follow. What would it mean if the null hypothesis, which says the variables gender and decision are unrelated, was true? It would mean each banker would decide whether to promote the candidate without regard to the gender indicated on the file. That is, the difference in the promotion percentages would be due to the way the files were randomly allocated to the bankers, and the randomization just happened to give rise to a relatively large difference of 29.2%. Consider the alternative hypothesis: bankers were influenced by which gender was listed on the personnel file. If this was true, and especially if this influence was substantial, we would expect to see some difference in the promotion rates of male and female candidates. If this gender bias was against females, we would expect a smaller fraction of promotion recommendations for female personnel files relative to the male files. We will choose between the two competing claims by assessing if the data conflict so much with $$H_0$$ that the null hypothesis cannot be deemed reasonable. If data and the null claim seem to be at odds with one another, and the data seem to support $$H_A,$$ then we will reject the notion of independence and conclude that the data provide strong evidence of discrimination. #### Variability of the statistic Table 5.1 shows that 35 bank supervisors recommended promotion and 13 did not. Now, suppose the bankers’ decisions were independent of gender. Then, if we conducted the experiment again with a different random assignment of gender to the files, differences in promotion rates would be based only on random fluctuation. We can actually perform this randomization, which simulates what would have happened if the bankers’ decisions had been independent of gender but we had distributed the file genders differently.109 In the simulation, we thoroughly shuffle 48 personnel files, 35 labelled promoted and 13 labelled not promoted, and we deal files into two stacks. Note that by keeping 35 promoted and 13 not promoted, we are assuming that 35 of the bank managers would have promoted the individual whose content is contained in the file independent of gender. We will deal 24 files into the first stack, which will represent the 24 “female” files. The second stack will also have 24 files, and it will represent the 24 “male” files. Figure 5.2 highlights both the shuffle and the reallocation to the sham gender groups. Then, as we did with the original data, we tabulate the results and determine the fraction of personnel files designated as “male” and “female” who were promoted. Since the randomization of files in this simulation is independent of the promotion decisions, any difference in the two promotion rates is entirely due to chance. Table 5.2 show the results of one such simulation. Table 5.2: Simulation results, where the difference in promotion rates between male and female is purely due to random chance. decision gender promoted not promoted Total male 18 6 24 female 17 7 24 Total 35 13 48 What is the difference in promotion rates between the two simulated groups in Table 5.2 ? How does this compare to the observed difference 29.2% from the actual study?110 Figure 5.3 shows that the difference in promotion rates is much larger in the original data than it is in the simulated groups (0.292 >>> 0.042). The quantity of interest throughout this case study has been the difference in promotion rates. We call the summary value the statistic of interest (or often the test statistic). When we encounter different data structures, the statistic is likely to change (e.g., we might calculate an average instead of a proportion), but we will always want to understand how the statistic varies from sample to sample. #### Observed statistic vs. null statistics We computed one possible difference under the null hypothesis in Guided Practice, which represents one difference due to chance. While in this first simulation, we physically dealt out files, it is much more efficient to perform this simulation using a computer. Repeating the simulation on a computer, we get another difference due to chance: -0.042. And another: 0.208. And so on until we repeat the simulation enough times that we have a good idea of the shape of the distribution of differences from chance alone. Figure 5.4 shows a plot of the differences found from 100 simulations, where each dot represents a simulated difference between the proportions of male and female files recommended for promotion. Note that the distribution of these simulated differences in proportions is centered around 0. Because we simulated differences in a way that made no distinction between men and women, this makes sense: we should expect differences from chance alone to fall around zero with some random fluctuation for each simulation. How often would you observe a difference of at least 29.2% (0.292) according to Figure 5.4? Often, sometimes, rarely, or never? It appears that a difference of at least 29.2% due to chance alone would only happen about 2% of the time according to Figure 5.4. Such a low probability indicates that observing such a large difference from chance alone is rare. The difference of 29.2% is a rare event if there really is no impact from listing gender in the candidates’ files, which provides us with two possible interpretations of the study results: • If $$H_0,$$ the Null hypothesis is true: Gender has no effect on promotion decision, and we observed a difference that is so large that it would only happen rarely. • If $$H_A,$$ the Alternative hypothesis is true: Gender has an effect on promotion decision, and what we observed was actually due to equally qualified women being discriminated against in promotion decisions, which explains the large difference of 29.2%. When we conduct formal studies, we reject a null position (the idea that the data are a result of chance only) if the data strongly conflict with that null position.111 In our analysis, we determined that there was only a $$\approx$$ 2% probability of obtaining a sample where $$\geq$$ 29.2% more males than females get promoted by chance alone, so we conclude that the data provide strong evidence of gender discrimination against women by the supervisors. In this case, we reject the null hypothesis in favor of the alternative. Statistical inference is the practice of making decisions and conclusions from data in the context of uncertainty. Errors do occur, just like rare events, and the data set at hand might lead us to the wrong conclusion. While a given data set may not always lead us to a correct conclusion, statistical inference gives us tools to control and evaluate how often these errors occur. Before getting into the nuances of hypothesis testing, let’s work through another case study. ### 5.1.2 Opportunity cost case study How rational and consistent is the behavior of the typical American college student? In this section, we’ll explore whether college student consumers always consider the following: money not spent now can be spent later. In particular, we are interested in whether reminding students about this well-known fact about money causes them to be a little thriftier. A skeptic might think that such a reminder would have no impact. We can summarize the two different perspectives using the null and alternative hypothesis framework. • $$H_0:$$ Null hypothesis. Reminding students that they can save money for later purchases will not have any impact on students’ spending decisions. • $$H_A:$$ Alternative hypothesis. Reminding students that they can save money for later purchases will reduce the chance they will continue with a purchase. In this section, we’ll explore an experiment conducted by researchers that investigates this very question for students at a university in the southwestern United States.112 #### Observed data One-hundred and fifty students were recruited for the study, and each was given the following statement: Imagine that you have been saving some extra money on the side to make some purchases, and on your most recent visit to the video store you come across a special sale on a new video. This video is one with your favorite actor or actress, and your favorite type of movie (such as a comedy, drama, thriller, etc.). This particular video that you are considering is one you have been thinking about buying for a long time. It is available for a special sale price of $14.99. What would you do in this situation? Please circle one of the options below. Half of the 150 students were randomized into a control group and were given the following two options: 1. Buy this entertaining video. 1. Not buy this entertaining video. The remaining 75 students were placed in the treatment group, and they saw a slightly modified option (B): 1. Buy this entertaining video. 1. Not buy this entertaining video. Keep the$14.99 for other purchases. Would the extra statement reminding students of an obvious fact impact the purchasing decision? Table 5.3 summarizes the study results. The data from this study can be found in the openintro package: opportunity_cost. Table 5.3: Summary results of the opportunity cost study. decision control 56 19 75 treatment 41 34 75 Total 97 53 150 It might be a little easier to review the results using a visualisation. Figure 5.5 shows that a higher proportion of students in the treatment group chose not to buy the video compared to those in the control group. Another useful way to review the results from Table 5.3 is using row proportions, specifically considering the proportion of participants in each group who said they would buy or not buy the video. These summaries are given in Table 5.4. Table 5.4: The opportunity cost data are summarized using row proportions. Row proportions are particularly useful here since we can view the proportion of buy and not buy decisions in each group. decision control 0.747 0.253 1 treatment 0.547 0.453 1 We will define a success in this study as a student who chooses not to buy the video.113 Then, the value of interest is the change in video purchase rates that results by reminding students that not spending money now means they can spend the money later. We can construct a point estimate for this difference as ($$T$$ for treatment and $$C$$ for control): $\hat{p}_{T} - \hat{p}_{C} = \frac{34}{75} - \frac{19}{75} = 0.453 - 0.253 = 0.200$ The proportion of students who chose not to buy the video was 20 percentage points higher in the treatment group than the control group. However, is this result statistically significant? In other words, is a 20% difference between the two groups so prominent that it is unlikely to have occurred from chance alone? #### Variability of the statistic The primary goal in this data analysis is to understand what sort of differences we might see if the null hypothesis were true, i.e., the treatment had no effect on students. For this, we’ll use the same procedure we applied in Section 5.1.1: randomization. Let’s think about the data in the context of the hypotheses. If the null hypothesis $$(H_0)$$ was true and the treatment had no impact on student decisions, then the observed difference between the two groups of 20% could be attributed entirely to random chance. If, on the other hand, the alternative hypothesis $$(H_A)$$ is true, then the difference indicates that reminding students about saving for later purchases actually impacts their buying decisions. #### Observed statistic vs. null statistics Just like with the gender discrimination study, we can perform a statistical analysis. Using the same randomization technique from the last section, let’s see what happens when we simulate the experiment under the scenario where there is no effect from the treatment. While we would in reality do this simulation on a computer, it might be useful to think about how we would go about carrying out the simulation without a computer. We start with 150 index cards and label each card to indicate the distribution of our response variable: decision. That is, 53 cards will be labeled “not buy video” to represent the 53 students who opted not to buy, and 97 will be labeled “buy video” for the other 97 students. Then we shuffle these cards thoroughly and divide them into two stacks of size 75, representing the simulated treatment and control groups. Any observed difference between the proportions of “not buy video” cards (what we earlier defined as success) can be attributed entirely to chance. If we are randomly assigning the cards into the simulated treatment and control groups, how many “not buy video” cards would we expect to end up in each simulated group? What would be the expected difference between the proportions of “not buy video” cards in each group? Since the simulated groups are of equal size, we would expect $$53 / 2 = 26.5,$$ i.e., 26 or 27, “not buy video” cards in each simulated group, yielding a simulated point estimate of the difference in proportions of 0% . However, due to random chance, we might also expect to sometimes observe a number a little above or below 26 and 27. The results of a single randomization from chance alone is shown in Table 5.5. Table 5.5: Summary of student choices against their simulated groups. The group assignment had no connection to the student decisions, so any difference between the two groups is due to chance. decision control 46 29 75 treatment 51 24 75 Total 97 53 150 From this table, we can compute a difference that occurred the first shuffle of the data (i.e., from chance alone): $\hat{p}_{T, shfl1} - \hat{p}_{C, shfl1} = \frac{24}{75} - \frac{29}{75} = 0.32 - 0.387 = - 0.067$ Just one simulation will not be enough to get a sense of what sorts of differences would happen from chance alone. We’ll simulate another set of simulated groups and compute the new difference: 0.04. And again: 0.12. And again: -0.013. We’ll do this 1,000 times. The results are summarized in a dot plot in Figure 5.6, where each point represents a simulation. Since there are so many points, it is more convenient to summarize the results in a histogram such as the one in Figure 5.7, where the height of each histogram bar represents the number of simulations resulting in an outcome of that magnitude. If there was no treatment effect, then we’d only observe a difference of at least +20% about 0.6% of the time. That is really rare! Instead, we will conclude the data provide strong evidence there is a treatment effect: reminding students before a purchase that they could instead spend the money later on something else lowers the chance that they will continue with the purchase. Notice that we are able to make a causal statement for this study since the study is an experiment, although we don’t know why the reminder induces a lower purchase rate. ### 5.1.3 Hypothesis testing In the last two sections, we utilized a hypothesis test, which is a formal technique for evaluating two competing possibilities. In each scenario, we described a null hypothesis, which represented either a skeptical perspective or a perspective of no difference. We also laid out an alternative hypothesis, which represented a new perspective such as the possibility that there has been a change or that there is a treatment effect in an experiment. The alternative hypothesis is usually the reason the scientists set out to do the research in the first place. Null and alternative hypotheses. The null hypothesis $$(H_0)$$ often represents either a skeptical perspective or a claim to be tested. The alternative hypothesis $$(H_A)$$ represents an alternative claim under consideration and is often represented by a range of possible values for the value of interest. If a person makes a somewhat unbelievable claim, we are initially skeptical. However, if there is sufficient evidence that supports the claim, we set aside our skepticism. The hallmarks of hypothesis testing are also found in the US court system. #### The US court system A US court considers two possible claims about a defendant: they are either innocent or guilty. If we set these claims up in a hypothesis framework, which would be the null hypothesis and which the alternative? The jury considers whether the evidence is so convincing (strong) that there is no reasonable doubt regarding the person’s guilt. That is, the skeptical perspective (null hypothesis) is that the person is innocent until evidence is presented that convinces the jury that the person is guilty (alternative hypothesis). Jurors examine the evidence to see whether it convincingly shows a defendant is guilty. Notice that if a jury finds a defendant not guilty, this does not necessarily mean the jury is confident in the person’s innocence. They are simply not convinced of the alternative that the person is guilty. This is also the case with hypothesis testing: even if we fail to reject the null hypothesis, we typically do not accept the null hypothesis as truth. Failing to find strong evidence for the alternative hypothesis is not equivalent to providing evidence that the null hypothesis is true. We will see this idea in greater detail in Section 6.2.2. #### p-value and statistical significance In Section 5.1.1 we encountered a study from the 1970’s that explored whether there was strong evidence that women were less likely to be promoted than men. The research question – are females discriminated against in promotion decisions? – was framed in the context of hypotheses: • $$H_0:$$ Gender has no effect on promotion decisions. • $$H_A:$$ Women are discriminated against in promotion decisions. The null hypothesis $$(H_0)$$ was a perspective of no difference. The data on gender discrimination provided a point estimate of a 29.2% difference in recommended promotion rates between men and women. We determined that such a difference from chance alone would be rare: it would only happen about 2 in 100 times. When results like these are inconsistent with $$H_0,$$ we reject $$H_0$$ in favor of $$H_A.$$ Here, we concluded there was discrimination against women. The 2-in-100 chance is what we call a p-value, which is a probability quantifying the strength of the evidence against the null hypothesis and in favor of the alternative. p-value. The p-value is the probability of observing data at least as favorable to the alternative hypothesis as our current dataset, if the null hypothesis were true. We typically use a summary statistic of the data, such as a difference in proportions, to help compute the p-value and evaluate the hypotheses. This summary value that is used to compute the p-value is often called the test statistic. In the gender discrimination study, the difference in discrimination rates was our test statistic. What was the test statistic in the opportunity cost study covered in Section 5.1.2? The test statistic in the opportunity cost study was the difference in the proportion of students who decided against the video purchase in the treatment and control groups. In each of these examples, the point estimate of the difference in proportions was used as the test statistic. When the p-value is small, i.e., less than a previously set threshold, we say the results are statistically significant. This means the data provide such strong evidence against $$H_0$$ that we reject the null hypothesis in favor of the alternative hypothesis. The threshold, called the significance level and often represented by $$\alpha$$ (the Greek letter alpha), is typically set to $$\alpha = 0.05,$$ but can vary depending on the field or the application. Using a significance level of $$\alpha = 0.05$$ in the discrimination study, we can say that the data provided statistically significant evidence against the null hypothesis. Statistical significance. We say that the data provide statistically significant evidence against the null hypothesis if the p-value is less than some reference value, often $$\alpha=0.05.$$ In the opportunity cost study in Section 5.1.2, we analyzed an experiment where study participants had a 20% drop in likelihood of continuing with a video purchase if they were reminded that the money, if not spent on the video, could be used for other purchases in the future. We determined that such a large difference would only occur 6-in-1000 times if the reminder actually had no influence on student decision-making. What is the p-value in this study? Was the result statistically significant? The p-value was 0.006. Since the p-value is less than 0.05, the data provide statistically significant evidence that US college students were actually influenced by the reminder. We often use a threshold of 0.05 to determine whether a result is statistically significant. But why 0.05? Maybe we should use a bigger number, or maybe a smaller number. If you’re a little puzzled, that probably means you’re reading with a critical eye – good job! We’ve made a video to help clarify why 0.05: https://www.openintro.org/book/stat/why05/ Sometimes it’s also a good idea to deviate from the standard. We’ll discuss when to choose a threshold different than 0.05 in Section 6.2.2. ### 5.1.4 Randomization test summary Figure 5.8 provides a visual summary of the randomization testing procedure. We can summarise the Randomization Test procedure as follows: • Frame the research question in terms of hypotheses. Hypothesis tests are appropriate for research questions that can be summarized in two competing hypotheses. The null hypothesis $$(H_0)$$ usually represents a skeptical perspective or a perspective of no difference. The alternative hypothesis $$(H_A)$$ usually represents a new view or a difference. • Collect data with an observational study or experiment. If a research question can be formed into two hypotheses, we can collect data to run a hypothesis test. If the research question focuses on associations between variables but does not concern causation, we would run an observational study. If the research question seeks a causal connection between two or more variables, then an experiment should be used. • Model the randomness as if the null hypothesis was true. In the examples above, the variability has been modeled as if the treatment (e.g., gender, opportunity) allocation was independent of the outcome of the study. The computer generated the null distribution from many different randomizations in order to quantify the null variability. • Analyze the data. Choose an analysis technique appropriate for the data and identify the p-value. So far, we’ve only seen one analysis technique: randomization. Throughout the rest of this textbook, we’ll encounter several new methods suitable for many other contexts. • Form a conclusion. Using the p-value from the analysis, determine whether the data provide statistically significant evidence against the null hypothesis. Also, be sure to write the conclusion in plain language so casual readers can understand the results. Table 5.6 is another look at the Randomization Test summary. Table 5.6: Summary of randomization tests as an inferential statistical method. Randomization Test What does it do? Shuffles the explanatory variable to mimic the natural variability found in a randomized experiment. What is the random process described? Randomized experiment. What other random processes can be approximated? Can also be used to describe random sampling in an observational model What is it best for? Hypothesis Testing (can be used for Confidence Intervals, but not covered in this text). What physical object represents the simulation process? Shuffling cards ### 5.1.5 Exercises Exercises for this section will be available in the 1st edition of this book, which will be available in Summer 2021. In the meantime, OpenIntro::Introduction to Statistics with Randomization and Simulation and OpenIntro::Statistics, both of which are available for free, have many exercises you can use alongside this book. ## 5.2 Bootstrap confidence intervals As seen in Section 5.1, Randomization is a statistical technique suitable for evaluating whether a difference in sample proportions is due to chance. Randomization tests are best suited for modeling experiments where the treatment (explanatory variable) has been randomly assigned to the observational units and there is an attempt to answer a simple yes/no research question. For example, consider the following research questions that can be well assessed with a randomization test: • Does this vaccine make it less likely that a person will get malaria? • Does drinking caffeine affect how quickly a person can tap their finger? • Can we predict whether candidate A will win the upcoming election? In this section, however, we are instead interested in a different approach to understanding population parameters. Instead of testing a claim, the goal now is to estimate the unknown value of a population parameter. For example, • How much less likely am I to get malaria if I get the vaccine? • How much faster (or slower) can a person tap their finger, on average, if they drink caffeine first? • What proportion of the vote will go to candidate A? Here, we explore the situation where focus is on a single proportion, and we introduce a new simulation method: bootstrapping. Bootstrapping is best suited for modeling studies where the data have been generated through random sampling from a population. As with randomization tests, our goal with bootstrapping is to understand variability of a statistic. Unlike randomization tests (which modeled how the statistic would change if the treatment had been allocated differently), the bootstrap will model how a statistic changes from repeated sampling. How a statistic varies from sample to sample will provide information about how different the statistic is from the parameter of interest. Quantifying the variability of a statistic from sample to sample is a hard problem. Fortunately, sometimes the mathematical theory for how a statistic varies (across different samples) is well-known; this is the case for the sample proportion as seen in Section 5.3. However, some statistics don’t have simple theory for how they vary, and bootstrapping provides a computational approach for providing interval estimates for almost any population parameter (we will revisit bootstrapping in Chapters 6, 7, and 8 so you’ll get plenty of practice as well as exposure to bootstrapping in many different data settings). Our goal with bootstrapping will be to produce an interval estimate (a range of plausible values) for the population parameter. If we could, we would measure the variability of the statistics by repeatedly taking sample data from the population compute the sample proportion. Then we could do it again. And again. And so on until we have a good sense of the variability of our original estimate. When the sampling variability is large, we would assume that the original statistic is possibly far from the true population parameter of interest (and the interval estimate will be wide). When the variability across the samples is small, we expect the sample statistic to be close to the true parameter of interest (and the interval estimate will be narrow). The ideal world where sampling data is free or extremely cheap is almost never the case, and taking repeated samples from a population is usually impossible. So, instead of using a “resample from the population” approach, bootstrapping uses a “resample from the sample” approach. The sections below provide examples and details about the bootstrapping process. ### 5.2.1 Medical consultant case study People providing an organ for donation sometimes seek the help of a special medical consultant. These consultants assist the patient in all aspects of the surgery, with the goal of reducing the possibility of complications during the medical procedure and recovery. Patients might choose a consultant based in part on the historical complication rate of the consultant’s clients. #### Observed data One consultant tried to attract patients by noting the average complication rate for liver donor surgeries in the US is about 10%, but her clients have had only 3 complications in the 62 liver donor surgeries she has facilitated. She claims this is strong evidence that her work meaningfully contributes to reducing complications (and therefore she should be hired!). We will let $$p$$ represent the true complication rate for liver donors working with this consultant. (The “true” complication rate will be referred to as the parameter.) We estimate $$p$$ using the data, and label the estimate $$\hat{p}.$$ The sample proportion for the complication rate is 3 complications divided by the 62 surgeries the consultant has worked on: $$\hat{p} = 3/62 = 0.048.$$ Is it possible to assess the consultant’s claim (that the reduction in complications is due to her work) using the data? No. The claim is that there is a causal connection, but the data are observational, so we must be on the lookout for confounding variables. For example, maybe patients who can afford a medical consultant can afford better medical care, which can also lead to a lower complication rate. While it is not possible to assess the causal claim, it is still possible to understand the consultant’s true rate of complications. Parameter. A parameter is the “true” value of interest. We typically estimate the parameter using a point estimate from a sample of data. The point estimate is also known as the statistic. For example, we estimate the probability $$p$$ of a complication for a client of the medical consultant by examining the past complications rates of her clients: $\hat{p} = 3 / 62 = 0.048~\text{is used to estimate}~p$ #### Variability of the statistic In the medical consultant case study, the parameter is $$p,$$ the true probability of a complication for a client of the medical consultant. There is no reason to believe that $$p$$ is exactly $$\hat{p} = 3/62,$$ but there is also no reason to believe that $$p$$ is particularly far from $$\hat{p} = 3/62.$$ By sampling with replacement from the dataset (a process called bootstrapping), the variability of the possible $$\hat{p}$$ values can be approximated. Most of the inferential procedures covered in this text are grounded in quantifying how one data set would differ from another when they are both taken from the same population. It doesn’t make sense to take repeated samples from the same population because if you have the means to take more samples, a larger sample size will benefit you more than separately evaluating two sample of the exact same size. Instead, we measure how the samples behave under an estimate of the population. Figure 5.9 shows how the unknown original population can be estimated by using the sample to approximate the proportion of successes and failures (in our case, the proportion of complications and no complications for the medical consultant). By taking repeated samples from the estimated population, the variability from sample to sample can be observed. In Figure 5.10 the repeated bootstrap samples are obviously different both from each other and from the original population. Recall that the bootstrap samples were taken from the same (estimated) population, and so the differences are due entirely to natural variability in the sampling procedure. By summarizing each of the bootstrap samples (here, using the sample proportion), we see, directly, the variability of the sample proportion, $$\hat{p},$$ from sample to sample. The distribution of $$\hat{p}_{boot}$$ for the example scenario is shown in Figure 5.11, and the full bootstrap distribution for the medical consultant data is shown in Figure 5.14. It turns out that in practice, it is very difficult for computers to work with an infinite population (with the same proportional breakdown as in the sample). However, there is a physical and computational model which produces an equivalent bootstrap distribution of the sample proportion in a computationally efficient manner. Consider the observed data to be a bag of marbles 3 of which are success (red) and 4 of which are failures (white). By drawing the marbles out of the bag with replacement, we depict the exact same sampling process as was done with the infinitely large estimated population. If we apply the bootstrap sampling process to the medical consultant example, we consider each client to be one of the marbles in the bag. There will be 59 white marbles (no complication) and 3 red marbles (complication). If we choose 62 marbles out of the bag (one at a time with replacement) and compute the proportion of simulated patients with complications, $$\hat{p}_{boot},$$ then this “bootstrap” proportion represents a single simulated proportion from the “resample from the sample” approach. In a simulation of 62 patients, about how many would we expect to have had a complication?114 One simulation isn’t enough to get a sense of the variability from one bootstrap proportion to another bootstrap proportion, so we repeat the simulation 10,000 times using a computer. Figure 5.14 shows the distribution from the 10,000 bootstrap simulations. The bootstrapped proportions vary from about zero to 11.3%. The variability in the bootstrapped proportions leads us to believe that the true probability of complication (the parameter, $$p$$) is somewhere between 0 and 11.3%. The range of values for the true proportion is called a bootstrap percentile confidence interval, and we will see it again in throughout the next few sections and chapters. The original claim was that the consultant’s true rate of complication was under the national rate of 10%. Does the interval estimate of 0 to 11.3% for the true probability of complication indicate that the surgical consultant has a lower rate of complications than the national average? Explain. No. Because the interval overlaps 10%, it might be that the consultant’s work is associated with a lower risk of complications, or it might be that the consultant’s work is associated with a higher risk (i.e., greater than 10%) of complications! Additionally, as previously mentioned, because this is an observational study, even if an association can be measured, there is no evidence that the consultant’s work is the cause of the complication rate (being higher or lower). ### 5.2.2 Tappers and listeners case study Here’s a game you can try with your friends or family: pick a simple, well-known song, tap that tune on your desk, and see if the other person can guess the song. In this simple game, you are the tapper, and the other person is the listener. #### Observed data A Stanford University graduate student named Elizabeth Newton conducted an experiment using the tapper-listener game.115 In her study, she recruited 120 tappers and 120 listeners into the study. About 50% of the tappers expected that the listener would be able to guess the song. Newton wondered, is 50% a reasonable expectation? In Newton’s study, only 3 out of 120 listeners ($$\hat{p} = 0.025$$) were able to guess the tune! That seems like quite a low number which leads the researcher to ask: what is the true proportion of people who can guess the tune? ### Variability of the statistic To answer the question, we will again use a simulation. To simulate 120 games, this time we use a bag of 120 marbles 3 are red (for those who guessed correctly) and 117 are white (for those who could not guess the song). Sampling from the bag 120 times (remembering to replace the marble back into the bag each time to keep constant the population proportion of red) produces one bootstrap sample. For example, we can start by simulating 5 tapper-listener pairs by sampling 5 marbles from the bag of 3 red and 117 white marbles. W W W R W Wrong Wrong Wrong Correct Wrong After selecting 120 marbles, we counted 2 red for $$\hat{p}_{boot1} = 0.0167.$$ As we did with the randomization technique, seeing what would happen with one simulation isn’t enough. In order to understand how far the observed proportion of 0.025 might be from the true parameter, we should generate more simulations. Here we’ve repeated the entire simulation ten times: $0.0417 \quad 0.0250 \quad 0.0250 \quad 0.0083 \quad 0.0500 \quad 0.0333 \quad 0.0250 \quad 0.000 \quad 0.0083 \quad 0.000$ As before, we’ll run a total of 10,000 simulations using a computer. As seen in Figure 5.15, the range of 95% of the resampled values of $$\hat{p}_{boot}$$ is 0.000 to 0.0583. That is, we expect that between 0% and 5.83% of people are truly able to guess the tapper’s tune. Do the data provide “statistically significant” evidence against the claim that 50% of listeners can guess the tapper’s tune?116 ### 5.2.3 Confidence intervals A point estimate provides a single plausible value for a parameter. However, a point estimate is rarely perfect; usually there is some error in the estimate. In addition to supplying a point estimate of a parameter, a next logical step would be to provide a plausible range of values for the parameter. #### Plausible range of values for the population parameter A plausible range of values for the population parameter is called a confidence interval. Using only a single point estimate is like fishing in a murky lake with a spear, and using a confidence interval is like fishing with a net. We can throw a spear where we saw a fish, but we will probably miss. On the other hand, if we toss a net in that area, we have a good chance of catching the fish. If we report a point estimate, we probably will not hit the exact population parameter. On the other hand, if we report a range of plausible values – a confidence interval – we have a good shot at capturing the parameter. If we want to be very certain we capture the population parameter, should we use a wider interval or a smaller interval?117 #### Bootstrap confidence interval As we saw above, a bootstrap sample is a sample of the original sample. In the case of the medical complications data, we proceed as follows: • Randomly sample one observation from the 62 patients (replace the marble back into the bag so as to keep constant the population). • Randomly sample a second observation from the 62 patients. Because we sample with replacement (i.e., we don’t actually remove the marbles from the bag), there is a 1-in-62 chance that the second observation will be the same one sampled in the first step! • Keep going one sampled observation at a time … • Randomly sample a 62nd observation from the 62 patients. Bootstrap sampling is often called sampling with replacement. A bootstrap sample behaves similarly to how an actual sample from a populationwould behave, and we compute the point estimate of interest (here, compute $$\hat{p}_{boot}$$). Due to theory that is beyond this text, we know that the bootstrap proportions $$\hat{p}_{boot}$$ vary around $$\hat{p}$$ in a similar way to how different sample proportions (i.e., values of $$\hat{p}$$) vary around the true parameter $$p.$$ Therefore, an interval estimate for $$p$$ can be produced using the $$\hat{p}_{boot}$$ values themselves. 95% Bootstrap percentile confidence interval for a parameter $$p.$$ The 95% bootstrap confidence interval for the parameter $$p$$ can be obtained directly using the ordered values $$\hat{p}_{boot}$$ values. Consider the sorted $$\hat{p}_{boot}$$ values. Call the 2.5% bootstrapped proportion value “lower,” and call the 97.5% bootstrapped proportion value “upper.” The 95% confidence interval is given by: (lower, upper) In Section 6.1.1 we will discuss different percentages for the confidence interval (e.g., 90% confidence interval or 99% confidence interval). Section 6.1.1 also provides a longer discussion on what “95% confidence” actually means. ### 5.2.4 Bootstrap summary We can summarise the Bootstrap process as follows: • Frame the research question in terms of a parameter to estimate. Confidence Intervals are appropriate for research questions that aim to estimate a number from the population (called a parameter). • Collect data with an observational study or experiment. If a research question can be formed as a query about the parameter, we can collect data to calculate a statistic which is the best guess we have for the value of the parameter. However, we know that the statistic won’t be exactly equal to the parameter due to natural variability. • Model the randomness by using the data values as a proxy for the population. In order to assess how far the statistic might be from the parameter, we take repeated resamples from the dataset to measure the variability in bootstrapped statistics. The variability of the bootstrapped statistics around the observed statistic (a quantity which can be measured through computational technique) should be approximately the same as the variability of many observed sample statistics around the parameter (a quantity which is very difficult to measure because in real life we only get exactly one sample). • Create the interval. After choosing a particular confidence level, use the variability of the bootstrapped statistics to create an interval estimate which will hope to capture the true parameter. While the interval estimate associated with the particular sample at hand may or may not capture the parameter, the researcher knows that over their lifetime, the confidence level will determine the percentage of their research confidence intervals that do capture the true parameter. • Form a conclusion. Using the confidence interval from the analysis, report on the interval estimate for the parameter of interest. Also, be sure to write the conclusion in plain language so casual readers can understand the results. Table 5.7 is another look at the Bootstrap process summary. Table 5.7: Summary of bootstrapping as an inferential statistical method. Bootstrapping What does it do? Resamples (with replacement) from the observed data to mimic the sampling variability found by collecting data from a population. What is the random process described? Random sampling from a population. What other random processes can be approximated? Can also be used to describe random allocation in an experiment What is it best for? Confidence Intervals (bootstrap HT for one proportion covered in Chapter 6). What physical object represents the simulation process? Pulling marbles from a bag ### 5.2.5 Exercises Exercises for this section will be available in the 1st edition of this book, which will be available in Summer 2021. In the meantime, OpenIntro::Introduction to Statistics with Randomization and Simulation and OpenIntro::Statistics, both of which are available for free, have many exercises you can use alongside this book. ## 5.3 Mathematical models ### 5.3.1 Central Limit Theorem We’ve encountered four case studies so far this chapter. While they differ in the settings, in their outcomes, and also in the technique we’ve used to analyze the data, they all have something in common: the general shape of the distribution of the statistics (called the sampling distribution). #### Null distribution Figure 5.17 shows the null distributions in each of the four case studies where we ran 10,000 simulations. Note that the null distribution is the sampling distribution of the statistic created under the setting where the null hypothesis is true. Therefore, the null distribution will always be centered at the value of the parameter given by the null hypothesis. In the case of the opportunity cost study, which originally had just 1,000 simulations, we’ve included an additional 9,000 simulations. Describe the shape of the distributions and note anything that you find interesting.118 The case study for the medical consultant is the only distribution with any evident skew. As we observed in Chapter 1, it’s common for distributions to be skewed or contain outliers. However, the null distributions we’ve so far encountered have all looked somewhat similar and, for the most part, symmetric. They all resemble a bell-shaped curve. The bell-shaped curve similarity is not a coincidence, but rather, is guaranteed by mathematical theory. Central Limit Theorem for proportions. If we look at a proportion (or difference in proportions) and the scenario satisfies certain conditions, then the sample proportion (or difference in proportions) will appear to follow a bell-shaped curve called the normal distribution. An example of a perfect normal distribution is shown in Figure 5.18. Imagine laying a normal curve over each of the four null distributions in Figure 5.17. While the mean (center) and standard deviation (width or spread) may change for each plot, the general shape remains roughly intact. Mathematical theory guarantees that if repeated samples are taken a sample proportion or a difference in sample proportions will follow something that resembles a normal distribution when certain conditions are met. (Note: we typically only take one sample, but the mathematical model lets us know what to expect if we had taken repeated samples.) These conditions fall into two general categories describing the independence between observations and the need to take a sufficiently large sample size. 1. Observations in the sample are independent. Independence is guaranteed when we take a random sample from a population. Independence can also be guaranteed if we randomly divide individuals into treatment and control groups. 2. The sample is large enough. The sample size cannot be too small. What qualifies as “small” differs from one context to the next, and we’ll provide suitable guidelines for proportions in Chapter 6. So far we’ve had no need for the normal distribution. We’ve been able to answer our questions somewhat easily using simulation techniques. However, soon this will change. Simulating data can be non-trivial. For example, some of the scenarios encountered in Chapters 3 and 4 would require complex simulations in order to make inferential conclusions. Instead, the normal distribution and other distributions like it offer a general framework for statistical inference that applies to a very large number of settings. Technical Conditions In order for the normal approximation to describe the sampling distribution of the sample proportion as it varies from sample to sample, two conditions must hold. If these conditions do not hold, it is unwise to use the normal distribution (and related concepts like Z scores, probabilities from the normal curve, etc.) for inferential analyses. 1. independent observations 2. large enough sample (for proportions, at least 10 successes and 10 failures should have been observed in the sample) #### Anticipating frequent use of the normal distribution Below we introduce three new settings where the normal distribution will be useful, and constructing suitable simulations can be difficult. The opportunity cost study determined that students are thriftier if they are reminded that saving money now means they can spend the money later. The study’s point estimate for the estimated impact was 20%, meaning 20% fewer students would move forward with a video purchase in the study scenario. However, as we’ve learned, point estimates aren’t perfect – they only provide an approximation of the truth. It would be useful if we could provide a range of plausible values for the impact, more formally known as a confidence interval. It is often difficult to construct a reliable confidence interval in many situations using simulations.119 However, doing so is reasonably straightforward using the normal distribution. Book prices were collected for 73 courses at UCLA in Spring 2010. Data were collected from both the UCLA Bookstore and Amazon. The differences in these prices are shown in Figure 5.19. The mean difference in the price of the books was \$12.76, and we might wonder, does this provide strong evidence that the prices differ between the two book sellers? Here again we can apply the normal distribution, this time in the context of numerical data. We’ll explore this example and construct such a hypothesis test in Section 7.3. Elmhurst College in Illinois released anonymized data for family income and financial support provided by the school for Elmhurst’s first-year students in 2011. Figure 5.20 shows a regression line fit to a scatterplot of a sample of the data. One question we will ask is, do the data show a real linear trend, or is the trend we observe reasonably explained by random chance? In Chapter 3 we learned how to apply least squares regression to quantify the trend. In Chapter 8 we will focus on whether or not that trend can be explained by chance alone. For this case study, we could again use the normal distribution to help us answer this question. These examples highlight the value of the normal distribution approach. However, before we can apply the normal distribution to statistical inference, it is necessary to become familiar with the mechanics of the normal distribution. In Section 5.3.2 we discuss characteristics of the normal distribution and explore examples of data that follow a normal distribution. In Section 5.3.3, we apply the new knowledge in the context of hypothesis tests and confidence intervals. ### 5.3.2 Normal Distribution Among all the distributions we see in statistics, one is overwhelmingly the most common. The symmetric, unimodal, bell curve is ubiquitous throughout statistics. It is so common that people know it as a variety of names including the normal curve, normal model, or normal distribution.120 Under certain conditions, sample proportions, sample means, and sample differences can be modeled using the normal distribution. Additionally, some variables such as SAT scores and heights of US adult males closely follow the normal distribution. Normal distribution facts. Many summary statistics and variables are nearly normal, but none are exactly normal. Thus the normal distribution, while not perfect for any single problem, is very useful for a variety of problems. We will use it in data exploration and to solve important problems in statistics. In this section, we will discuss the normal distribution in the context of data to become familiar with normal distribution techniques. In the following sections and beyond, we’ll move our discussion to focus on applying the normal distribution and other related distributions to model point estimates for hypothesis tests and for constructing confidence intervals. #### Normal distribution model The normal distribution always describes a symmetric, unimodal, bell-shaped curve. However, normal curves can look different depending on the details of the model. Specifically, the normal model can be adjusted using two parameters: mean and standard deviation. As you can probably guess, changing the mean shifts the bell curve to the left or right, while changing the standard deviation stretches or constricts the curve. Figure 5.21 shows the normal distribution with mean $$0$$ and standard deviation $$1$$ (which is commonly referred to as the standard normal distribution) on top. A normal distributions with mean $$19$$ and standard deviation $$4$$ is shown on the bottom. Figure 5.22 shows the same two normal distributions on the same axis. If a normal distribution has mean $$\mu$$ and standard deviation $$\sigma,$$ we may write the distribution as $$N(\mu, \sigma).$$ The two distributions in Figure 5.22 can be written as $N(\mu = 0, \sigma = 1)\quad\text{and}\quad N(\mu = 19, \sigma = 4)$ Because the mean and standard deviation describe a normal distribution exactly, they are called the distribution’s parameters. Write down the short-hand for a normal distribution with (a) mean 5 and standard deviation 3, (b) mean -100 and standard deviation 10, and (c) mean 2 and standard deviation 9.121 #### Standardizing with Z scores Table 5.8 shows the mean and standard deviation for total scores on the SAT and ACT. The distribution of SAT and ACT scores are both nearly normal. Suppose Ann scored 1800 on her SAT and Tom scored 24 on his ACT. Who performed better?122 Table 5.8: Mean and standard deviation for the SAT and ACT. SAT ACT Mean 1500 21 SD 300 5 The solution to the previous example relies on a standardization technique called a Z score, a method most commonly employed for nearly normal observations (but that may be used with any distribution). The Z score of an observation is defined as the number of standard deviations it falls above or below the mean. If the observation is one standard deviation above the mean, its Z score is 1. If it is 1.5 standard deviations below the mean, then its Z score is -1.5. If $$x$$ is an observation from a distribution $$N(\mu, \sigma),$$ we define the Z score mathematically as $Z = \frac{x-\mu}{\sigma}$ Using $$\mu_{SAT}=1500,$$ $$\sigma_{SAT}=300,$$ and $$x_{Ann}=1800,$$ we find Ann’s Z score: $Z_{Ann} = \frac{x_{Ann} - \mu_{SAT}}{\sigma_{SAT}} = \frac{1800-1500}{300} = 1$ The Z score. The Z score of an observation is the number of standard deviations it falls above or below the mean. We compute the Z score for an observation $$x$$ that follows a distribution with mean $$\mu$$ and standard deviation $$\sigma$$ using $Z = \frac{x-\mu}{\sigma}$ If the observation $$x$$ comes from a normal distribution centered at $$\mu$$ with standard deviation of $$\sigma$$, then the Z score will distributed according to a normal distribution with a center of 0 and a standard deviation of 1. That is, the normality remains when transforming from $$x$$ to $$Z$$ with a shift in both the center as well as the spread. Use Tom’s ACT score, 24, along with the ACT mean and standard deviation to compute his Z score.123 Observations above the mean always have positive Z scores while those below the mean have negative Z scores. If an observation is equal to the mean (e.g., SAT score of 1500), then the Z score is $$0.$$ Let $$X$$ represent a random variable from $$N(\mu=3, \sigma=2),$$ and suppose we observe $$x=5.19.$$ (a) Find the Z score of $$x.$$ (b) Use the Z score to determine how many standard deviations above or below the mean $$x$$ falls.124 Head lengths of brushtail possums follow a nearly normal distribution with mean 92.6 mm and standard deviation 3.6 mm. Compute the Z scores for possums with head lengths of 95.4 mm and 85.8 mm.125 We can use Z scores to roughly identify which observations are more unusual than others. One observation $$x_1$$ is said to be more unusual than another observation $$x_2$$ if the absolute value of its Z score is larger than the absolute value of the other observation’s Z score: $$\|Z_1\| > \|Z_2\|.$$ This technique is especially insightful when a distribution is symmetric. Which of the two brushtail possum observations in the previous guided practice is more unusual?126 #### Normal probability calculations Ann from the SAT Guided Practice earned a score of 1800 on her SAT with a corresponding $$Z=1.$$ She would like to know what percentile she falls in among all SAT test-takers. Ann’s percentile is the percentage of people who earned a lower SAT score than Ann. We shade the area representing those individuals in Figure 5.24. The total area under the normal curve is always equal to 1, and the proportion of people who scored below Ann on the SAT is equal to the area shaded in Figure 5.24: 0.8413. In other words, Ann is in the $$84^{th}$$ percentile of SAT takers. We can use the normal model to find percentiles or probabilities. A normal probability table, which lists Z scores and corresponding percentiles, can be used to identify a percentile based on the Z score (and vice versa). Statistical software can also be used. Normal probabilities are most commonly found using statistical software which we will show here using R. We use the software to identify the percentile corresponding to any particular Z score. For instance, the percentile of $$Z=0.43$$ is 0.6664, or the $$66.64^{th}$$ percentile. The pnorm() function is available in default R and will provide the percentile associated with any cutoff on a normal curve. The normTail() function is available in the OpenIntro R package and will draw the associated curve if it is helpful. pnorm(0.43, mean = 0, sd = 1) #> [1] 0.666 openintro::normTail(0.43, m = 0, s = 1) We can also find the Z score associated with a percentile. For example, to identify Z for the $$80^{th}$$ percentile, we use qnorm() which identifies the quantile for a given percentage. The quantile represents the cutoff value. (To remember the function qnorm() as providing a cutoff, notice that both qnorm() and “cutoff” start with the sound “kuh.” To remember the pnorm() function as providing a probability from a given cutoff, notice that both pnorm() and probability start with the sound “puh.”) We determine the Z score for the $$80^{th}$$ percentile using qnorm(): 0.84. qnorm(0.80, mean = 0, sd = 1) #> [1] 0.842 openintro::normTail(0.84162, m = 0, s = 1) Determine the proportion of SAT test takers who scored better than Ann on the SAT.127 #### Normal probability examples Cumulative SAT scores are approximated well by a normal model, $$N(\mu=1500, \sigma=300).$$ Shannon is a randomly selected SAT taker, and nothing is known about Shannon’s SAT aptitude. What is the probability that Shannon scores at least 1630 on her SATs? First, always draw and label a picture of the normal distribution. (Drawings need not be exact to be useful.) We are interested in the chance she scores above 1630, so we shade the upper tail. See the normal curve below. The $$x$$-axis identifies the mean and the values at 2 standard deviations above and below the mean. The simplest way to find the shaded area under the curve makes use of the Z score of the cutoff value. With $$\mu=1500,$$ $$\sigma=300,$$ and the cutoff value $$x=1630,$$ the Z score is computed as $Z = \frac{x - \mu}{\sigma} = \frac{1630 - 1500}{300} = \frac{130}{300} = 0.43$ We use software to find the percentile of $$Z=0.43,$$ which yields 0.6664. However, the percentile describes those who had a Z score lower than 0.43. To find the area above $$Z=0.43,$$ we compute one minus the area of the lower tail, as seen below. The probability Shannon scores at least 1630 on the SAT is 0.3336. Always draw a picture first, and find the Z score second. For any normal probability situation, always always always draw and label the normal curve and shade the area of interest first. The picture will provide an estimate of the probability. After drawing a figure to represent the situation, identify the Z score for the observation of interest. If the probability of Shannon scoring at least 1630 is 0.3336, then what is the probability she scores less than 1630? Draw the normal curve representing this exercise, shading the lower region instead of the upper one.128 Edward earned a 1400 on his SAT. What is his percentile? First, a picture is needed. Edward’s percentile is the proportion of people who do not get as high as a 1400. These are the scores to the left of 1400. The mean $$\mu=1500,$$ the standard deviation $$\sigma=300,$$ and the cutoff for the tail area $$x=1400$$ are used to compute the Z score: $Z = \frac{x - \mu}{\sigma} = \frac{1400 - 1500}{300} = -0.33$ Statistical software can be used to find the proportion of the $$N(0,1)$$ curve to the left of $$-0.33$$ which is 0.3707. Edward is at the $$37^{th}$$ percentile. Use the results of the previous example to compute the proportion of SAT takers who did better than Edward. Also draw a new picture. If Edward did better than 37% of SAT takers, then about 63% must have done better than him. Areas to the right. Most statistical software, as well as normal probability tables in most books, give the area to the left. If you would like the area to the right, first find the area to the left and then subtract the amount from one. Stuart earned an SAT score of 2100. Draw a picture for each part. (a) What is his percentile? (b) What percent of SAT takers did better than Stuart?129 Based on a sample of 100 men,130 the heights of male adults between the ages 20 and 62 in the US is nearly normal with mean 70.0’’ and standard deviation 3.3’’. Mike is 5’7’’ and Jim is 6’4’’. (a) What is Mike’s height percentile? (b) What is Jim’s height percentile? Also draw one picture for each part.131 The last several problems have focused on finding the probability or percentile for a particular observation. What if you would like to know the observation corresponding to a particular percentile? Erik’s height is at the $$40^{th}$$ percentile. How tall is he? As always, first draw the picture. In this case, the lower tail probability is known (0.40), which can be shaded on the diagram. We want to find the observation that corresponds to the known probability of 0.4. As a first step in this direction, we determine the Z score associated with the $$40^{th}$$ percentile. Because the percentile is below 50%, we know $$Z$$ will be negative. Statistical software provides the $$Z$$ value to be $$-0.25.$$ Here, we show the format for calculating the value of $$Z$$ using the R statistical software. qnorm(0.4, mean = 0, sd = 1) #> [1] -0.253 Knowing $$Z_{Erik}=-0.25$$ and the population parameters $$\mu=70$$ and $$\sigma=3.3$$ inches, the Z score formula can be set up to determine Erik’s unknown height, labeled $$x_{Erik}$$: $-0.25 = Z_{Erik} = \frac{x_{Erik} - \mu}{\sigma} = \frac{x_{Erik} - 70}{3.3}$ Solving for $$x_{Erik}$$ yields the height 69.18 inches. That is, Erik is about 5’9’’ (this is notation for 5-feet, 9-inches). What is the adult male height at the $$82^{nd}$$ percentile? Again, we draw the figure first. And calculate the Z value associated with the $$82^{nd}$$ percentile: qnorm(0.82, m = 0, s = 1) #> [1] 0.915 Next, we want to find the Z score at the $$82^{nd}$$ percentile, which will be a positive value (because the percentile is bigger than 50%). Using qnorm(), the $$82^{nd}$$ percentile corresponds to $$Z=0.92.$$ Finally, the height $$x$$ is found using the Z score formula with the known mean $$\mu,$$ standard deviation $$\sigma,$$ and Z score $$Z=0.92$$: $0.92 = Z = \frac{x-\mu}{\sigma} = \frac{x - 70}{3.3}$ This yields 73.04 inches or about 6’1’’ as the height at the $$82^{nd}$$ percentile. 1. What is the $$95^{th}$$ percentile for SAT scores? 2. What is the $$97.5^{th}$$ percentile of the male heights? As always with normal probability problems, first draw a picture.132 1. What is the probability that a randomly selected male adult is at least 6’2’’ (74 inches)? 2. What is the probability that a male adult is shorter than 5’9’’ (69 inches)?133 What is the probability that a randomly selected adult male is between 5’9’’ and 6’2’’? These heights correspond to 69 inches and 74 inches. First, draw the figure. The area of interest is no longer an upper or lower tail. The total area under the curve is 1. If we find the area of the two tails that are not shaded (from the previous Guided Practice, these areas are $$0.3821$$ and $$0.1131$$), then we can find the middle area: That is, the probability of being between 5’9’’ and 6’2’’ is 0.5048. What percent of SAT takers get between 1500 and 2000?134 What percent of adult males are between 5’5’’ and 5’7’’?135 #### 68-95-99.7 rule Here, we present a useful general rule for the probability of falling within 1, 2, and 3 standard deviations of the mean in the normal distribution. The rule will be useful in a wide range of practical settings, especially when trying to make a quick estimate without a calculator or Z table. Use pnorm() (or a Z table) to confirm that about 68%, 95%, and 99.7% of observations fall within 1, 2, and 3, standard deviations of the mean in the normal distribution, respectively. For instance, first find the area that falls between $$Z=-1$$ and $$Z=1,$$ which should have an area of about 0.68. Similarly there should be an area of about 0.95 between $$Z=-2$$ and $$Z=2.$$136 It is possible for a normal random variable to fall 4, 5, or even more standard deviations from the mean. However, these occurrences are very rare if the data are nearly normal. The probability of being further than 4 standard deviations from the mean is about 1-in-30,000. For 5 and 6 standard deviations, it is about 1-in-3.5 million and 1-in-1 billion, respectively. SAT scores closely follow the normal model with mean $$\mu = 1500$$ and standard deviation $$\sigma = 300.$$ (a) About what percent of test takers score 900 to 2100? (b) What percent score between 1500 and 2100 ?137 ### 5.3.3 Hypothesis testing case studies The approach for using the normal model in the context of inference is very similar to the practice of applying the model to individual observations that are nearly normal. We will replace null distributions we previously obtained using the randomization or simulation techniques and verify the results once again using the normal model. When the sample size is sufficiently large, the normal approximation generally provides us with the same conclusions as the simulation model. #### 5.3.3.1 Standard error Point estimates vary from sample to sample, and we quantify this variability with what is called the standard error (SE). The standard error is equal to the standard deviation associated with the statistic. So, for example, to quantify the variability of a point estimate from one sample to the next, the variability is called the standard error of the point estimate. Almost always, the standard error is itself an estimate, calculated from the sample of data. The way we determine the standard error varies from one situation to the next. However, typically it is determined using a formula based on the Central Limit Theorem. #### Opportunity cost ##### Observed data In Section 5.1.2 we were introduced to the opportunity cost study, which found that students became thriftier when they were reminded that not spending money now means the money can be spent on other things in the future. Let’s re-analyze the data in the context of the normal distribution and compare the results. ##### Variability of the statistic Figure 5.26 summarizes the null distribution as determined using the randomization method. The best fitting normal distribution for the null distribution has a mean of 0. We can calculate the standard error of this distribution by borrowing a formula that we will become familiar with in Section 6.2, but for now let’s just take the value $$SE = 0.078$$ as a given. Recall that the point estimate of the difference was 0.20, as shown in Figure 5.26. Next, we’ll use the normal distribution approach to compute the two-tailed p-value. ##### Observed statistic vs. null statistics As we learned in Section 5.3.2, it is helpful to draw and shade a picture of the normal distribution so we know precisely what we want to calculate. Here we want to find the area of the tail beyond 0.2, representing the p-value. Next, we can calculate the Z score using the observed difference, 0.20, and the two model parameters. The standard error, $$SE = 0.078,$$ is the equivalent of the model’s standard deviation. $Z = \frac{\text{observed difference} - 0}{SE} = \frac{0.20 - 0}{0.078} = 2.56$ We can either use statistical software or look up $$Z = 2.56$$ in the normal probability table to determine the right tail area: 0.0052, which is about the same as what we got for the right tail using the randomization approach (0.006). Using this area as the p-value, we see that the p-value is less than 0.05, we conclude that the treatment did indeed impact students’ spending. Z score in a hypothesis test. In the context of a hypothesis test, the Z score for a point estimate is $Z = \frac{\text{point estimate} - \text{null value}}{SE}$ The standard error in this case is the equivalent of the standard deviation of the point estimate, and the null value comes from the claim made in the null hypothesis. We have confirmed that the randomization approach we used earlier and the normal distribution approach provide almost identical p-values and conclusions in the opportunity cost case study. Next, let’s turn our attention to the medical consultant case study. #### Medical consultant ##### Observed data In Section 5.2.1 we learned about a medical consultant who reported that only 3 of her 62 clients who underwent a liver transplant had complications, which is less than the more common complication rate of 0.10. In that work, we did not model a null scenario, but we will discuss a simulation method for a one proportion null distribution in Section 6.1.1, such a distribution is provided in Figure 5.27. We have added the best-fitting normal curve to the figure, which has a mean of 0.10. Borrowing a formula that we’ll encounter in Chapter 6, the standard error of this distribution was also computed: $$SE = 0.038.$$ ##### Variability of the statistic Before we begin, we want to point out a simple detail that is easy to overlook: the null distribution we generated from the simulation is slightly skewed, and the histogram is not particularly smooth. In fact, the normal distribution only sort-of fits this model. ##### Observed statistic vs. null statistics As always, we’ll draw a picture before finding the normal probabilities. Below is a normal distribution centered at 0.10 with a standard error of 0.038. Next, we can calculate the Z score using the observed complication rate, $$\hat{p} = 0.048$$ along with the mean and standard deviation of the normal model. Here again, we use the standard error for the standard deviation. $Z = \frac{\hat{p} - p_0}{SE_{\hat{p}}} = \frac{0.048 - 0.10}{0.038} = -1.37$ Identifying $$Z = -1.37$$ using statistical software or in the normal probability table, we can determine that the left tail area is 0.0853 which is the estimated p-value for the hypothesis test. There is a small problem: the p-value of 0.0853 is slightly different from the simulation p-value or 0.1222 which will be calculated in Section 6.1.1. The discrepancy is explained by the normal model’s poor representation of the null distribution in Figure 5.27. As noted earlier, the null distribution from the simulations is not very smooth, and the distribution itself is slightly skewed. That’s the bad news. The good news is that we can foresee these problems using some simple checks. We’ll learn more about these checks in the following chapters. In Section 5.3.1 we noted that the two common requirements to apply the Central Limit Theorem are (1) the observations in the sample must be independent, and (2) the sample must be sufficiently large. The guidelines for this particular situation – which we will learn in Section 6.1 – would have alerted us that the normal model was a poor approximation. #### Conditions for applying the normal model The success story in this section was the application of the normal model in the context of the opportunity cost data. However, the biggest lesson comes from the less successful attempt to use the normal approximation in the medical consultant case study. Statistical techniques are like a carpenter’s tools. When used responsibly, they can produce amazing and precise results. However, if the tools are applied irresponsibly or under inappropriate conditions, they will produce unreliable results. For this reason, with every statistical method that we introduce in future chapters, we will carefully outline conditions when the method can reasonably be used. These conditions should be checked in each application of the technique. After covering the introductory topics in this course, advanced study may lead to working with complex models which, for example, bring together many variables with different variability structure. Working with data that come from normal populations makes higher-order models easier to estimate and interpret. There are times when simulation, randomization, or bootstrapping are unwieldy in either structure or computational demand. Normality can often lead to excellent approximations of the data using straightforward modeling techniques. ### 5.3.4 Confidence interval case study A point estimate is our best guess for the value of the parameter, so it makes sense to build the confidence interval around that value. The standard error, which is a measure of the uncertainty associated with the point estimate, provides a guide for how large we should make the confidence interval. The 68-95-99.7 rule tells us that, in general, 95% of observations are within 2 standard errors of the mean. Here, we use the value 1.96 to be slightly more precise. Constructing a 95% confidence interval. When the sampling distribution of a point estimate can reasonably be modeled as normal, the point estimate we observe will be within 1.96 standard errors of the true value of interest about 95% of the time. Thus, a 95% confidence interval for such a point estimate can be constructed: $\text{point estimate} \pm 1.96 \times SE$ We can be 95% confident this interval captures the true value. Compute the area between -1.96 and 1.96 for a normal distribution with mean 0 and standard deviation 1.138 The point estimate from the opportunity cost study was that 20% fewer students would buy a video if they were reminded that money not spent now could be spent later on something else. The point estimate from this study can reasonably be modeled with a normal distribution, and a proper standard error for this point estimate is $$SE = 0.078.$$ Construct a 95% confidence interval.139 Since the conditions for the normal approximation have already been verified, we can move forward with the construction of the 95% confidence interval: $\text{point estimate} \pm 1.96 \times SE = 0.20 \pm 1.96 \times 0.078 = (0.047, 0.353)$ We are 95% confident that the video purchase rate resulting from the treatment is between 4.7% and 35.3% lower than in the control group. Since this confidence interval does not contain 0, it is consistent with our earlier result where we rejected the notion of “no difference” using a hypothesis test. #### Stents ##### Observed data Consider an experiment that examined whether implanting a stent in the brain of a patient at risk for a stroke helps reduce the risk of a stroke. The results from the first 30 days of this study, which included 451 patients, are summarized in Table 5.9. These results are surprising! The point estimate suggests that patients who received stents may have a higher risk of stroke: $$p_{trmt} - p_{ctrl} = 0.090.$$ Table 5.9: Descriptive statistics for 30-day results for the stent study. stroke no event Total treatment 33 191 224 control 13 214 227 Total 46 405 451 ##### Variability of the statistic Consider the stent study and results. The conditions necessary to ensure the point estimate $$p_{trmt} - p_{ctrl} = 0.090$$ is nearly normal have been verified for you, and the estimate’s standard error is $$SE = 0.028.$$ Construct a 95% confidence interval for the change in 30-day stroke rates from usage of the stent. The conditions for applying the normal model have already been verified, so we can proceed to the construction of the confidence interval: $\text{point estimate} \pm 1.96 \times SE = 0.090 \pm 1.96 \times 0.028 = (0.035, 0.145)$ We are 95% confident that implanting a stent in a stroke patient’s brain increased the risk of stroke within 30 days by a rate of 0.035 to 0.145. This confidence interval can also be used in a way analogous to a hypothesis test: since the interval does not contain 0 (is completely above 0), it means the data provide statistically significant evidence that the stent used in the study increases the risk of stroke within 30 days. As with hypothesis tests, confidence intervals are imperfect. About 1-in-20 properly constructed 95% confidence intervals will fail to capture the parameter of interest, simply due to natural variability in the observed data. Figure 5.28 shows 25 confidence intervals for a proportion that were constructed from 25 different datasets that all came from the same population where the true proportion was $$p = 0.3.$$ However, 1 of these 25 confidence intervals happened not to include the true value. The interval which does not capture $$p=0.3$$ is not due to bad science. Instead, it is due to natural variability, and we should expect some of our intervals to miss the parameter of interest. Indeed, over a lifetime of creating 95% intervals, you should expect 5% of your reported intervals to miss the parameter of interest (unfortunately, you will not ever know which of your reported intervals captured the parameter and which missed the parameter). In Figure 5.28, one interval does not contain the true proportion, $$p = 0.3.$$ Does this imply that there was a problem with the datasets that were selected?140 #### Interpreting confidence intervals A careful eye might have observed the somewhat awkward language used to describe confidence intervals. Correct confidence interval interpretation: We are XX% confident that the population parameter is between lower and upper (where lower and upper are both numerical values). Incorrect language might try to describe the confidence interval as capturing the population parameter with a certain probability. This is one of the most common errors: while it might be useful to think of it as a probability, the confidence level only quantifies how plausible it is that the parameter is in the interval. Another especially important consideration of confidence intervals is that they only try to capture the population parameter. Our intervals say nothing about the confidence of capturing individual observations, a proportion of the observations, or about capturing point estimates. Confidence intervals provide an interval estimate for and attempt to capture population parameters. ### 5.3.5 Mathematical model summary We can summarise the normal model as follows: • Frame the research question. The mathematical model can be applied to both the hypothesis testing and the confidence interval framework. Make sure that your research question is being addressed by the most appropriate inference procedure. • Collect data with an observational study or experiment. To address the research question, collect data on the variables of interest. Note that your data may be a random sample from a population or may be part of a randomized experiment. • Model the randomness of the statistic. In many cases, the normal distribution will be an excellent model for the randomness associated with the statistic of interest. The Central Limit Theorem tells us that if the sample size is large enough, sample averages (which can be calculated as either a proportion or a sample mean) will be approximately normally distributed when describing how the statistics change from sample to sample. • Calculate the variability of the statistic. Using formulas, come up with the standard deviation (or more typically, an estimate of the standard deviation called the standard error) of the statistic. The SE of the statistic will give information on how far the observed statistic is from the null hypothesized value (if performing a hypothesis test) or from the unknown population parameter (if creating a confidence interval). • Use the normal distribution to quantify the variability. The normal distribution will provide a probability which measures how likely it is for your observed and hypothesized (or observed and unknown) parameter to differ by the amount measured. The unusualness (or not) of the descrepancy will form the conclusion to the research question. • Form a conclusion. Using the p-value or the confidence interval from the analysis, report on the research question of interest. Also, be sure to write the conclusion in plain language so casual readers can understand the results. Table 5.10 is another look at the mathematical model approach to inference.. Table 5.10: Summary Mathematical Models as inferential statistical methods. Mathematical Model What does it do? Uses theory (primarily the Central Limit Theorem) to describe the hypothetical variability resulting from either repeated randomized experiments or random samples. What is the random process described? Randomized experiment or random sampling. What other random processes can be approximated? Randomized experiment or random sampling. What is it best for? Quick analyses through, for example, calculating a Z score. What physical object represents the simulation process? Not applicable ### 5.3.6 Exercises Exercises for this section will be available in the 1st edition of this book, which will be available in Summer 2021. In the meantime, OpenIntro::Introduction to Statistics with Randomization and Simulation and OpenIntro::Statistics, both of which are available for free, have many exercises you can use alongside this book. ## 5.4 Chapter review ### 5.4.1 Summary In this chapter, we have provided three different methods for statistical inference. We will continue to build on all three of the methods throughout the text, and by the end, you should have an understanding of their similarities and differences between them. Meanwhile, it is important to note that the methods are designed to mimic variability with data, and we know that variability can come from different sources (e.g., random sampling vs. random allocation, see Figure 1.11). In Table 5.11, we have summarized some of the ways the inferential procedures feature specific sources of variability. We hope that you refer back to the table often as you dive more deeply into inferential ideas in future chapters. Table 5.11: Summary and comparison of Randomization Tests, Bootstrapping, and Mathematical Models as inferential statistical methods. Randomization Test Bootstrapping Mathematical Model What does it do? Shuffles the explanatory variable to mimic the natural variability found in a randomized experiment. Resamples (with replacement) from the observed data to mimic the sampling variability found by collecting data from a population. Uses theory (primarily the Central Limit Theorem) to describe the hypothetical variability resulting from either repeated randomized experiments or random samples. What is the random process described? Randomized experiment. Random sampling from a population. Randomized experiment or random sampling. What other random processes can be approximated? Can also be used to describe random sampling in an observational model Can also be used to describe random allocation in an experiment Randomized experiment or random sampling. What is it best for? Hypothesis Testing (can be used for Confidence Intervals, but not covered in this text). Confidence Intervals (bootstrap HT for one proportion covered in Chapter 6). Quick analyses through, for example, calculating a Z score. What physical object represents the simulation process? Shuffling cards Pulling marbles from a bag Not applicable ### 5.4.2 Terms We introduced the following terms in the chapter. If you’re not sure what some of these terms mean, we recommend you go back in the text and review their definitions. We are purposefully presenting them in alphabetical order, instead of in order of appearance, so they will be a little more challenging to locate. However you should be able to easily spot them as bolded text. 95% confidence interval hypothesis test p-value simulation 95% confident independent parameter standard error alternative hypothesis normal curve percentile standard normal distribution bootstrap percentile confidence interval normal distribution permutation test statistic bootstrap sample normal model point estimate statistically significant bootstrapping normal probability table randomization test success Central Limit Theorem null distribution sampling distribution test statistic confidence interval null hypothesis sampling with replacement Z score ### 5.4.3 Chapter exercises Exercises for this section will be available in the 1st edition of this book, which will be available in Summer 2021. In the meantime, OpenIntro::Introduction to Statistics with Randomization and Simulation and OpenIntro::Statistics, both of which are available for free, have many exercises you can use alongside this book. ### 5.4.4 Interactive R tutorials Navigate the concepts you’ve learned in this chapter in R using the following self-paced tutorials. All you need is your browser to get started! You can also access the full list of tutorials supporting this book here. ### 5.4.5 R labs Further apply the concepts you’ve learned in this chapter in R with computational labs that walk you through a data analysis case study.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8665291666984558, "perplexity": 595.2100781417631}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038464065.57/warc/CC-MAIN-20210417222733-20210418012733-00207.warc.gz"}
https://lavelle.chem.ucla.edu/forum/viewtopic.php?p=81177	## The Third Law Boltzmann Equation for Entropy: $S = k_{B} \ln W$ Hector Acosta Discussion 1H Posts: 51 Joined: Fri Sep 29, 2017 7:04 am ### The Third Law Can someone explain to me the third law of thermodynamics? Cam Bear 2F Posts: 60 Joined: Thu Jul 27, 2017 3:01 am ### Re: The Third Law The third law of thermodynamics states that entropy of a perfect crystal is zero when the temperature is zero Kelvin. If it isn't a perfect crystal or if it is at a different temperature there will be residual entropy. Cam Bear 2F Posts: 60 Joined: Thu Jul 27, 2017 3:01 am ### Re: The Third Law A perfect crystal only has one microstate so w=1. When you plug 1 into the equation S=kb*ln(w) and solve, you get zero. Miguel Velasco 2J Posts: 40 Joined: Fri Sep 29, 2017 7:07 am Been upvoted: 1 time ### Re: The Third Law we know the micro state is w=1 because there exists no movement at 0 Kelvin therefore resulting in entropy equal to 0. Return to “Third Law of Thermodynamics (For a Unique Ground State (W=1): S -> 0 as T -> 0) and Calculations Using Boltzmann Equation for Entropy” ### Who is online Users browsing this forum: No registered users and 1 guest	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5197122693061829, "perplexity": 3470.3734256516536}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655880616.1/warc/CC-MAIN-20200706104839-20200706134839-00130.warc.gz"}
http://www.jiskha.com/search/index.cgi?query=Assume+that+the+three+blocks+portrayed+in+Figure+P4.27+move+on+a+frictionless+surface+and+that+a+F+%3D+42+N+force+acts+as+shown+on+the+m+%3D+2.5+kg+block	Wednesday January 28, 2015 # Search: Assume that the three blocks portrayed in Figure P4.27 move on a frictionless surface and that a F = 42 N force acts as shown on the m = 2.5 kg block Number of results: 55,206 Physics Assume that the three blocks in Figure P4.27 move on a frictionless surface and that a F = 46 N force acts as shown on the m = 2.5 kg block. Figure P4.27. (a) Determine the acceleration given this system. m/s2 (to the right) (b) Determine the tension in the cord connecting m ... February 23, 2012 by Avery Forces w/ tension Assume that three blocks portrayed below move on a frictionless surface and that a 42 N force acts on the 3.0 kg block. Determine (a) the acecleration given the system, (b) the tension inthe cord connecting the 3.0kg and the 1.0 kg blocks, and (c) the force exerted by the 1.... December 7, 2006 by Armando physics Two blocks with masses m1 = 10.9 kg and m2 = 79.3 kg, shown in the figure, are free to move. The coefficent of static friction between the blocks is 0.66 but the surface beneath m2 is frictionless. What is the minimum force F required to hold m1 against m2? November 7, 2011 by lisa physics Two blocks with masses m1 = 20.7 kg and m2 = 55.5 kg, shown in the figure, are free to move. The coefficent of static friction between the blocks is 0.74 but the surface beneath m2 is frictionless. What is the minimum force F required to hold m1 against m2? February 8, 2012 by Katie physics Two blocks with masses m1 = 13.4 kg and m2 = 74.2 kg, shown in the figure, are free to move. The coefficient of static friction between the blocks is 0.55 but the surface beneath m2 is frictionless. What is the minimum force F required to hold m1 against m2? October 21, 2014 by DD Physics Three blocks rest on a frictionless, horizontal table (see figure below), with m1 = 8 kg and m3 = 20 kg. A horizontal force F = 101 N is applied to block 1, and the acceleration of all three blocks is found to be 3.5 m/s2. Find m2. What is the normal force between blocks 2 and 3? January 25, 2011 by Lauren physics Pleaseee help explain how to draw the free body diagrams for this problem!!! Two blocks with masses m1 = 10.9 kg and m2 = 79.3 kg, shown in the figure (in the figure the 79.3kg block(m2) is on a flat surface, the 10.9kg(m1) block is pinned against the block with the greater ... November 9, 2011 by dave college physics Three blocks of mass 1kg,2kg and 3kg move on a frictionless surface and a horizontal force 46 N acts on the 3kg block.1kg and 2kg blocks are in contact with each other while 1kg and 3kg blocks are connected by a chord. (a) Determine the acceleration of the system (b) Determine... September 21, 2008 by Sandhya physics Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface by a horizontal force . (Figure 1) The magnitude of the tension in the string between blocks B and C is = 3.00 . Assume that each block has mass = 0.400 . Part A What is ... September 29, 2012 by sammy Physics-Mechaincs A force of 23.52 N pushes and pulls to blocks as shown in the figure below. The vertical contact surfaces between the two blocks are frictionless. The contact between the blocks and the horizontal surface has a coefficient of friction of 0.29. The acceleration of gravity is 9.... September 24, 2010 by Genevieve Physics Consider two blocks that are resting one on top of the other. The lower block has mass m2 = 3.5 kg and is resting on a frictionless table. The upper block has mass m1 = 2.7 kg. Suppose the coefficient of static friction between the two blocks is given by μs = 0.5. Part a... October 10, 2013 by Anonymous Physics Three objects are connected as shown in the figure below. They move along a horizontal, frictionless surface, and are pulled to the right with a force Fext = 1.3 N. With the three mass values given as m1 = 726 g, m2 = 633 g, and m3 = 782 g. Calculate the magnitude of the ... October 2, 2009 by Sam Physics Three objects are connected as shown in the figure below. They move along a horizontal, frictionless surface, and are pulled to the right with a force Fext = 2.4 N. With the three mass values given as m1 = 604 g, m2 = 744 g, and m3 = 693 g. Calculate the magnitude of the ... October 6, 2009 by Hannah Physics Three blocks are located on a horizontal frictionless table. They are connected by a massless cord, as shown in the figure, and pulled to the right. The masses of the three blocks are m1 = 22 kg, m2 = 21 kg, and m3 = 33 kg. The pulling force is equal to T3 = 53 N. What is the ... September 23, 2012 by jameson physics Two blocks with masses m1 = 1.10 kg and m2 = 3.10 kg are connected by a massless string, as shown in the Figure (the figure shows m1 on top of a box and m2 hanging off the side of the box). They are released from rest. The coefficent of kinetic friction between the upper block... February 28, 2012 by meyer physics Two blocks with masses m1 = 1.10 kg and m2 = 3.10 kg are connected by a massless string, as shown in the Figure (the figure shows m1 on top of a box and m2 hanging off the side of the box). They are released from rest. The coefficent of kinetic friction between the upper block... February 28, 2012 by meyer PHYSICS Three objects are connected as shown in the figure below. They move along a horizontal, frictionless surface, and are pulled to the right with a force Fext = 2.4 N. With the three mass values given as m1 = 604 g, m2 = 744 g, and m3 = 693 g. Calculate the magnitude of the ... October 6, 2009 by Hannah Physics Two blocks with masses m1 = 1.20 kg and m2 = 2.90 kg are connected by a massless string, as shown in the Figure. They are released from rest. The coefficent of kinetic friction between the upper block and the surface is 0.300. Assume that the pulley has a negligible mass and ... December 2, 2014 by Anonymous physics Two blocks with masses m1 = 1.20 kg and m2 = 2.90 kg are connected by a massless string, as shown in the Figure. They are released from rest. The coefficent of kinetic friction between the upper block and the surface is 0.300. Assume that the pulley has a negligible mass and ... December 2, 2014 by Anonymous Physics Two blocks with masses m1 = 1.40 kg and m2 = 3.00 kg are connected by a massless string, as shown in the Figure. They are released from rest. The coefficent of kinetic friction between the upper block and the surface is 0.390.In the figure m1 is on top of a horizontal table ... March 6, 2013 by Heidi physics Two blocks of mass m1 = 1.2 kg and m2 = 1.7 kg are connected by a massless string, as shown in the Figure. They are released from rest. The coefficent of kinetic friction between the upper block and the surface is 0.45. Calculate the speed of the blocks after they have moved a... December 11, 2007 by anonymous Physics/mats Two blocks with masses m1 = 1.40 kg and m2 = 3.00 kg are connected by a massless string, as shown in the Figure. They are released from rest. The coefficent of kinetic friction between the upper block and the surface is 0.390.In the figure m1 is on top of a horizontal table ... March 7, 2013 by HP Physics Three blocks on a frictionless horizontal surface are in contact with each other A force F is applied to block 1 (m1) Draw a free body diagram for each block ok for the diagram is the force F applied horizontal to mass one does this force act on m2 all the blocks are lines up ... July 11, 2009 by Physics Physics1 Two blocks are initially held at rest on 30° frictionless ramps . The 4 kg block is 1.25 m from the base of the ramp and the 3 kg block is 5 m above the base of the ramp. The two blocks are then released and slide down the ramps and onto a frictionless horizontal surface. The ... November 17, 2009 by Jon Routh Physics Three blocks rest on a frictionless, horizontal table, with m1 = 9 kg and m3 = 16 kg. A horizontal force F = 104 N is applied to block 1, and the acceleration of all three blocks is found to be 3.3 m/s2. 1) Find m2 2)What is the normal force between 2 and 3? September 1, 2011 by Logan physics Two blocks of mass m1 = 1.0 kg and m2 = 2.5 kg are connected by a massless string.M1 is on the surface and mass 2 is hanging on the surface. They are released from rest. The coefficent of kinetic friction between the upper block and the surface is 0.40. Calculate the speed of ... December 4, 2010 by sky Physics Three identical blocks, fastened together by a string, are pulled across a frictionless surface by a constant force. Compare the tension on string A to magnitude of applied force F. August 5, 2010 by Shaila physics Three blocks on a frictionless horizontal surface are in contact with each other. A force F is applied to block A and the blocks start to slide to the right of their initial position. Determine the acceleration of the system, if m_A = 12 kg, m_B = 38 kg, m_C = 4700 g, and F = ... February 21, 2014 by sean Physics Three identical blocks, A, B, and C, are on a horizontal frictionless table. The blocks are connected by strings of negligible mass, with block B between the other two blocks. If block C is pulled horizontally by a force of magnitude F = 28 N, find the tension in the string ... Physics Consider a force F = 815 N pulling 3 blocks of masses m1 = 7.94 kg, m2 = 15.3 kg, and m3 = 32.4 kg along a frictionless horizontal surface. Find the acceleration a of the blocks. Answer in units of m/s2. October 9, 2012 by Priscilla Physics The two blocks (m = 37 kg and M = 109 kg) in the figure below are not attached to each other. The coefficient of static friction between the blocks is µs = 0.55, but the surface beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force ... October 28, 2009 by Jane physics Three blocks on a frictionless surface are connected by massless strings, with M1 = 1.40 kg, M2 = 2.40 kg, and M3 = 3.60 kg. Due to the force F acting on M3, as shown, the system accelerates to the right. Given that T1 is 3.50 N, calculate T2 February 12, 2014 by Carly Physics A 4kg and a 2kg block are moving along a horizontal frictionless surface. The 4 kg block is moving to the right with a speed of 6 m/s and the 2 kg block is moving to the left with a speed of 3 m/s. The two blocks collide inelastically and then continue to move together along ... November 17, 2009 by Jon Routh physics Three blocks are located on a horizontal table. The coefficient of kinetic friction between the blocks and the table is 0.276. They are connected by a massless cord, as shown in the figure below, and pulled to the right. The masses of the three blocks are = 9.0 kg, = 0.5 kg, ... February 13, 2008 by shelby physics Three blocks are located on a horizontal table. The coefficient of kinetic friction between the blocks and the table is 0.276. They are connected by a massless cord, as shown in the figure below, and pulled to the right. The masses of the three blocks are = 9.0 kg, = 0.5 kg, ... February 12, 2008 by shelby physics Two blocks of mass m1 = 1.0 kg and m2 = 2.5 kg are connected by a massless string. They are released from rest. The coefficent of kinetic friction between the upper block and the surface is 0.40. Calculate the speed of the blocks after they have moved a distance 72 cm. Assume ... December 4, 2010 by lucy physics Three blocks are in contact with each other on a frictionless, horizontal surface, as shown below. A horizontal force is applied to m1. Take m1 = 2.00 kg, m2 = 3.00 kg, m3 = 5.00 kg, and F = 22.0 N March 3, 2010 by diamond physics The mass of the heavier block is 28 kg and the mass of the lighter blocks is 14 kg and the magnitude of the force of the connecting string on the smaller block is 24 N. Assume: g = 9.8 m/s^2 and the horizontal surface on which the objects slide is frictionless. Determine the ... September 28, 2012 by michelle Phys Three blocks on a frictionless horizontal surface are in contact with each other. A force F is applied to block A (mass mA). (a) Draw a free body diagram for each block. I've drawn it and it looks like this, but I'm not sure if I'm including everything. ^normal force F-->\|... February 7, 2013 by anonymous physics Two blocks connected by a string are on a horizontal frictionless surface. The blocks are connected to a hanging weight by means of a string that passes over a pulley as shown in the figure below, where m1 = 1.75 kg, m2 = 2.85 kg, and m3 = 4.95 kg. (a) Find the tension T in ... February 8, 2011 by Anonymous physics The masses of blocks A and B are 4.5 kg and 3.7 kg respectively. The blocks are initially at rest and are connected by a massless string passing over a massless, frictionless pulley. The system is released from rest. a. What is the acceleration of the blocks? b. What is the ... November 24, 2013 by Nickoli The masses of blocks A and B are 4.5 kg and 3.7 kg respectively. The blocks are initially at rest and are connected by a massless string passing over a massless, frictionless pulley. The system is released from rest. a. What is the acceleration of the blocks? b. What is the ... November 24, 2013 by Nickoli Physics A block of mass 3m is placed on a frictionless horizontal surface, and a second block of mass m is placed on top of the first block. The surfaces of the blocks are rough. A constant force of magnitude F is applied to the first block as shown in the figure. (a) Construct free-... October 17, 2012 by Brette two blocks of masses m1 and m2 (m1>m2) are placed on a frictionless table in contact with each other. A horizontal force of magnitude F is applied to the block of mass m1. if P is the magnitude of the contact force between the blocks, what are the net forces acting on m1 ... October 11, 2012 by Jack university of redlands Two blocks connected by a string are on a horizontal frictionless surface. The blocks are connected to a hanging weight by means of a string that passes over a pulley as shown in the figure below, where m1 = 1.85 kg, m2 = 2.80 kg, and m3 = 5.05 kg. September 24, 2012 by Anonymous Physics. Really stuck! two blocks of masses m1 and m2 (m1>m2) are placed on a frictionless table in contact with each other. A horizontal force of magnitude F is applied to the block of mass m1. if P is the magnitude of the contact force between the blocks, what are the net forces acting on m1 ... October 8, 2012 by Lindsay Physics The two blocks in the figure, of mass m and M respectively, are not attached, but there is a coefficient of static friction u between them. The surface below the heavier block M is frictionless. What is the minimum force magnitude F required to keep the smaller block m from ... May 16, 2011 by John AP Physics Three blocks of masses 8.2 kg, 5.88 kg, and 2.19 kg are connected by light strings that pass over frictionless pulleys as shown in the ﬁgure. The acceleration of the 5.88 kg block is 2.18 m/s 2 to the left and the surfaces are rough. The acceleration of gravity is 9.8 m... February 5, 2012 by . physics Three blocks are in contact with each other on a frictionless horizontal surface. A 696 N horizontal force is applied to the block with mass of 4.7 kg as shown in the ﬁgure below. The acceleration of gravity is 9.8 m/s 2 . 4.7 kg 5.5 kg 7.1 kg d) What is the magnitude ... October 19, 2012 by Anonymous physics Two blocks, joined by a string, have masses of 6 and 9kg. They rest on frictionless horizontal surface. A 2nd string, attached only to the 9kg block, has a horizontal force = 30N applied to it. Both blocks accelerate. Find the tension in the string between the blocks. October 19, 2008 by Tiffany physics Three blocks are in contact with each other on a frictionless horizontal surface. A 696 N horizontal force is applied to the block with mass of 4.7 kg as shown in the ﬁgure below. The acceleration of gravity is 9.8 m/s 2 . 4.7 kg 5.5 kg 7.1 kg F a) What is the net force... October 19, 2012 by Anonymous physics Three blocks are in contact with each other on a frictionless horizontal surface. A 696 N horizontal force is applied to the block with mass of 4.7 kg as shown in the ﬁgure below. The acceleration of gravity is 9.8 m/s 2 . 4.7 kg 5.5 kg 7.1 kg ) What is the resultant ... October 19, 2012 by Anonymous Physics 2 blocks are in contact on a horizontal table. A force is applied on the first block at a 30* angle. The blocks move to the right side. If m1 = 2kg and m2 = 1kg and F = 6 N kinetic friction at the middle of the 2 blocks and the table = 0.250 Find the "contact force" between ... December 8, 2011 by Tom Physics2 2 blocks are in contact on a horizontal table. A force is applied on the first block at a 30* angle. The blocks move to the right side. If m1 = 2kg and m2 = 1kg and F = 6 N kinetic friction at the middle of the 2 blocks and the table = 0.250 Find the "contact force" between ... December 9, 2011 by Jim Physics A 10 kg block sits on a flat surface whose μs=0.60 and whose μk is 0.40 a. What horizontal force is required to get the block move? b.If we continue to apply the same force as in part a. what will the blocks acceleration be? In the answer: force=.6mg to move net ... August 26, 2012 by Lianne AP physics i really need help on this problem!! Three blocks are connected,on a horizontal frictionless table and pulled to the right with a force T3 = 64.4 N. Assume that m1 = 12.5 kg, m2 = 25.0 kg, and m3 = 31.7 kg. (a) Calculate the acceleration of the system (b)Calculate the tensions... September 24, 2010 by annamaria College physics (simple) Two blocks (one on top of the other), each of mass m = 2.4 kg, are pushed along the horizontal surface of a table by a horizontal force P of magnitude 6.8 N, directed to the right. The blocks move together to the right at constant velocity. (a) Find the frictional force ... September 27, 2011 by Kellie College physics (simple) Two blocks (one on top of the other), each of mass m = 2.4 kg, are pushed along the horizontal surface of a table by a horizontal force P of magnitude 6.8 N, directed to the right. The blocks move together to the right at constant velocity. (a) Find the frictional force ... September 27, 2011 by Kellie Physics Two blocks (on top of one another), each of mass m = 2.4 kg, are pushed along the horizontal surface of a table by a horizontal force of magnitude 6.8 N, directed to the right. The blocks move together to the right at constant velocity. (a) Find the frictional force exerted on... September 27, 2011 by Kellie Physics Three blocks are in contact with each other on a frictionless horizontal surface. A 417 N horizontal force is applied to the block with mass of 3.7 kg as shown in the ﬁgure below. The acceleration of gravity is 9.8 m/s^2. (the picture looks like this) F ----->[3.7 ... November 16, 2012 by alice physical three blocks,each with same mass, stacked one upon the other. the bottom block rest on a frictionlesshorizontal surface and is being pulled by a force F that is parrallel to this surface.the surface where the blocks touch each other have identical coefficients of static ... July 26, 2012 by nkosingiphile Physics HELP Two blocks having mass m1 = 6 kg(m1 on ramp of 30 degrees) and m2 =3 kg are connected by a light rope and slide on a frictionless surface as in the figure below. A force F = 10 N acts on m2 at 20 degrees relative the horizontal. Find the acceleration of the system and the ... October 7, 2014 by Sabrina Physics "Two wooden blocks A and B have respective masses of 3.0kg and 4.0kg and are connected with an inextensible cord. If the blocks are placed on a horizontal frictionless surface and a force of 8.0N is applied to A, find the tension in the connecting cord." July 28, 2010 by Stuck Physics Two metal blocks are attached by a cable as shown in the figure below and are submerged at rest near the surface of a lake. If the volumes are V1 = 2.1 m3 and V2 = 1.1 m3, what is the total buoyant force on the two blocks? July 25, 2012 by Sierra physics The figure below shows an object of mass M = 1,276 g. It is free to move along a horizontal, frictionless surface. This object is further connected to a second object with a mass of m = 1,362 g by means of a massless string that extends around a massless, frictionless pulley. ... October 10, 2009 by m2a Physics Two blocks (M1 = 2.57 kg and M2 = 6.71 kg) are in contact on a frictionless, horizontal tabletop. An external force, $\vec{F}$, is applied to block 1, and the two blocks are moving with a constant acceleration of 2.59 m/s2. What is the contact force between the blocks? What is... September 22, 2013 by Lyra Physics Two blocks of masses 40.0kg and 20.0kg are stacked on a table with the heavier block on top. The coefficient of static friction is 0.600 between the top and bottom blocks and 0.300 between the bottom block and the table. What is the required magnitude of a horizontal force ... October 31, 2006 by Eric physics A,horizontial,force,of,40N,actingon,a,block,of,frictionless,level,surface,produces,an,acceleration,of,2.5m/s^2.A,second,block,with,a,mass,of,4.0kg,is,dropped,onto,the,first,.What,is,the,magnitude,of,acceleration,of,the,combination,of,blocks,if,the,same,force,continues,to,act... January 19, 2008 by melissa Physics 1. Two blocks on a frictionless horizontal surface are connected by a light string. where m1 = 6.21 kg and m2 = 19.5 kg. A force of 48.4 N 6.21kg --T-- 19.5kg ----->48.4 N The acceleration of gravity is 9.8 m/s^2. Find the acceleration of the system. Answer in units of m/s^... Physics 1. Two blocks on a frictionless horizontal surface are connected by a light string. where m1 = 6.21 kg and m2 = 19.5 kg. A force of 48.4 N 6.21kg --T-- 19.5kg ----->48.4 N The acceleration of gravity is 9.8 m/s^2. Find the acceleration of the system. Answer in units of m/s^... March 6, 2014 by Fabricus Physics A small bug is nestled between a 1-kg block and a 2-kg block on a frictionless table. A horizontal force can be applied to either of the blocks as shown in figure Q5.24 (i) In which situation illustrated in the figure (a) or (b), does the bug have a better chance of survival, ... September 18, 2012 by Avery Physics Three blocks on a frictionless horizontal surface are in contact with each other, as shown below. A force F is applied to block A (mass mA). (a) Draw a free-body diagram for each block. Determine (b) the acceleration of the system (in terms of mA, mB, mC), (c) the net force on... October 22, 2010 by Anonymous Physics Ok I got a question I asked before except there are other parts that I didn't ask so here we go Three blocks on a frictionless horizontal surface are in contact with each other A force F is applied to block 1 (mass m1). Draw a free-body diagram for each block ok I did this the... July 12, 2009 by Physics Physics A block of mass m1 = 41.3 kg on a horizontal surface is connected to a mass m2 = 13.2 kg that hangs vertically as shown in the figure below. The two blocks are connected by a string of negligible mass passing over a frictionless pulley. Assume that the horizontal surface is ... October 27, 2014 by alex Physics A 4 kg block resting on a horizontal surface is attached to an 8 kg block that hangs freely by a cord passing over a frictionless pulley. The coefficient of kinetic friction between the block and the horizontal surface is 0.4. Find the acceleration of the blocks and the ... November 18, 2006 by Vv Physics The two blocks (m = 13 kg and M = 89 kg) are not attached to each other. The coefficient of static friction between the blocks is μs = 0.50, but the surface beneath the larger block is frictionless. What is the minimum magnitude of the horizontal force (F) required to ... October 10, 2010 by Alaina physics Two blocks of masses m1 = 4.00 kg and m2 = 3.00 kg are placed in contact with each other on a frictionless horizontal surface. A constant force F = 9.00 N is applied to the block of mass m1. a) Determine the magnitude of the acceleration of the two-block system. b) Determine ... February 11, 2012 by michael Physics In the figure below, assume that the slope is frictionless and that the two blocks are connected by a massless cord. Assume the following: θ1 = 37° θ2 = 45° m1=3kg m2=0.86kg. What is the tension in the cord?. February 29, 2012 by Ariel phy Three blocks are suspended at rest by the system of strings and frictionless pulleys shown in the figure below, where W = 29.0 N, and è = 26.6°. What are the weights w1 and w2? October 25, 2012 by anthony physics Three blocks are suspended at rest by the system of strings and frictionless pulleys shown in the figure below, where W = 29.0 . What are the weights w1 and w2? October 25, 2012 by anthony A 3.0kg- block sits on top of a 5.0kg block which is on a horizontal surface. The 5.0-kg block is pulled to the right with a force as shown in the figure . The coefficient of static friction between all surfaces is 0.65 and the kinetic coefficient is 0.42. PART A: What is the ... May 8, 2012 by jeni A 3.0kg- block sits on top of a 5.0kg block which is on a horizontal surface. The 5.0-kg block is pulled to the right with a force as shown in the figure . The coefficient of static friction between all surfaces is 0.65 and the kinetic coefficient is 0.42. PART A: What is the ... May 8, 2012 by jeni college physics Two blocks of masses m1 = 4.00 kg and m2 = 3.00 kg are placed in contact with each other on a frictionless horizontal surface. A constant force F = 9.00 N is applied to the block of mass m1. a) Determine the magnitude of the acceleration of the two-block system. b) Determine ... February 11, 2012 by lacrosse Physics The builders of the Great Pyramids of Egypt are thought to have used ramps to move the large 20,000 kg (22 ton) stone blocks into place at the construction site. To reduce friction, the Egyptians are assumed to have used rollers between the ramp and each block, enabling the ... June 23, 2013 by Anonymous physics A block of mass 4.0 kg is put on top of a block of mass M = 6.0 kg. To cause the top block to slip on the bottom one, while the bottom one is held fixed, a horizontal force of at least 19 N must be applied to the top block. The assembly of blocks is now placed on a horizontal... February 18, 2010 by tripp Physics Block B has a mass of 4.2 kg and block A has a mass of 2.6 kg. They are in contact and slide over a frictionless horizontal surface. A force of 11 N acts on B.(force applied on block b then block a , they are beside each other) what is the force on B due to A if the blocks are... October 6, 2014 by Sabrina physics Two blocks are pushed along a horizontal frictionless surface by a force of 20 newtons to the right. The force acts on the 3 kg block, which in turn pushes the 2kg block sitting next to it. The force that the 2-kilogram block exerts on the 3-kilogram block is...... January 20, 2008 by Hannah physics The two blocks in the sketch are connected by a light cord over a frictionless pulley and are initially held in place. The block m1 has a mass of 2,00 kg and m2 has a mass of 3,00 kg. The inclined plane is frictionless and the coefficient of kinetic friction between block m1 ... June 8, 2014 by Lysha Math Two blocks of mass 0.1 kg and 0.2 kg approach each other on a frictionless surface at velocities of 0.4 and 1 m/s respectively. If the blocks collide and remain together, calculate their joint velocity after the collision. April 13, 2014 by Nam-kung hoon physics Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them as shown in the figure below. A cord initially holding the blocks together is burned; ... January 23, 2011 by Jackie physics Two blocks of masses M and 3M are placed on a horizontal, frictionless surface. A light spring is attached to one of them, and the blocks are pushed together with the spring between them as shown in the figure below. A cord initially holding the blocks together is burned; ... January 23, 2011 by Jackie physics A 4.0 kg block is put on top of a 5.0 kg block. To cause the top block to slip on the bottom one while the bottom one is held fixed, a horizontal force of at least 16 N must be applied to the top block. The assembly of blocks is now placed on a horizontal, frictionless table... Physics. A block of mass 3m is placed on a frictionless horizontal surface, and a second block of mass m is placed on top of the first block. The surfaces of the blocks are rough. A constant force of magnitude F is applied to the first block. a) Identify the horizontal force that ... October 16, 2012 by Kelsey Physics Two blocks, with masses M1 = 1.4 kg and M2 = 9.9 kg, and a spring with spring constant k = 228 N/m are arranged on a horizontal, frictionless surface. The coefficient of static friction between the two blocks is 0.59. What is the maximum possible amplitude of the simple ... April 27, 2008 by help? AP PHYSICS MECH. In Figure 9-62, block 2 (mass 1.3 kg) is at rest on a frictionless surface and touching the end of an unstretched spring of spring constant 160 N/m. The other end of the spring is fixed to a wall. Block 1 (mass 2.1 kg), traveling at speed v1 = 4.0 m/s, collides with block 2, ... February 14, 2011 by vm Physics Blocks of mass 4, 8, and 24 kg are lined up from left to right in that order on a frictionless surface so each block is touching the next one. A rightward-pointing force of magnitude 15 N is applied to the left-most block. Suppose now that the left-right order of the blocks is... February 20, 2011 by Raji physics three identical blocks are pulled on a horizontal frictionless surface. if the tension in the rope held by the habd is 30N what is the tension in the other ropes? February 2, 2011 by joy physics A 3.0kg- block sits on top of a 5.0kg block which is on a horizontal surface. The 5.0-kg block is pulled to the right with a force as shown in the figure . The coefficient of static friction between all surfaces is 0.65 and the kinetic coefficient is 0.42. Part a: What is the ... May 8, 2012 by kle Physics Two blocks are in contact on a frictionless table. A horizontal force F is applied to M2, as shown. If M1 = 1.06 kg, M2 = 3.80 kg, and F = 4.85 N, find the size of the contact force between the two blocks. If instead an equal but oppositely directed force is applied to M1 ... May 20, 2013 by Kayleigh Physics Two blocks are in contact on a frictionless table. A horizontal force F is applied to M2, as shown. If M1 = 1.06 kg, M2 = 3.80 kg, and F = 4.85 N, find the size of the contact force between the two blocks. If instead an equal but oppositely directed force is applied to M1 ... May 20, 2013 by Kayleigh Pages: 1 \| 2 \| 3 \| 4 \| 5 \| 6 \| 7 \| 8 \| 9 \| 10 \| 11 \| 12 \| 13 \| 14 \| 15 \| Next>> Members	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8822792768478394, "perplexity": 372.8107553540607}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422122034298.3/warc/CC-MAIN-20150124175354-00059-ip-10-180-212-252.ec2.internal.warc.gz"}
http://physics.stackexchange.com/questions/12258/why-is-pseudorapidity-defined-as-log-tan-theta-2/12259	# Why is pseudorapidity defined as $-\log \tan \theta/2$ Why the log? Is it there to make the growth of the function slower? As this is a common experimental observable, it doesn't seem reasonable to take the range from $[0,\infty)$ to $(-\infty,\infty)$ (For a particle emitted along the beam axis after collision $\theta = 0$ wouldn't be better to have a number that says how close it is to zero rather than one that says how large a number it is. I hope that makes the question clear.) - The advantage of this particular definition is that differences in pseudorapidity are invariant under boosts along the $z$ axis. Specifically, consider a Lorentz transformation corresponding to a boost by velocity $\beta\hat{z}$. Since the tangent is basically a transverse distance over a longitudinal distance, it transforms under a Lorentz boost along the longitudinal axis with a factor $\gamma$: $$\tan\phi \sim\frac{\Delta x_T}{\Delta x_L} \qquad\to\qquad \tan\phi' = \frac{\Delta x_T}{\Delta x_L/\gamma} = \gamma\tan\phi$$ and if you put that in the pseudorapidity formula, you find $$\eta = -\log\biggl(\tan\frac{\theta}{2}\biggr) \qquad\to\qquad \eta' = -\log\biggl(\tan\frac{\theta}{2}\biggr) - \log\gamma$$ The first term is a function of the particle's trajectory, but the second term is a function of the boost parameter only - it doesn't depend on the particle at all. So if you have two particles coming out of a collision with pseudorapidities $\eta_1$ and $\eta_2$, the $\log\gamma$ term is the same for both, and thus when you take the difference it cancels out: $$\eta_1 - \eta_2 = \eta_1' - \eta_2'$$ The reason why it's so important to keep the pseudorapidity difference invariant is that in particle physics, people like to make plots called "lego plots" which show the directional distribution of the particles detected after a collision. When you do this, you could plot the particle detections vs. the polar and azimuthal angles $\theta$ and $\phi$. But if you use pseudorapidity instead of the angle $\theta$, the fact that $\Delta\eta$ is invariant means that you can perform a Lorentz boost on your data by just translating the whole graph along the $\eta$ axis. This is useful because in hadron collisions, it's often the case that one of the individual quarks or gluons involved in the collision may have a lot more momentum than the other, so all the particles produced come out near one end of the detector. But by translating the graph appropriately, you can effectively shift to the center-of-mass frame of the colliding quarks or gluons, where the particles come out symmetrically distributed, and it's a lot easier to analyze. By the way, the reason it's $\tan\frac{\theta}{2}$ rather than just $\tan\theta$ is that we'd like a jet which comes out of the collision at $\theta \approx \frac{\pi}{2}$, where the resolution is best, to have the same shape in the lego plot as it does in physical space. In particular, a circular jet should appear circular on the graph. This requires that the two coordinates be scaled the same way. If we were using $(\theta,\phi)$ as the directional coordinates, this wouldn't be a problem, since both are measured in radians, so we just need to choose a scaling for $\eta$ such that a small increment in $\theta$ near $\frac{\pi}{2}$ corresponds to the same numerical increment in $\eta$: $$\biggl\|\frac{\mathrm{d}\eta}{\mathrm{d}\theta}\biggr\|\biggl(\theta=\frac{\pi}{2}\biggr) = 1$$ The argument in the first part of the post (along with some common-sense conditions) basically requires that psuedorapidity be defined as $$\eta = -\log(\tan a\theta)$$ for some constant $a$. Plugging into the derivative gives $$\biggl\|\frac{\mathrm{d}\eta}{\mathrm{d}\theta}\biggr\|_{\frac{\pi}{2}} = \biggl\|\frac{a\,\sec^2(a\theta)}{\tan(a\theta)}\biggr\|_{\frac{\pi}{2}} = \biggl\|\frac{a}{\sin(a\theta)\cos(a\theta)}\biggr\|_{\frac{\pi}{2}} = \frac{2a}{\sin(2a\pi/2)} = 1$$ (I'm abusing the notation a bit by using vertical bars for both absolute value and substitution, but hopefully the meaning is clear.) This is a transcendental equation, so you can't solve it analytically, but with a little mathematical reasoning it's not hard to convince yourself that $a = \pm\frac{1}{2}$ are the only nonzero solutions. Having a negative argument to a logarithm brings in an extra imaginary term, though it would cancel out anyway, so we might as well choose the positive one. - Thanks a lot, David. This is a great answer. I had been looking for an involved experimental perspective as well and this is better than most stuff I read. – yayu Jul 15 '11 at 5:42 Oh god.. I remember stressing over this one when I started in particle physics. :) Regarding the use of the log: This is just a hyperbolic trig thing. First write down the pseudorapidity using momenta perpendicular and parallel to the beam line like they do in the second expression here: http://en.wikipedia.org/wiki/Pseudorapidity Then use the inverse hyperbolic identities you find here: http://en.wikipedia.org/wiki/Hyperbolic_cosine and you can get back to the angle. Regarding it's use as an experimental observable: There are two reasons high energy guys prefer to use it (from wikipedia): • Pseudorapidity depends only on the polar angle of its trajectory, and not on the energy of the particle. (nice sometimes when you're comparing data from one detector to the next) • In hadron collider physics, the rapidity (or pseudorapidity) is preferred over the polar angle θ because, loosely speaking, particle production is constant as a function of rapidity. One speaks of the "forward" direction in a hadron collider experiment, which refers to regions of the detector that are close to the beam axis, at high \| η \| . -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9216017127037048, "perplexity": 256.3138831142269}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-41/segments/1412037663218.28/warc/CC-MAIN-20140930004103-00490-ip-10-234-18-248.ec2.internal.warc.gz"}
https://www.physicsforums.com/threads/help-distance-between-mu-lep-nihal.26821/	# Help! Distance between Mu lep & Nihal? 1. May 21, 2004 ### MonstersFromTheId "Dammit Jim! I'm a writer, not a stellar cartographer!" Doin some homework for a SF story. I badly need to know the approximate distance between Mu Leporis and Nihal. Also useful: Distance from Sol to Mu Lep, distance from Sol to Nihal, warnings about any known odd ball physical effects or interstellar objects between Mu Lep and Nihal that shouldn't be overlooked in a chapter covering a trip between those two stars. My impression is that there's no reason to expect a trip between Nihal and Mu Lep would involve passing through any known physical obstacles, that left uncovered in such a story, could quickly get my :-) "undying prose" covered by the remains of a knowledgeable reader’s lunch Tx in advance for any help... Monsters 2. May 22, 2004 ### Ahmes been there lately? Nihal (Beta Leporis) is about 172 lightyears away from us. Mu Leporis is 175 lightyears away, but not exactly in the same direction. If you want to know the approximate distance between these two stars, then it will be a bit harder to compute. 3. May 22, 2004 ### Ahmes lucky for you i have a math test soon... The two stars should be 17.83 lightyears apart (drop the .83, it's not accurate anyway)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.887833297252655, "perplexity": 3720.557788457277}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646636.25/warc/CC-MAIN-20180319081701-20180319101701-00076.warc.gz"}
https://ramp.studio/problems/MNIST_simplified	MNIST classification Current events on this problem Keywords MNIST_simplified_starting_kit # Paris Saclay Center for Data ScienceÂ¶ ## RAMP MNIST handwritten digit classificationÂ¶ Mehdi Cherti (CNRS), Balázs Kégl (CNRS) ## DataÂ¶ The goal of this RAMP is to classify correctly handwritten digits. For each submission, you will have to provide an image classifier (versus the original setup that required a transformer and a batch classifier). The images are usually big so loading them into the memory at once may be impossible. The image classifier therefore will access them through an img_loader function which can load one image at a time. ## HintsÂ¶ Setting up an AWS instance is easy, just follow this tutorial. For learning the nuts and bolts of convolutional nets, we suggest that you follow Andrej Karpathy’s excellent course. In [1]: import os import numpy as np import pandas as pd from sklearn.model_selection import StratifiedShuffleSplit from sklearn.metrics import accuracy_score import matplotlib.pyplot as plt from mpl_toolkits.axes_grid1 import AxesGrid from matplotlib import cm %matplotlib inline pd.set_option('display.max_rows', 500) # The dataÂ¶ If the images are not yet in data/imgs, change the type of the net cell to "Code" and run it. In [2]: df = pd.read_csv('data/train.csv') X_df = df['id'] y_df = df['class'] X = X_df.values y = y_df.values The class distribution is balanced. In [3]: labels_counts_df = df.groupby('class').count() labels_counts_df Out[3]: id class 0 4742 1 5370 2 4795 3 4914 4 4675 5 4337 6 4709 7 4998 8 4707 9 4753 It is worthwhile to look at some image panels, grouped by label. In [4]: nb_rows = 4 nb_cols = 4 nb_elements = nb_rows * nb_cols label = 8 df_given_label = df[df['class']==label] subsample = np.random.choice(df_given_label['id'], replace=False, size=nb_elements) fig = plt.figure(figsize=(4, 4)) grid = AxesGrid(fig, 111, # similar to subplot(141) nrows_ncols = (nb_rows, nb_cols), label_mode = "1", ) for i, image_id in enumerate(subsample): filename = 'data/imgs/{}'.format(image_id) im = grid[i].imshow(image, cmap='Greys', interpolation='nearest') grid[i].axis('off') plt.tight_layout() /Users/kegl/anaconda/lib/python2.7/site-packages/matplotlib/figure.py:1999: UserWarning: This figure includes Axes that are not compatible with tight_layout, so results might be incorrect. warnings.warn("This figure includes Axes that are not compatible " All images have size 28 $\times$ 28. In [5]: image.shape Out[5]: (28, 28) In [6]: n_subsample = 1000 shapes = np.empty((n_subsample, 2)) for i, image_id in enumerate(X_df[:n_subsample]): filename = 'data/imgs/{}'.format(image_id) shapes[i] = image.shape In [7]: shapes_df = pd.DataFrame(shapes, columns=['height', 'width']) shapes_df['count'] = 0 shapes_df.groupby(['height', 'width']).count().sort_values('count', ascending=False) Out[7]: count height width 28.0 28.0 1000 In [8]: shapes_df['height'].hist() Out[8]: <matplotlib.axes._subplots.AxesSubplot at 0x1c165c6090> # Image preprocessingÂ¶ In the first workflow element image_preprocessor.py you can resize, crop, or rotate the images. This is an important step. Neural nets need standard-size images defined by the dimension of the input layer. MNIST images are centered and resized, so these operations are unlikely to be useful but rotation may help. In [9]: filename = 'data/imgs/{}'.format(X_df[161]) plt.imshow(image, cmap='Greys', interpolation='nearest') plt.show() Here we resize the images to different resolutions, then blow them up so the difference can be visible. In [10]: from skimage.transform import resize nb_rows = 1 nb_cols = 2 nb_elements = nb_rows * nb_cols fig = plt.figure(figsize=(4, 4)) grid = AxesGrid(fig, 111, # similar to subplot(141) nrows_ncols = (nb_rows, nb_cols), label_mode = "1", ) grid[0].imshow( resize(resize(image, (16, 16)), (224, 224), order=0), cmap='Greys', interpolation='nearest') grid[0].axis('off') grid[1].imshow( resize(resize(image, (8, 8)), (224, 224), order=0), cmap='Greys', interpolation='nearest') grid[1].axis('off') plt.tight_layout() /Users/kegl/anaconda/lib/python2.7/site-packages/skimage/transform/_warps.py:84: UserWarning: The default mode, 'constant', will be changed to 'reflect' in skimage 0.15. warn("The default mode, 'constant', will be changed to 'reflect' in " Here we rotate the image. Explore options in skimage. In [11]: from skimage.transform import rotate nb_rows = 1 nb_cols = 4 nb_elements = nb_rows * nb_cols fig = plt.figure(figsize=(10, 10)) grid = AxesGrid(fig, 111, # similar to subplot(141) nrows_ncols = (nb_rows, nb_cols), label_mode = "1", ) grid[0].imshow(rotate(image, 30), cmap='Greys', interpolation='nearest') grid[0].axis('off') grid[1].imshow(rotate(image, 45), cmap='Greys', interpolation='nearest') grid[1].axis('off') grid[2].imshow(rotate(image, 60), cmap='Greys', interpolation='nearest') grid[2].axis('off') grid[3].imshow(rotate(image, 75), cmap='Greys', interpolation='nearest') grid[3].axis('off') plt.tight_layout() All these tansformations should be implemented in the transform function found in the image_preprocessor workflow element that you will submit. ## The pipelineÂ¶ For submitting at the RAMP site, you will have to write a single ImageClassifier class implementing a fit and a predict_proba function. Note that the following code cells are not executed in the notebook. The notebook saves their contents in the file specified in the first line of the cell, so you can edit your submission before running the local test below and submitting it at the RAMP site. ### The starting kit image classifierÂ¶ The starting kit implements a simple keras neural net. Since MNIST is a small set of small images, we can actually load them into the memory. MNIST contains well-centered and aligned images so _transform only needs to scale the pixels into [0, 1]. In [18]: %%file submissions/starting_kit/image_classifier.py import numpy as np from keras.models import Model from keras.layers import Input from keras.layers import Dense from keras.layers import Flatten from keras.optimizers import SGD class ImageClassifier(object): def __init__(self): inp = Input((28, 28, 1)) x = Flatten(name='flatten')(inp) x = Dense(100, activation='relu', name='fc1')(x) out = Dense(10, activation='softmax', name='predictions')(x) self.model = Model(inp, out) self.model.compile( loss='categorical_crossentropy', optimizer=SGD(lr=1e-4), metrics=['accuracy']) def _transform(self, x): # adding channel dimension at the last position x = np.expand_dims(x, axis=-1) # bringing input between 0 and 1 x = x / 255. return x # load the full data into memory # make a 4D tensor: # number of images x width x height x number of channels X = np.zeros((nb, 28, 28, 1)) # one-hot encoding of the labels to set NN target Y = np.zeros((nb, 10)) for i in range(nb): X[i] = self._transform(x) # since labels are [0, ..., 9], label is the same as label index Y[i, y] = 1 self.model.fit(X, Y, batch_size=32, validation_split=0.1, epochs=1) X = np.zeros((nb, 28, 28, 1)) for i in range(nb): return self.model.predict(X) Overwriting submissions/starting_kit/image_classifier.py ### A simple keras convnetÂ¶ In [19]: %%file submissions/keras_convnet/image_classifier.py import numpy as np from keras.models import Model from keras.layers import Input from keras.layers import Dense from keras.layers import Conv2D from keras.layers import MaxPooling2D from keras.layers import Flatten class ImageClassifier(object): def __init__(self): inp = Input((28, 28, 1)) # Block 1 x = Conv2D( name='block1_conv1')(inp) x = Conv2D( name='block1_conv2')(x) x = MaxPooling2D( (2, 2), strides=(2, 2), name='block1_pool')(x) # dense x = Flatten( name='flatten')(x) x = Dense( 512, activation='relu', name='fc1')(x) out = Dense(10, activation='softmax', name='predictions')(x) self.model = Model(inp, out) self.model.compile( loss='categorical_crossentropy', metrics=['accuracy']) def _transform(self, x): # adding channel dimension at the last position x = np.expand_dims(x, axis=-1) # bringing input between 0 and 1 x = x / 255. return x # load the full data into memory # make a 4D tensor: # number of images x width x height x number of channels X = np.zeros((nb, 28, 28, 1)) # one-hot encoding of the labels to set NN target Y = np.zeros((nb, 10)) for i in range(nb): X[i] = self._transform(x) # since labels are [0, ..., 9], label is the same as label index Y[i, y] = 1 self.model.fit(X, Y, batch_size=32, validation_split=0.1, epochs=1) X = np.zeros((nb, 28, 28, 1)) for i in range(nb): return self.model.predict(X) Overwriting submissions/keras_convnet/image_classifier.py ### The same keras convnet using generatorsÂ¶ In [21]: %%file submissions/keras_generator/image_classifier.py import numpy as np from keras.models import Model from keras.layers import Input from keras.layers import Dense from keras.layers import Flatten from rampwf.workflows.image_classifier import get_nb_minibatches class ImageClassifier(object): def __init__(self): inp = Input((28, 28, 1)) x = Flatten(name='flatten')(inp) x = Dense(100, activation='relu', name='fc1')(x) out = Dense(10, activation='softmax', name='predictions')(x) self.model = Model(inp, out) self.model.compile( loss='categorical_crossentropy', metrics=['accuracy']) self.batch_size = 64 np.random.seed(24) nb_train = int(nb * 0.9) nb_valid = nb - nb_train indices = np.arange(nb) np.random.shuffle(indices) ind_train = indices[0:nb_train] ind_valid = indices[nb_train:] gen_train = self._build_train_generator( indices=ind_train, batch_size=self.batch_size, shuffle=True ) gen_valid = self._build_train_generator( indices=ind_valid, batch_size=self.batch_size, shuffle=True ) self.model.fit_generator( gen_train, steps_per_epoch=get_nb_minibatches(nb_train, self.batch_size), epochs=1, max_queue_size=16, workers=1, use_multiprocessing=True, validation_data=gen_valid, validation_steps=get_nb_minibatches(nb_valid, self.batch_size), verbose=1 ) return self.model.predict_generator( gen_test, steps=get_nb_minibatches(nb_test, self.batch_size), max_queue_size=16, workers=1, use_multiprocessing=True, verbose=0 ) shuffle=False): indices = indices.copy() nb = len(indices) X = np.zeros((batch_size, 28, 28, 1)) Y = np.zeros((batch_size, 10)) while True: if shuffle: np.random.shuffle(indices) for start in range(0, nb, batch_size): stop = min(start + batch_size, nb) # load the next minibatch in memory. # The size of the minibatch is (stop - start), # which is batch_size for the all except the last # minibatch, which can either be batch_size if # nb is a multiple of batch_size, or nb % batch_size. bs = stop - start Y[:] = 0 for i, img_index in enumerate(indices[start:stop]): x = self._transform(x) X[i] = x Y[i, y] = 1 yield X[:bs], Y[:bs] X = np.zeros((batch_size, 28, 28, 1)) while True: for start in range(0, nb, batch_size): stop = min(start + batch_size, nb) # load the next minibatch in memory. # The size of the minibatch is (stop - start), # which is batch_size for the all except the last # minibatch, which can either be batch_size if # nb is a multiple of batch_size, or nb % batch_size. bs = stop - start for i, img_index in enumerate(range(start, stop)): x = self._transform(x) X[i] = x yield X[:bs] def _transform(self, x): x = np.expand_dims(x, axis=-1) x = x / 255. return x Overwriting submissions/keras_generator/image_classifier.py ### A simple pytorch convnetÂ¶ In [10]: %%file submissions/pytorch_convnet/image_classifier.py from __future__ import division import time import math import numpy as np import torch import torch.nn as nn import torch.optim as optim is_cuda = torch.cuda.is_available() def _make_variable(X): variable = Variable(torch.from_numpy(X)) if is_cuda: variable = variable.cuda() return variable def _flatten(x): return x.view(x.size(0), -1) class Net(nn.Module): def __init__(self): super(Net, self).__init__() self.block1 = nn.Sequential( nn.ReLU(inplace=True), nn.ReLU(inplace=True), nn.MaxPool2d(kernel_size=2, stride=2) ) self.fc = nn.Sequential( nn.Linear(32 * 14 * 14, 512), nn.ReLU(True), nn.Linear(512, 10), ) self._initialize_weights() def forward(self, x): x = self.block1(x) x = _flatten(x) x = self.fc(x) return x def _initialize_weights(self): # Source: https://github.com/pytorch/vision/blob/master/torchvision/ # models/vgg.py for m in self.modules(): if isinstance(m, nn.Conv2d): n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels m.weight.data.normal_(0, math.sqrt(2. / n)) if m.bias is not None: m.bias.data.zero_() elif isinstance(m, nn.Linear): n = m.weight.size(1) m.weight.data.normal_(0, 0.01) m.bias.data.zero_() class ImageClassifier(object): def __init__(self): self.net = Net() if is_cuda: self.net = self.net.cuda() def _transform(self, x): # adding channel dimension at the first position x = np.expand_dims(x, axis=0) # bringing input between 0 and 1 x = x / 255. return x def _get_acc(self, y_pred, y_true): y_pred = y_pred.cpu().data.numpy().argmax(axis=1) y_true = y_true.cpu().data.numpy() return (y_pred == y_true) n_minibatch_images = len(indexes) X = np.zeros((n_minibatch_images, 1, 28, 28), dtype=np.float32) # one-hot encoding of the labels to set NN target y = np.zeros(n_minibatch_images, dtype=np.int) X[i] = self._transform(x) # since labels are [0, ..., 9], label is the same as label index X = _make_variable(X) y = _make_variable(y) return X, y n_minibatch_images = len(indexes) X = np.zeros((n_minibatch_images, 1, 28, 28), dtype=np.float32) X[i] = self._transform(x) X = _make_variable(X) return X validation_split = 0.1 batch_size = 32 nb_epochs = 1 lr = 1e-4 criterion = nn.CrossEntropyLoss().cuda() if is_cuda: criterion = criterion.cuda() for epoch in range(nb_epochs): t0 = time.time() self.net.train() # train mode nb_trained = 0 train_loss = [] train_acc = [] n_images = len(img_loader) * (1 - validation_split) i = 0 while i < n_images: indexes = range(i, min(i + batch_size, n_images)) i += len(indexes) # zero-out the gradients because they accumulate by default y_pred = self.net(X) loss = criterion(y_pred, y) optimizer.step() # update params # Loss and accuracy train_acc.extend(self._get_acc(y_pred, y)) train_loss.append(loss.data[0]) nb_trained += X.size(0) if nb_updates % 100 == 0: print( 'Epoch [{}/{}], [trained {}/{}], avg_loss: {:.4f}' ', avg_train_acc: {:.4f}'.format( epoch + 1, nb_epochs, nb_trained, n_images, np.mean(train_loss), np.mean(train_acc))) self.net.eval() # eval mode valid_acc = [] while i < n_images: indexes = range(i, min(i + batch_size, n_images)) i += len(indexes) y_pred = self.net(X) valid_acc.extend(self._get_acc(y_pred, y)) delta_t = time.time() - t0 print('Finished epoch {}'.format(epoch + 1)) print('Time spent : {:.4f}'.format(delta_t)) print('Train acc : {:.4f}'.format(np.mean(train_acc))) print('Valid acc : {:.4f}'.format(np.mean(valid_acc))) # We need to batch load also at test time batch_size = 32 i = 0 y_proba = np.empty((n_images, 10)) while i < n_images: indexes = range(i, min(i + batch_size, n_images)) i += len(indexes) y_proba[indexes] = nn.Softmax()(self.net(X)).cpu().data.numpy() return y_proba Overwriting submissions/pytorch_convnet/image_classifier.py In [20]: %%file submissions/pytorch_convnet_parallel/image_classifier.py from __future__ import division import time import math import numpy as np import torch import torch.nn as nn import torch.optim as optim is_cuda = torch.cuda.is_available() def _make_variable(X): variable = Variable(torch.from_numpy(X)) if is_cuda: variable = variable.cuda() return variable def _flatten(x): return x.view(x.size(0), -1) class Net(nn.Module): def __init__(self): super(Net, self).__init__() self.block1 = nn.Sequential( nn.ReLU(inplace=True), nn.ReLU(inplace=True), nn.MaxPool2d(kernel_size=2, stride=2) ) self.fc = nn.Sequential( nn.Linear(32 * 14 * 14, 512), nn.ReLU(True), nn.Linear(512, 10), ) self._initialize_weights() def forward(self, x): x = self.block1(x) x = _flatten(x) x = self.fc(x) return x def _initialize_weights(self): # Source: https://github.com/pytorch/vision/blob/master/torchvision/ # models/vgg.py for m in self.modules(): if isinstance(m, nn.Conv2d): n = m.kernel_size[0] * m.kernel_size[1] * m.out_channels m.weight.data.normal_(0, math.sqrt(2. / n)) if m.bias is not None: m.bias.data.zero_() elif isinstance(m, nn.Linear): n = m.weight.size(1) m.weight.data.normal_(0, 0.01) m.bias.data.zero_() class ImageClassifier(object): def __init__(self): self.net = Net() if is_cuda: self.net = self.net.cuda() def _transform(self, x): # adding channel dimension at the first position x = np.expand_dims(x, axis=0) # bringing input between 0 and 1 x = x / 255. return x def _get_acc(self, y_pred, y_true): y_pred = y_pred.cpu().data.numpy().argmax(axis=1) y_true = y_true.cpu().data.numpy() return (y_pred == y_true) transforms = [{'name': 'rotate', 'l_angle': -30, 'u_angle': 30}] X = np.array([self._transform(x) for x in X], dtype=np.float32) X = _make_variable(X) y = np.array(y) y = _make_variable(y) return X, y X = np.array([self._transform(x) for x in X], dtype=np.float32) X = _make_variable(X) return X validation_split = 0.1 batch_size = 32 nb_epochs = 1 lr = 1e-4 criterion = nn.CrossEntropyLoss().cuda() if is_cuda: criterion = criterion.cuda() for epoch in range(nb_epochs): t0 = time.time() self.net.train() # train mode nb_trained = 0 train_loss = [] train_acc = [] n_images = len(img_loader) * (1 - validation_split) i = 0 while i < n_images: indexes = range(i, min(i + batch_size, n_images)) i += len(indexes) # zero-out the gradients because they accumulate by default y_pred = self.net(X) loss = criterion(y_pred, y) optimizer.step() # update params # Loss and accuracy train_acc.extend(self._get_acc(y_pred, y)) train_loss.append(loss.data[0]) nb_trained += X.size(0) if nb_updates % 100 == 0: print( 'Epoch [{}/{}], [trained {}/{}], avg_loss: {:.4f}' ', avg_train_acc: {:.4f}'.format( epoch + 1, nb_epochs, nb_trained, n_images, np.mean(train_loss), np.mean(train_acc))) self.net.eval() # eval mode valid_acc = [] while i < n_images: indexes = range(i, min(i + batch_size, n_images)) i += len(indexes) y_pred = self.net(X) valid_acc.extend(self._get_acc(y_pred, y)) delta_t = time.time() - t0 print('Finished epoch {}'.format(epoch + 1)) print('Time spent : {:.4f}'.format(delta_t)) print('Train acc : {:.4f}'.format(np.mean(train_acc))) print('Valid acc : {:.4f}'.format(np.mean(valid_acc))) batch_size = 32 i = 0 y_proba = np.empty((n_images, 10)) while i < n_images: indexes = range(i, min(i + batch_size, n_images)) i += len(indexes) y_proba[indexes] = nn.Softmax()(self.net(X)).cpu().data.numpy() return y_proba Overwriting submissions/pytorch_convnet_parallel/image_classifier.py ## Local testing (before submission)Â¶ It is important that you test your submission files before submitting them. For this we provide a unit test. Note that the test runs on your files in submissions/starting_kit, not on the classes defined in the cells of this notebook. First pip install ramp-workflow or install it from the github repo. Make sure that the python file image_classifier.py is in the submissions/starting_kit folder, and the data train.csv and test.csv are in data. If you haven't yet, download the images by executing python download_data.py. Then run ramp_test_submission If it runs and print training and test errors on each fold, then you can submit the code. In [1]: !ramp_test_submission Testing MNIST classification Reading train and test files from ./data ... Training ./submissions/starting_kit ... Using TensorFlow backend. Train on 34560 samples, validate on 3840 samples Epoch 1/1 W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use SSE4.1 instructions, but these are available on your machine and could speed up CPU computations. W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use SSE4.2 instructions, but these are available on your machine and could speed up CPU computations. W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use AVX instructions, but these are available on your machine and could speed up CPU computations. W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use AVX2 instructions, but these are available on your machine and could speed up CPU computations. W tensorflow/core/platform/cpu_feature_guard.cc:45] The TensorFlow library wasn't compiled to use FMA instructions, but these are available on your machine and could speed up CPU computations. 34560/34560 [==============================] - 3s - loss: 2.3441 - acc: 0.1071 - val_loss: 2.2978 - val_acc: 0.1289 CV fold 0 train acc = 0.132 valid acc = 0.132 test acc = 0.129 train nll = 2.294 valid nll = 2.294 test nll = 2.293 ---------------------------- train acc = 0.132 ± 0.0 train nll = 2.294 ± 0.0 valid acc = 0.132 ± 0.0 valid nll = 2.294 ± 0.0 test acc = 0.129 ± 0.0 test nll = 2.293 ± 0.0 ## Submitting to ramp.studioÂ¶ Once you found a good feature extractor and classifier, you can submit them to ramp.studio. First, if it is your first time using RAMP, sign up, otherwise log in. Then find an open event on the particular problem, for example, the event MNIST for this RAMP. Sign up for the event. Both signups are controled by RAMP administrators, so there can be a delay between asking for signup and being able to submit. Once your signup request is accepted, you can go to your sandbox and copy-paste (or upload) image_preprocessor.py and batch_classifier.py from submissions/starting_kit. Save it, rename it, then submit it. The submission is trained and tested on our backend in the same way as ramp_test_submission does it locally. While your submission is waiting in the queue and being trained, you can find it in the "New submissions (pending training)" table in my submissions. Once it is trained, you get a mail, and your submission shows up on the public leaderboard. If there is an error (despite having tested your submission locally with ramp_test_submission), it will show up in the "Failed submissions" table in my submissions. You can click on the error to see part of the trace. After submission, do not forget to give credits to the previous submissions you reused or integrated into your submission. The data set we use at the backend is usually different from what you find in the starting kit, so the score may be different. The usual way to work with RAMP is to explore solutions, add feature transformations, select models, perhaps do some AutoML/hyperopt, etc., locally, and checking them with ramp_test_submission. The script prints mean cross-validation scores ---------------------------- train acc = 0.132 ± 0.0 train nll = 2.294 ± 0.0 valid acc = 0.132 ± 0.0 valid nll = 2.294 ± 0.0 test acc = 0.129 ± 0.0 test nll = 2.293 ± 0.0 The official score in this RAMP (the first score column after "historical contributivity" on the leaderboard) is balanced accuracy aka macro-averaged recall, so the line that is relevant in the output of ramp_test_submission is valid acc = 0.132 ± 0.0. When the score is good enough, you can submit it at the RAMP.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20403161644935608, "perplexity": 25144.27930539029}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826892.78/warc/CC-MAIN-20181215152912-20181215174912-00060.warc.gz"}
https://solvable.group/posts/anomalous-curves-1/	# Anomalous Curves Part 1: Don't be clever with your elliptic curve order $$\def\F{\mathbb{F}}$$ Have you ever been confused by the numbers $p,q,r$ in a paper dealing with elliptic curves? Some paper use $q$ for the order of the elliptic curve over a field of order $p$. Conveniently, other papers use the exact opposite notation, while some get original and use $r$ for the field size, or the order of a subgroup of the curve, or something else… What if I told you there are curves where $p=q=r$? We could decide to only use these curves and never have to go back on page 2 of a paper to see what are $p,q$ or $r$! Joke aside, these curves actually exist and go by the name of anomalous curves, that is, curves $E(\mathbb{F}_p)$ with $\# E(\F_p)=p$. If you know Hasse’s Theorem, you’ll understand why these curves are also called curves of trace one. Here is an example: E: y^2 = x^3 + 425706413842211054102700238164133538302169176474*x + 203362936548826936673264444982866339953265530166 p = 730750818665451459112596905638433048232067471723 Regardless of my rant on inconsistent notations for elliptic curves, using such curves could result in more elegant notation, or even a Nothing up my sleeve mechanism for choosing elliptic curves. Moreover, they could be use to derive efficient recursive proof systems without having to use cycles of elliptic curves. It turns out that these curves are actually totally worthless for cryptography. Namely, the discrete logarithm problem can be solved in $O(\log p)$ on these curves. So these curves are secure only if their field arithmetic is intractable. Clearly not ideal. This was discovered independently by Smart and Semaev in 1998-99. In a coming series of posts, I will try to explore how these attacks work. I think they use some interesting math that is not commonly used in current cryptographic schemes. For example, in pairing-based cryptography, we regularly use a field extension $\F_p \subset \F_{p^k}$ to, for example, capture the torsion points. In Smart’s attack, we use a dual of some kind; we look at a map $E(\mathbb{Q}_p) \to \tilde{E}(\F_p)$ and lift points over $\F_p$ to points over $\mathbb{Q}_p$. In the next post, I’ll explain what this means and how to use it to break ECDLP.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6972286105155945, "perplexity": 431.15405339684077}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585201.94/warc/CC-MAIN-20211018093606-20211018123606-00327.warc.gz"}
http://cms.math.ca/cjm/kw/rationalization	location: Publications → journals Search results Search: All articles in the CJM digital archive with keyword rationalization Expand all Collapse all Results 1 - 1 of 1 1. CJM 2004 (vol 56 pp. 1290) Scull, Laura Equivariant Formality for Actions of Torus Groups This paper contains a comparison of several definitions of equivariant formality for actions of torus groups. We develop and prove some relations between the definitions. Focusing on the case of the circle group, we use $S^1$-equivariant minimal models to give a number of examples of $S^1$-spaces illustrating the properties of the various definitions. Keywords:Equivariant homotopy, circle action, minimal model,, rationalization, formalityCategories:55P91, 55P62, 55R35, 55S45 top of page \| contact us \| privacy \| site map \|	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40998411178588867, "perplexity": 4526.392030067848}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-36/segments/1471982295854.33/warc/CC-MAIN-20160823195815-00229-ip-10-153-172-175.ec2.internal.warc.gz"}
http://121.43.60.238/sxwlxbA/article/2021/1003-3998/sxwlxb-41-5-1296.shtml	## High Order Sign Preserving Entropy Stable Schemes Zheng Supei,, Xu Xia,, Feng Jianhu,, Jia Dou, College of Science, Chang'an University, Xi'an 710064 基金资助: 国家自然科学基金. 11971075陕西省自然科学基金. 2020JQ-338陕西省自然科学基金. 2019JM-243 Fund supported: the NSFC. 11971075the NSF of Shaanxi Province. 2020JQ-338the NSF of Shaanxi Province. 2019JM-243 Abstract Ensuring the sign preserving on entropy variable after the high-order reconstruction is fundamental in constructing the high-order entropy stable schemes. In this paper, we construct the 3rd order compact CWENO-type entropy stable schemes (Fjordholm's the 3rd order entropy conservative schemes with sign preserving compact CWENO reconstruction for the entropy variable) and prove the sign preserving on entropy variable with the 3rd order compact CWENO reconstruction. Numerical results show that the schemes can achieve third-order accuracy, and have high resolution, robustness and non-oscillation. Keywords： Sign preserving ; Compact CWENO reconstruction ; Entropy stable schemes Zheng Supei, Xu Xia, Feng Jianhu, Jia Dou. High Order Sign Preserving Entropy Stable Schemes. Acta Mathematica Scientia[J], 2021, 41(5): 1296-1310 doi: ## 1 引言 ### 2 预备知识 $$$\begin{array}{ll} {\bf u}_t+{\bf f(u)}_x = 0, & {\forall}\ (x, t)\in {{\Bbb R}} \times {{\Bbb R}} _+, \\ {\bf u}(x, 0) = {\bf u}_0(x), & {\forall}\ x\in {{\Bbb R}} , \end{array}$$$ $$$\eta({\bf u})_t+q({\bf u})_x \le 0,$$$ $$$\frac{\rm d}{{\rm d}t}{\bf u}_i (t) = -\frac{1}{h_i}(\hat{{\bf f}}_{i+\frac{1}{2}}-\hat{{\bf f}}_{i-\frac{1}{2}}),$$$ $$$\frac{\rm d}{{\rm d}t}\eta({\bf u}_i(t))+\frac{1}{h_i}(\hat{q}_{i+\frac{1}{2}}-\hat{q}_{i-\frac{1}{2}}) = 0,$$$ $$$\hat{q}_{i+\frac{1}{2}} = \hat{q}({\bf u}_{i-p+1}, \cdots, {\bf u}_{i+p}), \ \ \hat{q}({\bf u}, {\bf u}, \cdots, {\bf u}) = q({\bf u}).$$$ ### 2.1 熵守恒通量 $$$[{\bf v}]_{i+\frac{1}{2}}\cdot\hat{{\bf f}}_{i+\frac{1}{2}} = [\psi]_{i+\frac{1}{2}},$$$ $$$q_{i+\frac{1}{2}} = \bar{{\bf v}}_{i+\frac{1}{2}}\cdot\hat{{\bf f}}_{i+\frac{1}{2}}-\bar{\psi}_{i+\frac{1}{2}}.$$$ ### 4 数值算例 $$$\begin{array}{ll} u^{(1)} = u^n+\Delta t L(u^n), \\ { } u^{(2)} = \frac{3}{4}u^n+\frac{1}{4}u^{(1)}+\frac{1}{4}\Delta t L(u^{(1)}), \\ { }u^{n+1} = \frac{1}{3}u^n+\frac{2}{3}u^{(2)}+\frac{2}{3}\Delta t L(u^{(2)}), \end{array}$$$ ### 4.1 线性对流方程 $$$u_t+u_x = 0.$$$ $(1)$光滑初始条件 $$$u(x, 0) = \sin(\pi x), \ \ \|x\|\leq1.$$$ $(2)$间断初始条件 $$$u(x, 0) = \left\{\begin{array}{ll} 1, {\quad} &{ } \|x\|\leqslant \frac{1}{3}, \\ 0, &{ } \frac{1}{3}\leqslant \|x\|\leqslant 1.\end{array}\right.$$$ N L1 error Rate L∞ error Rate 40 0.001979313043305 3.629516311932702e-04 80 2.726027476503843e-04 2.86 7.092855086397350e-05 2.36 160 3.522356279884232e-05 2.95 9.975669895746602e-06 2.83 320 4.405706993699641e-06 3.00 1.260137438287312e-06 2.99 640 5.373835462491922e-07 3.01 1.576597490888024e-07 3.00 ### 4.2 Burgers方程 $$$u_t+\bigg(\frac{u^2}{2}\bigg)_x = 0.$$$ $(1)$光滑初始条件 $$$u(x, 0) = u_0-u_1\sin(\pi x), \ \ \|x\|\leq1.$$$ $(2)$间断初始条件 $$$u(x, 0) = \left\{\begin{array}{ll} 1, &{ } \|x\|\leqslant \frac{1}{3}, \\ -1, {\quad} &{ } \frac{1}{3}\leqslant \|x\|\leqslant 1.\end{array}\right.$$$ $$$u(x, 0) = 1+\frac{1}{2}\sin(\pi x), \ \ \|x\|\leq1.$$$ Burgers方程是一类非线性标量问题, 取熵函数$\eta(u) = \frac{u^2}{2}$, 则熵通量函数为$q(u) = \frac{u^3}{3}$, 可得二阶熵守恒通量 $$$\tilde{f}(u_i, u_{i+1}) = \frac{u_i^2+u_iu_{i+1}+u_{i+1}^2}{6}.$$$ $$${\bf D}_{i+\frac{1}{2}} = \|\bar{u}_{i+\frac{1}{2}}\|+\frac{1}{6}\|[u]_{i+\frac{1}{2}}\|.$$$ N L1 error Rate L∞ error Rate 40 1.827054747602715e-04 1.448773504797440e-04 80 2.851024314352313e-05 2.68 1.785661053588239e-05 3.02 160 3.845862448196772e-06 2.89 2.226299234296333e-06 3.00 320 4.929538860536765e-07 2.96 2.782109209450295e-07 3.00 640 6.139221843903657e-08 3.01 3.478015911254420e-08 3.00 ### 4.3 Euler方程 $$${\bf u}_t+{\bf f}({\bf u})_x = 0,$$$ $$${\bf u} = \left( \begin{array}{c} \rho\\ \rho u \\ E \end{array} \right), \ {\bf f}({\bf u}) = \left( \begin{array}{c} \rho u\\ \rho u^2+p \\ \rho uH \end{array} \right).$$$ $$$\eta({\bf u}) = \frac{-\rho s}{\gamma-1}, \ q({\bf u}) = \frac{-\rho us}{\gamma-1},$$$ Ismail和Roe[9]为Euler方程构造了${\bf v}^{\rm T}\tilde{{\bf f}} = [\psi]$的显式解. 定义参数向量${\bf z}$ $$${\bf z} = \left( \begin{array}{c} z_1\\ z_2 \\ z_3 \end{array} \right) = \sqrt{\frac{\rho}{p}}\left( \begin{array}{c} 1\\ u \\ p \end{array} \right),$$$ $$$\tilde{{\bf f}}_{i+\frac{1}{2}} = \left( \begin{array}{c} \hat{\rho}\hat{u}\\ \hat{\rho}\hat{u}^2+\hat{p}_1 \\ \hat{\rho}\hat{u}\hat{H} \end{array} \right)_{i+\frac{1}{2}},$$$ $$$\left(\ast\right)_{i+\frac{1}{2}}^{\ln} = \frac{[\ast]_{i+\frac{1}{2}}}{[\ln(\ast)]_{i+\frac{1}{2}}} .$$$ (1) Sod激波管问题，初始条件为 $$$\left\{ \begin{array}{ll} \left(\rho_l, u_l, p_l\right) = \left(1, 0, 1\right), \ &x\leq0.5, \\ \left(\rho_r, u_r, p_r\right) = \left(0.125, 0, 0.1\right), \ &x>0.5. \end{array} \right.$$$ Sod激波管问题的初始间断包含左稀疏波, 接触间断和右激波. 本文计算了$T = 0.16$时刻$[0, 1]$区间上的解. 即扰动到达计算区域边界之前的解. 从图 4可以清晰地看到: 与ES格式相比, CCWENO3格式能更好地捕捉激波, 稀疏波和接触间断, 分辨率更高, 鲁棒性更好, 且不产生伪振荡. ### 图 4 (2) Lax激波管问题，初始条件为 $$$\left\{\begin{array}{ll}\left(\rho_l, u_l, p_l\right) = \left(0.445, 0.698, 3.528\right), \ &x\leq0.5, \\\left(\rho_r, u_r, p_r\right) = \left(0.5, 0, 0.571\right), \ &x>0.5.\end{array} \right.$$$ Lax激波管问题包含了真正的非线性场(稀疏波, 激波)和线性退化场(接触间断). 其计算区间均为$[0, 1]$, 终止时刻为$T = 0.16,$CFL条件为0.25. 图 5表明: 与ES格式相比, CCWENO3格式可以避免过度抹平现象, 提高了数值结果的分辨率, 具有更好的鲁棒性. ### 图 5 (3) Shu-Osher问题, 初始条件为 $$$\left\{ \begin{array}{ll} \left(\rho_l, u_l, p_l\right) = \left(3.857143, 2.629369, 10.3333\right), \ &x\leq0.1, \\ \left(\rho_r, u_r, p_r\right) = \left((1+0.2\sin(50x)), 0, 1\right), \ &x>0.1. \end{array} \right.$$$ ### 4.4 浅水波方程 $$${\bf u}_t+{\bf f}({\bf u})_x = 0,$$$ $$${\bf u} = \left(\begin{array}{c}h \\ hu\end{array}\right), \; \; \{\bf f}({\bf u}) = \left(\begin{array}{c}hu \\{ } hu^2+\frac{1}{2}gh^2\end{array}\right),$$$ $$$\eta({\bf u}) = \frac{hu^2+gh^2}{2}, \q({\bf u}) = \frac{hu^3}{2}+guh^2.$$$ $$${\bf v} = \left(\begin{array}{c}{ } gh-\frac{u^2}{2} \\ u\end{array}\right), \\psi({\bf u}) = \frac{1}{2}guh^2.$$$ $$$\tilde{{\bf f}}_{i+\frac{1}{2}} = \left(\begin{array}{c}\bar{h}\bar{u}\\{ } \bar{h}\bar{u}^2+\frac{g}{2}\bar{h^2}\end{array}\right)_{i+\frac{1}{2}},$$$ $$${\bf R}_{i+\frac{1}{2}} = \frac{1}{\sqrt{2g}}\left(\begin{array}{cc}1{\quad} & 1 \\\bar{u}-\sqrt{g\bar{h}}{\quad} & \bar{u}+\sqrt{g\bar{h}}\end{array}\right)_{i+\frac{1}{2}},$$$ $$${\bf \tilde{\Lambda}}_{i+\frac{1}{2}} = \left(\begin{array}{cc}{ }\|\bar{u}-\sqrt{g\bar{h}}\|+\frac{1}{6}[u-\sqrt{gh}]{\quad} & 0 \\0{\quad} &{ } \|\bar{u}+\sqrt{g\bar{h}}\|+\frac{1}{6}[u+\sqrt{gh}]\end{array}\right)_{i+\frac{1}{2}}.$$$ (1) 溃坝问题, 初始条件为 $$$h(x, 0) = \left\{\begin{array}{ll}2, \ \ &x<0 \\1, \ \ &x>0\end{array} \right. , \ \ \u(x, 0)\equiv0.$$$ ### 图 7 (2) 大型溃坝问题, 初始条件为 $$$h(x, 0) = \left\{\begin{array}{ll}15, \ \ &x<0 \\1, \ \ &x>0\end{array}\right. , \ \ \u(x, 0)\equiv0.$$$ ## 5 总结 (1) 对于双曲守恒律方程组的光滑解可以达到任意阶精度. (2) 满足离散熵不等式, 是严格熵稳定的. (3) 每个单元交界面上重构的跳跃与相应单元格值的跳跃具有相同的符号. (4) 保留紧致CWENO格式的优点, 重构跳跃值具有对称性且计算经济, 即在相同精度要求下所用节点少. (5) 精准捕捉解的结构, 有效避免非物理现象, 间断附近基本无振荡, 高分辨率, 且具有良好的鲁棒性等. ## 参考文献原文顺序文献年度倒序文中引用次数倒序被引期刊影响因子 Lax P D . Weak solutions of nonlinear hyperbolic equation and their numerical computation Commun Pur Appl Math, 1954, 7 (1): 159- 193 Lax P D . Hyperbolic systems of conservation laws and the mathematical theory of shock waves Reg Conf Ser Appl Math, 1973, 11, 1- 48 The numerical viscosity of entropy stable schemes for systems of conservation laws I Math Comp, 1987, 49 (179): 91- 103 Lefloch P G , Mercier J M , Rohde C . Fully discrete, entropy conservative schemes of arbitrary order SIAM J Numer Anal, 2002, 40 (5): 1968- 1992 Cheng X , Nie Y . A third-order entropy stable scheme for hyperbolic conservation laws J Hyperbol Differ Eq, 2016, 13 (1): 129- 145 Fjordholm U S , Mishra S , Tadmor E . 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https://worldwidescience.org/topicpages/l/liepaja+plant+prospects.html	#### Sample records for liepaja plant prospects 1. Capacity of Building Energy Efficiency in Liepaja Lilita Ābele 2014-04-01 Full Text Available Ventilation with recuperation is a means of reducing heat consumption per square meter below 50 (kWh/m2 in Latvia through proper project design and trained personnel. The aim of this research is to show necessity for a ventilation system with recuperation. This research would further permit preparing recommendations for responsible decision-makers. There are no regulatory enactments that would provide ventilations indispensability during the renovation process in Latvia. The recommendation for ventilation with recuperation should be incorporated during the renovation as a mandatory requirement in Latvia. Renovated buildings with European co-financing in Liepaja city have been used as a research basis. Different renovated building groups are compared: those without ventilation, with ventilation, ventilation with recuperation. Each one of these building groups will have more than one object. The obtained data will be heat consumption per square meter (kWh/m2. It is not possible to achieve good results with badly designed projects as well as with non-trained personnel, therefore this system is quite often either not used or ignored. Ventilation with recuperation is to be a mandatory requirement in renovated buildings. During the research it has been realized that the available information is not sufficient to compare renovation processes in other countries of comparable climatic conditions. It would be preferable to meet researchers working on similar themes to be able to share mutual experience and to promote co-operation in this field. 2. Capacity of Building Energy Efficiency in Liepaja L. Ābele 2014-03-01 Full Text Available Ventilation with recuperation is a means of reducing heat consumption per square meter below 50 (kWh/m2 in Latvia through proper project design and trained personnel. The aim of this research is to show necessity for a ventilation system with recuperation. This research would further permit preparing recommendations for responsible decision-makers. There are no regulatory enactments that would provide ventilations indispensability during the renovation process in Latvia. The recommendation for ventilation with recuperation should be incorporated during the renovation as a mandatory requirement in Latvia. Renovated buildings with European co-financing in Liepaja city have been used as a research basis. Different renovated building groups are compared: those without ventilation, with ventilation, ventilation with recuperation. Each one of these building groups will have more than one object. The obtained data will be heat consumption per square meter (kWh/m2. It is not possible to achieve good results with badly designed projects as well as with non-trained personnel, therefore this system is quite often either not used or ignored. Ventilation with recuperation is to be a mandatory requirement in renovated buildings. During the research it has been realized that the available information is not sufficient to compare renovation processes in other countries of comparable climatic conditions. It would be preferable to meet researchers working on similar themes to be able to share mutual experience and to promote co-operation in this field.DOI: http://dx.doi.org/10.5755/j01.erem.67.1.5858 3. Establishment of educational module “Climate Change” in the University of Liepaja Ivars Javaitis 2016-01-01 Full Text Available Increase of awareness and high knowledge base of society in the field of climate change and environment in general in global and local ranges is vital to prevent future possible increase of climate changes in the world. In order to more involve society in prevention of future climate changes, national government has come up with National Climate Policy [1], which includes possibility for educational institutions such as University of Liepaja to develop educational programs, including lifelong and distance education programs. To achieve given objective, educational module “Climate Change” is created by University of Liepaja. Goal of this activity is to increase knowledge and capacity of governmental institutions, municipalities, scientific and educational institutions, private businesses, societies and foundations as well as separate members of society. Besides overall information on greenhouse gas emissions and adaptation to climate change, University of Liepaja concentrates more on practical questions, since, in our opinion, practical knowledge on how to use renewable resources, reduce greenhouse gas emissions or even reuse them in industry will create larger impact on achieving the objective. Therefore University of Liepaja concentrates on following topics: practical use of different technical solutions in industry, technical equipment used in industry of renewable energy, technologies used to prevent greenhouse gas emissions and mathematical modeling of possible scenarios, when pollution occurs in populated areas. Developed materials will be available for society, especially for the members of the target group for educational purposes. Materials also can and will be used for distance education. 4. Establishment of educational module “Climate Change” in the University of Liepaja Ivars Javaitis 2016-01-01 Increase of awareness and high knowledge base of society in the field of climate change and environment in general in global and local ranges is vital to prevent future possible increase of climate changes in the world. In order to more involve society in prevention of future climate changes, national government has come up with National Climate Policy [1], which includes possibility for educational institutions such as University of Liepaja to develop educational programs, including lifelong... 5. Establishment of educational module “Climate Change” in the University of Liepaja Ivars Javaitis 2016-01-01 Increase of awareness and high knowledge base of society in the field of climate change and environment in general in global and local ranges is vital to prevent future possible increase of climate changes in the world. In order to more involve society in prevention of future climate changes, national government has come up with National Climate Policy [1], which includes possibility for educational institutions such as University of Liepaja to develop educational programs, including lifelong... 6. [Plant hydroponics and its application prospect in medicinal plants study]. Zeng, Yan; Guo, Lan-Ping; Huang, Lu-Qi; Sun, Yu-Zhang 2007-03-01 This article introduced the theorem and method of hydroponics. Some examples of studies in agriculture and forestry were presented, the effects of elements, environmental stress and hormones on physiology of medicinal plants by using hydroponics were analyzed. It also introduced the feasibility and advantage of hydroponics in intermediate propagation and allelopathy of medicinal plant. And finally it made the conclusion that the way of hydroponics would be widely used in medicinal plant study. 7. Metabolomics for Plant Improvement: Status and Prospects Rakesh Kumar 2017-08-01 Full Text Available Post-genomics era has witnessed the development of cutting-edge technologies that have offered cost-efficient and high-throughput ways for molecular characterization of the function of a cell or organism. Large-scale metabolite profiling assays have allowed researchers to access the global data sets of metabolites and the corresponding metabolic pathways in an unprecedented way. Recent efforts in metabolomics have been directed to improve the quality along with a major focus on yield related traits. Importantly, an integration of metabolomics with other approaches such as quantitative genetics, transcriptomics and genetic modification has established its immense relevance to plant improvement. An effective combination of these modern approaches guides researchers to pinpoint the functional gene(s and the characterization of massive metabolites, in order to prioritize the candidate genes for downstream analyses and ultimately, offering trait specific markers to improve commercially important traits. This in turn will improve the ability of a plant breeder by allowing him to make more informed decisions. Given this, the present review captures the significant leads gained in the past decade in the field of plant metabolomics accompanied by a brief discussion on the current contribution and the future scope of metabolomics to accelerate plant improvement. 8. Energy from plants: problems and prospects Khoshoo, T.N. 1982-01-01 This article contains the presidential address to the Section of Botany (VI). After an introduction and a brief account of the process and efficiency of photosynthesis, the address describes terrestrial and aquatic biomass, biological hydrogen production and bioconversion (the conversion of biomass and organic wastes into energy and also into fertilizers, food and chemicals). The section on terrestial biomass is with particular reference to India and examines fuel plantations, the possibility of covered energy farms (such as the growth of alfalfa in greenhouses), the production of agricultural alcohol, the use of vegetable oils as fuel, the production and use of jojoba (Simmondsia chinensis) wax, and hydrocarbon producing plants (rubber, Euphorbia spp., various Leguminosae etc.). 9. Engineering resistance to plant viruses: Present status and future prospects Plant viruses cause severe crop losses across the globe. Resistant cultivars together with pesticide application are commonly used to avoid the losses caused by plant viruses. However, very limited success has been achieved at diminishing the impact of plant viruses. Use of virus resistant plant is ... 10. Progress and prospects for phosphoric acid fuel cell power plants Bonville, L.J.; Scheffler, G.W.; Smith, M.J. [International Fuel Cells Corp., South Windsor, CT (United States) 1996-12-31 International Fuel Cells (IFC) has developed the fuel cell power plant as a new, on-site power generation source. IFCs commercial fuel cell product is the 200-kW PC25{trademark} power plant. To date over 100 PC25 units have been manufactured. Fleet operating time is in excess of one million hours. Individual units of the initial power plant model, the PC25 A, have operated for more than 30,000 hours. The first model {open_quotes}C{close_quotes} power plant has over 10,000 hours of operation. The manufacturing, application and operation of this power plant fleet has established a firm base for design and technology development in terms of a clear understanding of the requirements for power plant reliability and durability. This fleet provides the benchmark against which power plant improvements must be measured. 11. Trichoderma genes in plants for stress tolerance- status and prospects. Nicolás, Carlos; Hermosa, Rosa; Rubio, Belén; Mukherjee, Prasun K; Monte, Enrique 2014-11-01 Many filamentous fungi from the genus Trichoderma are well known for their anti-microbial properties. Certain genes from Trichoderma spp. have been identified and transferred to plants for improving biotic and abiotic stress tolerance, as well for applications in bioremediation. Several Trichoderma genomes have been sequenced and many are in the pipeline, facilitating high throughput gene analysis and increasing the availability of candidate transgenes. This, coupled with improved plant transformation systems, is expected to usher in a new era in plant biotechnology where several genes from these antagonistic fungi can be transferred into plants to achieve enhanced stress tolerance, bioremediation activity, herbicide tolerance, and reduction of phytotoxins. In this review, we illustrate the major achievements made by transforming plants with Trichoderma genes as well as their possible mode of action. Moreover, examples of efficient application of genetically modified plants as biofactories to produce active Trichoderma enzymes are indicated. 12. [Prospects of the cultivated medical plants in Georgia]. Nanobashvili, N B; Lobzhanidze, M I 2009-05-01 The aim of the research is to give botanic description, to analyze chemical composition and medical properties of plants. The names of plants in Russian are also provided. The main areas of propagation of medicinal plants are identified. The period of collection is recommended. The most important features of raw materials and extracts are represented. The information about the therapeutic effectiveness of drugs is depicted. 13. Commercializing plant tissue culture processes: economics, problems and prospects Sahai, O.; Knuth, M. 1985-03-01 Novel tissue culture techniques and a range of process schemes may be considered for commercial production of plant derived drugs, chemicals, flavors and cosmetics. Plant cell immobilization, in conjunction with strain selection and product leakage, represents a major technological advancement, with significant economic implications. Conventional batch processes produce high value products at low production capacities, whereas continuous biocatalytic processes can potentially enable production of plant derived chemicals in the $20-$25/kg price range. 14. Medicinal Plants: A Prospect in Developing Male Fertility Enhancing Agent 2015-10-01 Full Text Available Medicinal plants have been a revolutionary breakthrough in the treatment of male sexual dysfunction. Traditional medicine based on a holistic philosophy is quite different with the practice of “western” medicine. Phytochemical substances focus their mechanisms of healing to the root of cause, i.e. the inability of controlling the proper function of the whole body system. Hence, medicinal plants manage sexual dysfunction and male fertility in the frame of sexual dysfunction as a whole entity. Some previous researches prove that the use of medicinal plants have a good impact in the treatment of a variety of male sexual problems. This paper will discuss several important aspects of aphrodisiac plants and preliminary study regarding them in Indonesia. Difficulties inherent to activity guided isolation and the specific requirements of bioassays are also discussed. 15. Prospects for advanced coal-fuelled fuel cell power plants Jansen, D.; Vanderlaag, P. C.; Oudhuis, A. B. J.; Ribberink, J. S. 1994-04-01 As part of ECN's in-house R&D programs on clean energy conversion systems with high efficiencies and low emissions, system assessment studies have been carried out on coal gasification power plants integrated with high-temperature fuel cells (IGFC). The studies also included the potential to reduce CO2 emissions, and to find possible ways for CO2 extraction and sequestration. The development of this new type of clean coal technology for large-scale power generation is still far off. A significant market share is not envisaged before the year 2015. To assess the future market potential of coal-fueled fuel cell power plants, the promise of this fuel cell technology was assessed against the performance and the development of current state-of-the-art large-scale power generation systems, namely the pulverized coal-fired power plants and the integrated coal gasification combined cycle (IGCC) power plants. With the anticipated progress in gas turbine and gas clean-up technology, coal-fueled fuel cell power plants will have to face severe competition from advanced IGCC power plants, despite their higher efficiency. 16. Energy-rich Plant Research in China: Overview and Prospect WU Guojiang; LIU Jie; LOU Zhiping; KANG Le 2006-01-01 @@ The energy crisis is an enormous challenge to the human race.Consequently, the technology development and utilization of biomass energy have become a new "hot spot"in the international arena.This article gives an overview on the current status of the research on energy plants and puts forward several suggestions on how to reasonably develop them in China. 17. Development, Operation, and Future Prospects for Implementing Biogas Plants Lybæk, Rikke 2014-01-01 , as is the case of biomass from nature conservation, straw, deep litter, etc. Further, the chapter discusses whether or not biogas technology can create new job opportunities in rural areas that lack development. Economic results from operating centralized biogas plants in Denmark now also stress the importance... 18. Prospect of indegenous plant extracts in tea pest management M.S.A. Mamun 2011-12-01 Full Text Available Tea is a popular beverage made from the leaves of evergreen shrub or tree Camellia sinensis, under the family Theaceae. Tea plant is subjected to the attack of insects, mites, nematodes and some plant pathogenic diseases. Tea production is greatly hindered due to thesemaladies. About 10-15% crop loss occurred by these pests per annum. In severe cases, it would be 100%. To combat these problems different groups of pesticides have been used in the tea fields since 1960. As tea is a consumable commodity, the effect of residue of pesticides in made tea is harmful to human health. In this context, biopesticides are being considered as environmentally safe, selective, biodegradable, economical and renewable alternatives for use in IPM programmes. Biopesticides are natural plant products and may be grown by the planters with minimum cost and extracted by indigenous methods.Biopesticides are secondary metabolites, which include alkaloids, terpenoids, phenolics, and minor secondary chemicals. It is estimated that as many as 2121 plant species have been reported to posses’ pest control properties. Botanicals like neem, ghora-neem, mahogoni,karanja, adathoda, sweet flag, tobacco, derris, annona, smart weed, bar weed, datura, calotropis, bidens, lantana, chrysanthemum, artemisia, marigold, clerodendrum, wild sunflower and many others may be grown by planters with minimum expense and extracted by indigenous methods. These botanical materials can be used as an alternative to chemical pesticides. These botanical extracts will help in controlling major pests of tea such as Helopeltis, red spider mite, aphids, thrips, jassid, flushworm, termites, nematodes etc. Thepresent note reviews the information of most widely available indigenous plants that may be used for the control of insect pests of tea as a component of IPM. 19. Metal hyperaccumulation in plants: Biodiversity prospecting for phytoremediation technology 2003-01-01 The importance of biodiversity (below and above ground) is increasingly considered for the cleanup of the metal contaminated and polluted ecosystems. This subject is emerging as a cutting edge area of research gaining commercial significance in the contemporary field of environmental biotechnology. Several microbes, including mycorrhizal and non-mycorrhizal fungi, agricultural and vegetable crops, ornamentals, and wild metal hyperaccumulating plants are being tested both in lab and field cond... 20. Metal hyperaccumulation in plants: Biodiversity prospecting for phytoremediation technology Vara Prasad,Majeti Narasimha; de Oliveira Freitas,Helena Maria 2003-01-01 The importance of biodiversity (below and above ground) is increasingly considered for the cleanup of the metal contaminated and polluted ecosystems. This subject is emerging as a cutting edge area of research gaining commercial significance in the contemporary field of environmental biotechnology. Several microbes, including mycorrhizal and non-mycorrhizal fungi, agricultural and vegetable crops, ornamentals, and wild metal hyperaccumulating plants are being tested both in lab and field cond... 1. Problems and prospects of nuclear power plants construction Pergamenshhik Boris Klimentyevich 2014-02-01 Full Text Available 60 years ago, in July 1954 in the city of Obninsk near Moscow the world's first nuclear power plant was commissioned with a capacity of 5 MW. Today more than 430 nuclear units with a total capacity of almost 375000 MW are in operation in dozens of the countries worldwide. 72 electrical power units are currently under construction, 8 of them are located in the Russian Federation. There will be no alternative to nuclear energy in the coming decades. Among the factors contributing to the construction of nuclear power plants reckon limited fossil fuel supply, lack of air and primarily carbon dioxide emissions. The holding back factors are breakdown, hazard, radioactive wastes, high construction costs and long construction period. Nuclear accidents in the power plant of «Three-Mile-Island» in the USA, in Chernobyl and in Japan have resulted in termination of construction projects and closure of several nuclear power plants in the Western Europe. The safety systems have become more complex, material consumption and construction costs have significantly increased. The success of modern competing projects like EPR-1600, AP1000, ABWR, national ones AES-2006 and VVER-TOI, as well as several others, depends not only on structural and configuration but also on construction and technological solutions. The increase of the construction term by one year leads to growth of estimated total costs by 3—10 %. The main improvement potentials include external plate reinforcement, pre-fabricated large-block assembly, production and installation of the equipment packages and other. One of the crucial success factors is highly skilled civil engineers training. 2. The magic and menace of metagenomics: prospects for the study of plant growth-promoting rhizobacteria Leveau, J.H.J. 2007-01-01 This article aims to be a pragmatic primer into the field of metagenomics with special emphasis on the prospective contributions of metagenomics to the study of plant growth-promoting rhizobacteria (PGPR). After an introduction into the concepts and methodologies of metagenomics and a discussion of 3. Arbuscular mycorrhizal symbiosis and active ingredients of medicinal plants: current research status and prospectives. Zeng, Yan; Guo, Lan-Ping; Chen, Bao-Dong; Hao, Zhi-Peng; Wang, Ji-Yong; Huang, Lu-Qi; Yang, Guang; Cui, Xiu-Ming; Yang, Li; Wu, Zhao-Xiang; Chen, Mei-Lan; Zhang, Yan 2013-05-01 Medicinal plants have been used world-wide for thousands of years and are widely recognized as having high healing but minor toxic side effects. The scarcity and increasing demand for medicinal plants and their products have promoted the development of artificial cultivation of medicinal plants. Currently, one of the prominent issues in medicinal cultivation systems is the unstable quality of the products. Arbuscular mycorrhiza (AM) affects secondary metabolism and the production of active ingredients of medicinal plants and thus influence the quality of herbal medicines. In this review, we have assembled, analyzed, and summarized the effects of AM symbioses on secondary metabolites of medicinal plants. We conclude that symbiosis of AM is conducive to favorable characteristics of medicinal plants, by improving the production and accumulation of important active ingredients of medicinal plants such as terpenes, phenols, and alkaloids, optimizing the composition of different active ingredients in medicinal plants and ultimately improving the quality of herbal materials. We are convinced that the AM symbiosis will benefit the cultivation of medicinal plants and improve the total yield and quality of herbal materials. Through this review, we hope to draw attention to the status and prospects of, and arouse more interest in, the research field of medicinal plants and mycorrhiza. 4. Conservation and sustainable use of medicinal plants: problems, progress, and prospects. Chen, Shi-Lin; Yu, Hua; Luo, Hong-Mei; Wu, Qiong; Li, Chun-Fang; Steinmetz, André 2016-01-01 Medicinal plants are globally valuable sources of herbal products, and they are disappearing at a high speed. This article reviews global trends, developments and prospects for the strategies and methodologies concerning the conservation and sustainable use of medicinal plant resources to provide a reliable reference for the conservation and sustainable use of medicinal plants. We emphasized that both conservation strategies (e.g. in situ and ex situ conservation and cultivation practices) and resource management (e.g. good agricultural practices and sustainable use solutions) should be adequately taken into account for the sustainable use of medicinal plant resources. We recommend that biotechnical approaches (e.g. tissue culture, micropropagation, synthetic seed technology, and molecular marker-based approaches) should be applied to improve yield and modify the potency of medicinal plants. 5. Review article: commercialization of whole-plant systems for biomanufacturing of protein products: evolution and prospects. Davies, H Maelor 2010-10-01 6. PROSPECTS OF SMALL HYDROPOWER PLANTS IN THE PIEDMONT AND MOUNTAIN STREAMS Grigorash O. V. 2015-10-01 Full Text Available The article reveals the advantages of low energy in comparison with other renewable energy sources. It is shown that broad prospects are visible for small (100 - 1000 kW and micro hydropower plants (up to 100 kW when used in the foothill and mountain areas. At the same time, the construction of hydropower plants of sleeve-type has improved the operational and technical characteristics, among other types of small-scale power plants. The article presents main analytical expressions for calculating hydroelectric power generator and it has built graphic dependences for the power generator of pressure and water flow. To improve the performance of small hydroelectric power plants we have proposed using unregulated water turbine and non-contact induction generator in their construction, thus, we could stabilize voltage and frequency directly by the frequency converter. Depending on the requirements of consumers to power supply reliability and electricity quality, we have offered several options for structural and circuit solutions of autonomous systems of electrosupply, made using small hydroelectric power plants. Thus, we can greatly enhance the efficiency of such systems if they are used with other types of renewable sources, such as windfarms or solar power plants 7. [Application prospect and expectation of fungistatic agents of plants in preservation of Chinese herbal medicines]. Li, Yan-jun; Kong, Wei-jun; Hu, Yi-chen; Zhao, Lian-hua; Yang, Shi-hai; Yang, Mei-hua 2015-10-01 During the process of growth, harvesting, transportation, processing and storage, Chinese herbal medicines (CHMs) can be easily contaminated by fungi and their metabolites like mycotoxins, which not only express negative effects on the quality and safety of CHMs and their processed products, but also pose great threats to human health. Now, some chemical synthetic fungicides have been frequently used to control the growth of fungi and accumulation of mycotoxins in the preservation of CHMs. However, the concentration and type of chemical fungicides allowed for postharvest application are restricted due to the disadvantages of their high residual toxicity, long degradation period and pollution to the environment and so on. Therefore, it is critical to research and develop some highly effective, safe and non-toxic, natural, environment-friendly fungistatic agents from plants to prevent CHMs from being contaminated by fungi and mycotoxins. The paper reviews mycotoxins and their harmfulness, the effective compounds of fungistatic plants as well as the antifungal mechanism to provide scientific evidences for developing novel and effective fungistatic agents plants. Then, the application prospect of fungistatic agents from plants in the preservation of CHMs was discussed. 8. Bio-prospecting of Plants and Marine Organisms in Saudi Arabia for New Potential Bioactivity Hajjar, Dina A. 2016-12-08 The natural resources offer a unique opportunity for the discovery of active compounds, due to the complexity and biodiversity of their chemical structures. Natural resources have been used as medicines throughout human history. Saudi Arabia’s natural resources, for instance its terrestrial medicinal plants and the Red Sea sponges, have not been extensively investigated with regard to their biological activities. To better identify the diversity of compounds with bioactive potential, new techniques are also necessary in order to improve the drug discovery path. This study comprises three sections. The first section examines Juniperus phoenicea (Arar), Anastatica hierochuntica (Kaff Maryam) and Citrullus colocynthis (Hanzal); these herbal plants were screened for potential bioactivity using a newly developed pipeline based on a high-content screening technique. We report a new cell-based high-throughput phenotypic screening for the bio-prospecting of unknown natural products from Saudi Arabian plants, in order to reveal their biological activities. The second section investigates Avicennia marina plants, screened for reverse transcriptase anti-HIV bioactivity using biochemical assay. Image-based high-content screening with a set of cellular stains was used to investigate the phenotypic results of toxicity and cell cycle arrest. The third section considers the isolation of Actinomycetes from Red Sea Sponges. Actinomycetes bacterial isolates were tested for bioactivity against West Nile Virus NS3 Protease. Analytical chemical techniques such as liquid chromatography–mass spectrometry (LC-MS), gas chromatography–mass spectrometry (GC-MS) and nuclear magnetic resonance (NMR) were used to gain more understanding of the possible chemical compounds responsible for this bioactivity. Overall, the aim of this work is to investigate the potential bioactive effect of several Saudi Arabian plants and Red Sea sponges against cancer cells and viral infections. Our study 9. WD40-repeat proteins in plant cell wall formation: current evidence and research prospects Gea eGuerriero 2015-12-01 Full Text Available The metabolic complexity of living organisms relies on supramolecular protein structures which ensure vital processes, such as signal transduction, transcription, translation and cell wall synthesis. In eukaryotes WD40-repeat (WDR proteins often function as molecular hubs mediating supramolecular interactions. WDR proteins may display a variety of interacting partners and participate in the assembly of complexes involved in distinct cellular functions. In plants, the formation of lignocellulosic biomass involves extensive synthesis of cell wall polysaccharides, a process that requires the assembly of large transmembrane enzyme complexes, intensive vesicle trafficking, interactions with the cytoskeleton, and coordinated gene expression. Because of their function as supramolecular hubs, WDR proteins could participate in each or any of these steps, although to date only few WDR proteins have been linked to the cell wall by experimental evidence. Nevertheless, several potential cell wall-related WDR proteins were recently identified using in silico aproaches, such as analyses of co-expression, interactome and conserved gene neighbourhood. Notably, some WDR genes are frequently genomic neighbours of genes coding for GT2-family polysaccharide synthases in eukaryotes, and this WDR-GT2 collinear microsynteny is detected in diverse taxa. In angiosperms, two WDR genes are collinear to cellulose synthase genes, CESAs, whereas in ascomycetous fungi several WDR genes are adjacent to chitin synthase genes, chs. In this Perspective we summarize and discuss experimental and in silico studies on the possible involvement of WDR proteins in plant cell wall formation. The prospects of biotechnological engineering for enhanced biomass production are discussed. 10. [Status and prospects for development of medical equipment at the state-of-the-art "Axion Holding" "Izhevskiy Motor Plant"]. Makarov, A N; Mubarakshin, R G 2002-01-01 The joint stock company "Izhevsky Motor Plant "AXION-HOLDING" is a large manufacturer in different industrial branches, including medical equipment. The paper presents data on the status-of-the-art and prospects of development in producing medical equipment in several areas, including information on specific articles that are manufactured and promising. 11. The “Hidden Diversity” of Medicinal Plants in Northeastern Brazil: Diagnosis and Prospects for Conservation and Biological Prospecting Cavalcanti, Deyvson Rodrigues; Albuquerque, Ulysses Paulino 2013-01-01 Increases in ethnobotanical studies and knowledge in recent decades have led to a greater and more accurate interpretation of the overall patterns related to the use of medicinal plants, allowing for a clear identification of some ecological and cultural phenomena. “Hidden diversity” of medicinal plants refers in the present study to the existence of several species of medicinal plants known by the same vernacular name in a given region. Although this phenomenon has previously been observed in a localized and sporadic manner, its full dimensions have not yet been established. In the present study, we sought to assess the hidden diversity of medicinal plants in northeastern Brazil based on the ethnospecies catalogued by local studies. The results indicate that there are an average of at least 2.78 different species per cataloged ethnospecies in the region. Phylogenetic proximity and its attendant morphological similarity favor the interchangeable use of these species, resulting in serious ecological and sanitary implications as well as a wide range of options for conservation and bioprospecting. PMID:24228056 12. The “Hidden Diversity” of Medicinal Plants in Northeastern Brazil: Diagnosis and Prospects for Conservation and Biological Prospecting Deyvson Rodrigues Cavalcanti 2013-01-01 Full Text Available Increases in ethnobotanical studies and knowledge in recent decades have led to a greater and more accurate interpretation of the overall patterns related to the use of medicinal plants, allowing for a clear identification of some ecological and cultural phenomena. “Hidden diversity” of medicinal plants refers in the present study to the existence of several species of medicinal plants known by the same vernacular name in a given region. Although this phenomenon has previously been observed in a localized and sporadic manner, its full dimensions have not yet been established. In the present study, we sought to assess the hidden diversity of medicinal plants in northeastern Brazil based on the ethnospecies catalogued by local studies. The results indicate that there are an average of at least 2.78 different species per cataloged ethnospecies in the region. Phylogenetic proximity and its attendant morphological similarity favor the interchangeable use of these species, resulting in serious ecological and sanitary implications as well as a wide range of options for conservation and bioprospecting. 13. Synthesis in plants and plant extracts of silver nanoparticles with potent antimicrobial properties: current status and future prospects. Mashwani, Zia-ur-Rehman; Khan, Tariq; Khan, Mubarak Ali; Nadhman, Akhtar 2015-12-01 Synthesis of silver nanoparticles by plants and plant extracts (green synthesis) has been developed into an important innovative biotechnology, especially in the application of such particles in the control of pathogenic bacteria. This is a safer technology, biologically and environmentally, than synthesis of silver nanoparticles by chemical or physical methods. Plants are preferable to microbes as agents for the synthesis of silver nanoparticles because plants do not need to be maintained in cell culture. The antibacterial activity of bionanoparticles has been extensively explored during the past decade. This review examines studies published in the last decade that deal with the synthesis of silver nanoparticles in plants and their antibacterial activity. 14. Status and prospects of plant virus control through interference with vector transmission Bragard, C.; Caciagli, P.; Lemaire, O.; Lopez-Moya, J.J.; MacFarlane, S.; Peters, D.; Susi, P.; Torrance, L. 2013-01-01 Most plant viruses rely on vector organisms for their plant-to-plant spread. Although there are many different natural vectors, few plant virus–vector systems have been well studied. This review describes our current understanding of virus transmission by aphids, thrips, whiteflies, leafhoppers, pla 15. Status and prospects of plant virus control through interference with vector transmission Bragard, C.; Caciagli, P.; Lemaire, O.; Lopez-Moya, J.J.; MacFarlane, S.; Peters, D.; Susi, P.; Torrance, L. 2013-01-01 Most plant viruses rely on vector organisms for their plant-to-plant spread. Although there are many different natural vectors, few plant virus–vector systems have been well studied. This review describes our current understanding of virus transmission by aphids, thrips, whiteflies, leafhoppers, 16. Arsenic accumulation in native plants of West Bengal, India: prospects for phytoremediation but concerns with the use of medicinal plants. Tripathi, Preeti; Dwivedi, Sanjay; Mishra, Aradhana; Kumar, Amit; Dave, Richa; Srivastava, Sudhakar; Shukla, Mridul Kumar; Srivastava, Pankaj Kumar; Chakrabarty, Debasis; Trivedi, Prabodh Kumar; Tripathi, Rudra Deo 2012-05-01 Arsenic (As) is a widespread environmental and food chain contaminant and class I, non-threshold carcinogen. Plants accumulate As due to ionic mimicry that is of importance as a measure of phytoremediation but of concern due to the use of plants in alternative medicine. The present study investigated As accumulation in native plants including some medicinal plants, from three districts [Chinsurah (Hoogly), Porbosthali (Bardhman), and Birnagar (Nadia)] of West Bengal, India, having a history of As pollution. A site-specific response was observed for Specific Arsenic Uptake (SAU; mg kg(-1) dw) in total number of 13 (8 aquatic and 5 terrestrial) collected plants. SAU was higher in aquatic plants (5-60 mg kg(-1) dw) than in terrestrial species (4-19 mg kg(-1) dw). The level of As was lower in medicinal plants (MPs) than in non-medicinal plants, however it was still beyond the WHO permissible limit (1 mg kg(-1) dw). The concentration of other elements (Cu, Zn, Se, and Pb) was found to be within prescribed limits in medicinal plants (MP). Among the aquatic plants, Marsilea showed the highest SAU (avg. 45 mg kg(-1) dw), however, transfer factor (TF) of As was the maximum in Centella asiatica (MP, avg. 1). Among the terrestrial plants, the maximum SAU and TF were demonstrated by Alternanthera ficoidea (avg. 15) and Phyllanthus amarus (MP, avg. 1.27), respectively. In conclusion, the direct use of MP or their by products for humans should not be practiced without proper regulation. In other way, one fern species (Marsilea) and some aquatic plants (Eichhornia crassipes and Cyperus difformis) might be suitable candidates for As phytoremediation of paddy fields. 17. Mechanisms for flowering plants to benefit arthropod natural enemies of insect pests: prospects for enhanced use in agriculture. Lu, Zhong-Xian; Zhu, Ping-Yang; Gurr, Geoff M; Zheng, Xu-Song; Read, Donna M Y; Heong, Kong-Luen; Yang, Ya-Jun; Xu, Hong-Xing 2014-02-01 Reduction of noncrop habitats, intensive use of pesticides and high levels of disturbance associated with intensive crop production simplify the farming landscape and bring about a sharp decline of biodiversity. This, in turn, weakens the biological control ecosystem service provided by arthropod natural enemies. Strategic use of flowering plants to enhance plant biodiversity in a well-targeted manner can provide natural enemies with food sources and shelter to improve biological control and reduce dependence on chemical pesticides. This article reviews the nutritional value of various types of plant-derived food for natural enemies, possible adverse effects on pest management, and the practical application of flowering plants in orchards, vegetables and field crops, agricultural systems where most research has taken place. Prospects for more effective use of flowering plants to maximize biological control of insect pests in agroecosystem are good but depend up on selection of optimal plant species based on information on the ecological mechanisms by which natural enemies are selectively favored over pest species. 18. Plant Growth Promoting Bacteria Associated with Langsdorffia hypogaea-Rhizosphere-Host Biological Interface: A Neglected Model of Bacterial Prospection Felestrino, Érica B.; Santiago, Iara F.; Freitas, Luana da Silva; Rosa, Luiz H.; Ribeiro, Sérvio P.; Moreira, Leandro M. 2017-01-01 Soil is a habitat where plant roots and microorganisms interact. In the region of the Brazilian Iron Quadrangle (IQ), studies involving the interaction between microbiota and plants have been neglected. Even more neglected are the studies involving the holoparasite plant Langsdorffia hypogaea Mart. (Balanophoraceae). The geomorphological peculiarities of IQ soil, rich in iron ore, as well as the model of interaction between L. hypogaea, its hosts and the soil provide a unique niche that acts as selective pressure to the evolution of plant growth-promoting bacteria (PGPB). The aim of this study was to prospect the bacterial microbiota of holoparasitic plant L. hypogaea, its plant host and corresponding rhizosphere of IQ soil, and to analyze the potential of these isolates as PGPB. We obtained samples of 11 individuals of L. hypogaea containing fragments of host and rhizosphere remnants, resulting in 81 isolates associated with Firmicutes and Proteobacteria phyla. The ability to produce siderophores, hydrocyanic acid (HCN), indole-3-acetic acid (IAA), nitrogen (N2) fixation, hydrolytic enzymes secretion and inhibition of enteropathogens, and phytopathogens were evaluated. Of the total isolates, 62, 86, and 93% produced, respectively, siderophores, IAA, and were able to fix N2. In addition, 27 and 20% of isolates inhibited the growth of enteropathogens and phytopathogens, respectively, and 58% were able to produce at least one hydrolytic activity investigated. The high number of isolates that produce siderophores and indole-3-acetic acid suggests that this microbiota may be important for adaptation of plants to IQ. The results demonstrate for the first time the biological importance of Brazilian IQ species as reservoirs of specific microbiotas that might be used as PGPB on agricultural land or antropized soils that needs to be reforested. PMID:28239369 19. The role of chemistry in poisonous plant research: Current status and future prospects Poisonous plants are a major cause of economic loss to livestock producers in many parts of the world. Losses include deaths, abortions, birth defects, reduced production and lost forage value. The USDA-ARS-Poisonous Plant Research Lab in collaboration with the Inner Mongolia Agricultural Univers... 20. Current status and prospects of ex situ cultivation and conservation of plants in China Zheng Zhang 2012-09-01 Full Text Available This review paper summarizes the history of plant introduction and acclimatization in China, and reviews the current status and progress of plant ex situ conservation. Overall, a total of 23,340 species belonging to 3,633 genera, and 396 families are maintained in botanical gardens, whereas 412,000 accessions of 1,890 crop or crop relatives species are preserved in Chinese national crop germplasm banks and 54,000 accessions of 7,271 wild plants in Chinese germplasm bank of wild species. The paper also discussed problems and challenges in plant ex situ conservation and outlooked further development in future: (1 initiation of “Ex situ Cultivated Flora of China project”; (2 development of integrating research of ex situ and in situ plant conservation; (3 enhancing research in ex situ conservation theory and methodology for endemic plants of China; (4 facilitating restoration and recovery of rare and endangered plants into wild on basis of ex situ conservation; and (5 strengthening evaluation and utilization of economic important plants. 1. Production of novel biopolymers in plants: recent technological advances and future prospects. Snell, Kristi D; Singh, Vijay; Brumbley, Stevens M 2015-04-01 The production of novel biopolymers in plants has the potential to provide renewable sources of industrial materials through agriculture. In this review we will highlight recent progress with plant-based production of polyhydroxyalkanoates (PHAs), silk, elastin, collagen, and cyanophycin with an emphasis on the synthesis of poly[(R)-3-hydroxybutyrate] (PHB), a renewable biodegradable PHA polymer with potential commercial applications in plastics, chemicals, and feed markets. Improved production of PHB has required manipulation of promoters driving expression of transgenes, reduction in activity of endogenous enzymes in competing metabolic pathways, insertion of genes to increase carbon flow to polymer, and basic plant biochemistry to understand metabolic limitations. These experiments have increased our understanding of carbon availability and partitioning in different plant organelles, cell types, and organs, information that is useful for the production of other novel molecules in plants. 2. Functions and toxicity of nickel in plants: recent advances and future prospects Chen, Cuiyun [Institute of Molecular Ecology, Key Laboratory of Arid and Grassland Ecology, School of Life Sciences, Lanzhou University, Lanzhou (China); Huang, Dejun [School of Life Sciences, Lanzhou University, Lanzhou (China); Liu, Jianquan 2009-04-15 Nickel is an essential nutrient for plants. However, the amount of Ni required for normal growth of plants is very low. Hence, with the level of Ni pollution in the environment increasing, it is essential to understand the functional roles and toxic effects of Ni in plants. We briefly review advances in relevant research over the past 20 years. Based on the available data, two new indirect pathways of Ni toxicity in plants are proposed. These are (i) interference with other essential metal ions and (ii) induction of oxidative stress. Research should focus on these mechanisms at the protein and molecular levels. Further research should also be directed at plant species that are capable of accumulating Ni at high concentration, so-called hyperaccumulators. Such species can provide model systems to study the mechanisms of Ni tolerance and can also be used for phytoremediation by removing nickel from polluted environment. (Abstract Copyright [2009], Wiley Periodicals, Inc.) 3. Phytosequestration: Carbon biosequestration by plants and the prospects of genetic engineering Jansson, C.; Wullschleger, S.D.; Kalluri, U.C.; Tuskan, G.A. 2010-07-15 Photosynthetic assimilation of atmospheric carbon dioxide by land plants offers the underpinnings for terrestrial carbon (C) sequestration. A proportion of the C captured in plant biomass is partitioned to roots, where it enters the pools of soil organic C and soil inorganic C and can be sequestered for millennia. Bioenergy crops serve the dual role of providing biofuel that offsets fossil-fuel greenhouse gas (GHG) emissions and sequestering C in the soil through extensive root systems. Carbon captured in plant biomass can also contribute to C sequestration through the deliberate addition of biochar to soil, wood burial, or the use of durable plant products. Increasing our understanding of plant, microbial, and soil biology, and harnessing the benefits of traditional genetics and genetic engineering, will help us fully realize the GHG mitigation potential of phytosequestration. 4. Genetically engineered virus-resistant plants in developing countries: current status and future prospects. Reddy, D V R; Sudarshana, M R; Fuchs, M; Rao, N C; Thottappilly, G 2009-01-01 Plant viruses cause severe crop losses worldwide. Conventional control strategies, such as cultural methods and biocide applications against arthropod, nematode, and plasmodiophorid vectors, have limited success at mitigating the impact of plant viruses. Planting resistant cultivars is the most effective and economical way to control plant virus diseases. Natural sources of resistance have been exploited extensively to develop virus-resistant plants by conventional breeding. Non-conventional methods have also been used successfully to confer virus resistance by transferring primarily virus-derived genes, including viral coat protein, replicase, movement protein, defective interfering RNA, non-coding RNA sequences, and protease, into susceptible plants. Non-viral genes (R genes, microRNAs, ribosome-inactivating proteins, protease inhibitors, dsRNAse, RNA modifying enzymes, and scFvs) have also been used successfully to engineer resistance to viruses in plants. Very few genetically engineered (GE) virus resistant (VR) crops have been released for cultivation and none is available yet in developing countries. However, a number of economically important GEVR crops, transformed with viral genes are of great interest in developing countries. The major issues confronting the production and deregulation of GEVR crops in developing countries are primarily socio-economic and related to intellectual property rights, biosafety regulatory frameworks, expenditure to generate GE crops and opposition by non-governmental activists. Suggestions for satisfactory resolution of these factors, presumably leading to field tests and deregulation of GEVR crops in developing countries, are given. 5. Prospects and Challenges for Harnessing Opportunities in Medicinal Plants Sector in India Harbir Singh 2006-09-01 Full Text Available The importance of the medicinal plants sector can be gauged from the fact that herbal medicines serve the healthcare needs of about 80 per cent of the world's population. India, with approximately eight percent of world's biodiversity including plant genetic diversity with medicinal properties, has the potential of becoming a major global player in market for medicinal plants-based herbal formulations and products. However, prior to establishment of Medicinal Plants Board, there was no nodal agency to look into medicinal plants as an economic 'sector' and different organisations dealt with different aspects of medicinal plants without any clear cut focus and coordination. This lack of co-ordination led to critical research gaps relating to socio-economic and policy aspects of medicinal plants. At the same time, absence of formal marketing linkages and effective buy-back arrangements hindered the development of medicinal plants sector. Developing appropriate varieties for cultivation which could ensure uniform quality and continuous supply of raw material for processing industry would not only meet the industry demand but also halt the degradation of natural resource base. To capitalize on expanding opportunities in the international market, we need to focus on scientific methods of cultivation, harvesting, processing, grading, transport, storage, labeling and marketing practices involved in the entire supply chain for medicinal plants. Policy and institutional issues particularly related to co-ordination among various stake holders are one of the major constraints faced by this sector. Species- specific and socio-economic environment specific research would be helpful for identification of an optimal institutional framework to take care of needs of various stakeholders and also cater to social needs without adverse implications for equity and environment. 6. CRISPR/Cas9 for plant genome editing: accomplishments, problems and prospects. Paul, Joseph W; Qi, Yiping 2016-07-01 The increasing burden of the world population on agriculture requires the development of more robust crops. Dissecting the basic biology that underlies plant development and stress responses will inform the design of better crops. One powerful tool for studying plants at the molecular level is the RNA-programmed genome editing system composed of a clustered regularly interspaced short palindromic repeats (CRISPR)-encoded guide RNA and the nuclease Cas9. Here, some of the recent advances in CRISPR/Cas9 technology that have profound implications for improving the study of plant biology are described. These tools are also paving the way towards new horizons for biotechnologies and crop development. 7. Potential ecosystem service delivery by endemic plants in New Zealand vineyards: successes and prospects Morgan W. Shields 2016-06-01 Full Text Available Vineyards worldwide occupy over 7 million hectares and are typically virtual monocultures, with high and costly inputs of water and agro-chemicals. Understanding and enhancing ecosystem services can reduce inputs and their costs and help satisfy market demands for evidence of more sustainable practices. In this New Zealand work, low-growing, endemic plant species were evaluated for their potential benefits as Service Providing Units (SPUs or Ecosystem Service Providers (ESPs. The services provided were weed suppression, conservation of beneficial invertebrates, soil moisture retention and microbial activity. The potential Ecosystem Dis-services (EDS from the selected plant species by hosting the larvae of a key vine moth pest, the light-brown apple moth (Epiphyas postvittana, was also quantified. Questionnaires were used to evaluate winegrowers’ perceptions of the value of and problems associated with such endemic plant species in their vineyards. Growth and survival rates of the 14 plant species, in eight families, were evaluated, with Leptinella dioica (Asteraceae and Acaena inermis ‘purpurea’ (Rosaceae having the highest growth rates in terms of area covered and the highest survival rate after 12 months. All 14 plant species suppressed weeds, with Leptinella squalida, Geranium sessiliforum (Geraniaceae, Hebe chathamica (Plantaginaceae, Scleranthus uniflorus (Caryophyllaceae and L. dioica, each reducing weed cover by >95%. Plant species also differed in the diversity of arthropods that they supported, with the Shannon Wiener diversity index (H′ for these taxa ranging from 0 to 1.3. G. sessiliforum and Muehlenbeckia axillaris (Polygonaceae had the highest invertebrate diversity. Density of spiders was correlated with arthropod diversity and G. sessiliflorum and H. chathamica had the highest densities of these arthropods. Several plant species associated with higher soil moisture content than in control plots. The best performing species 8. Status and prospects of plant virus control through interference with vector transmission. Bragard, C; Caciagli, P; Lemaire, O; Lopez-Moya, J J; MacFarlane, S; Peters, D; Susi, P; Torrance, L 2013-01-01 Most plant viruses rely on vector organisms for their plant-to-plant spread. Although there are many different natural vectors, few plant virus-vector systems have been well studied. This review describes our current understanding of virus transmission by aphids, thrips, whiteflies, leafhoppers, planthoppers, treehoppers, mites, nematodes, and zoosporic endoparasites. Strategies for control of vectors by host resistance, chemicals, and integrated pest management are reviewed. Many gaps in the knowledge of the transmission mechanisms and a lack of available host resistance to vectors are evident. Advances in genome sequencing and molecular technologies will help to address these problems and will allow innovative control methods through interference with vector transmission. Improved knowledge of factors affecting pest and disease spread in different ecosystems for predictive modeling is also needed. Innovative control measures are urgently required because of the increased risks from vector-borne infections that arise from environmental change. 9. Boosting the globalization of plant proteomics through INPPO: current developments and future prospects. Agrawal, Ganesh Kumar; Sarkar, Abhijit; Agrawal, Raj; Ndimba, Bongani Kaiser; Tanou, Georgia; Dunn, Michael J; Kieselbach, Thomas; Cramer, Rainer; Wienkoop, Stefanie; Chen, Sixue; Rafudeen, Mohammed Suhail; Deswal, Renu; Barkla, Bronwyn J; Weckwerth, Wolfram; Heazlewood, Joshua L; Renaut, Jenny; Job, Dominique; Chakraborty, Niranjan; Rakwal, Randeep 2012-02-01 The International Plant Proteomics Organization (INPPO) is a non-profit-organization consisting of people who are involved or interested in plant proteomics. INPPO is constantly growing in volume and activity, which is mostly due to the realization among plant proteomics researchers worldwide for the need of such a global platform. Their active participation resulted in the rapid growth within the first year of INPPO's official launch in 2011 via its website (www.inppo.com) and publication of the 'Viewpoint paper' in a special issue of PROTEOMICS (May 2011). Here, we will be highlighting the progress achieved in the year 2011 and the future targets for the year 2012 and onwards. INPPO has achieved a successful administrative structure, the Core Committee (CC; composed of President, Vice-President, and General Secretaries), Executive Council (EC), and General Body (GB) to achieve INPPO objectives. Various committees and subcommittees are in the process of being functionalized via discussion amongst scientists around the globe. INPPO's primary aim to popularize the plant proteomics research in biological sciences has also been recognized by PROTEOMICS where a section dedicated to plant proteomics has been introduced starting January 2012, following the very first issue of this journal devoted to plant proteomics in May 2011. To disseminate organizational activities to the scientific community, INPPO has launched a biannual (in January and July) newsletter entitled 'INPPO Express: News & Views' with the first issue published in January 2012. INPPO is also planning to have several activities in 2012, including programs within the Education Outreach committee in different countries, and the development of research ideas and proposals with priority on crop and horticultural plants, while keeping tight interactions with proteomics programs on model plants such as Arabidopsis thaliana, rice, and Medicago truncatula. Altogether, the INPPO progress and upcoming activities 10. Prospects and Problems for Identification of Poisonous Plants in China using DNA Barcodes XIE Lei; WANG YingWei; GUAN ShanYue; XIE LiJing; LONG Xin; SUN ChengYe 2014-01-01 ObjectivePoisonous plants are a deadly threat to public health in China. The traditional clinical diagnosis of the toxic plants isinefficient, fallible, and dependent upon experts. In this study, we tested the performance of DNA barcodes for identification of the most threatening poisonous plants in China. MethodsSeventy-four accessions of 27 toxic plant species in 22 genera and 17 families were sampled andthree DNA barcodes (matK,rbcL, and ITS) were amplified, sequenced and tested.Three methods, Blast,pairwise global alignment (PWG)distance, and Tree-Building were tested for discrimination power. ResultsThe primer universality of all the three markers was high. Except in the case of ITS for Hemerocallisminor, the three barcodes were successfully generated from all the selected species. Among the three methodsapplied, Blast showed the lowest discrimination rate,whereasPWGDistance and Tree-Building methods were equally effective. The ITS barcode showed highest discrimination rates using the PWG Distance and Tree-Building methods. When the barcodes were combined, discrimination rates were increased for the Blast method. ConclusionDNA barcoding technique provides us a fast tool for clinical identification of poisonous plants in China.We suggestmatK,rbcL, ITS used in combination as DNA barcodes for authentication of poisonous plants. 11. Plant Developmental Biology in Spain: from the origins to our days and prospects for the future. Beltrán, José-Pío 2009-01-01 The origins of modern Plant Developmental Biology in Spain can be traced back to a handful of scientists settled in Madrid, Barcelona, Valencia and Sevilla, who devoted themselves to plant biochemistry, molecular biology and genetics, and also to Drosophila developmental biology, which influenced, often unintentionally, the pioneers of this field. To reach the present day situation, the experience acquired in centres abroad has also been important, especially in plant research institutes in the USA, Germany (Max-Planck Institute für Züchtungsforschung) and United Kingdom (John Innes Centre). The contributions of Spanish scientists to the advancement of Plant Developmental Biology appears to be imbalanced towards reproductive biology, although relevant publications have also been reported on embryogenesis and seed development, shoot branching, tuberization, vascular morphogenesis, leaf development, regulation of development by light, signal transduction and hormone action and the connection between growth and development. Plant Developmental Biology in Spain is going through a flourishing time, with its future being highly dependent on i) appropriate funding conditions to its young scientists, ii) the opening of new areas of research, iii) the incorporation of technological breakthroughs into laboratories and iv) the carrying out of cooperative research by means of networking. Currently, besides many Departments of the Spanish universities, several centres in which competitive research in plant Developmental Biology can be accomplished, exist: the CNB and CBGP in Madrid, the LGMV CSIC-IRTA in Barcelona, the IBMCP CSIC-UPV, in Valencia and the IBVF CSIC-USE in Sevilla. Let's go for more! 12. Accumulation of uranium by aquatic plants in field conditions: prospects for phytoremediation. Favas, Paulo J C; Pratas, João; Varun, Mayank; D'Souza, Rohan; Paul, Manoj S 2014-02-01 A study was undertaken to determine Uranium concentrations in water and aquatic plants in the uraniferous region of Beiras, Central Portugal. Samples were collected from running water (n=200) at places where aquatic species were observed. Plant samples were collected from 28 species of submerged, free-floating and rooted emergent plants including 2 bryophytes and 1 pteridophyte. Uranium concentrations in surface waters ranged from 0.23 to 1,217 μg L(-1). The aquatic plant species studied, including several previously untested species, exhibited the ability to accumulate U in concentrations many times that of the ambient water. In general submerged plants exhibited higher U content followed by rooted emergent and free floating species. The highest U concentrations were observed in the bryophyte Fontinalis antipyretica (up to 4,979 mg kg(-1)) followed by Callitriche stagnalis (1963mgkg(-1)), Callitriche hamulata (379 mg kg(-1)), Ranunculus peltatus subsp. saniculifolius (243 mg kg(-1)), Callitriche lusitanica (218 mg kg(-1)), and Ranunculus trichophyllus (65.8 mg kg(-1)). In two out of three rooted emergent species U seemed to be preferentially partitioned in rhizome/roots with highest rhizome U content recorded in Typha latifolia (380 mg kg(-1)). Among the free-floating species, the highest U content (42.5 mg kg(-1)) was seen in Lemna minor. The bryophyte F. antipyretica and Callitrichaceae members seem to be promising candidates for the development of phytofiltration methodologies based on U accumulation, abundance and biomass production. 13. Prospects for pilot plants based on the tokamak, spherical tokamak and stellarator Menard, J. E.; Bromberg, L.; Brown, T.; Burgess, T.; Dix, D.; El-Guebaly, L.; Gerrity, T.; Goldston, R. J.; Hawryluk, R. J.; Kastner, R.; Kessel, C.; Malang, S.; Minervini, J.; Neilson, G. H.; Neumeyer, C. L.; Prager, S.; Sawan, M.; Sheffield, J.; Sternlieb, A.; Waganer, L.; Whyte, D.; Zarnstorff, M. 2011-10-01 A potentially attractive next-step towards fusion commercialization is a pilot plant, i.e. a device ultimately capable of small net electricity production in as compact a facility as possible and in a configuration scalable to a full-size power plant. A key capability for a pilot-plant programme is the production of high neutron fluence enabling fusion nuclear science and technology (FNST) research. It is found that for physics and technology assumptions between those assumed for ITER and nth-of-a-kind fusion power plant, it is possible to provide FNST-relevant neutron wall loading in pilot devices. Thus, it may be possible to utilize a single facility to perform FNST research utilizing reactor-relevant plasma, blanket, coil and auxiliary systems and maintenance schemes while also targeting net electricity production. In this paper three configurations for a pilot plant are considered: the advanced tokamak, spherical tokamak and compact stellarator. A range of configuration issues is considered including: radial build and blanket design, magnet systems, maintenance schemes, tritium consumption and self-sufficiency, physics scenarios and a brief assessment of research needs for the configurations. 14. Ergodynamics in the Reliability of Power Plant Operators and Prospective Hybrid Intelligence Systems. Venda; Chachko 1996-01-01 Based on ergodynamics and the hybrid intelligence theory, an analysis of the nuclear power plant operator's performance is given at the levels of strategies, tactics, and actions. Special attention is paid to the strategies used in the course of severe accidents at nuclear power plants. Data from Ukrainian and Russian power plants and training centres, and from accidents around the world were collected and processed. It is shown that in an emergency it is essential for the human operator to be flexible. This flexibility includes two main training and personal factors: a large set of strategies and tactics the operator manages to use, and quick transformations between the strategies (tactics). It was also found that some emergency tasks are too complicated: They require simultaneous use of different strategies, with time strictly limited by nuclear power plant dynamics. Those tasks cannot be successfully solved by any individual operator. Hybrid intelligence systems involving different specialists should be used in those cases in order to avoid failures in emergency problem solving and macroergonomic organizational design. 15. Omics and biotechnology of arsenic stress and detoxification in plants: current updates and prospective. Kumar, Smita; Dubey, Rama Shanker; Tripathi, Rudra Deo; Chakrabarty, Debasis; Trivedi, Prabodh Kumar 2015-01-01 Arsenic (As), a naturally occurring metallic element, is a dreadful health hazard to millions of people across the globe. Arsenic is present in low amount in the environment and originates from anthropogenic impact and geogenic sources. The presence of As in groundwater used for irrigation is a worldwide problem as it affects crop productivity, accumulates to different tissues and contaminates food chain. The consumption of As contaminated water or food products leads to several diseases and even death. Recently, studies have been carried out to explore the biochemical and molecular mechanisms which contribute to As toxicity, accumulation, detoxification and tolerance acquisition in plants. This information has led to the development of the biotechnological tools for developing plants with modulated As tolerance and detoxification to safeguard cellular and genetic integrity as well as to minimize food chain contamination. This review aims to provide current updates about the biochemical and molecular networks involved in As uptake by plants and the recent developments in the area of functional genomics in terms of developing As tolerant and low As accumulating plants. Copyright © 2014 Elsevier Ltd. All rights reserved. 16. Disease induction by human microbial pathogens in plant-model systems: potential, problems and prospects Baarlen, van P.; Belkum, van A.; Thomma, B.P.H.J. 2007-01-01 Relatively simple eukaryotic model organisms such as the genetic model weed plant Arabidopsis thaliana possess an innate immune system that shares important similarities with its mammalian counterpart. In fact, some human pathogens infect Arabidopsis and cause overt disease with human symptomology. 17. Accumulation of uranium by aquatic plants in field conditions: Prospects for phytoremediation Favas, Paulo J.C., E-mail: pjcf@utad.pt [School of Life Sciences and the Environment, University of Trás-os-Montes e Alto Douro, 5001-801 Vila Real (Portugal); IMAR-CMA Marine and Environmental Research Centre, Faculty of Sciences and Technology, University of Coimbra, 3001-401 Coimbra (Portugal); Pratas, João [Department of Earth Sciences, Faculty of Sciences and Technology, University of Coimbra, 3001-401 Coimbra (Portugal); IMAR-CMA Marine and Environmental Research Centre, Faculty of Sciences and Technology, University of Coimbra, 3001-401 Coimbra (Portugal); Varun, Mayank; D' Souza, Rohan; Paul, Manoj S. [Department of Botany, St. John' s College, Agra 282 002 (India) 2014-02-01 A study was undertaken to determine Uranium concentrations in water and aquatic plants in the uraniferous region of Beiras, Central Portugal. Samples were collected from running water (n = 200) at places where aquatic species were observed. Plant samples were collected from 28 species of submerged, free-floating and rooted emergent plants including 2 bryophytes and 1 pteridophyte. Uranium concentrations in surface waters ranged from 0.23 to 1217 μg L{sup −1}. The aquatic plant species studied, including several previously untested species, exhibited the ability to accumulate U in concentrations many times that of the ambient water. In general submerged plants exhibited higher U content followed by rooted emergent and free floating species. The highest U concentrations were observed in the bryophyte Fontinalis antipyretica (up to 4979 mg kg{sup −1}) followed by Callitriche stagnalis (1963 mg kg{sup −1}), Callitriche hamulata (379 mg kg{sup −1}), Ranunculus peltatus subsp. saniculifolius (243 mg kg{sup −1}), Callitriche lusitanica (218 mg kg{sup −1}), and Ranunculus trichophyllus (65.8 mg kg{sup −1}). In two out of three rooted emergent species U seemed to be preferentially partitioned in rhizome/roots with highest rhizome U content recorded in Typha latifolia (380 mg kg{sup −1}). Among the free-floating species, the highest U content (42.5 mg kg{sup −1}) was seen in Lemna minor. The bryophyte F. antipyretica and Callitrichaceae members seem to be promising candidates for the development of phytofiltration methodologies based on U accumulation, abundance and biomass production. - Highlights: • Exploration of U contamination extent in uraniferous province of Central Portugal • A group of previously untested species with the ability to accumulate U was assessed • U accumulation patterns in the species indicate their potential in bioindication and phytoremediation of U-contaminated water. 18. Prospects for using combined engineered bacterial enzymes and plant systems to rhizoremediate polychlorinated biphenyls. Sylvestre, Michel 2013-03-01 The fate of polychlorinated biphenyls (PCBs) in soil is driven by a combination of interacting biological processes. Several investigations have brought evidence that the rhizosphere provides a remarkable ecological niche to enhance the PCB degradation process by rhizobacteria. The bacterial oxidative enzymes involved in PCB degradation have been investigated extensively and novel engineered enzymes exhibiting enhanced catalytic activities toward more persistent PCBs have been described. Furthermore, recent studies suggest that approaches involving processes based on plant-microbe associations are very promising to remediate PCB-contaminated sites. In this review emphasis will be placed on the current state of knowledge regarding the strategies that are proposed to engineer the enzymes of the PCB-degrading bacterial oxidative pathway and to design PCB-degrading plant-microbe systems to remediate PCB-contaminated soil. 19. Prospects for the use of plant cell cultures in food biotechnology. Davies, Kevin M; Deroles, Simon C 2014-04-01 Plant cell cultures can offer continuous production systems for high-value food and health ingredients, independent of geographical or environmental variations and constraints. Yet despite many improvements in culture technologies, cell line selection, and bioreactor design, there are few commercial successes. This is principally due to the culture yield and market price of food products not being sufficient to cover the plant cell culture production costs. A better understanding of the underpinning biological mechanisms that control the target metabolite biosynthetic pathways may allow the metabolic engineering of cell lines to provide for economically competitive product yields. However, uncertainty around the regulatory and public acceptance of products derived from engineered cell cultures presents a barrier to the uptake of the technology by food product companies. Copyright © 2014 Elsevier Ltd. All rights reserved. 20. Mechanisms underlying plant resilience to water deficits: prospects for water-saving agriculture. Chaves, M M; Oliveira, M M 2004-11-01 Drought is one of the greatest limitations to crop expansion outside the present-day agricultural areas. It will become increasingly important in regions of the globe where, in the past, the problem was negligible, due to the recognized changes in global climate. Today the concern is with improving cultural practices and crop genotypes for drought-prone areas; therefore, understanding the mechanisms behind drought resistance and the efficient use of water by the plants is fundamental for the achievement of those goals. In this paper, the major constraints to carbon assimilation and the metabolic regulations that play a role in plant responses to water deficits, acting in isolation or in conjunction with other stresses, is reviewed. The effects on carbon assimilation include increased resistance to diffusion by stomata and the mesophyll, as well as biochemical and photochemical adjustments. Oxidative stress is critical for crops that experience drought episodes. The role of detoxifying systems in preventing irreversible damage to photosynthetic machinery and of redox molecules as local or systemic signals is revised. Plant capacity to avoid or repair membrane damage during dehydration and rehydration processes is pivotal for the maintenance of membrane integrity, especially for those that embed functional proteins. Among such proteins are water transporters, whose role in the regulation of plant water status and transport of other metabolites is the subject of intense investigation. Long-distance chemical signalling, as an early response to drought, started to be unravelled more than a decade ago. The effects of those signals on carbon assimilation and partitioning of assimilates between reproductive and non-reproductive structures are revised and discussed in the context of novel management techniques. These applications are designed to combine increased crop water-use efficiency with sustained yield and improved quality of the products. Through an understanding of 1. Plants as bioindicators for archaeological prospection: a case of study from Domitian's Stadium in the Palatine (Rome, Italy). Ceschin, S; Caneva, G 2013-06-01 In this study, we analyzed the relationship between buried archaeological remains (masonries, pavements, and ancient ruins) and spontaneous vegetation growing above them. We carried out several vegetation surveys in the Domitian's Stadium at the archaeological site of the Palatine (Rome). Vegetation data were collected using the Braun-Blanquet approach and elaborated using statistical analyses (cluster analysis) to assess the similarity among surveys. Structural, chorological, and ecological features of the plant communities were analyzed. Results showed that the vegetation responds significantly to the presence of sub-emerging ancient remains. The plant bioindication of this phenomenon occurs through the following floristic-vegetation variations: phenological alterations in single individuals (reduction in height, displacement of flowering/fruiting period), increase of annual species and decrease of perennial ones, decrease of total plant coverage, reduction of maturity level of the vegetation which remains blocked at a pioneer evolutive stage. The presence of sub-surfacing ruins manifests itself through the dominant occurrence of xerophilous and not-nitrophilous species (e.g., Hypochaeris achyrophorus L., Aira elegantissima Schur, Trifolium scabrum L. ssp. scabrum, Trifolium stellatum L., Plantago lagopus L., Medicago minima (L.) L., and Catapodium rigidum (L.) C.E. Hubb. ex Dony ssp. rigidum) and in a rarefaction of more mesophilous and nitrophilous species (e.g., Plantago lanceolata L., Trifolium pratense L. ssp. pratense, Trifolium repens L. ssp. repens, and Poa trivialis L.). Therefore, the vegetation can be used as bioindicator for the detection of buried ruins, contributing in the archaeological prospection for a general, fast, and inexpensive interpretation of the underground. 2. The assessment of physiology parameters of willow plants as a criterion for selection of prospective clones Rodzkin Aleh I. 2015-01-01 Full Text Available Bioenergy production based on short rotation coppice willow plantations (SRC is an effective direction both for economic and environment profit. The yield of willow wood can amount to 10-15 tons per hectare of dry biomass per year and the cost of thus obtained energy is lower in comparison with other energy crops. In order to achieve high yield and profitability, the use of special willow clones is necessary. Species most often used in selection for biomass production are shrub type willows: Salix viminalis, Salix dasyclados and Salix schwerini, while the clones tested in this paper were also of tree species Salix alba. The productivity and some physiology characteristics of Serbian selection clones of Salix alba (Bačka, Volmianka and Drina and Swedish selection clone Jorr (Salix viminalis were investigated in greenhouses and in field conditions. As the result of testing three clones of Salix alba - Bačka, Volmianka and Drina, having special preferences and adaptability to different environmental conditions, these were included in State register of Republic of Belarus in 2013. In our experiment it was also satisfactory that specific properties of willows (intensity of transpiration and photosynthesis, water use efficiency and others, were conserved both in greenhouses and in field conditions. This factor gives opportunity to select prospective clones of willows at an early stage of ontogenesis for further testing. 3. Remote sensing of plant emissions of volatile isoprenoids with PRI. Prospects for upscaling (Invited) Penuelas, J. 2013-12-01 Josep Peñuelas*1,2, Giovanni Marino1,2,3,4, Joan LLusia1,2, Catherine Morfopoulos1,2,5, Gerard Farre-Armengol1,2, Shawn Kefauver, Alex Guenther6 , Francesca Rapparini7 , Roger Seco1,2,6, Marc Estiarte1,2, Mónica Mejia-Chang1,2, Romà Ogaya1,2, Jordi Sardans1,2 , Andrew Turnipseed6, Peter Harley6, Osvaldo Facini7, Rita Baraldi7, Jim Greenberg6 , Iolanda Filella1,2 1 CSIC, Global Ecology Unit CREAF-CEAB-UAB, Cerdanyola del Vallés 08193, Catalonia, Spain 2 CREAF, Cerdanyola del Vallés 08193, Catalonia, Spain 3 Dipartimento di Bioscienze e Territorio, Università degli Studi del Molise, Contrada Fonte Lappone, 86090 Pesche (IS), Italy 4 Institute for Plant Protection, National Research Council, Via Madonna del Piano 10, 50019 Sesto Fiorentino (FI), Italy 5 Division of Ecology and Evolution, Imperial College, Silwood Park, Ascot, SL5 7PY, UK 6 Atmospheric Chemistry Division, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307-3000, USA 7 Biometeorology Institute, IBIMET-CNR, Via P. Gobetti 101, Bologna, Italy Abstract Terrestrial plants re-emit around 1-2% of the carbon they fix as isoprene and monoterpenes. These emissions play major roles in the ecological relationships among living organisms and in atmospheric chemistry and climate, and yet their actual quantification at the ecosystem level in different regions is far from being resolved. Phenomenological models are used to estimate the emission rates, but the limited understanding of the function and regulation of these emissions leads to large uncertainties in such estimations. Many measurements have been made at the foliar but few at the ecosystem level, and those that do exist are limited in space and time. We here provide evidence that a simple remote sensing index, the photochemical reflectance index (PRI), which is indicative of light use efficiency (LUE), is a good indirect estimator of foliar isoprenoid emissions and therefore can be used to sense them remotely. These results open 4. Bacterial disease management: challenges, experience, innovation and future prospects: Challenges in Bacterial Molecular Plant Pathology. Sundin, George W; Castiblanco, Luisa F; Yuan, Xiaochen; Zeng, Quan; Yang, Ching-Hong 2016-12-01 Plant diseases caused by bacterial pathogens place major constraints on crop production and cause significant annual losses on a global scale. The attainment of consistent effective management of these diseases can be extremely difficult, and management potential is often affected by grower reliance on highly disease-susceptible cultivars because of consumer preferences, and by environmental conditions favouring pathogen development. New and emerging bacterial disease problems (e.g. zebra chip of potato) and established problems in new geographical regions (e.g. bacterial canker of kiwifruit in New Zealand) grab the headlines, but the list of bacterial disease problems with few effective management options is long. The ever-increasing global human population requires the continued stable production of a safe food supply with greater yields because of the shrinking areas of arable land. One major facet in the maintenance of the sustainability of crop production systems with predictable yields involves the identification and deployment of sustainable disease management solutions for bacterial diseases. In addition, the identification of novel management tactics has also come to the fore because of the increasing evolution of resistance to existing bactericides. A number of central research foci, involving basic research to identify critical pathogen targets for control, novel methodologies and methods of delivery, are emerging that will provide a strong basis for bacterial disease management into the future. Near-term solutions are desperately needed. Are there replacement materials for existing bactericides that can provide effective disease management under field conditions? Experience should inform the future. With prior knowledge of bactericide resistance issues evolving in pathogens, how will this affect the deployment of newer compounds and biological controls? Knowledge is critical. A comprehensive understanding of bacterial pathosystems is required to not 5. Status and prospects for household biogas plants in Ghana – lessons, barriers, potential, and way forward Edem Cudjoe Bensah, Moses Mensah, Edward Antwi 2011-09-01 Full Text Available Ghana is a country faced with pressing developmental challenges on energy, sanitation, environment and agriculture. The development of a large scale, enterprise-based biogas programme in Ghana will improve sanitation, produce clean energy, reduce greenhouse gas emissions, promote nutrient recovery, and create jobs. While aforementioned benefits of biogas are known, the biogas industry is still not growing at rates that would enable its impact on sanitation, agriculture and energy usage to be felt, owing to challenges such as low awareness creation and poor biogas supply chain, lack of well-trained personnel, poor follow-up services, and high cost of biogas digesters – USD 235- 446 per cubic meter. This paper looks at the chronology of biogas developmental in Ghana, technical and market potential of household biogas plants, strengths and weaknesses of main biogas service providers, human resource development, quality issues, and risks involved in developing a large scale household biogas programme. From the paper, the technical and market potential of dung-based, household biogas digesters in Ghana are estimated at 162,066 and 16,207 units respectively. In order to take full advantage of biogas technology, the paper recommends the development of standardized digesters, increase in awareness programmes on the life-long benefits of biogas systems, introduction of flexible payment schemes, and stepping-up of follow-up services. Finally, there is an urgent need for a "promoter" who will engage all stakeholders to ensure that a national action plan on biogas technology is initiated and implemented. 6. Status and prospects for household biogas plants in Ghana: lessons, barriers, potential, and way forward Bensah, Edem Cudjoe [Chemical Engineering Department, Kumasi Polytecnic, Kumasi (Ghana); Mensah, Moses [Chemical Engineering Department, KNUST, PMB, Kumasi (Ghana); Antwi, Edward [Mechanical Engineering Department, Kumasi Polytechnic, Kumasi (Ghana) 2011-07-01 Ghana is a country faced with pressing developmental challenges on energy, sanitation, environment and agriculture. The development of a large scale, enterprise-based biogas programme in Ghana will improve sanitation, produce clean energy, reduce greenhouse gas emissions, promote nutrient recovery, and create jobs. While aforementioned benefits of biogas are known, the biogas industry is still not growing at rates that would enable its impact on sanitation, agriculture and energy usage to be felt, owing to challenges such as low awareness creation and poor biogas supply chain, lack of well-trained personnel, poor follow-up services, and high cost of biogas digesters -- USD 235- 446 per cubic meter. This paper looks at the chronology of biogas developmental in Ghana, technical and market potential of household biogas plants, strengths and weaknesses of main biogas service providers, human resource development, quality issues, and risks involved in developing a large scale household biogas programme. From the paper, the technical and market potential of dung-based, household biogas digesters in Ghana are estimated at 162,066 and 16,207 units respectively. In order to take full advantage of biogas technology, the paper recommends the development of standardized digesters, increase in awareness programmes on the life-long benefits of biogas systems, introduction of flexible payment schemes, and stepping-up of follow-up services. Finally, there is an urgent need for a 'promoter' who will engage all stakeholders to ensure that a national action plan on biogas technology is initiated and implemented. 7. Prospects for including L'Vovsk-Volynsk coals in carbonization blends for Ukrainian plants Tyutyunnikov, Yu.B.; Koyuda, V.A.; Kaftan, Yu.S.; Drozdnik, I.D.; Pustovoit, M.I.; Shifrin, S.I.; Pivnyak, V.I. 1981-01-01 The Ukrainian coking industry is currently experiencing difficulties over coal supplies. It is therefore necessary to consider the possibility of carbonizing coals from the L'vovsk-Volynsk coalfield. The mining costs in the L'vovsk-Volynsk coalfield are much lower than in the Donbas (by 36 to 37%) but higher than in the Kuzbas (by 4 to 7%). The cost of coal mined by the Ukrzapadugol Combine in 1977 for example was 10.59 rubles/ton. In June 1978, it was decided to include L'vovsk-Volynsk coals in the blend carbonized at the Dneprodzerzhinsk C and CW. These coals were substituted for 10 to 14% of coals from the Samarskaya pit (Western Donbas), leaving the proportions of the other coals in the blend virtually unchanged. The material balance for the coke ovens showed increased yields of coke-oven gas (0.2% up) and crude benzol (0.05% up). More coke-oven gas was produced during the experimental period, although the volatile matter of the charge was lower. The reason lies in the lower thermal stability of the vapor phase formed by the volatile substances; this is confirmed by the 0.4% increment in the hydrogen content of the coke-oven gas formed under comparable carbonization conditions. The introduction of L'vovsk-Volynsk coals in the blend carbonized at the Dneprodzerzhinsk C and CW increased the yield of >25 mm coke and reduced that of <10 mm coke. The M25 strength index was improved by 0.2%, while the M10 index was 0.07% poorer.The overall economic effect of introducing L'vovsk-Volynsk coals (after correction for the change in coke quality) amounted to savings in 1978 of 896,100 rubles. The coals mined in the Velikomostovsk and Mezherechensk regions of the L'vovsk-Volynsk coalfield, which have hitherto been used solely as fuels, should be reserved for the Ukrainian coking plants and used to produce metallurgical coke. 8. Biodiversity Prospecting. Sittenfeld, Ana; Lovejoy, Annie 1994-01-01 Examines the use of biodiversity prospecting as a method for tropical countries to value biodiversity and contribute to conservation upkeep costs. Discusses the first agreement between a public interest organization and pharmaceutical company for the extraction of plant and animal materials in Costa Rica. (LZ) 9. Developing Process and Applying Prospects of Nuclear Power Plant%核电站的发展历程及应用前景林宗虎 2012-01-01 自1954年苏联建成第1个核电站以来,全球已出现了为数众多装有各种反应堆的核电站.本文简述了反应堆的主要结构及核电站的发展历程.根据核电站的特点,论述了核电站在未来能源中的地位及应用前景.%Since the first nuclear power plant established by the So.viet Union in 1954. many nuclear power plants with different types of nuclear reactors have been presented on the world.Main constructions of nuclear reactors and the developing process of the nuclear power plant are briefly described in this paper. According to features of the nuclear power plant, its position in the future energy and applying prospects are also mentioned. 10. Is time running out for US energy merchant companies? Part III: The prospects for principal recovery, by region and plant type Rigby, P. [McGraw-Hill Co. (USA). Standard & Poor' s 2003-03-01 Parts I and II of this article detailed the signs of distress in the US energy merchant sector that lenders should look for and the analytic issues they should consider in estimating load-recovery prospects if a generator defaults. This final instalment presents three examples that illustrate how Standard and Poor's loss recovery valuation analyses for secured power loans take into account variations in regional markets and plant type. Coal-MAAC, which is an example of how favourable recoveries in default could be, is a baseload, coal-fired plant that has undergone extensive retrofit work since its former owner divested it. 3 figs. 11. 75 FR 53321 - Prospective Grant of a Co-Exclusive License: Natural Plant Extracts From Incense Cedar as Pest... 2010-08-31 ... HUMAN SERVICES Centers for Disease Control and Prevention Prospective Grant of a Co-Exclusive License... Valent BioSciences Corporation, having places of business in San Diego, CA and Libertyville, IL... 8, 2000. The prospective co-exclusive licenses will be royalty-bearing and will comply with the... 12. Prospects for optimizing soil microbial functioning to improve plant nutrient uptake and soil carbon sequestration under elevated CO2 Nie, M.; Pendall, E. G. 2013-12-01 Potential to mitigate climate change through increasing plant productivity and its carbon (C) input to soil may be limited by soil nitrogen (N) availability. Using a novel 13C-CO2 and 15N-soil dual labeling method, we investigated whether plant growth-promoting bacteria would interact with atmospheric CO2 concentration to alter plant productivity and soil C storage. We grew Bouteloua gracilis under ambient (380 ppm) or elevated CO2 (700 ppm) in climate-controlled chambers, and plant individuals were grown with or without Pseudomonas fluorescens inoculum, which can produce N catabolic enzymes. We observed that both eCO2 and P. fluorescens increased plant productivity and its C allocation to soil. P. fluorescens relative to eCO2 enhanced plant N uptake from soil organic matter, which highly correlated with soil N enzyme activities and rhizosphere exudate C. More importantly, P. fluorescens increased microbial biomass and deceased specific microbial respiration in comparison with eCO2. These results indicate that application of plant growth-promoting bacteria can increase microbial C utilization efficiency with subsequent N mineralization from soil organic matter, and may improve plant N availability and soil C sequestration. Together, our findings highlight the potential of plant growth-promoting bacteria for global change mitigation by terrestrial ecosystems. 13. Pilot projects of network wind power plants in the eisk region of Krasnodar krai: the state and prospects Gordeev, I. G.; Ermolenko, G. V.; Nikomarova, A. V.; Ryzhenkov, M. A.; Tskhomariya, V. N. 2012-11-01 The market of electric energy in the Krasnodar krai and the specific features of electric power supply in the Eisk region are analyzed. The basic aspects of designing wind power plants are considered. The main technical, economic, and environmental indicators of the wind power plants being designed are presented. 14. Biogeochemical anomaly above oil-containing structures in an arid zone. [Growth stimulation of plants by sodium naphthenate used for prospecting Grishchenko, O.M. 1983-01-01 Visual biological anomalies above the oil-containing structures are characterized by bright green coloring of the vegetation cover, gigantism of the plants, extended vegetation period of the plants, deformity of the plants, etc. Biological anomalies are associated with geological features and are observed only above the zone of fault disorders of the earth's crust, above deep faults. A conclusion is drawn about the presence above the oil-bearing structures in the arid zone of a biogeochemical anomaly whose origin is explained by the biological activity of oil and its derivatives. The petroleum growth matter is the sodium salt of naphthene acid, a growth stimulator of plants and animals. The oils of the USSR contain 0.8-4.8% naphthene acids, which effuse through the faults into the root area levels of the soil. As a result of stimulation of growth and development by the petroleum growth matter, the vegetation period of the plants is prolonged. Under the influence of natural petroleum growth substances, the height and productivity of the anomalous plants increases 2-3-fold. Formation and manifestation of signs of biogeochemical anomalies above the oil-bearing structures in the arid zone predetermine the following conditions: presence of fault disorders of the earth's crust; salinity of the root area of the soil layer necessary for neutralization of the naphthene acids with subsequent formation of the biologically active naphthenates; aridity of the desert landscape; plain relief excluding color diversity in vegetation cover because of nonuniform wetting, etc. The established biogeochemical anomaly can be used in prospecting and exploration of oil, gas and bitumen, and also in determining the fault disorders of the earth's crust. 15. Application of CG animation system to plant designing and its future prospect. Plant sekkei eno CG animation system no katsuyo to shorai tenbo Kumazawa, T. (JGC Corp., Tokyo (Japan)) 1994-03-05 This paper introduces an outline of four-dimensional real-time CG (computer graphics) animation system, which is applicable to the plant designing. It also describes a new type engineering work environment using a decision support system for the plant designing. This animation system is applied to the visualization of dynamic simulation analysis, preparation of presentation data at the stage of basic designing, arrangement of equipments, etc. Are illustrated examples of the application of this system to the multiform variable production type plant, physical distribution simulation, and multipurpose batch plant. Furthermore, effectiveness of the virtual space decision support system is emphasized, which is a visual design support system using the latest element technologies, such as CG, VR (virtual reality), hologram, tele-existence, telepresence, multimedia, etc. 6 refs., 10 figs. 16. The prospect of applying chemical elicitors and plant strengtheners to enhance the biological control of crop pests. Sobhy, Islam S; Erb, Matthias; Lou, Yonggen; Turlings, Ted C J 2014-04-05 An imminent food crisis reinforces the need for novel strategies to increase crop yields worldwide. Effective control of pest insects should be part of such strategies, preferentially with reduced negative impact on the environment and optimal protection and utilization of existing biodiversity. Enhancing the presence and efficacy of native biological control agents could be one such strategy. Plant strengthener is a generic term for several commercially available compounds or mixtures of compounds that can be applied to cultivated plants in order to 'boost their vigour, resilience and performance'. Studies into the consequences of boosting plant resistance against pests and diseases on plant volatiles have found a surprising and dramatic increase in the plants' attractiveness to parasitic wasps. Here, we summarize the results from these studies and present new results from assays that illustrate the great potential of two commercially available resistance elicitors. We argue that plant strengtheners may currently be the best option to enhance the attractiveness of cultivated plants to biological control agents. Other options, such as the genetic manipulation of the release of specific volatiles may offer future solutions, but in most systems, we still miss fundamental knowledge on which key attractants should be targeted for this approach. 17. Prospecting the utility of a PMI/mannose selection system for the recovery of transgenic sugarcane (Saccharum spp. hybrid) plants. Jain, Mukesh; Chengalrayan, Kudithipudi; Abouzid, Ahmed; Gallo, Maria 2007-05-01 For the first time, the phosphomannose isomerase (PMI, EC 5.3.1.8)/mannose-based "positive" selection system has been used to obtain genetically engineered sugarcane (Saccharum spp. hybrid var. CP72-2086) plants. Transgenic lines of sugarcane were obtained following biolistic transformation of embryogenic callus with an untranslatable sugarcane mosaic virus (SCMV) strain E coat protein (CP) gene and the Escherichia coli PMI gene manA, as the selectable marker gene. Postbombardment, transgenic callus was selectively proliferated on modified MS medium containing 13.6 microM 2,4-D, 20 g l(-1) sucrose and 3 g l(-1) mannose. Plant regeneration was obtained on MS basal medium with 2.5 microM TDZ under similar selection conditions, and the regenerants rooted on MS basal medium with 19.7 microM IBA, 20 g l(-1) sucrose, and 1.5 g l(-1) mannose. An increase in mannose concentration from permissive (1.5 g l(-1)) to selective (3 g l(-1)) conditions after 3 weeks improved the overall transformation efficiency by reducing the number of selection escapes. Thirty-four vigorously growing putative transgenic plants were successfully transplanted into the greenhouse. PCR and Southern blot analyses showed that 19 plants were manA-positive and 15 plants were CP-positive, while 13 independent transgenics contained both transgenes. Expression of manA in the transgenic plants was evaluated using a chlorophenol red assay and enzymatic analysis. 18. Bacteria used in the biological control of plant-parasitic nematodes: populations, mechanisms of action, and future prospects. Tian, Baoyu; Yang, Jinkui; Zhang, Ke-Qin 2007-08-01 As a group of important natural enemies of nematode pests, nematophagous bacteria exhibit diverse modes of action: these include parasitizing; producing toxins, antibiotics, or enzymes; competing for nutrients; inducing systemic resistance of plants; and promoting plant health. They act synergistically on nematodes through the direct suppression of nematodes, promoting plant growth, and facilitating the rhizosphere colonization and activity of microbial antagonists. This review details the nematophagous bacteria known to date, including parasitic bacteria, opportunistic parasitic bacteria, rhizobacteria, Cry protein-forming bacteria, endophytic bacteria and symbiotic bacteria. We focus on recent research developments concerning their pathogenic mechanisms at the biochemical and molecular levels. Increased understanding of the molecular basis of the various pathogenic mechanisms of the nematophagous bacteria could potentially enhance their value as effective biological control agents. We also review a number of molecular biological approaches currently used in the study of bacterial pathogenesis in nematodes. We discuss their merits, limitations and potential uses. 19. Effects of climate change on plant-insect interactions and prospects for resistance breeding using genetic resources Pritchard, J.; Broekgaarden, C.; Vosman, B. 2014-01-01 This chapter describes the components (elevated CO2, temperature and drought) of climate change and their direct and indirect effects on plant-insect interactions. The genetic resources (such as wild relatives and traditional, locally adapted landraces) important for increasing pest/disease resistan 20. Effects of climate change on plant-insect interactions and prospects for resistance breeding using genetic resources Pritchard, J.; Broekgaarden, C.; Vosman, B. 2014-01-01 This chapter describes the components (elevated CO2, temperature and drought) of climate change and their direct and indirect effects on plant-insect interactions. The genetic resources (such as wild relatives and traditional, locally adapted landraces) important for increasing pest/disease 1. Gender diphasy in plant species:progresses and prospects%性二相植物研究进展与展望朱艳; 张志强 2015-01-01 植物性的多样性一直是植物进化生物学研究的重要议题。其中，性二相植物在被子植物中极为罕见，该类植物的性别是环境决定的，它们的每个个体可以根据环境状况在不同年际间表现为雄性或雌性，因此被称为变性植物。综述了性二相植物的研究进展，并对未来的发展方向进行了展望。认为未来此方面的研究应该强调对更多植物的自然种群进行观察，在阐明变性植物性别转变机制的基础上加强性二相植物与非变性近缘植物的对比。%Understanding sexual-system diversity is a prominent research theme in plant evolution biology. The plants with gender dishasy is rare in angiosperm because the plants exhibit sexual system depend on their environments,which means the plant individuals exhibit male or female according with its environments in vari-ous years.The paper summurized the current researches on gender diphasy and highlight prospects in the fu-ture. 2. 光伏电站的投资前景分析%Analysis on investment prospects of photovoltaic power plants 欧惠; 查国君; 李黎明; 刘澄宇 2012-01-01 在世界各国对太阳能光伏发电鼓励政策引导下,近年来太阳能光伏发电产业呈现出快速发展的势头.文章就建立光伏电站所涉及的电站成本、相关政策和市场状况问题进行了研究分析.在不考虑政府财政补贴的情况下,2008年投资光伏电站每年平均损失115.5万元/MW,当前投资光伏电站每年可平均获得利润33万元/MW.在国内太阳能电站的收益率水平迅速提升的形势下,预计未来5年将是我国太阳能电站投资的黄金时期,建议政府和相关企业抓住机遇,加大光伏电站的投入和建设.%In recent years, through the guidance of incentives in various countries, the solar photovoltaic power industry shows a rapid development trend. The key issues on the construction of photovoltaic power plant were investigated, including the cost of photovoltaic power plant, related policy and market situation. The results indicate that, without considering the government financial subsidies, an average annual loss of 1.155 million yuan was obtained from the investment in each 1 MW photovoltaic power plant in 2008, however, an average annual profit of 330 thousand yuan could be made in present. With the rapid rise of photovoltaic power plant yields in China, the golden age of the photovoltaic power plant investment will be coming in next 5 years. It was suggested that the government and related enterprises would seize the opportunity to increase the investment and construction of photovoltaic power plant. 3. Soil-plant relationship of Pteropyrum olivieri, a serpentine flora of Wadh, Balochistan, Pakistan and its use in mineral prospecting Shahid Naseem 2009-09-01 Full Text Available Biogeochemical investigation of Pteropyrum olivieri, a flora of Wadh area in perspective of plant-soil-rock relationship has been made. It is a native of Irano-Turanian region which extended into Saharo-Sindian region of Pakistan. The distribution of P. olivieri and some other co-ecological flora in relation to lithology was also discussed. Field observations showed its controlled population on the serpentine soil. The average abundance of Mg and Ca in soil was estimated as 2.43% and 5.46 respectively. The Mg/Ca ratio of the soils of the study area was below unity (0.445, indicating pedogenesis from serpentinite. Quantitative estimation of Cr, Ni, Co and Cu in soils and plant ash was made. Distribution of these elements has been discussed in context with soil chemistry, average abundance in plant ash and the exclusion mechanism of the flora. The concentration of Cr, Ni and Co in the twigs of P. olivieri is more than the average abundance in the plant ash, while Cu concentration was less. Relationship among Cr, Ni, Co and Cu has been established using scatter-grams to evaluate biogeochemistry of the P. olivieri. Bio-concentration factor (BCF of the specie attributed Co>Cu>Ni>Cr trend. Present study signifies a number of anomalous zones which can be utilized for the exploration of new hidden mineral deposits in and around Wadh area. The rocks in the anomalous zone served as good host for podiform chromite and associated mineralization. 4. Parametric study of prospective early commercial MHD power plants (PSPEC). General Electric Company, task 1: Parametric analysis Marston, C. H.; Alyea, F. N.; Bender, D. J.; Davis, L. K.; Dellinger, T. C.; Hnat, J. G.; Komito, E. H.; Peterson, C. A.; Rogers, D. A.; Roman, A. J. 1980-01-01 The performance and cost of moderate technology coal-fired open cycle MHD/steam power plant designs which can be expected to require a shorter development time and have a lower development cost than previously considered mature OCMHD/steam plants were determined. Three base cases were considered: an indirectly-fired high temperature air heater (HTAH) subsystem delivering air at 2700 F, fired by a state of the art atmospheric pressure gasifier, and the HTAH subsystem was deleted and oxygen enrichment was used to obtain requisite MHD combustion temperature. Coal pile to bus bar efficiencies in ease case 1 ranged from 41.4% to 42.9%, and cost of electricity (COE) was highest of the three base cases. For base case 2 the efficiency range was 42.0% to 45.6%, and COE was lowest. For base case 3 the efficiency range was 42.9% to 44.4%, and COE was intermediate. The best parametric cases in bases cases 2 and 3 are recommended for conceptual design. Eventual choice between these approaches is dependent on further evaluation of the tradeoffs among HTAH development risk, O2 plant integration, and further refinements of comparative costs. 5. Abscisic Acid Signaling and Abiotic Stress Tolerance in Plants: A Review on Current Knowledge and Future Prospects Vishwakarma, Kanchan; Upadhyay, Neha; Kumar, Nitin; Yadav, Gaurav; Singh, Jaspreet; Mishra, Rohit K.; Kumar, Vivek; Verma, Rishi; Upadhyay, R. G.; Pandey, Mayank; Sharma, Shivesh 2017-01-01 Abiotic stress is one of the severe stresses of environment that lowers the growth and yield of any crop even on irrigated land throughout the world. A major phytohormone abscisic acid (ABA) plays an essential part in acting toward varied range of stresses like heavy metal stress, drought, thermal or heat stress, high level of salinity, low temperature, and radiation stress. Its role is also elaborated in various developmental processes including seed germination, seed dormancy, and closure of stomata. ABA acts by modifying the expression level of gene and subsequent analysis of cis- and trans-acting regulatory elements of responsive promoters. It also interacts with the signaling molecules of processes involved in stress response and development of seeds. On the whole, the stress to a plant can be susceptible or tolerant by taking into account the coordinated activities of various stress-responsive genes. Numbers of transcription factor are involved in regulating the expression of ABA responsive genes by acting together with their respective cis-acting elements. Hence, for improvement in stress-tolerance capacity of plants, it is necessary to understand the mechanism behind it. On this ground, this article enlightens the importance and role of ABA signaling with regard to various stresses as well as regulation of ABA biosynthetic pathway along with the transcription factors for stress tolerance. PMID:28265276 6. Purslane Weed (Portulaca oleracea: A Prospective Plant Source of Nutrition, Omega-3 Fatty Acid, and Antioxidant Attributes Md. Kamal Uddin 2014-01-01 Full Text Available Purslane (Portulaca oleracea L. is an important plant naturally found as a weed in field crops and lawns. Purslane is widely distributed around the globe and is popular as a potherb in many areas of Europe, Asia, and the Mediterranean region. This plant possesses mucilaginous substances which are of medicinal importance. It is a rich source of potassium (494 mg/100 g followed by magnesium (68 mg/100 g and calcium (65 mg/100 g and possesses the potential to be used as vegetable source of omega-3 fatty acid. It is very good source of alpha-linolenic acid (ALA and gamma-linolenic acid (LNA, 18 : 3 w3 (4 mg/g fresh weight of any green leafy vegetable. It contained the highest amount (22.2 mg and 130 mg per 100 g of fresh and dry weight, resp. of alpha-tocopherol and ascorbic acid (26.6 mg and 506 mg per 100 g of fresh and dry weight, resp.. The oxalate content of purslane leaves was reported as 671–869 mg/100 g fresh weight. The antioxidant content and nutritional value of purslane are important for human consumption. It revealed tremendous nutritional potential and has indicated the potential use of this herb for the future. 7. Some prospects for the use of ash and slag wastes of coal power plants for production of building materials Bryukhan Fedor 2016-01-01 Full Text Available Coal-fired thermal power plants (TPP generate large amounts of ash and slag wastes (ASW, therefore ecological problems related to ASW storage and disposal for such power plants come to the fore. To obtain new data on ASW properties analysis of a number of ASW samples from ash dump No. 4 of Cherepet’ TPP was carried out as part of engineering surveys. The purpose of this study included determiantion of the ASW granulometrical and mineralogical composition, as well as their physical and chemical properties. During field works 4 ASW samples were taken from the surface layer of the ash dump plus one sample of ash froth for further laboratory analysis. Laboratory analysis enabled determination of the granulometrical, mineralogical and chemical composition of ASW. Assessment of the ASW corrosiveness toward various materials determined necessary limitations in utilization of ASW-based bulding materiasls in contact with steel and aluminum. The content of natural radionuclides of K40, Ra226, Th232 and man-made Cs137 in ASW was determined. The detected increased activity of Ra226 and Th232 necessitates additional studies of radon and thoron emissions from ASW. Microspheres recovered from ash froth during ASW utilization have special usage value. 8. Thematic strategy on sustainable use of plant protection products. Prospects and requirements for transferring proposals for plant protection products to biocides Gartiser, Stefan [Hydrotox GmbH, Freiburg im Breisgau (Germany); Lueskow, Heike [Institut fuer Oekologie und Politik GmbH (OEKOPOL), Hamburg (Germany); Gross, Rita [Oeko-Institut e.V. - Institut fuer Angewandte Oekologie e.V., Freiburg im Breisgau (Germany) 2012-03-15 The sustainable use of pesticides pursues, independent of the authorisation of single products, the aim to minimise existing environmental risks of pesticide use and therefore contribute to the reduction of its impact on the environmental protection goals. The Thematic Strategy (TS) and the Framework Directive 2009/128/EC (FWD) on sustainable use of pesticides have so far only been implemented for plant protection products (PPP). For biocides there exists no harmonised approach. Within the project the possibilities and requirements for transferring measures of the FWD to the biocide area have been analysed, with specific focus on wood preservatives, insecticides, and antifouling products. Several biocidal active substances are found in the outlets of sewage treatment plants and in surface water, but an inventory of the present environmental impact as well as reliable data on biocide consumption and use patterns, which could be used to identify key action areas, are generally missing. These data are urgently needed for the development of suitable indicators and the definition of the objectives. Sustainable use of biocides addresses the three issues; social, environmental and economic impact at which the ecological background assigns the borderline and beam barrier of the economic and social development. A systematic analysis of the instruments for improving sustainable use of pesticides described in TS and FWD indicated that many issues can be transferred to the biocide area. This concerns e.g. education and training, requirements for sales, the establishment of awareness programmes, control of the machinery for biocide application, the development of best practice standards based on integrated pest management principles, and the collection of statistics on biocide consumption. Some biocide specific characteristics need to be considered: E.g. unlike PPP, the intended use of some biocides is to be directly applied in water bodies or indoors. Furthermore for some 9. Phytoremediation: State-of-the-art and a key role for the plant microbiome in future trends and research prospects. Thijs, Sofie; Sillen, Wouter; Weyens, Nele; Vangronsveld, Jaco 2017-01-02 Phytoremediation is increasingly adopted as a more sustainable approach for soil remediation. However, significant advances in efficiency are still necessary to attain higher levels of environmental and economic sustainability. Current interventions do not always give the expected outcomes in field settings due to an incomplete understanding of the multicomponent biological interactions. New advances in -omics are gradually implemented for studying microbial communities of polluted land in situ. This opens new perspectives for the discovery of biodegradative strains and provides us new ways of interfering with microbial communities to enhance bioremediation rates. This review presents retrospectives and future perspectives for plant microbiome studies relevant to phytoremediation, as well as some knowledge gaps in this promising research field. The implementation of phytoremediation in soil clean-up management systems is discussed, and an overview of the promoting factors that determine the growth of the phytoremediation market is given. Continuous growth is expected since elimination of contaminants from the environment is demanded. The evolution of scientific thought from a reductionist view to a more holistic approach will boost phytoremediation as an efficient and reliable phytotechnology. It is anticipated that phytoremediation will prove the most promising for organic contaminant degradation and bioenergy crop production on marginal land. 10. Status of plant protein drinks, prospects and innovative ideas%植物蛋白饮料的现状、前景及创新思路曾友明; 丁泉水 2011-01-01 按我国的分类方法,植物蛋白饮料属于软饮料,本文分析了植物蛋白饮料的现状:1.在软饮料中属于资产规模较小的行业;2.近些年来的发展速度很快;3.相对于软饮料的其它行业及液态乳行业,属于全国性品牌相对较弱,市场集中度相对较低,竞争性相对较小的行业.对其前景进行了展望:1.消费者对其健康性认识将越来越高,市场需求越来越大;2.未来几年仍属于高速发展时期;3.未来十年是形成全国性强势品牌的关键时期.并就其产品的创新思路进行了探讨:1.进行营养强化,针对其营养缺陷进行必要的强化或突出其最主要的功能;2.复合化,多种植物蛋白原料复合,或与牛奶、果蔬复合,使其营养更全面.%According to the classification, plant protein drinks are soft drinks. In this paper, status of plant protein drinks are analyzed: 1. In the soft drinks industry, it s relatively small asset size; 2. Fast development in recent years; 3. Relative in other soft drinks industry and liquid dairy industry, it's a national brand is relatively weak, the market concentration is relatively low, competitive is relatively small industry. Its prospect: 1. Knowledge of the health of consumers will be increasingly high, growing market demand; 2. The next few years is still a period of rapid development; 3. The next ten years is the formation of a strong national critical period of the brand. And innovative ideas for their products were discussed: 1. Were fortified, nutritional deficiencies, as necessary for its enhancement or highlight its main function; 2. Composite, a variety of plant protein raw material compound, or with milk, fruit Vegetable compound to make it more comprehensive nutrition. 11. Autoluminescent plants. Alexander Krichevsky Full Text Available Prospects of obtaining plants glowing in the dark have captivated the imagination of scientists and layman alike. While light emission has been developed into a useful marker of gene expression, bioluminescence in plants remained dependent on externally supplied substrate. Evolutionary conservation of the prokaryotic gene expression machinery enabled expression of the six genes of the lux operon in chloroplasts yielding plants that are capable of autonomous light emission. This work demonstrates that complex metabolic pathways of prokaryotes can be reconstructed and function in plant chloroplasts and that transplastomic plants can emit light that is visible by naked eye. 12. A case study of a sugar and alcohol plant: prospects for the production of alcohol and exceeding energy; Um estudo de caso de uma usina de acucar e alcool: perspectivas para a producao de alcool e energia excedente Halmeman, Maria Cristina Rodrigues; Oliveira, Franciene Gois; Seraphim, Odivaldo Jose [Universidade Estadual Paulista (UNESP), Botucatu, SP (Brazil)], E-mail: cristhalmeman@gmail.com; Halmenan, Radames Juliano [Universidade Tecnologica Federal do Parana (UTFPR), Campo Mourao, PR (Brazil); Michels, Roger Nabeyama [Instituto Federal de Santa Catarina (IFSC), Luzerna, SC (Brazil) 2010-07-01 Brazil stands out in the world scene as the largest producer and exporter of sugar and the main producer of ethanol derived from sugar cane, which generates the bagasse used to produce electrical energy for the plant as well as for electricity companies. Energy products from sugar cane, such as ethanol and bagasse have contributed significantly to reduce the gases that contribute to the greenhouse effect by replacing fossil fuels, that is, gasoline and diesel. The research is defined as exploratory and descriptive, the data were obtained in June, 2009 in a sugar cane and alcohol plant located in the state of Sao Paulo, Brazil. It was sought through direct interviews, to check what the prospects for the processing of sugar cane, alcohol production and generation of exceeding energy are. Therefore, the purpose of this study is to contextualize the current production of alcohol and electrical energy, with projections up to 2016. (author) 13. Intake of total, animal and plant proteins, and their food sources in 10 countries in the European Prospective Investigation into Cancer and Nutrition Halkjaer, J.; Olsen, A.; Bjerregaard, L. J.; Deharveng, G.; Tjonneland, A.; Welch, A. A.; Crowe, F. L.; Wirfalt, E.; Hellstrom, V.; Niravong, M.; Touvier, M.; Linseisen, J.; Steffen, A.; Ocke, M. C.; Peeters, P. H. M.; Chirlaque, M. D.; Larranaga, N.; Ferrari, P.; Contiero, P.; Frasca, G.; Engeset, D.; Lund, E.; Misirli, G.; Kosti, M.; Riboli, E.; Slimani, N.; Bingham, S. 2009-01-01 Objective: To describe dietary protein intakes and their food sources among 27 redefined centres in 10 countries participating in the European Prospective Investigation into Cancer and Nutrition (EPIC). Methods: Between 1995 and 2000, 36 034 persons, aged between 35 and 74 years, were administered a 14. Plant virus emergence and evolution: origins, new encounter scenarios, factors driving emergence, effects of changing world conditions, and prospects for control. Jones, Roger A C 2009-05-01 This review focuses on virus-plant pathosystems at the interface between managed and natural vegetation, and describes how rapid expansion in human activity and climate change are likely to impact on plants, vectors and viruses causing increasing instability. It starts by considering virus invasion of cultivated plants from their wild ancestors in the centres of plant domestication in different parts of the world and subsequent long distance movement away from these centres to other continents. It then describes the diverse virus-plant pathosystem scenarios possible at the interface between managed and natural vegetation and gives examples that illustrate situations where indigenous viruses emerge to damage introduced cultivated plants and newly introduced viruses become potential threats to biodiversity. These examples demonstrate how human activities increasingly facilitate damaging new encounters between plants and viruses worldwide. The likely effects of climate change on virus emergence are emphasised, and the major factors driving virus emergence, evolution and greater epidemic severity at the interface are analysed and explained. Finally, the kinds of challenges posed by rapidly changing world conditions to achieving effective control of epidemics of emerging plant viruses, and the approaches needed to address them, are described. 15. PROSPECTING EXPLORATION 2008-01-01 <正>20082879 Chen Yaoyu(No.3 Geology and Mineral Exploration Team,Gansu Provincial Bureau of Geology and Mineral Exploration and Development,Lanzhou 730050,China); Gong Quansheng Discussion on the Division of Deposit Scale and the Index of Ore Prospecting(Gansu Geology,ISSN 1004—4116,CN62—1191/P,16(3),2007,p.6—11,4 tables,6 refs.) Key words:prospecting and exploration of mineral 16. Planning small hydroelectric power plants, considering private sector prospects; O planejamento de pequenas centrais hidreletricas face as perspectivas da iniciativa privada Martinez, Carlos B. [Minas Gerais Univ., Belo Horizonte, MG (Brazil). Dept. de Engenheria Hidraulica e Recursos Hidricos; Bajay, Sergio V. [Universidade Estadual de Campinas, SP (Brazil) 1996-12-31 The participation of the private sector in the generation of electric power in Brazil and the experiences of private groups in the construction and operation of small hydroelectric power plants are analysed. 10 refs., 2 figs., 2 tabs 17. 香蕉根际促生菌的研究展望%Progress and Prospect on Plant Growth - promoting Rhizobacteria of Banana Rhizosphere 李文英; 彭智平; 于俊红; 黄继川; 宋慧敏 2011-01-01 植物根际促生菌(plant growth-promoting rhizobacteria,PGPR)是一类具有促进作物生长并增加产量的作用,兼有抑制植物病原菌、根际有害微生物的根际微生物,作为生物肥料和生物农药的重要资源库,PGPR相关研究受到越来越多的重视.着重从PGPR的概念演变、功能机制、研究手段及应用现状等方面进行综述,并在分析香蕉根际促生菌研究现状的基础上,对香蕉PGPR研究的理论意义和现实意义提出讨论与展望.%Plant growth-promoting rhizobacteria (PGPR) are microorganisms colonized in the plant rhizosphere, which can promote the plant growth and yield, and inhibit plant pathogens.As an important resource of biofertilizer and biocontrol agents, PGPR have been paid more and more attention by researchers in the sustainable agriculture.This paper reviewed progresses on the concept development, functioning mechanisms, study techniques and the application of PGPR.In addition, the theoretical and practical significance of banana PG PR were disscused, and some future directions in PGPR study were suggested. 18. Plants as De-Worming Agents of Livestock in the Nordic Countries: Historical Perspective, Popular Beliefs and Prospects for the Future Ingebrigtsen K 2001-03-01 Full Text Available Preparations derived from plants were the original therapeutic interventions used by man to control diseases (including parasites, both within humans and livestock. Development of herbal products depended upon local botanical flora with the result that different remedies tended to develop in different parts of the world. Nevertheless, in some instances, the same or related plants were used over wide geographic regions, which also was the result of communication and/or the importation of plant material of high repute. Thus, the Nordic countries have an ancient, rich and diverse history of plant derived anthelmintic medications for human and animal use. Although some of the more commonly used herbal de-wormers were derived from imported plants, or their products, many are from endemic plants or those that thrive in the Scandinavian environment. With the advent of the modern chemotherapeutic era, and the discovery, development and marketing of a seemingly unlimited variety of highly efficacious, safe synthetic chemicals with very wide spectra of activities, herbal remedies virtually disappeared from the consciousness – at least in the Western world. This attitude is now rapidly changing. There is a widespread resurgence in natural product medication, driven by major threats posed by multi-resistant pest, or disease, organisms and the diminishing public perceptions that synthetic chemicals are the panacea to health and disease control. This review attempts to provide a comprehensive account of the depth of historical Nordic information available on herbal de-wormers, with emphasis on livestock and to provide some insights on potentially rewarding areas of "re-discovery" and scientific evaluation in this field. 19. Application Status and Development Prospect of Plant Growth Regulator Brassinolide in Agriculture%植物生长调节剂芸苔素内酯在农业上的应用现状及前景陈秀; 方朝阳 2015-01-01 介绍了植物生长调节剂芸苔素内酯目前在国内的登记情况,简述了芸苔素内酯作为植物生长调节剂的生理功能,综述了芸苔素内酯商品化以来在国内农业上的应用现状及应用效果,并对其未来的发展前景进行了简要分析.%The paper reported the current registration information of the plant growth regulator Brassinolide in China, briefly described its physiological function, reviewed its application status and effects in agriculture and then analyzed its development prospect in the future. 20. Suitability of non-lethal marker and marker-free systems for development of transgenic crop plants: present status and future prospects. Manimaran, P; Ramkumar, G; Sakthivel, K; Sundaram, R M; Madhav, M S; Balachandran, S M 2011-01-01 Genetically modified crops are one of the prudent options for enhancing the production and productivity of crop plants by safeguarding from the losses due to biotic and abiotic stresses. Agrobacterium-mediated and biolistic transformation methods are used to develop transgenic crop plants in which selectable marker genes (SMG) are generally deployed to identify 'true' transformants. The commonly used SMG obtained from prokaryotic sources when employed in transgenic plants pose risks due to their lethal nature during selection process. In the recent past, some non-lethal SMGs have been identified and used for selection of transformants with increased precision and high selection efficiency. Considering the concerns related to bio-safety of the environment, it is desirable to remove the SMG in order to maximize the commercial success through wide adoption and public acceptance of genetically modified (GM) food crops. In this review, we examine the availability, and the suitability of wide range of non-lethal selection markers and elimination of SMG methods to develop marker-free transgenics for achieving global food security. As the strategies for marker-free plants are still in proof-of-concept stage, adaptation of new genomics tools for identification of novel non-lethal marker systems and its application for developing marker-free transgenics would further strengthen the crop improvement program. 1. Silicon occurrence, uptake, transport and mechanisms of heavy metals, minerals and salinity enhanced tolerance in plants with future prospects: A review. 2016-12-01 Recently, heavy metals pollution due to industrialization and urbanization, use of untreated wastewater and unreasonable use of pesticides and fertilizers is increasing rapidly, resulting in major threat to the environment and contaminate soils. Silicon (Si) is the second most abundant element in the earth crust after oxygen. Although it's higher accumulation in plants, yet Si has not been listed as essential nutrient however, considered as beneficial element for growth of plants particularly in stressed environment. Research to date has demonstrated that silicon helps the plants to alleviate the various biotic and abiotic stresses. This review article presents a comprehensive update about Si and heavy metals, minerals and salinity stresses, and contained the progress about Si so far done worldwide in the light of previous studies to evaluate the ecological importance of Si. Moreover, this review will also be helpful to understand the Si uptake ability and its benefits on plants grown under stressed environment. Further research needs for Si-mediated mitigation of heavy metals and mineral nutrients stresses are also discussed. Copyright © 2016 Elsevier Ltd. All rights reserved. 2. Development and Prospect of the Water Culture of Ornamental Plants%水培观赏植物的发展与展望李景蕻; 戴月; 张洪权 2012-01-01 无土栽培是提高设施农业生产效率的重要手段，其中，水培是一种新型的植物无土栽培方式，是一种需大力推广的具有规模化和精准化生产优势的现代植物生产技术，在21世纪中国生物产业崛起的大背景下，水培观赏植物的发展面临着机遇与挑战并存，还需要对不同水培观赏植物开展多学科、多角度、深层次的理论研究，为观赏植物的水培种植和工厂化生产提供理论依据和技术参考。%Soilless culture an important means of the facilities efficiency of agricultural production, hydroponics is a new plant soilless culture the way, is a need to promote the scale and precision production advantages modem plant production technology, the background of the rise of China＇s biotechnology industry in the 21 st century, the development of ornamental plants hydroponic facing both opportunities and challenges, different hydroponic ornamental plants to carry out multi-disci- plinary, multi-angle, deep-level theoretical studies of water for ornamental plantsPearson cultivation and industrial produc- tion to provide a theoretical basis and technical reference. 3. Resurrection plants of the genus Ramonda: prospective survival strategies - unlock further capacity of adaptation, or embark on the path of evolution? Rakić, Tamara; Lazarević, Maja; Jovanović, Zivko S; Radović, Svetlana; Siljak-Yakovlev, Sonja; Stevanović, Branka; Stevanović, Vladimir 2014-01-10 Paleoendemic species of the monophyletic genus Ramonda (R. myconi, R. serbica and R.~nathaliae) are the remnants of the Tertiary tropical and subtropical flora in Europe. They are the rare resurrection plants of Northern Hemisphere temperate zone. Ramonda serbica and R. nathaliae are chorologically differentiated in the Balkan Peninsula and occupy similar habitats in calcareous, northward slopes in canyons and mountainsides. They remain well-hydrated during spring, late autumn and even in winter. In summer and early autumn when plants are subjected to drought and thermal stress, their desiccation tolerance comes into operation and they fall into anabiosis. Investigations revealed the permanent presence of ubiquitine and its conjugates, high amounts of oxalic acid and proline. Both species are homoiochlorophyllous. It enables them to rapidly resume photosynthesis upon rehydration, but also makes them susceptible to reactive oxygen species formation. Dehydration induces activation of antioxidative enzymes (ascorbate peroxidase, glutathione reductase, polyphenol oxidase), increase in amounts of AsA and GSH, phenolic acids, dehydrins, sucrose, and inorganic ions. Plasma membranes, characterized by high amount of cholesterol, are subjected to decrease in membrane fluidity mostly on account of increased level of lipid saturation. Cytogenetic analysis revealed that R. nathaliae is a diploid (2n = 48) and probably evolutionary older species, while R. serbica is a hexaploid (2n = 144). Two species live together in only two localities forming hybrid individuals (2n = 96). Polyploidization is the major evolutionary mechanism in the genus Ramonda that together with hybridization ability indicates that these relict species which have preserved an ancient survival strategy are not the evolutionary "dead end."The species of the genus Ramonda are promising sources of data important for understanding the complex strategy of resurrection plants' survival, appraised through a prism 4. Spectral reflectance and emissivity features of broad leaf plants: Prospects for remote sensing in the thermal infrared (8.0-14.0 μm) Ribeiro da Luz, Beatriz; Crowley, James K. 2007-01-01 Field emissivity measurements were made of leaves collected from nine deciduous tree and agricultural plant species. The data show, for the first time, that it is possible to discriminate subtle spectral emissivity features of leaves from the natural background emission. Under conditions of controlled measurement geometry (leaves arranged to cover a flat surface), the field emissivity spectra agreed fairly well with emissivity values calculated from laboratory directional hemispherical reflectance measurements. Spectral features associated with a variety of leaf chemical constituents, including cellulose, cutin, xylan, silica, and oleanolic acid could be identified in the field emissivity data. Structural aspects of leaf surfaces also influenced spectral behavior, notably the abundance of trichomes, as well as wax thickness and texture. 5. Problems and prospects connected with development of high-temperature filtration technology at nuclear power plants equipped with VVER-1000 reactors Shchelik, S. V.; Pavlov, A. S. 2013-07-01 Results of work on restoring the service properties of filtering material used in the high-temperature reactor coolant purification system of a VVER-1000 reactor are presented. A quantitative assessment is given to the effect from subjecting a high-temperature sorbent to backwashing operations carried out with the use of regular capacities available in the design process circuit in the first years of operation of Unit 3 at the Kalinin nuclear power plant. Approaches to optimizing this process are suggested. A conceptual idea about comprehensively solving the problem of achieving more efficient and safe operation of the high-temperature active water treatment system (AWT-1) on a nuclear power industry-wide scale is outlined. 6. Resurrection plants of the genus Ramonda: prospective survival strategies – unlock further capacity of adaptation, or embark on the path of evolution? Tamara eRakic 2014-01-01 Full Text Available Paleoendemic species of the monophyletic genus Ramonda (R. myconi, R. serbica and R. nathaliae are the remnants of the Tertiary tropical and subtropical flora in Europe. They are the rare resurrection plants of Northern Hemisphere temperate zone. Ramonda serbica and R. nathaliae are chorologically differentiated in the Balkan Peninsula and occupy similar habitats in calcareous, northward slopes in canyons and mountainsides. They remain well-hydrated during spring, late autumn and even in winter. In summer and early autumn when plants are subjected to drought and thermal stress, their desiccation tolerance comes into operation and they fall into anabiosis. Investigations revealed the permanent presence of ubiquitine and its conjugates, high amounts of oxalic acid and proline. Both species are homoiochlorophyllous. It enables them to rapidly resume photosynthesis upon rehydration, but also makes them susceptible to ROS formation. Dehydration induces activation of antioxidative enzymes (APX, GR, PPO, increase in amounts of AsA and GSH, phenolic acids, dehydrins, sucrose and inorganic ions. Plasma membranes, characterized by high amount of cholesterol, are subjected to decrease in membrane fluidity mostly on account of increased level of lipid saturation.Cytogenetic analysis revealed that R. nathaliae is a diploid (2n=48 and probably evolutionary older species, while R. serbica is a hexaploid (2n=144. Two species live together in only two localities forming hybrid individuals (2n=96. Polyploidization is the major evolutionary mechanism in the genus Ramonda that together with hybridization ability indicates that these relict species which have preserved an ancient survival strategy are not the evolutionary „dead end.The species of the genus Ramonda are promising sources of data important for understanding the complex strategy of resurrection plants’ survival, appraised through a prism of their evolutionary and adaptive potential for multiple 7. 植物生长调节剂在高尔夫草坪上的应用%Application prospect of plant growth regulators on gol f turf 夏发生; 刘刚 2013-01-01 高尔夫球场草坪养护成本增加和效益降低已成为草坪养护管理者所面临的一个严峻问题。在草坪养护中，合理应用植物生长调节剂能有效地减少能源消耗和机械磨损，节省劳动力资源，提高草坪质量。植物生长调节剂能够促进高尔夫草坪种子萌发、幼苗生长和加速成坪；延缓高尔夫草坪生长，减少修剪；促进高尔夫草坪着色，延长绿期，提高草坪观赏性；促进草坪生根，增加分蘖，提高草坪草的抗逆性。%It has become a serious problem for turfgrass manager that the cost is increasing where as out-come is dropping in turfgrass maintenance and management.In the turf maintenance process,proper application of plant growth regulators can effectively reduce the energy consumption and mechanical wear,save labor usage and improve turf quality.Plant growth regulators can effectively promote the golf turf seed germination,rate seedling growth;reduce vain growth and mowing frequency;promote golf turf coloring,prolong green period;stimulate the root growth,improve tiller numbers;increase the resistance of turf. 8. Resurrection plants of the genus Ramonda: prospective survival strategies – unlock further capacity of adaptation, or embark on the path of evolution? Rakić, Tamara; Lazarević, Maja; Jovanović, Živko S.; Radović, Svetlana; Siljak-Yakovlev, Sonja; Stevanović, Branka; Stevanović, Vladimir 2014-01-01 Paleoendemic species of the monophyletic genus Ramonda (R. myconi, R. serbica and R.~nathaliae) are the remnants of the Tertiary tropical and subtropical flora in Europe. They are the rare resurrection plants of Northern Hemisphere temperate zone. Ramonda serbica and R. nathaliae are chorologically differentiated in the Balkan Peninsula and occupy similar habitats in calcareous, northward slopes in canyons and mountainsides. They remain well-hydrated during spring, late autumn and even in winter. In summer and early autumn when plants are subjected to drought and thermal stress, their desiccation tolerance comes into operation and they fall into anabiosis. Investigations revealed the permanent presence of ubiquitine and its conjugates, high amounts of oxalic acid and proline. Both species are homoiochlorophyllous. It enables them to rapidly resume photosynthesis upon rehydration, but also makes them susceptible to reactive oxygen species formation. Dehydration induces activation of antioxidative enzymes (ascorbate peroxidase, glutathione reductase, polyphenol oxidase), increase in amounts of AsA and GSH, phenolic acids, dehydrins, sucrose, and inorganic ions. Plasma membranes, characterized by high amount of cholesterol, are subjected to decrease in membrane fluidity mostly on account of increased level of lipid saturation. Cytogenetic analysis revealed that R. nathaliae is a diploid (2n = 48) and probably evolutionary older species, while R. serbica is a hexaploid (2n = 144). Two species live together in only two localities forming hybrid individuals (2n = 96). Polyploidization is the major evolutionary mechanism in the genus Ramonda that together with hybridization ability indicates that these relict species which have preserved an ancient survival strategy are not the evolutionary “dead end.”The species of the genus Ramonda are promising sources of data important for understanding the complex strategy of resurrection plants’ survival, appraised through a 9. Power storage system technology development. Toshiba's achievements and prospects of storage testing equipment in the Tatsumi plant of the Kansai Electric Power Co. , Ltd 1988-07-01 In the Tatsumi substation, Toshiba corporation built a power storage testing plant using revised lead batteries and has been test-running it since 1986. The storage system consists of (1) 526 revised-type lead batteries connected in series, (2) an AC/DC converter for connection to a DC system using a self-excited converter, and a measuring/monitoring operation control system. The converter synthesizes single-phase bridge fundamental units by using a transformer, thus eliminating all waves except higher harmonic waves. The system uses a vacuum circuit breaker for connection to AC lines, an output transformer for increasing converter voltage, and a DC high-speed circuit breader for DC circuits. The system achieves (a) a minimum charge/discharge energy efficiency of 70 % during constant-power operation at 500 kW or 1,000 kW, (b) a maximum response time of 10 seconds with regard to ordinary step changes in the effective/ineffective power setting, (c) and an overall voltage distortion factor of 2 %. Test results related to protective system behavior and environmental measurements were also satisfactory. (2 figs, 3 tabs) 10. Prospecting plant growth promoting bacteria and cyanobacteria as options for enrichment of macro- and micronutrients in grains in rice–wheat cropping sequence Anuj Rana 2015-12-01 Full Text Available The influence of plant growth promoting bacteria (PGPB and cyanobacteria, alone and in combination, was investigated on micronutrient enrichment and yield in rice–wheat sequence, over a period of two years. Analysis of variance (ANOVA in both crops indicated significant differences in soil dehydrogenase activity and micronutrient enrichment in grains (Fe, Zn in rice, and Cu, Mn in wheat. The combined inoculation of Anabaena oscillarioides CR3, Brevundimonas diminuta PR7, and Ochrobactrum anthropi PR10 (T6 significantly increased nitrogen, phosphorus, and potassium (NPK content and improved rice yield by 21.2%, as compared to the application of recommended dose of NPK fertilizers (T2. The treatment T5 (Providencia sp. PR3 + B. diminuta PR7 + O. anthropi PR10 recorded an enhancement of 13–16% in Fe, Zn, Cu, and Mn concentrations, respectively, in rice grains. In wheat, Providencia sp. PW5 (T6 recorded the highest yield (5.23 Mg ha−1 and significantly higher enrichment of Fe and Cu (44–45% in the grains. This study highlighted the promise of combinations of cyanobacteria/bacteria and their synergistic action in biofortification and providing savings of 40–60 kg N ha−1. Future focus needs to be towards integrating such promising environment-friendly and environmentally sustainable options in nutrient management strategies for this cropping sequence. 11. 立架种植葡萄修剪机的研制与展望%Development and Prospect of Vertical planting grape Pruning Machine 阿尔孜古丽·吾买尔 2016-01-01 结合新疆葡萄园的种植模式特点，设计了一种往复式葡萄修剪机，可以解决劳动生产的耗费时间长，人工成本高，作业量大等问题，以来提高葡萄产业的竞争优势。并对往复式葡萄修剪机提出了一种方案设计，使往复式修剪机不仅可以用于葡萄园的修剪，也可以用于其他果园和园林的修剪和整形，具有很好的社会效益和经济效益，可以得到很大的推广。%Combining with the characteristics of the planting patterns of the vineyard in Xinjiang,this paper designs a recip-rocating grape trimmer which can solve problems such as long labor production time,high labor costs,huge homework and so on to improve the competitive advantage of the grape industry.In this paper,a kind of scheme design for the reciprocating grape pruning machine is put forward,reciprocating cutting machine not only can be used for the trim of the vineyard,but also can be used for other pruning and shaping of orchards and gardens, which has very good social benefit and economic benefit. 12. Research progress and prospects for controlling plant diseases using Pseudomonas fluorescens%荧光假单胞菌防治植物病害研究现状与展望孙广正; 姚拓; 赵桂琴; 卢虎; 马文彬 2015-01-01 Biological control agents,especially Pseudomonas fluorescens ,have become one of the most impor-tant and useful options for plant disease management.This study reviews the culture characteristics of P .fluo-rescens ,including the morphological characteristics,physiological and biochemical characteristics,culture con-ditions and the similarities or differences with other bacteria also isolated from various plant groups to control diseases.The disease control efficiency of P .fluorescens when used alone or together with other bacteria or treatment preparations is summarized.The modes of action of both P .fluorescens and bio-active substances used for controlling plant diseases are elucidated.Hazards of P .fluorescens in medicine,agriculture and envi-ronmental protection are discussed.The outlook and prospects for biological control in the field are also evalua-ted and a field risk assessment presented.%随着植物病害的日趋严重，生物防治已经成为国内外学者研究的重点，其中，荧光假单胞菌尤为重要。本研究综述了荧光假单胞菌的培养特征（形态特征、生理生化特性、培养条件和与其他菌的异同）；从不同类群的植物分离到防治病害的荧光假单胞菌；荧光假单胞菌的生防效果（单独使用和与其他菌或物质交互使用的防治效果）；荧光假单胞菌及活性物质防治植物病害的作用方式和作用机理；荧光假单胞菌在医学、农业和环保领域中的危害。对其风险和在生物防治领域的发展前景做了评价和展望。 13. Site-specific analysis of geothermal development-data files of prospective sites. Vol. III Williams, F.; Cohen, A.; Pfundstein, R.; Pond, S. 1978-02-01 Development scenarios for 37 hydrothermal and geopressured prospects in the United States were analyzed. This third of three volumes presents site-specific data and sample development schedules for the first plant on line at each of the 37 prospects. 14. Bioenergy Plants: Hopes, Concerns and Prospectives Martin A.J.Parry; Hai-Chun Jing 2011-01-01 @@ There are major concerns over both the security of energy supplies (declining supplies and political control) and the en-vironmental costs associated with energy generation and use.The global consumption of carbon-containing fossil fuels for heat, electricity, transport and the manufacture of chemicals is not sustainable. 15. Kenaf: its prospect in Indonesia Estri Laras Arumingtyas 2015-09-01 Full Text Available Kenaf is a plant fibre with high potential as source of material industry. Originally, kenaf usage in Indonesia is still limited only for jute sacks material, which is then displaced by plastic sacks production. While at international scale, kenaf has been started to be developed as pulp material, polypropylene composite, fibreglass replacement, and particle board for automotive industry materials. Indonesia is a tropical country this condition which suitable for kenaf cultivation. However, research reports about kenaf potential usages are still few and limited in domestic level only. Whereas, Indonesian kenaf plant information is needed by international community to understand comprehensively about the potential of tropical plants. This article aims to provide an overview about kenaf cultivation potential and usages in Indonesia as well as the possibility of future development. Key words: kenaf, fibre, prospect, potential. 16. MRI of plants and foods As, van H.; Duynhoven, van J.P.M. 2013-01-01 The importance and prospects for MRI as applied to intact plants and to foods are presented in view of one of humanity's most pressing concerns, the sustainable and healthy feeding of a worldwide increasing population. Intact plants and foods have in common that their functionality is determined by 17. Psychophysiology of prospective memory. Rothen, Nicolas; Meier, Beat 2014-01-01 Prospective memory involves the self-initiated retrieval of an intention upon an appropriate retrieval cue. Cue identification can be considered as an orienting reaction and may thus trigger a psychophysiological response. Here we present two experiments in which skin conductance responses (SCRs) elicited by prospective memory cues were compared to SCRs elicited by aversive stimuli to test whether a single prospective memory cue triggers a similar SCR as an aversive stimulus. In Experiment 2 we also assessed whether cue specificity had a differential influence on prospective memory performance and on SCRs. We found that detecting a single prospective memory cue is as likely to elicit a SCR as an aversive stimulus. Missed prospective memory cues also elicited SCRs. On a behavioural level, specific intentions led to better prospective memory performance. However, on a psychophysiological level specificity had no influence. More generally, the results indicate reliable SCRs for prospective memory cues and point to psychophysiological measures as valuable approach, which offers a new way to study one-off prospective memory tasks. Moreover, the findings are consistent with a theory that posits multiple prospective memory retrieval stages. 18. Clinical Effect of Antioxidant Glasses Containing Extracts of Medicinal Plants in Patients with Dry Eye Disease: A Multi-Center, Prospective, Randomized, Double-Blind, Placebo-Controlled Trial. Choi, Won; Kim, Jae Chan; Kim, Won Soo; Oh, Han Jin; Yang, Jee Myung; Lee, Jee Bum; Yoon, Kyung Chul 2015-01-01 To investigate the clinical efficacy and safety of wearable antioxidant glasses containing extracts of medicinal plants in patients with mild dry eye disease (DED). Fifty patients with mild DED were randomly assigned to wear either extracts of antioxidant medicinal plants containing (N = 25) or placebo glasses (N = 25). Patients wore the glasses for 15 min three times daily. The ocular surface disease index (OSDI) score, tear film break up time (BUT), and Schirmer's test were evaluated and compared within the group and between the groups at baseline, 4 weeks, and 8 weeks after treatment. OSDI score and tear film BUT were significantly improved in the treatment group at 4 and 8 weeks after wearing glasses (all P plants were effective in improving in DED both subjectively and objectively. Wearing antioxidants glasses might be a safe and adjunctive therapeutic option for DED. ISRCTN registry 71217488. 19. Phytoextraction of heavy metals by potential native plants and their microscopic observation of root growing on stabilised distillery sludge as a prospective tool for in situ phytoremediation of industrial waste. Chandra, Ram; Kumar, Vineet 2017-01-01 The safe disposal of post-methanated distillery sludge (PMDS) in the environment is challenging due to high concentrations of heavy metals along with other complex organic pollutants. The study has revealed that PMDS contained high amounts of Fe (2403), Zn (210), Mn (126), Cu (73.62), Cr (21.825), Pb (16.33) and Ni (13.425 mg kg(-1)) along with melanoidins and other co-pollutants. The phytoextraction pattern in 15 potential native plants growing on sludge showed that the Blumea lacera, Parthenium hysterophorous, Setaria viridis, Chenopodium album, Cannabis sativa, Basella alba, Tricosanthes dioica, Amaranthus spinosus L., Achyranthes sp., Dhatura stramonium, Sacchrum munja and Croton bonplandianum were noted as root accumulator for Fe, Zn and Mn, while S. munja, P. hysterophorous, C. sativa, C. album, T. dioica, D. stramonium, B. lacera, B. alba, Kalanchoe pinnata and Achyranthes sp. were found as shoot accumulator for Fe. In addition, A. spinosus L. was found as shoot accumulator for Zn and Mn. Similarly, all plants found as leaf accumulator for Fe, Zn and Mn except A. spinosus L. and Ricinus communis. Further, the BCF of all tested plants were noted 1. This revealed that metal bioavailability to plant is poor due to strong complexation of heavy metals with organic pollutants. This gives a strong evidence of hyperaccumulation for the tested metals from complex distillery waste. Furthermore, the TEM observations of root of P. hysterophorous, C. sativa, Solanum nigrum and R. communis showed formation of multi-nucleolus, multi-vacuoles and deposition of metal granules in cellular component of roots as a plant adaptation mechanism for phytoextraction of heavy metal-rich polluted site. Hence, these native plants may be used as a tool for in situ phytoremediation and eco-restoration of industrial waste-contaminated site. 20. The PROSPECT Physics Program Ashenfelter, J; Band, H R; Barclay, G; Bass, C D; Berish, D; Bowden, N S; Bowes, A; Bryan, C D; Brodsky, J P; Cherwinka, J J; Chu, R; Classen, T; Commeford, K; Davee, D; Dean, D; Deichert, G; Diwan, M V; Dolinski, M J; Dolph, J; Gaison, J K; Galindo-Uribarri, A; Gilje, K; Glenn, A; Goddard, B W; Green, M; Han, K; Hans, S; Heeger, K M; Heffron, B; Jaffe, D E; Jones, D; Langford, T J; Littlejohn, B R; Caicedo, D A Martinez; McKeown, R D; Mendenhall, M P; Mueller, P; Mumm, H P; Napolitano, J; Neilson, R; Norcini, D; Pushin, D; Qian, X; Romero, E; Rosero, R; Seilhan, B S; Sharma, R; Sheets, S; Surukuchi, P T; Varner, R L; Viren, B; Wang, W; White, B; White, C; Wilhelmi, J; Williams, C; Wise, T; Yao, H; Yeh, M; Yen, Y -R; Zangakis, G; Zhang, C; Zhang, X 2015-01-01 The Precision Reactor Oscillation and Spectrum Experiment, PROSPECT, is designed to make a precise measurement of the antineutrino spectrum from a highly-enriched uranium reactor and probe eV-scale sterile neutrinos by searching for neutrino oscillations over meter-long distances. PROSPECT is conceived as a 2-phase experiment utilizing segmented $^6$Li-doped liquid scintillator detectors for both efficient detection of reactor antineutrinos through the inverse beta decay reaction and excellent background discrimination. PROSPECT Phase I consists of a movable 3-ton antineutrino detector at distances of 7 - 12 m from the reactor core. It will probe the best-fit point of the $\ 1. 植物内生菌对柑橘溃疡病的生物防治作用及应用前景%Biological Control Effect of Plant Endophyte on Citrus Bacterial Canker Disease and Its Prospects 金玲莉; 匡全; 王彦波 2012-01-01 This paper summarized the disease -resistant mechanism and biological control effect of plant endophyte, discussed the mechanism and superiority of plant endophyte in the control of citrus bacterial canker disease, and looked forward its application in the biological control.%从植物内生菌的抗病机理及生物防治病害作用方面综述了利用植物内生菌防治柑橘溃疡病的机理与优势,并对其生物防治应用前景进行了展望. 2. Prospective ergonomics: origin, goal, and prospects. Robert, Jean-Marc; Brangier, Eric 2012-01-01 So far ergonomics has been concerned with two categories of activities: correction and design. We propose to add a third category: prospection, and by so doing, we introduce a new series of activities that opens up the future of ergonomics. Corrective ergonomics relates to the past and comes with a demand and a client. It is turned towards the correction of existing situations and aims to reduce or eliminate problems. Here, after delimiting and defining the problem, the challenge is to find the best solution. Ergonomics for design relates to the present and also comes with a demand and a client. It is turned towards the design of new artefacts that have already been identified by a client, and that will allow users to do some activity and attain their goals. Here, after defining the scope of the project and the functional requirements, the challenge is to do the best design. Finally, prospective ergonomics relates to the future and does not come with a demand and a client. It is turned towards the creation of future things that have not been identified yet. Here the challenge is to detect existing user needs or anticipate future ones, and imagine solutions. These three categories of activities overlap and are not exclusive of each other. In this paper we define prospective ergonomics and compare it with corrective ergonomics and ergonomics for design. We describe its origin, goal, and prospects, we analyze its impacts on education and practice, and we emphasize the need of new collaboration between ergonomics and other disciplines. 3. Application Prospect of Harmless Disposal Technology for Garden Plant Wastes in Taiyuan City%太原市园林废弃物无害化处理技术应用展望高玉平 2014-01-01 This paper expounds the present situation of and existing problems in the harmless disposal technology for garden plant wastes in Taiyuan City, analyzes the biological benefit and social benefit of the harmless disposal technology for garden plant wastes, probes into the features of the harmless disposal of garden plant wastes and the technical principle and the main equipment of the harmless disposal, and puts forward the solution for the harmless disposal of garden plant wastes.%阐述了太原市园林植物废弃物无害化处理技术的应用现状和存在的问题，分析了园林废弃物处理的生态效益和社会效益，探讨了园林废弃物无害化处理技术的特点以及园林废弃物处理的工艺原理与主要设备，提出了园林废弃物处理的解决方案。 4. Problems, Prospects And Challenges. Urban Road Transportation in Nigeria From 1960 To 2006: Problems, Prospects And Challenges. ... Ethiopian Journal of Environmental Studies and Management ... The paper suggested the construction of more motor-able roads within cities ... 5. Forage Oat Production Investigation and Analysis of Planting Prospect in Ar Horqin%阿旗草用燕麦生产调查及种植前景分析赵世锋; 巴图巴根; 任长忠; 秦佳滨; 满都拉 2015-01-01 Ar Horqin Banner has vast prairie area, which is the important breeding base of cow and sheep. And the climate is suitable for growing oat. The artificial grasslands of alfalfa and green mass of oat have developed rapidly in recent years. The aim of this study was to better solve the problem of oat production in this area, and accurately get the picture of oat cultivation and its economic benefits. The artificial grassland of the oat production was investigated and the different methods'influence on the planting of green mass of oat was studied. The results were as follows:(1) Oat could be used as the protect crop in sand. The oat root crop could reduce soil erosion and cover the soil surface on the severe desertification grassland. It could avoid sand erosion of alfalfa seeds and ensure the seedlings completing, uniformity and robustness of alfalfa planted in the oat root crop field. And oat could be used as protecting crop and planted with alfalfa. Alfalfa planting time could be ahead of schedule for two months, so green mass of oat and alfalfa could be harvested once a year to improve the overall benefits. (2) Oats could be used as rotation crop of alfalfa. The artificial grasslands planted alfalfa, but the grass yield began to drop when the clover entered high yield period, so timely crop rotation with oat was needed. (3) The grazing grassland could be built with a mixed type of oat and alfalfa forage planting. The mixed seeding of oat and alfalfa was a mature technology at home and abroad. The grazing grassland could be built by mix-sowing of Medicago and Bromus inermis, and economic benefits could be obtained in that very year. (4) Oat and hay were the high grade forage grasses of animal husbandry, and their seed was the high quality feed for livestock. Oat could grow in various soil type blocks and suitable varieties should be chosen according to the planting time and environment, in order to obtain high economic benefits. (5) Grass with oat planting had 6. Clinical Effect of Antioxidant Glasses Containing Extracts of Medicinal Plants in Patients with Dry Eye Disease: A Multi-Center, Prospective, Randomized, Double-Blind, Placebo-Controlled Trial. Won Choi Full Text Available To investigate the clinical efficacy and safety of wearable antioxidant glasses containing extracts of medicinal plants in patients with mild dry eye disease (DED.Fifty patients with mild DED were randomly assigned to wear either extracts of antioxidant medicinal plants containing (N = 25 or placebo glasses (N = 25. Patients wore the glasses for 15 min three times daily. The ocular surface disease index (OSDI score, tear film break up time (BUT, and Schirmer's test were evaluated and compared within the group and between the groups at baseline, 4 weeks, and 8 weeks after treatment.OSDI score and tear film BUT were significantly improved in the treatment group at 4 and 8 weeks after wearing glasses (all P < 0.001. Compared to the placebo group, the OSDI scores were significantly lower in the treatment group at 8 weeks (P = 0.007. The results of the Schirmer's test showed significant improvement in the treatment group at 4 weeks (P = 0.035, however there were no significant differences between the other groups or within the groups. No adverse events were reported during the study.Antioxidant glasses containing extracts of medicinal plants were effective in improving in DED both subjectively and objectively. Wearing antioxidants glasses might be a safe and adjunctive therapeutic option for DED.ISRCTN registry 71217488. 7. The technique of Solar Tower and its Application Prospect Power Plant in China%塔式太阳能热发电技术及其在我国的应用前景分析杨艳玲; 叶丽 2012-01-01 介绍了塔式太阳能热发电的结构原理、关键技术，并结合国内外相关研究的基础上，针对中国的能源情况和自然资源情况，论述了我国发展塔式太阳能热发电的必要性和可行性，并对我国发展塔式太阳能发电技术进行风险分析，提出相关建议。%The concentrated solar power a kind of potential technology for energy. In this paper, the mech- anism for solar tower power plant and its key technologies were introduced at first. The status of develop- ments of solar tower power plant at home and abroad was summarized then. It is concluded that the de- velopment of technology of solar tower power plant is necessary and feasible according to the analysis of energy and natural resources distribution in China. The risk analysis for solar tower was carried out at last and some of advices were put forward for the technology. 8. Opportunities, Challenges and Prospects of Utilization of Plant Biomass for Energy in Constructed Wetland%人工湿地植物能源化利用的机遇、挑战与展望刘冬; 欧阳琰; 林乃峰; 葛滢; 常杰; 邹长新 2013-01-01 综合概述了利用人工湿地植物进行能源化再生产的方式、优势、存在问题和发展趋势。人工湿地植物具有生长不需额外施肥、较高的生物量、物种多样化等优势，是一种较好的生物质资源，可通过生物质固体成型燃料技术、沼气技术和燃料乙醇技术加以利用，进而建立人工湿地植物生物质能源化利用模式，实现应对能源挑战、进行污水处理和强化环境保护三者的有机统一。%A review was conducted on models of production, strengths, existing problems and development trend in using wetland plants for energy production. The plants grown in constructed wetland are advantageous due to no need for extra fertilization, high biomass production, and high species diversity, they can be used as one of the suitable raw material resources for biomass briquette fuel, biogas and bioethanol production. Models of using plant biomass for bioenergy production will be developed to achieve the harmonization among energy need, wastewater treatment and environmental protection. 9. Current Development Situation and Prospects of Blueberry in Guangdong Province Lixia; GAO; Hualan; XIAO; Sen; LI; Fengmin; LIU; Aiqiong; MO 2015-01-01 With high nutrition and health value,blueberry receives much concern in recent years. Blueberry experts in the world are cultivating new blueberry varieties. They have come up with constructive theoretical support and planting technology researches and are constantly devoted to expanding blueberry planting latitudes. This paper elaborated researches of blueberry at home and abroad,current development situation of blueberry in China and Guangdong Province,analyzed strengths of planting blueberry in Guangdong. Besides,it came up with recommendations for development of blueberry industry. Finally,it discussed development prospects of blueberry planting in Guangdong. 10. Cumulative Impact Evaluation in Central Part of Liepaja with Comulative Pollution Index Method and Air Pollution Dispersion Modelling Kalniņš Viesturs 2015-07-01 Full Text Available Cumulative impact evaluation is one of the most actual problems in air quality monitoring. At the same time, it is also the most problematic factor to evaluate due to lack of appropriate methodology. The aim of this study was to assess the opportunity to use a new method – Cumulative Pollution Index (CPI in cumulative impact calculation from two different sets of data – bioindication survey with Index of Atmospheric Purity method and air pollution dispersion modelling. Results show that the usage of modelling data, instead of measurements, in cumulative impact evaluation can be quite difficult due to the fact that dispersion models not always give sufficiently accurate data. Despite the issues with modelling specifics, the use of dispersion modelling in CPI calculation shows that the use of this approach not only gives plausible data – obtained values correlate with pollution level and forming strong clustering in spatial distribution, but also reveals new facts about cumulative impact – demonstrates the city microclimate importance in forming of cumulative effect due to geometry of street canyons. 11. The PROSPECT physics program Ashenfelter, J.; Balantekin, A. B.; Band, H. R.; Barclay, G.; Bass, C. D.; Berish, D.; Bignell, L.; Bowden, N. S.; Bowes, A.; Brodsky, J. P.; Bryan, C. D.; Cherwinka, J. J.; Chu, R.; Classen, T.; Commeford, K.; Conant, A. J.; Davee, D.; Dean, D.; Deichert, G.; Diwan, M. V.; Dolinski, M. J.; Dolph, J.; DuVernois, M.; Erikson, A. S.; Febbraro, M. T.; Gaison, J. K.; Galindo-Uribarri, A.; Gilje, K.; Glenn, A.; Goddard, B. W.; Green, M.; Hackett, B. T.; Han, K.; Hans, S.; Heeger, K. M.; Heffron, B.; Insler, J.; Jaffe, D. E.; Jones, D.; Langford, T. J.; Littlejohn, B. R.; Martinez Caicedo, D. A.; Matta, J. T.; McKeown, R. D.; Mendenhall, M. P.; Mueller, P. E.; Mumm, H. P.; Napolitano, J.; Neilson, R.; Nikkel, J. A.; Norcini, D.; Pushin, D.; Qian, X.; Romero, E.; Rosero, R.; Seilhan, B. S.; Sharma, R.; Sheets, S.; Surukuchi, P. T.; Trinh, C.; Varner, R. L.; Viren, B.; Wang, W.; White, B.; White, C.; Wilhelmi, J.; Williams, C.; Wise, T.; Yao, H.; Yeh, M.; Yen, Y.-R.; Zangakis, G. Z.; Zhang, C.; Zhang, X.; PROSPECT Collaboration 2016-11-01 The precision reactor oscillation and spectrum experiment, PROSPECT, is designed to make a precise measurement of the antineutrino spectrum from a highly-enriched uranium reactor and probe eV-scale sterile neutrinos by searching for neutrino oscillations over a distance of several meters. PROSPECT is conceived as a 2-phase experiment utilizing segmented 6Li-doped liquid scintillator detectors for both efficient detection of reactor antineutrinos through the inverse beta decay reaction and excellent background discrimination. PROSPECT Phase I consists of a movable 3 ton antineutrino detector at distances of 7-12 m from the reactor core. It will probe the best-fit point of the {ν }e disappearance experiments at 4σ in 1 year and the favored region of the sterile neutrino parameter space at \\gt 3σ in 3 years. With a second antineutrino detector at 15-19 m from the reactor, Phase II of PROSPECT can probe the entire allowed parameter space below 10 eV2 at 5σ in 3 additional years. The measurement of the reactor antineutrino spectrum and the search for short-baseline oscillations with PROSPECT will test the origin of the spectral deviations observed in recent {θ }13 experiments, search for sterile neutrinos, and conclusively address the hypothesis of sterile neutrinos as an explanation of the reactor anomaly. 12. Encapsulation plant at Forsmark Nystroem, Anders 2007-08-15 SKB has already carried out a preliminary study of an encapsulation plant detached from Clab (Central interim storage for spent fuels). This stand-alone encapsulation plant was named FRINK and its assumed siting was the above-ground portion of the final repository, irrespective of the repository's location. The report previously presented was produced in cooperation with BNFL Engineering Ltd in Manchester and the fuel reception technical solution was examined by Gesellschaft fuer Nuklear-Service mbH (GNS) in Hannover and by Societe Generale pour les Techniques Nouvelles (SGN) in Paris. This report is an update of the earlier preliminary study report and is based on the assumption that the encapsulation plant and also the final repository will be sited in the Forsmark area. SKB's main alternative for siting the encapsulation plant is next to Clab. Planning of this facility is ongoing and technical solutions from the planning work have been incorporated in this report. An encapsulation plant placed in proximity to any final repository in Forsmark forms part of the alternative presentation in the application for permission to construct and operate an installation at Clab. The main technical difference between the planned encapsulation plant at Clab and an encapsulation plant at a final repository at Forsmark is how the fuel is managed and prepared before actual encapsulation. Fuel reception at the encapsulation plant in Forsmark would be dry, i.e. there would be no water-filled pools at the facility. Clab is used for verificatory fuel measurements, sorting and drying of the fuel before transport to Forsmark. This means that Clab will require a measure of rebuilding and supplementary equipment. In purely technical terms, the prospects for building an encapsulation plant sited at Forsmark are good. A description of the advantages and drawbacks of siting the encapsulation plant at Clab as opposed to any final repository at Forsmark is presented in a separate 13. 土壤-植物体系中农药和重金属污染研究现状及展望%Proceedings and Prospects of Pesticides and Heavy Metals Contamination in Soil-Plant System 潘攀; 杨俊诚; 邓仕槐; 姜慧敏; 张建峰; 李玲玲; 沈飞 2011-01-01 农药、重金属已成为当今农业生态系统中重要的污染物质,国内外科学家对其进行了大量卓有建树的研究,特别是在土壤-植物系统中的研究受到较多关注.通过就农药和重金属对土壤微生物、土壤动物、土壤酶活性和植物的生理生化指标的影响进行的综合分析和阐述,系统剖析了其产生毒害机理和影响的因素,在此基础上提出今后相关研究中有待加强的重点,包括农药对非靶标生物毒害机理、农药降解中间产物的环境风险以及农药和重金属的迁移转化机理等.%Pesticides and heavy metals beeing considered as serious pollutants in agro-ecosystem, it had been studied massively over the world, especially in soil-plant system. The impact of pesticides and heavy metals on soil microbes, soil animals, soil enzymatic activity, and physiological and biochemical characters of plant were analyzed and discussed in this review, as well as their toxicological mechanism and influencing factors. Based on above, toxicological mechanism of pesticides on non-target, environmental risk of pesticides degradation products, and transformation mechanism of pesticides and heavy metals in soil-plant system were proposed as key areas in further study. 14. 生物滤池去除污水处理厂臭气的应用及展望%Application and prospects of the biofilter for the removal of malodors in wastewater treatment plant 韩力超; 刘建广; 罗培 2011-01-01 The malodor pollution has already become a very important problem of environmental pollution in the wastewater treatment plant and the study and application of deodorization technology have already become a focus. Biological deodorization method uses microbial metabolism to transform malodorous substances without secondary pollution, so it is suitable to deal with the malodor from wastewater treatment plants. The biofilter technology is widely used to control the malodor in wastewater treatment plant. The paper introduces the components and source of malodors and the overview of biofilter process and elaborates the influencing factors of the biofilter. At last,it summarizes the existing problems and development direction of biofilter technology by comparing with other deodorization technology and engineering practice in recent years.%污水处理厂中恶臭气体污染已成为环境污染的重大问题,除臭技术的研究与应用已经成为一个热点.生物除臭法利用微生物的代谢作用转化致臭物质,不会产生二次污染,适于处理污水处理厂的臭气.生物滤池除臭技术在污水处理厂中应用广泛.介绍了污水处理厂恶臭物质的成分、来源及生物滤池工艺的概况,详细阐述了生物滤池的影响因素,与其他除臭工艺的比较以及最近几年的工程实例,最后概述了生物滤池工艺存在的问题以及发展方向. 15. The technological prospective of non nuclear channels; La prospective technologique des filieres non nucleaires Claverie, M.; Clement, D.; Girard, C 2000-07-15 This prospective study concerns the electric power demand in 2050. It examines the three non nuclear sectors of production: the natural gas combined cycle power plants, the wind turbines among the renewable energies and the cogeneration electric power - heat in the ternary and building sector. The necessity of the network adaptation to the european competition and the decentralized production of electric power will suppose new investments of transport and storage. (A.L.B.) 16. 金堆城百花岭选矿厂重大技术进步回顾与展望%REVIEW AND PROSPECT OF MAJOR TECHNOLOGY PROGRESS IN BAIHUALING DRESSING PLANT 刘迎春 2013-01-01 介绍了百花岭选矿厂近30年来新工艺、新设备、新药剂等方面的重大技术进步.对已取得的成就进行了总结并就公司今后如何加快企业科技创新,增强企业竞争力提出了建议.%Major technological advances of new technologies,new equipment,new pharmaceuticals in past 30 years in Baihualing Dressing Plant were introduced.The achievements were summarized.Meanwhile,how to accelerate enterprises innovation of science and technology in the future and enhance the competitiveness of enterprises were recommended. 17. Rhododendron plants in Nanling mountains along an altitudinal gradient and the prospect of landscape greening%南岭山地杜鹃花沿海拔梯度的分布及其园林应用前景张璐; 敬小丽; 苏志尧; 杜伟静 2014-01-01 [目的]从植物资源利用的角度，定量研究南岭山地杜鹃花沿海拔梯度的分布，以期为城乡园林绿化推荐可供引种的潜在杜鹃花种类．[方法]在南岭山地海拔700～1900 m范围内，采用样方法设置样地，运用相关分析和双向指示种分析（ TWINSPAN）探讨南岭山地垂直带谱上的杜鹃花分异特征．[结果和结论]基于15600 m2样方数据，南岭山地共有杜鹃花属植物7种，皆为小径阶的常绿灌木或小乔木；TWINSPAN将7种杜鹃花分为3大类，第1大类由刺毛杜鹃Rhododendron championae、猴头杜鹃R．simiarum和龙山杜鹃R．chunii组成，第2大类由多花杜鹃R． cavaleriei、广东杜鹃R．kwangtungense和腺萼马银花R．bachii组成，云锦杜鹃R．fortunei自成第3大类，分类结果反映出南岭山地杜鹃花属沿海拔梯度的变化，揭示采用数量分类方法能够根据植被组成反映环境特点的生态原理；垂直带谱上，多花杜鹃分布最为广泛，其次为腺萼马银花，刺毛杜鹃和猴头杜鹃出现在多个海拔段．%[Objective]The objective was to determine the altitudinal pattern of Rhododendron plant distri-bution and the potential of using indigenous Rhododendron plant resource in landscape greening .[Meth-od] The continuous transect sampling method was employed and a total area of 15 600 m2 was surveyed . A horizontal transect (10 m ×120 m) was placed at an 100 m altitudinal interval from 700 m to 1 900 m a.s.l., representing the altitudinal range of Rhododendron in Nanling mountains of north Guangdong . The contiguous grid quadrat sampling method was used for plant census in each transect , which consisted of 12 quadrats (10 m ×10 m).Correlation analysis and two-way indicator species analysis (TWINS-PAN) were used to analyze the altitudinal patterns of Rhododendron species.[Result and conclusion]Seven Rhododendron species were found in the 15 600 m2 plot, all of which were perennial 18. Jojoba: an assessment of prospects Walters, P.R.; MacFarlane, W.; Spensley, P.C. 1979-01-01 Jojoba (Simmondsia chinensis) is a crop that might be cultivated profitably in the arid and semi-arid zones of certain cultivated profitably in the arid and semi-arid zones of certain developing countries. This report assesses the present state of research on the crop and gives an opinion as to its prospects of being of economic benefit to these areas. The report is divided into five sections. In Section 1 the plant and its natural habitats are described and current research and the problems to be overcome in cultivating the crop are outlined. In Section 2 the chemistry of jojoba and other waxes is discussed. In Section 3 consideration is given to the end-use potential of jojoba and an attempt is made to forecast the future market demand and price for jojoba oil, both as a liquid and as a solid wax. In Section 4 the economics of jojoba production are discussed in light of the findings in the earlier sections. Finally, in Section 5, the wider aspects of plant introductions are considered briefly and conclusions drawn regarding jojoba's potential and its future research needs. It will be essential to increase jojoba yield significantly before cultivation will be viable except on a small scale. A satisfactory mechanized harvesting system also needs to be developed. The market for jojoba oil at various levels of production is estimated at production of less than 1000 tons (pounds-sterling 5500- pounds-sterling 7700 per ton); production of 2000 to 5000 tons (pounds-sterling 900- pounds-sterling 950 per ton); and production up to 20,000 tons (pounds-sterling 500-pounds-sterling 600 per ton). 19. Efficiency of Modern Power Plants of Thermal Power Stations B. V. Yakovlev 2007-01-01 Full Text Available The paper considers efficiency and prospects in development of different types of fossil-fuel power plants – gas turbine, steam turbine and combined (gas and steam cycles.The paper provides information on plant selection, fuel consumption, specific output cost. It describes main advantages of various power plants. 20. Applications and Prospects of Fluorescence in situ Hybridization on Plant Molecular Cytogenetics%荧光原位杂交技术（FISH）及其在植物分子细胞遗传学中的应用与展望林秀琴; 毛钧; 陆鑫; 刘新龙; 马丽; 蔡青 2012-01-01 Fluorescence in situ hybridization （FISH） is a most effective method of detecting alien chromatin at molecular level. It plays an increasing important role in a variety of research fields, such as plant molecular cytogenetics, gene amplification, gene mapping, evolution and identification of the relation ships of different species. In this paper, the probes used in this technique, probes label methods and chromosome preparation were introduced. The application of FISH in plant genomic physical atlas estimation, functional gene location, for distant hybrid identification and alien chromatin detection, analysis of chromosome behavior in meiosis, origination of species are summarized and prospected.%荧光原位杂交是在分子水平上检测外源染色质的一种有效方法。该技术在研究植物分子细胞遗传学、基因扩增、基因作图及植物进化和亲缘关系的鉴定上已广泛应用。本文简要介绍了荧光原位杂交探针类型、探针标记方法和染色体制片技术等，概述了荧光原位杂交技术在构建植物基因组物理图谱，功能基因定位，远缘杂种的鉴定及外源染色质的检测，减数分裂时期染色体行为研究和探讨种的起源中的应用与展望。 1. North American tidal power prospects Wayne, W. W., Jr. 1981-07-01 Prospects for North American tidal power electrical generation are reviewed. Studies by the US Army Corps of Engineers of 90 possible generation schemes in Cobscook Bay, ME, indicated that maximum power generation rather than dependable capacity was the most economic method. Construction cost estimates for 15 MW bulb units in a single effect mode from basin to the sea are provided; five projects were considered ranging from 110-160 MW. Additional tidal power installations are examined for: Half-Moon Cove, ME (12 MW, 18 ft tide); Cook Inlet, AK, which is shown to pose severe environmental and engineering problems due to fish migration, earthquake hazards, and 300 ft deep silt deposits; and the Bay of Fundy, Canada. This last has a 17.8 MW plant under construction in a 29 ft maximum tide area. Other tidal projects of the Maritime Provinces are reviewed, and it is noted that previous economic evaluations based on an oil price of$16/barrel are in need of revision. 2. a prospective study Rörster, Elisa geb. Pätel 2012-01-01 Bulk fractures only occur on very rare occasions in bilayered all-ceramic crowns, where as veneer fractures, above all chippings, still present a frequent amount of clinical complications. The purpose of the current prospective study was to examine the clinical performance of an anatomically modified framework for a period of two years. All crowns were manufactured following the Cercon process (DeguDent GmbH, Hanau). As is common practice, the frameworks for the control group were made of ... 3. Bright Economic Prospects Zhang Minqiu 2004-01-01 @@ India is expected to register an 8.2% growth rate for the 2003-04 fiscal year. The overall economic situation this year has been satisfactory despite the scaled down 6-6.5% growth rate for the new fiscal year due to oil price hikes, reduced monsoon volume and some 7% inflation. Judging from the following factors, bright prospects are in store for the country down the road. 4. Prospecting for lunar resources Taylor, G.; Martel, L. Large space settlements on the Moon (thousands of people) will require use of indigenous resources to build and maintain the infrastructure and generate products for export. Prospecting for these resources is a crucial step in human migration to space and needs to begin before settlement and the establishment of industrial complexes. We are devising a multi-faceted approach to prospect for resources. A central part of this work is developing the methodology for prospecting the Moon and other planetary bodies. This involves a number of investigations: (1) It is essential to analyze the economics of planetary ore deposits. Ore deposits are planetary materials that we can mine, process, and deliver to customers at a profit. The planetary context tosses in some interesting twists to this definition. (2) We are also making a comprehensive theoretical assessment of potential lunar ore deposits. Our understanding of the compositions, geological histories, and geological processes on the Moon will lead to significant differences in how we assess wh a t types of ores could be present. For example, the bone-dry nature of the Moon (except at the poles) eliminates all ore deposits associated with hydrothermal fluids. (3) We intend to search for resources using existing data for the Moon. Thus, prospecting can begin immediately. We have a wealth of remote sensing data for the Moon. We also have a good sampling of the Moon by the Apollo and Luna missions, and from lunar meteorites. We can target specific types of deposits already identified (e.g. lunar pyroclastic deposits) and look for other geological settings that might have produced ores and other materials of economic value. Another approach we will take is to examine all data available to look for anomalies. Examples are unusual spectral properties, large disagreements between independent techniques that measure the same property, unusual elemental ratios, or simply exceptional properties such as elemental abundances much 5. Chloroplast thioredoxin systems: prospects for improving photosynthesis. Nikkanen, Lauri; Toivola, Jouni; Diaz, Manuel Guinea; Rintamäki, Eevi 2017-09-26 Thioredoxins (TRXs) are protein oxidoreductases that control the structure and function of cellular proteins by cleavage of a disulphide bond between the side chains of two cysteine residues. Oxidized thioredoxins are reactivated by thioredoxin reductases (TR) and a TR-dependent reduction of TRXs is called a thioredoxin system. Thiol-based redox regulation is an especially important mechanism to control chloroplast proteins involved in biogenesis, in regulation of light harvesting and distribution of light energy between photosystems, in photosynthetic carbon fixation and other biosynthetic pathways, and in stress responses of plants. Of the two plant plastid thioredoxin systems, the ferredoxin-dependent system relays reducing equivalents from photosystem I via ferredoxin and ferredoxin-thioredoxin reductase (FTR) to chloroplast proteins, while NADPH-dependent thioredoxin reductase (NTRC) forms a complete thioredoxin system including both reductase and thioredoxin domains in a single polypeptide. Chloroplast thioredoxins transmit environmental light signals to biochemical reactions, which allows fine tuning of photosynthetic processes in response to changing environmental conditions. In this paper we focus on the recent reports on specificity and networking of chloroplast thioredoxin systems and evaluate the prospect of improving photosynthetic performance by modifying the activity of thiol regulators in plants.This article is part of the themed issue 'Enhancing photosynthesis in crop plants: targets for improvement'. © 2017 The Authors. 6. Applied Astronomy: Asteroid Prospecting Elvis, M. 2013-09-01 In the age of asteroid mining the ability to find promising ore-bearing bodies will be valuable. This will give rise to a new discipline- "Applied Astronomy". Just as most geologists work in industry, not in academia, the same will be true of astronomers. Just how rare or common ore-rich asteroids are likely to be, and the skills needed to assay their value, are discussed here, with an emphasis on remote - telescopic - methods. Also considered are the resources needed to conduct extensive surveys of asteroids for prospecting purposes, and the cost and timescale involved. The longer-term need for applied astronomers is also covered. 7. Poisonous Plants ... Publications and Products Programs Contact NIOSH NIOSH POISONOUS PLANTS Recommend on Facebook Tweet Share Compartir Photo courtesy ... U.S. Department of Agriculture Many native and exotic plants are poisonous to humans when ingested or if ... 8. International prospects for clean coal technologies (Focus on Asia) Gallaspy, D.T. [Southern Energy, Inc., Atlanta, GA (United States) 1997-12-31 The purpose of this paper is to propose Asia as a focus market for commercialization of CCTs; describe the principles for successful penetration of CCTs in the international market; and summarize prospects for CCTs in Asia and other international markets. The paper outlines the following: Southern Companys clean coal commitment; acquisition of Consolidated Electric Power Asia (CEPA); the prospects for CCTs internationally; requirements for CCTs widespread commercialization; CEPAs application of CCTs; and gas turbine power plants as a perfect example of a commercialization driver. 9. Aquatic plants 2006-01-01 Aquatic fl owering plants form a relatively young plant group on an evolutionary timescale. The group has developed over the past 80 million years from terrestrial fl owering plants that re-colonised the aquatic environment after 60-100 million years on land. The exchange of species between...... terrestrial and aquatic environments continues today and is very intensive along stream banks. In this chapter we describe the physical and chemical barriers to the exchange of plants between land and water.... 10. Manufacturing Plants TANG YUANKAI 2010-01-01 @@ Sunshine, air and soil are indispensable for green plants. This might be axi-omatic but not in a plant factory. By creating a plant factory, scientists are trying to grow plants where natural elements are deficient or absent, such as deserts,islands, water surfaces, South and North poles and space, as well as in human habi-tats such as skyscrapers in modern cities. 11. Manufacturing Plants 2010-01-01 China starts to produce vegetables and fruits in a factory sunshine,air and soil are indispensable for green plants. This might be axiomatic but not in a plant factory. By creating a plant factory,scientists are trying to grow plants where natural elements are deficient or absent,such as deserts, islands,water surfaces,South and North poles and space,as well as in human habitats such as skyscrapers in modern cities. 12. Astronautics summary and prospects Kiselev, Anatoly Ivanovich; Menshikov, Valery Alexandrovich 2003-01-01 The monograph by A.I.Kiselev, A.A. Medvedev and Y.A.Menshikov, Astronautics: Summary and Prospects, aroused enthusiasm both among experts and the public at large. This is due to the felicitous choice of presentation that combines a simple description of complex space matters with scientificsubstantiation of the sub jectmatter described. The wealth of color photos makes the book still more attractive, and it was nominated for an award at the 14th International Moscow Book Fair, being singled out as the "best publication of the book fair". The book's popularity led to a second edition, substantially revised and enlarged. Since the first edition did not sufficiently cover the issues of space impact on ecology and the prospective development of space systems, the authors revised the entire volume, including in it the chapter "Space activity and ecology" and the section "Multi-function space systems". Using the federal monitoring system, now in the phase of system engi neering, as an example, the authors consi... 13. Medicinal Plants. Phillipson, J. David 1997-01-01 Highlights the demand for medicinal plants as pharmaceuticals and the demand for health care treatments worldwide and the issues that arise from this. Discusses new drugs from plants, anticancer drugs, antiviral drugs, antimalarial drugs, herbal remedies, quality, safety, efficacy, and conservation of plants. Contains 30 references. (JRH) 14. Plant volatiles. Baldwin, Ian T 2010-05-11 Plant volatiles are the metabolites that plants release into the air. The quantities released are not trivial. Almost one-fifth of the atmospheric CO2 fixed by land plants is released back into the air each day as volatiles. Plants are champion synthetic chemists; they take advantage of their anabolic prowess to produce volatiles, which they use to protect themselves against biotic and abiotic stresses and to provide information - and potentially disinformation - to mutualists and competitors alike. As transferors of information, volatiles have provided plants with solutions to the challenges associated with being rooted in the ground and immobile. 15. Prospect Theory and Coercive Bargaining Butler, Christopher K. 2007-01-01 Despite many applications of prospect theory's concepts to explain political and strategic phenomena, formal analyses of strategic problems using prospect theory are rare. Using Fearon's model of bargaining, Tversky and Kahneman's value function, and an existing probability weighting function, I construct a model that demonstrates the differences… 16. [Plant hormones, plant growth regulators]. Végvári, György; Vidéki, Edina 2014-06-29 Plants seem to be rather defenceless, they are unable to do motion, have no nervous system or immune system unlike animals. Besides this, plants do have hormones, though these substances are produced not in glands. In view of their complexity they lagged behind animals, however, plant organisms show large scale integration in their structure and function. In higher plants, such as in animals, the intercellular communication is fulfilled through chemical messengers. These specific compounds in plants are called phytohormones, or in a wide sense, bioregulators. Even a small quantity of these endogenous organic compounds are able to regulate the operation, growth and development of higher plants, and keep the connection between cells, tissues and synergy between organs. Since they do not have nervous and immume systems, phytohormones play essential role in plants' life. 17. Legume proteomics: Progress, prospects, and challenges. Rathi, Divya; Gayen, Dipak; Gayali, Saurabh; Chakraborty, Subhra; Chakraborty, Niranjan 2016-01-01 Legumes are the major sources of food and fodder with strong commercial relevance, and are essential components of agricultural ecosystems owing to their ability to carry out endosymbiotic nitrogen fixation. In recent years, legumes have become one of the major choices of plant research. The legume proteomics is currently represented by more than 100 reference maps and an equal number of stress-responsive proteomes. Among the 48 legumes in the protein databases, most proteomic studies have been accomplished in two model legumes, soybean, and barrel medic. This review highlights recent contributions in the field of legume proteomics to comprehend the defence and regulatory mechanisms during development and adaptation to climatic changes. Here, we attempted to provide a concise overview of the progress in legume proteomics and discuss future developments in three broad perspectives: (i) proteome of organs/tissues; (ii) subcellular compartments; and (iii) spatiotemporal changes in response to stress. Such data mining may aid in discovering potential biomarkers for plant growth, in general, apart from essential components involved in stress tolerance. The prospect of integrating proteome data with genome information from legumes will provide exciting opportunities for plant biologists to achieve long-term goals of crop improvement and sustainable agriculture. 18. Current and Prospective Methods for Plant Disease Detection Yi Fang 2015-08-01 Full Text Available Food losses due to crop infections from pathogens such as bacteria, viruses and fungi are persistent issues in agriculture for centuries across the globe. In order to minimize the disease induced damage in crops during growth, harvest and postharvest processing, as well as to maximize productivity and ensure agricultural sustainability, advanced disease detection and prevention in crops are imperative. This paper reviews the direct and indirect disease identification methods currently used in agriculture. Laboratory-based techniques such as polymerase chain reaction (PCR, immunofluorescence (IF, fluorescence in-situ hybridization (FISH, enzyme-linked immunosorbent assay (ELISA, flow cytometry (FCM and gas chromatography-mass spectrometry (GC-MS are some of the direct detection methods. Indirect methods include thermography, fluorescence imaging and hyperspectral techniques. Finally, the review also provides a comprehensive overview of biosensors based on highly selective bio-recognition elements such as enzyme, antibody, DNA/RNA and bacteriophage as a new tool for the early identification of crop diseases. 19. Principles, requirements and prospects of genetic mapping in plants AJB SERVER Genetic mapping (also known as linkage mapping or meiotic mapping) refers to the determination of the relative ..... F2 is more powerful for detecting QTLs of additive effect, and can also be .... In general, cross pollinating ..... chromosome deletion stocks (Fox et al., 2001). ..... The cytological basis of genetical interference. 20. Development, Operation, and Future Prospects for Implementing Biogas Plants Lybæk, Rikke 2014-01-01 of developing new gas boosters to support a further development of the biogas sector. The chapter ends with a discussion of new trends in biogas production, for example, how new organizational models can be designed as well as how the use of alternative boosters—like blue biomass—can be applied. Finally, biogas... 1. Electronic plants Stavrinidou, Eleni; Gabrielsson, Roger; Gomez, Eliot; Crispin, Xavier; Nilsson, Ove; Simon, Daniel T.; Berggren, Magnus 2015-01-01 The roots, stems, leaves, and vascular circuitry of higher plants are responsible for conveying the chemical signals that regulate growth and functions. From a certain perspective, these features are analogous to the contacts, interconnections, devices, and wires of discrete and integrated electronic circuits. Although many attempts have been made to augment plant function with electroactive materials, plants’ “circuitry” has never been directly merged with electronics. We report analog and digital organic electronic circuits and devices manufactured in living plants. The four key components of a circuit have been achieved using the xylem, leaves, veins, and signals of the plant as the template and integral part of the circuit elements and functions. With integrated and distributed electronics in plants, one can envisage a range of applications including precision recording and regulation of physiology, energy harvesting from photosynthesis, and alternatives to genetic modification for plant optimization. PMID:26702448 2. Development Prospect of Aromatherapy Industry in Yunnan Province Ziyun; PENG; Dantong; LI; Rui; CHEN; Min; QIAN; Yiqi; CHEN; Hongjun; YANG 2014-01-01 This paper firstly introduced domestic and foreign supply of products processed by aromatherapy plant. On the basis of predicting market demand of aromatherapy plant,it analyzed current development situation of the plant in Yunnan Province. It arrived at the conclusion that the industry has broad market prospect. Then,it analyzed competitive advantages and risk factors of aromatherapy plant in Yunnan Province. There are climate,location and price advantages,but due to lack of product standard,it is difficult to guarantee quality,and there are certain market risks. Finally,it put forward recommendations for development of aromatherapy industry:( 1) taking full advantage of preferential policies to set up leading enterprises and realize radiated development;( 2) bringing into play of resource advantages and introducing capitals and technologies;( 3) Fostering market and driving the industrial development. Dobre, M.; ATLAS Collaboration 2017-01-01 After the successful operation at the centre-of-mass energies of 7 and 8 TeV in 2010-2012, the LHC was ramped up and successfully took data at the centre-of-mass energies of 13 TeV in 2015 and 2016. Meanwhile, plans are actively advancing for a series of upgrades of the accelerator, culminating roughly ten years from now in the high-luminosity LHC (HL-LHC) project, which will deliver of the order of five times the LHC nominal instantaneous luminosity along with luminosity levelling. The ultimate goal is to extend the dataset from about few hundred fb ‑1 expected for LHC running by the end of 2018 to 3000 fb ‑1 by around 2035 for ATLAS and CMS. The challenge of coping with the HL-LHC instantaneous and integrated luminosity, along with the associated radiation levels, requires further major changes to the ATLAS detector. The designs are developing rapidly for a new all-silicon tracker, significant upgrades of the calorimeter and muon systems, as well as improved triggers and data acquisition. ATLAS is also examining potential benefits of extensions to larger pseudorapidity, particularly in tracking and muon systems. This report summarizes various improvements to the ATLAS detector required to cope with the anticipated evolution of the LHC luminosity during this decade and the next. A brief overview is also given on physics prospects with a pp centre-of-mass energy of 14 TeV. 4. German energy technology prospects. Popp, M 1982-12-24 After more than 25 years of development of nuclear power and almost 10 years of research and development in numerous areas of nonnuclear energy, there is now a good basis for judging the future prospects of energy technologies in the Federal Republic of Germany. The development of nuclear power has provided an important and economically advantageous new source of energy. Further efforts are needed to establish the nuclear fuel cycle in all stages and to exploit the potential of advanced reactors. In all other areas of energy technology, including energy conservation, new energy sources, and coal, economics has turned out to be the key problem, even at today's energy prices. Opportunities to overcome these economic problems through additional R & D are limited. There is some potential for special applications, and there are many technologies that could contribute to the energy supply of developing countries. In general, however, progress in energy conservation and the use of renewable energy sources will depend on the degree to which energy policy measures can improve their economic basis. For some technologies, such as solar thermal power stations and coal liquefaction, large-scale economic deployment cannot be foreseen today. Instead of establishing costly demonstration projects, emphasis will be put on improving key components of these technologies with the aim of having the most advanced technology available when the economic parameters are more favorable. 5. ANAIS: Status and prospects Amaré, Julio; Cuesta, Clara; García, Eduardo; Ginestra, Carlos; Martínez, María; Oliván, Miguel A; Ortigoza, Ysrael; de Solórzano, Alfonso Ortíz; Pobes, Carlos; Puimedón, Jorge; Sarsa, María Luisa; Villar, José Ángel; Villar, Patricia 2015-01-01 ANAIS experiment will look for dark matter annual modulation with large mass of ultra-pure NaI(Tl) scintillators at the Canfranc Underground Laboratory (LSC), aiming to confirm the DAMA/LIBRA positive signal in a model-independent way. Two 12.5 kg each NaI(Tl) crystals provided by Alpha Spectra are currently taking data at the LSC. Present status of ANAIS detectors background and general performance is summarized; in particular, thanks to the high light collection efficiency prospects of lowering the threshold down to 1 keVee are reachable. Crystal radiopurity goals are fulfilled for $^{232}$Th and $^{238}$U chains and $^{40}$K activity, although higher than original goal, could be accepted; however, high $^{210}$Pb contamination out-of-equilibrium has been identified. More radiopure detectors are being built by Alpha Spectra. The ongoing high quantum efficiency PMT tests and muon veto characterization are also presented. Finally, the sensitivity of the experiment for the annual modulation in the WIMP signal,... 6. IPY Progress and Prospects Carlson, D. 2008-12-01 We can summarize the IPY goals as: (a) make major advances in polar knowledge and understanding; (b) leave a legacy of new or enhanced observational systems, facilities and infrastructure; (c) excite a new generation of polar scientists and engineers, and (d) elicit exceptional interest and participation from polar residents, schoolchildren, the general public, and decision-makers, worldwide. This talk reports on the progress and prospects in each of those areas from an overall international view; separate talks will describe details of future researcher and the IPY outreach efforts. To achieve major advances in knowledge, IPY has entrained the intellectual resources of thousands of scientists, many more than expected, often from 'non- polar' nations, and representing an unprecedented breadth of scientific specialties; integration of those efforts across disciplines to achieve integrated system-level understanding remains a substantial challenge. Many national and international organizations prepare plans to sustain new and improved observational systems, but clear outcomes and the necessary resources remain elusive. International outreach networks gradually build breadth and strength, largely through IPY Polar Science Days and other internationally- coordinated IPY events. A new Association of Polar Early Career Scientists (APECS) devotes talent and energy to shaping the future of polar research. These activities and networks may, with time and with continued international coordination, achieve an exceptional level of interest and participation. In all areas, much work remains. 7. Intellectual Property for Plant innovation in Europe Nordberg, Ana; Sonne, Maria Lillie 2017-01-01 Innovation in plant bioscience offers prospects for solving important and urgent issues regarding the future of mankind: Food security, renewable energy sources, and medicines. It is also connected closely to questions of environmental protection, global warming, biodiversity, sustainable devel-o... 8. Plant Behavior Liu, Dennis W. C. 2014-01-01 Plants are a huge and diverse group of organisms, ranging from microscopic marine phytoplankton to enormous terrestrial trees epitomized by the giant sequoia: 300 feet tall, living 3000 years, and weighing as much as 3000 tons. For this plant issue of "CBE-Life Sciences Education," the author focuses on a botanical topic that most… 9. Plant Behavior Liu, Dennis W. C. 2014-01-01 Plants are a huge and diverse group of organisms, ranging from microscopic marine phytoplankton to enormous terrestrial trees epitomized by the giant sequoia: 300 feet tall, living 3000 years, and weighing as much as 3000 tons. For this plant issue of "CBE-Life Sciences Education," the author focuses on a botanical topic that most… 10. Plant minichromosomes. Birchler, James A; Graham, Nathaniel D; Swyers, Nathan C; Cody, Jon P; McCaw, Morgan E 2016-02-01 Plant minichromosomes have the potential for stacking multiple traits on a separate entity from the remainder of the genome. Transgenes carried on an independent chromosome would facilitate conferring many new properties to plants and using minichromosomes as genetic tools. The favored method for producing plant minichromosomes is telomere-mediated chromosomal truncation because the epigenetic nature of centromere function prevents using centromere sequences to confer the ability to organize a kinetochore when reintroduced into plant cells. Because haploid induction procedures are not always complete in eliminating one parental genome, chromosomes from the inducer lines are often present in plants that are otherwise haploid. This fact suggests that minichromosomes could be combined with doubled haploid breeding to transfer stacked traits more easily to multiple lines and to use minichromosomes for massive scale genome editing. 11. Labour: A Prospective, Descriptive Study Symphysis Fundus Height Measurements during Labour: A Prospective, Descriptive Study 49. Introduction ... 800g in about 50% of cases,2 and in term preg- nancies to be as .... Discussion. Prematurity and low birthweight are major causes. 12. Prospect of ultralight airplanes development 2015-09-01 Full Text Available The article presents characteristic of ultralight airplanes, rules and current interest of them. The purpose is to determine prospect of ultralight airplanes development on the basis of Civil Aviation Authority statistics analysis and trend of aviation market. 13. MRI of plants and foods Van As, Henk; van Duynhoven, John 2013-04-01 The importance and prospects for MRI as applied to intact plants and to foods are presented in view of one of humanity's most pressing concerns, the sustainable and healthy feeding of a worldwide increasing population. Intact plants and foods have in common that their functionality is determined by complex multiple length scale architectures. Intact plants have an additional level of complexity since they are living systems which critically depend on transport and signalling processes between and within tissues and organs. The combination of recent cutting-edge technical advances and integration of MRI accessible parameters has the perspective to contribute to breakthroughs in understanding complex regulatory plant performance mechanisms. In food science and technology MRI allows for quantitative multi-length scale structural assessment of food systems, non-invasive monitoring of heat and mass transport during shelf-life and processing, and for a unique view on food properties under shear. These MRI applications are powerful enablers of rationally (re)designed food formulations and processes. Limitations and bottlenecks of the present plant and food MRI methods are mainly related to short T2 values and susceptibility artefacts originating from small air spaces in tissues/materials. We envisage cross-fertilisation of solutions to overcome these hurdles in MRI applications in plants and foods. For both application areas we witness a development where MRI is moving from highly specialised equipment to mobile and downscaled versions to be used by a broad user base in the field, greenhouse, food laboratory or factory. 14. [Interactive effects between plant allelochemicals, plant allelopathic potential and soil nutrients]. Xiao, Huilin; Peng, Shaolin; Zheng, Yuji; Mo, Jiangming; Luo, Wei; Zeng, Xiaoduo; He, Xiaoxia 2006-09-01 Plant allelopathy relates to many ecological factors. The deficit of soil nutrients can influence the production of plant allelochemicals, and thus, influence plant allelopathic potential, while plant allelochemicals can influence the form and level of soil nutrients by the ways of complexation, adsorption, acid dissolution, competition, inhibition, and others. In this paper, the interactive effects between plant allelochemicals, plant allelopathic potential and soil nutrients were summarized, and further research aspects in this field were prospected. It was suggested that following aspects should be strengthened: (1) the integration of plant allelopathy and soil-plant nutrition research to more precisely and deeply interpret the relationships between plant allelochemicals, plant allelopathic potential and soil nutrients, (2) the integration of plant allelopathy and ecosystem nutrient cycling research to simulate the plant nutrients disturbance in nature and make the allelopathy research results more true and more reliable, and (3) the allelopathy research with soils containing excessive nutrients or polluted to provide new ideas and scientific basis in revealing the mechanisms of plants interaction and biomass variation in agricultural and forestry production, and in ecological protection. 15. Plant Macrofossils National Oceanic and Atmospheric Administration, Department of Commerce — Records of past vegetation and environmental change derived from plant remains large enough to be seen without a microscope (macrofossils), such as leaves, needles,... 16. Seed planting US Fish and Wildlife Service, Department of the Interior — This report summarizes prairie seed plantings on Neal Smith National Wildlife Refuge (formerly Walnut Creek National Wildlife Refuge) between 1992 and 2009. 17. T Plant Federal Laboratory Consortium — Arguably the second most historic building at Hanford is the T Plant.This facility is historic in that it's the oldest remaining nuclear facility in the country that... 18. TRANSGENIC PLANTS MANAGEMENT OF INSECT PEST RESISTANCE WHILE USING ... Stratégies to delay the development of résistance while using Bt engineered plants are many and would need to be ..... training, pesticide use patterns change, and the. 19. Probiosis: concepts and prospects Lima R Barbosa 2010-12-01 Full Text Available The use of probiotics in animal and human feeding has been a subject of increasing interest both for the academia and the industry, mostly due to their potential positive effects on health and profitability. However, the knowledge on the composition of bacterial gastrointestinal communities in humans and animals, as well as its respective nutritional requirements, is far from being elucidated. Due to the ban of the use of antibiotic growth promoters in animal feeds, there has been an increasing interest on the utilization of probiotics to improve animal intestinal health under commercial settings. However, the possibility of horizontal transference of antibiotic-resistant genes between probiotic bacteria and pathogenic species has become a concern of poultry farmers and consumers around the world. Innovative ideas have emerged, such as the addition of essential oils, spices, and other plant extracts to feeds of monogastric animals to promote intestinal health. These natural compounds are considered ecologically adequate and safe for feeding purposes. This new reality will probably change the direction of research and of the use of additives in poultry production. 20. The application of biotechnology in medicinal plants breeding research in China. Huang, He-Ping; Li, Jin-Cai; Huang, Lu-Qi; Wang, Dian-Lei; Huang, Peng; Nie, Jiu-Sheng 2015-07-01 Breeding is not only an important area of medicinal plants research but also the foundation for the superior varieties acquirement of medicinal plants. The rise of modern biotechnology provides good opportunities and new means for medicinal plants breeding research in China. Biotechnology shows its technical advantages and new development prospects in breeding of new medicinal plants varieties with high and stable yield, good quality, as well as stress-resistance. In this paper, we describe recent advances, problems, and development prospects about the application of modern biotechnology in medicinal plants breeding research in China. 1. Homologous recombination in plants: an antireview. Lieberman-Lazarovich, Michal; Levy, Avraham A 2011-01-01 Homologous recombination (HR) is a central cellular process involved in many aspects of genome maintenance such as DNA repair, replication, telomere maintenance, and meiotic chromosomal segregation. HR is highly conserved among eukaryotes, contributing to genome stability as well as to the generation of genetic diversity. It has been intensively studied, for almost a century, in plants and in other organisms. In this antireview, rather than reviewing existing knowledge, we wish to underline the many open questions in plant HR. We will discuss the following issues: how do we define homology and how the degree of homology affects HR? Are there any plant-specific HR qualities, how extensive is functional conservation and did HR proteins acquire new functions? How efficient is HR in plants and what are the cis and the trans factors that regulate it? Finally, we will give the prospects for enhancing the rates of gene targeting and meiotic HR for plant breeding purposes. 2. Assessment of commercial prospects of molten carbonate fuel cells Dicks, Andrew; Siddle, Angie The commercial prospects of molten carbonate fuel cells have been evaluated. Market applications, and the commercial criteria that the MCFC will need to satisfy for these applications, were identified through interviews with leading MCFC developers. Strengths, weaknesses, opportunities and threats (SWOT) analyses were carried out to critically evaluate the prospects for commercialisation. There are many competing technologies, but it is anticipated that MCFCs can make significant penetration into markets where their attributes, such as quality of power, low emissions and availability, give them a leading position in comparison with, for example, engine and turbine-based power generation systems. Analysis suggests that choosing the size for MCFC plant is more important than the target market sector/niche. Opportunities will exist in many market sectors, though the commercial market would be easier to penetrate initially. Developers are optimistic about the commercial prospects for the MCFC. Most believe that early commercial MCFC plants may start to appear in the first decade of the next century, the earliest date suggested for initial market entry being 2002. 3. PROSPECTIVE ISLAMIC LAW IN INDONESIA Mohdar Yanlua 2015-02-01 Full Text Available This paper discusses the Prospective Islamic law in Indonesia. The enforcement of Islamic law in Indonesia experienced the ups and downs, ranging from the colonial period with the Government of Indonesia to the Netherlands in order to reform it.In this study it was found that a prospective law of Islam in Indonesia the development of any regime of the Government of Indonesia is experiencing developments. By the Government of Indonesia does not accept or reject the extremes, but instead selectively receive (not the totality and gradual.Such a step is done for the sake of maintaining the stability and integrity of the country. 4. Introduction prospects for rare species of flora in Crimea fur use in urban landscaping Pidgaynaya Elena 2016-12-01 Full Text Available The article presents introduction prospects for rare and endangered plants of the Crimean flora. The target of research puts together types of the Crimean natural flora included to the global and regional protection documents; such plants grow in the N. V. Bagrov Botanical Garden of the Taurida Academy, V. I. Vernadsky Crimean Federal University, in Simferopol. The observations were conducted in 2010-2016. As a result of an integral assessment of plants decorative features, 34 promising and 20 highly decorative species have been marked for wide cultivation and introduction into planting of the Crimean foothill. The studied species are recommended for use in planting of various flowerbeds’ types as accent, dominant, shading, and auxiliary plants. Some 24 of the proposed types are heliophyte plants and are recommended for planting the solar sites; 10 types are suitable for half-shaded and shaded areas. In the wild, the majority of these plants are adapted to dry growing conditions; this improves their cultivation prospects in the arid areas. 5. Toxic plants Reproductive performance is the single most important economic animal trait to the livestock industry and is reported to be 5 and 10 times more significant than carcass quality and growth traits respectively. Poisonous plants impact livestock reproductive function in a major way and have been shown... 6. Technical analysis of prospective photovoltaic systems in Utah. Quiroz, Jimmy Edward; Cameron, Christopher P. 2012-02-01 This report explores the technical feasibility of prospective utility-scale photovoltaic system (PV) deployments in Utah. Sandia National Laboratories worked with Rocky Mountain Power (RMP), a division of PacifiCorp operating in Utah, to evaluate prospective 2-megawatt (MW) PV plants in different locations with respect to energy production and possible impact on the RMP system and customers. The study focused on 2-MW{sub AC} nameplate PV systems of different PV technologies and different tracking configurations. Technical feasibility was evaluated at three different potential locations in the RMP distribution system. An advanced distribution simulation tool was used to conduct detailed time-series analysis on each feeder and provide results on the impacts on voltage, demand, voltage regulation equipment operations, and flicker. Annual energy performance was estimated. 7. PROSPECT FOR CHINA'S PETROLEUM INDUSTRY Cha Quanheng 2001-01-01 @@ Many people show concerns over the prospect forChina's petroleum industry.They may raise the question about whether the country's resources are on the brink of exhaustion. Such questions should be answered only by the exploration results because petroleum production is based on the reserves. 8. Job Prospects for Electrical Engineers. Basta, Nicholas 1986-01-01 Discusses the career outlook for electrical/electronics engineers. Explains that the number of bachelor degree graduates continues to rise, along with average starting salaries. Reveals that although the availability of jobs in the computer industry is leveling off, prospects in the robotics and telecommunication fields are growing. (TW) 9. Handbook for Prospective Single Parents. Marindin, Hope This handbook for prospective single adoptive parents provides information on locating and adopting a child, necessary clothing and supplies for children of various ages, health and day care arrangements, expenses incurred after adoption, various financial benefits and subsidies available to the adoptive parent, and legal and financial provisions… 10. Job Prospects for Civil Engineers. Basta, Nicholas 1985-01-01 Government programs and renewed industrial activity have combined with stable enrollments to create bright job prospects for civil engineers. Areas with good opportunities include highway reconstruction and rehabilitation, water-resource management, and new factory construction. The subspecialty of structural engineering has a growing need in… 11. Autism Research: Prospects and Priorities. Rutter, Michael 1996-01-01 Research prospects and priorities in autism are discussed with respect to: (1) diagnosis, classification, and epidemiology; (2) clinical research; (3) neuropsychological research; (4) genetics; (5) structural and functional brain imaging; (6) postmortem studies; (7) other biological research; and (8) treatment research. Application of research… 12. The UK Prospective Diabetes Study Olivarius, Niels de Fine; Andreasen, A.H. 1998-01-01 Læserbrev, som kritiserer det store UK Prospective Diabetes Study's forfattere for at overfortolke deres fund, idet marginalt signifikante p-værdier tages som udtryk for slående effekt (af at sænke blodsukkeret). Det sker selvom der f.eks. indgår effektvariabler, som kunne påvirkes af patienternes... 13. Rose breeding: past, present, prospects Vries, de D.P.; Dubois, L.A.M. 1996-01-01 In this review the PAST, PRESENT and PROSPECT will be considered as three separate periods in the history of the breeding and development of rose cultivars. The recurring theme is the genetic variation. This theme was chosen because there is justified doubt as to sufficient genetic variation 14. Job Prospects for Electrical Engineers. Basta, Nicholas 1986-01-01 Discusses the career outlook for electrical/electronics engineers. Explains that the number of bachelor degree graduates continues to rise, along with average starting salaries. Reveals that although the availability of jobs in the computer industry is leveling off, prospects in the robotics and telecommunication fields are growing. (TW) 15. Rose breeding: past, present, prospects Vries, de D.P.; Dubois, L.A.M. 1996-01-01 In this review the PAST, PRESENT and PROSPECT will be considered as three separate periods in the history of the breeding and development of rose cultivars. The recurring theme is the genetic variation. This theme was chosen because there is justified doubt as to sufficient genetic variation availab 16. RNAi-mediated plant protection against aphids. Yu, Xiu-Dao; Liu, Zong-Cai; Huang, Si-Liang; Chen, Zhi-Qin; Sun, Yong-Wei; Duan, Peng-Fei; Ma, You-Zhi; Xia, Lan-Qin 2016-06-01 Aphids (Aphididae) are major agricultural pests that cause significant yield losses of crop plants each year by inflicting damage both through the direct effects of feeding and by vectoring harmful plant viruses. Expression of double-stranded RNA (dsRNA) directed against suitable insect target genes in transgenic plants has been shown to give protection against pests through plant-mediated RNA interference (RNAi). Thus, as a potential alternative and effective strategy for insect pest management in agricultural practice, plant-mediated RNAi for aphid control has received close attention in recent years. In this review, the mechanism of RNAi in insects and the so far explored effective RNAi target genes in aphids, their potential applications in the development of transgenic plants for aphid control and the major challenges in this regard are reviewed, and the future prospects of using plant-mediated RNAi for aphid control are discussed. This review is intended to be a helpful insight into the generation of aphid-resistant plants through plant-mediated RNAi strategy. © 2016 Society of Chemical Industry. 17. Old Yet New--Pharmaceuticals from Plants Houghton, Peter J. 2001-02-01 Plants or their crude extracts have been used since prehistory to treat human ailments. Plants are still used in this way in many parts of the world, but Western scientific medicine has tended to isolate active compounds, or make derivatives of them, for use as drugs. Compounds produced by the plant have been important pharmaceuticals since the isolation of morphine almost two hundred years ago and new naturally occurring compounds such as paclitaxel are continually being introduced commercially. Bioactive molecules may also be produced from chemicals found in plants by chemical modification using synthetic chemistry or microorganisms (as in the production of steroids). A third major contribution of plant chemicals to drugs is their utilization as templates for the design of new compounds made by synthesis (e.g. the discovery of aspirin and related compounds from substances in willow bark). New pharmaceuticals from plants are being discovered by examining traditional medicines and by large-scale bioassay screening processes. In addition, the chemical survival systems of plants that exist in hostile environments are receiving increasing attention as leads to discover active compounds. The knowledge of botanical relationships helps find new sources of known compounds of interest and novel compounds with similar structures from related species. Future prospects for the discovery of new compounds from plants are broadened by the new technologies of gene manipulation, tissue culture, and combinatorial chemistry, so it is very likely that natural products from plants will continue to play an important role in the fight against disease. 18. Antioxidants, oxidative stress, and cardiovascular diseases : cross-cultural comparisons and prospective cohort studies Buijsse, B. 2008-01-01 Background: Antioxidants in plant foods have been proposed to reduce the risk of cardiovascular diseases (CVD) by reducing oxidative stress. The objective was to confirm prospective studies on CVD and traditional antioxidants (beta-carotene, alpha-tocopherol), and to investigate emerging antioxidant 19. Audubon Plant Study Program. National Audubon Society, New York, NY. Included are an illustrated student reader, "The Story of Plants and Flowers," an adult leaders' guide, and a large wall chart picturing 37 wildflowers and describing 23 major plant families. The student reader presents these main topics: The Plant Kingdom, The Wonderful World of Plants, Plants Without Flowers, Flowering Plants, Plants Make Food… 20. Biofuel Production by Fermentation of Water Plants and Agricultural Lignocellulosic by-Products Anker, Yaakov; Nakonechny, Faina; Niazov, Betty; Lugovskoy, Svetlana; Nisnevitch, Marina 2016-01-01 While at present most energy crops are depriving human feedstock, fermentation of agricultural residues and fast growing water plants possesses a good prospect to become a significant source for bio-fuel... Wagner, H; Nörr, H; Winterhoff, H 1994-06-01 2. Microfluidic platforms for plant cells studies. 2014-09-07 Conventional methods of plant cell analysis rely on growing plant cells in soil pots or agarose plates, followed by screening the plant phenotypes in traditional greenhouses and growth chambers. These methods are usually costly, need a large number of experiments, suffer from low spatial resolution and disorderly growth behavior of plant cells, with lack of ability to locally and accurately manipulate the plant cells. Microfluidic platforms take advantage of miniaturization for handling small volume of liquids and providing a closed environment, with the purpose of in vitro single cell analysis and characterizing cell response to external cues. These platforms have shown their ability for high-throughput cellular analysis with increased accuracy of experiments, reduced cost and experimental times, versatility in design, ability for large-scale and combinatorial screening, and integration with other miniaturized sensors. Despite extensive research on animal cells within microfluidic environments for high-throughput sorting, manipulation and phenotyping studies, the application of microfluidics for plant cells studies has not been accomplished yet. Novel devices such as RootChip, RootArray, TipChip, and PlantChip developed for plant cells analysis, with high spatial resolution on a micrometer scale mimicking the internal microenvironment of plant cells, offering preliminary results on the capability of microfluidics to conquer the constraints of conventional methods. These devices have been used to study different aspects of plant cell biology such as gene expression, cell biomechanics, cellular mechanism of growth, cell division, and cells fusion. This review emphasizes the advantages of current microfluidic systems for plant science studies, and discusses future prospects of microfluidic platforms for characterizing plant cells response to diverse external cues. 3. Prospects for Future Collider Physics Ellis, John 2016-01-01 One item on the agenda of future colliders is certain to be the Higgs boson. What is it trying to tell us? The primary objective of any future collider must surely be to identify physics beyond the Standard Model, and supersymmetry is one of the most studied options. it Is supersymmetry waiting for us and, if so, can LHC Run 2 find it? The big surprise from the initial 13-TeV LHC data has been the appearance of a possible signal for a new boson X with a mass ~750 GeV. What are the prospects for future colliders if the X(750) exists? One of the most intriguing possibilities in electroweak physics would be the discovery of non-perturbative phenomena. What are the prospects for observing sphalerons at the LHC or a future collider? 4. RNA interference and its application in plants 2008-01-01 RNA interference (RNAi), a process that inhibits gene expression by the double-stranded RNA (dsRNA), causes the deg-radation of target messenger RNA molecules. RNAi exists in almost all organisms. We review the recent history of RNAi studies,RNAi molecular mechanisms, characteristics and RNAi applications in higher plants. At the same time, the prospect of RNAi appli-cations in functional genomics and genetic improvement of higher plants and possible future problems and possibilities are also dis-cussed. 5. Review: Colchicine, current advances and future prospects MAHENDRA KUMAR RAI 2010-07-01 Full Text Available Ade R, Rai MK. 2010. Colchicine, current advances and future prospects. Nusantara Bioscience 2: 90-96. Colchicine is a toxic natural compound and secondary metabolite commonly produced by plants like Colchicum autumnale and Gloriosa superba. It is originally used to treat rheumatic complaints, especially gout, and still finds its uses for these purposes today despite dosing issues concerning its toxicity. It is also prescribed for its cathartic and emetic effects. Initially oral colchicine has not been approved as a drug by U.S. Food and Drug Administration (FDA. But now FDA approved colchicine as a drug for some disorders. Colchicine's present medicinal use is in the treatment of gout and familial mediterranean fever. It is also being investigated for its use as an anticancer drug. In neurons, axoplasmic transport is disrupted by colchicine. Due to all the pharmacological application of colchicine, there is urgent need to enhance the properties and increase the production of colchicine with the help of in vitro technologies. The present review is mainly focused on the chemistry of colchicine, its medicinal uses and toxicity. 6. Prospects of Cooperation between Russia and Turkey Elvin Aghayev 2017-06-01 Full Text Available Russian – Turkish relations go deep into the past. From the Cold War and the relations between the Soviet Union and the United States certainly there has not been a more complicated relationship in international relations. Both countries have different strategic positions, a different dominant religion, a different past, but their relationship largely depends on the future of Eurasia. This paper will deal with relations between the two countries since the establishment of the first diplomatic contacts in the 15th century, through the relationship during the time of Peter the Great, and will mention the periods of the First and Second World Wars, as well as the Cold War era. Special attention will be focused on the current relations between the two countries, especially after the conflict in 2015, when Turkey shot down a Russian plane over Syria. Special attention will be focused on energy policy and the potential for building a nuclear power plant in Mersin, and the continuation of Turkish stream. The paper will deal with economics and trade exchange, which have almost disappeared following the 2015 incident, security cooperation and Turkey’s plans to buy the defense system S-400 from Russia, as well as relations between the two countries towards NATO. The paper will end with the projection of the prospects for the economic relations between the two countries. 7. Prospects for de-automatization. Kihlstrom, John F 2011-06-01 Research by Raz and his associates has repeatedly found that suggestions for hypnotic agnosia, administered to highly hypnotizable subjects, reduce or even eliminate Stroop interference. The present paper sought unsuccessfully to extend these findings to negative priming in the Stroop task. Nevertheless, the reduction of Stroop interference has broad theoretical implications, both for our understanding of automaticity and for the prospect of de-automatizing cognition in meditation and other altered states of consciousness. 8. Atmospheric neutrinos: Status and prospects 2016-01-01 We present an overview of the current status of neutrino oscillation studies at atmospheric neutrino experiments. While the current data gives some tentalising hints regarding the neutrino mass hierarchy, octant of $\\theta_{23}$ and $\\delta_{CP}$, the hints are not statistically significant. We summarise the sensitivity to these sub-dominant three-generation effects from the next-generation proposed atmospheric neutrino experiments. We next present the prospects of new physics searches such a... 9. Prospects for nuclear safety research Beckjord, E.S. 1995-04-01 This document is the text of a paper presented by Eric S. Beckjord (Director, Nuclear Regulatory Research/NRC) at the 22nd Water Reactor Safety Meeting in Bethesda, MD in October 1994. The following topics are briefly reviewed: (1) Reactor vessel research, (2) Probabilistic risk assessment, (3) Direct containment heating, (4) Advanced LWR research, (5) Nuclear energy prospects in the US, and (6) Future nuclear safety research. Subtopics within the last category include economics, waste disposal, and health and safety. 10. Stress tolerant plants 2014-01-01 [EN] The invention relates to transgenic plants and methods for modulating abscisic acid (ABA) perception and signal transduction in plants. The plants find use in increasing yield in plants, particularly under abiotic stress. 11. Plant fertilizer poisoning Plant fertilizers and household plant foods are used to improve plant growth. Poisoning can occur if someone swallows these products. Plant fertilizers are mildly poisonous if small amounts are swallowed. ... 12. Stress tolerant plants Rubio, Vicente; Iniesto Sánchez, Elisa; Irigoyen Miguel, María Luisa 2014-01-01 [EN] The invention relates to transgenic plants and methods for modulating abscisic acid (ABA) perception and signal transduction in plants. The plants find use in increasing yield in plants, particularly under abiotic stress. 13. The many faces of plant chromatin: Meeting summary of the 4th European workshop on plant chromatin 2015, Uppsala, Sweden. Mozgová, Iva; Köhler, Claudia; Gaudin, Valérie; Hennig, Lars 2015-01-01 In June 2015, the fourth European Workshop on Plant Chromatin took place in Uppsala, Sweden, bringing together 80 researchers studying various aspects of plant chromatin and epigenetics. The intricate relationships between plant chromatin dynamics and gene expression change, chromatin organization within the plant cell nucleus, and the impact of chromatin structure on plant development were discussed. Among the main highlights of the meeting were an ever-growing list of newly identified players in chromatin structure establishment and the development of novel tools and approaches to foster our understanding of chromatin-mediated gene regulation, taking into account the context of the plant cell nucleus and its architecture. In this report, we summarize some of the main advances and prospects of plant chromatin research presented at this meeting. 14. The Development and Research on the Coordinate Control Strategy Between Turbine and Boiler in Fossil Power Plant WEI Shuangying 2006-01-01 Based on the research on domestic and international automatic technical development in fossil power plant, the paper analyses the recent situation of the coordinate control system between turbine and boiler of domestic fossil Power Plant, provides the development thought of coordinate control system between turbine and boiler, and describes the application prospect in control system of fossil power plant combining with the application experience. 15. Prospective economical study of the nuclear power file; Etude economique prospective de la filiere electrique nucleaire Charpin, J.M. [Commissariat General du Plan, 75 - Paris (France); Dessus, B. [Ecodev-CNRS, 92 - Meudon (France); Pellat, R. [CEA, 75 - Paris (France) 2000-07-01 On May 7, 1999 an economical study of the overall nuclear file, and in particular, of the back-end part of the fuel cycle and including the reprocessing, was requested by the French Prime Minister. This study includes the cost comparisons with the other means of power production and takes into consideration the environmental costs. The study is shared into five chapters dealing with: 1 - the legacy of the past: todays park of nuclear plants, economical and material status; 2 - the international evolution: the dynamics of nuclear policies worldwide (existing parks and R and D programs), the rise of environmental problems worldwide (CO{sub 2} and the climate convention, nuclear risks, attempts of including environment in the power costs), the choices made for the management of spent fuels in the main countries; 3 - the technological prospects for the power production and use: technologies for the mastery of power demand (residential, industrial and tertiary sectors, power transportation), technologies of power production (production from nuclear, fossil and renewable energies); 4 - prospective scenarios for France: two demand scenarios at the year 2050 vista (energy, electric power), power supply (supply structure with respect to scenarios, nuclear parks, power capacities), environmental aspects (CO{sub 2} emissions, plutonium and minor actinides production); 5 - the economical status of the different scenarios: data preparation, fossil fuel price scenarios, investment and operation costs of the different power production means (nuclear, fossil and renewable energies, natural gas and power distribution networks), comparison between fluxes and cumulated economic costs linked with the different scenarios (investments, exploitation, fuels, R and D, status for 2000 to 2050), time structure of expenditures with respect to the different scenarios (chronology, statuses, kWh costs, sensitivity with respect to the rate of discount, valorization of existing parks in 2050 16. Renewable energy prospects for implementation Jackson, Tim 1993-01-01 Renewable Energy: Prospects for Implementation contains papers that were originally commissioned by the journal Energy Policy for a series on renewable energy appearing between January 1991 to September 1992. In view of the fast-changing demands on conventional energy supply to meet environmental imperatives, it seemed timely to reproduce here a selection of those papers with a new introduction and a revised concluding chapter by the Editor of the series, Dr Tim Jackson, a research fellow with the Stockholm Environment Institute. The book is organized into four parts. The papers in Part I 17. Atmospheric Neutrinos: Status and Prospects Choubey, Sandhya 2016-01-01 We present an overview of the current status of neutrino oscillation studies at atmospheric neutrino experiments. While the current data gives some tentalising hints regarding the neutrino mass hierarchy, octant of $\\theta_{23}$ and $\\delta_{CP}$, the hints are not statistically significant. We summarise the sensitivity to these sub-dominant three-generation effects from the next-generation proposed atmospheric neutrino experiments. We next present the prospects of new physics searches such as non-standard interactions, sterile neutrinos and CPT violation studies at these experiments. 18. Atmospheric neutrinos: Status and prospects Choubey, Sandhya 2016-07-01 We present an overview of the current status of neutrino oscillation studies at atmospheric neutrino experiments. While the current data gives some tantalising hints regarding the neutrino mass hierarchy, octant of θ23 and δCP, the hints are not statistically significant. We summarise the sensitivity to these sub-dominant three-generation effects from the next-generation proposed atmospheric neutrino experiments. We next present the prospects of new physics searches such as non-standard interactions, sterile neutrinos and CPT violation studies at these experiments. 19. Space Colonization: Problems and Prospects Krichevskiy S. V. 2012-04-01 Full Text Available Space colonization is the top priority of mankind and the strategic target of manned cosmonautics. It is necessary to comprehend the outcome of human space flights and to give a new impulse to space expansion, scientific and practical solving the problem of space colonization by human beings. The attention is also paid to key issues, potentials, restrictions, forecasts, and prospects of space colonization as well as to the transformation of a man into "a man of the future", "homo cosmicus", and "a universal man", to the formation of "space mankind". 20. Prospects for K^+ \\to \\pi^+ \ Palladino, Vito 2015-01-01 The rare decays K+ -> p + n -n are excellent processes to make tests of new physics at the highest scale complementary to LHC thanks to their theoretically cleaness. The NA62 experiment at CERN SPS aims to collect of the order of 100 events in two years of data taking, keeping the background at the level of 10%. Part of the experimental apparatus has been commissioned during a technical run in 2012. The physics prospects and the status of the experiment will be reviewed after the commissioning run of 2014 and the data taking in 2015. 1. Research advances on transgenic plant vaccines. Han, Mei; Su, Tao; Zu, Yuan-Gang; An, Zhi-Gang 2006-04-01 In recent years, with the development of genetics molecular biology and plant biotechnology, the vaccination (e.g. genetic engineering subunit vaccine, living vector vaccine, nucleic acid vaccine) programs are taking on a prosperous evolvement. In particular, the technology of the use of transgenic plants to produce human or animal therapeutic vaccines receives increasing attention. Expressing vaccine candidates in vegetables and fruits open up a new avenue for producing oral/edible vaccines. Transgenic plant vaccine disquisitions exhibit a tempting latent exploiting foreground. There are a lot of advantages for transgenic plant vaccines, such as low cost, easiness of storage, and convenient immune-inoculation. Some productions converged in edible tissues, so they can be consumed directly without isolation and purification. Up to now, many transgenic plant vaccine productions have been investigated and developed. In this review, recent advances on plant-derived recombinant protein expression systems, infectious targets, and delivery systems are presented. Some issues of high concern such as biosafety and public health are also discussed. Special attention is given to the prospects and limitations on transgenic plant vaccines. 2. Caracterização de lodo gerado em estações de tratamento de água: perspectivas de aplicação agrícola Characterization of sludge generated in water treatment plants: prospects for agricultural application Wander Gustavo Botero 2009-01-01 Full Text Available The work reported here involved the characterization of sludges produced at water treatment plants in Jaboticabal-SP using FeCl3 as flocculant, and in Taquaritinga-SP and Manaus-AM using Al2(SO43 as flocculant. An evaluation was also made of the interaction of organic matter extracted from the sludges with different metal species. The results indicated that all the sludges produced at water treatment plants have an important agricultural potential and that their use depends on the characteristics of the raw water and the type of flocculant employed in conventional treatment. The humic substances extracted from the sludges showed different affinities for metal species, favoring eventual exchanges between potentially toxic metals and macro- and micronutrients. An alternative for the use of sludge in agriculture is to pretreat it to remove potentially toxic metals and enrich it with micro- and macronutrients that can be released to the plant. 3. BOILER MATERIALS FOR ULTRASUPERCRITICAL COAL POWER PLANTS R. Viswanathan; K. Coleman; R.W. Swindeman; J. Sarver; J. Blough; W. Mohn; M. Borden; S. Goodstine; I. Perrin 2003-10-20 The principal objective of this project is to develop materials technology for use in ultrasupercritical (USC) plant boilers capable of operating with 760 C (1400 F), 35 MPa (5000 psi) steam. This project has established a government/industry consortium to undertake a five-year effort to evaluate and develop of advanced materials that allow the use of advanced steam cycles in coal-based power plants. These advanced cycles, with steam temperatures up to 760 C, will increase the efficiency of coal-fired boilers from an average of 35% efficiency (current domestic fleet) to 47% (HHV). This efficiency increase will enable coal-fired power plants to generate electricity at competitive rates (irrespective of fuel costs) while reducing CO{sub 2} and other fuel-related emissions by as much as 29%. Success in achieving these objectives will support a number of broader goals. First, from a national prospective, the program will identify advanced materials that will make it possible to maintain a cost-competitive, environmentally acceptable coal-based electric generation option. High sulfur coals will specifically benefit in this respect by having these advanced materials evaluated in high-sulfur coal firing conditions and from the significant reductions in waste generation inherent in the increased operational efficiency. Second, from a national prospective, the results of this program will enable domestic boiler manufacturers to successfully compete in world markets for building high-efficiency coal-fired power plants. 4. Work ethics: An Islamic prospective Muhammad Shakil Ahmad 2011-02-01 Full Text Available Islamic principles completely cover all prospects of life including working in organization. The impact of management style used in an organization play an important role in employee commitment towards its work. This paper is an effort to explore impact of Islamic work ethic on human resource of organization including the prospective of work conflict, job satisfaction, job turn over, turnover intentions and organizational commitment. Data for current study was collected personally through questionnaires from 18 branches of seven banks of Pakistan who practices Islamic banking. In total, 150 Muslims employees were targeted as respondent of current study, while response rate was above 85%. Results show that there is significant impact of Islamic work ethics on organizational commitment, job satisfaction and rewards while Islamic work ethic has no significant relation with intention to quit job. Out of seven, only three hypotheses were fully supported, while two were partially supported, however number of rejected hypothesis were two. Islamic work ethics are source to built greater morale in employees resulting greater job satisfaction. Adopting Islamic work ethics improves organizational commitment, source of motivation as well as reduces the negative intentions of quitting job. 5. Mathematics for Water and Wastewater Treatment Plant Operators. Water and Wastewater Training Program. South Dakota Dept. of Environmental Protection, Pierre. This booklet is intended to aid the prospective waste treatment plant operator or drinking water plant operator in learning to solve mathematical problems, which is necessary for Class I certification. It deals with the basic mathematics which a Class I operator may require in accomplishing day-to-day tasks. The book also progresses into problems… 6. Association mapping of plant resistance to insects. Kloth, Karen J; Thoen, Manus P M; Bouwmeester, Harro J; Jongsma, Maarten A; Dicke, Marcel 2012-05-01 Association mapping is rapidly becoming an important method to explore the genetic architecture of complex traits in plants and offers unique opportunities for studying resistance to insect herbivores. Recent studies indicate that there is a trade-off between resistance against generalist and specialist insects. Most studies, however, use a targeted approach that will easily miss important components of insect resistance. Genome-wide association mapping provides a comprehensive approach to explore the whole array of plant defense mechanisms in the context of the generalist-specialist paradigm. As association mapping involves the screening of large numbers of plant lines, specific and accurate high-throughput phenotyping (HTP) methods are needed. Here, we discuss the prospects of association mapping for insect resistance and HTP requirements. 7. Plant host finding by parasitic plants: A new perspective on plant to plant communication Mark C. Mescher; Justin B. Runyon; Consuelo M. De Moraes 2006-01-01 Plants release airborne chemicals that can convey ecologically relevant information to other organisms. These plant volatiles are known to mediate a large array of, often complex, interactions between plants and insects. It has been suggested that plant volatiles may have similar importance in mediating interactions among plant species, but there are few well-... 8. Plant foods and plant-based diets: protective against childhood obesity? Newby, P K 2009-05-01 The objective of this article is to review the epidemiologic literature examining the role of plant foods and plant-based diets in the prevention of childhood obesity. Available data suggest a protective effect of ready-to-eat cereal on risk of obesity, although prospective studies are still needed. Studies on fruit and vegetables; grains other than cereal; high-protein foods, including beans, legumes, and soy; fiber; and plant-based dietary patterns are inconsistent or generally null. The evidence base is limited, and most studies are fraught with methodologic limitations, including cross-sectional design, inadequate adjustment for potential confounders, and lack of consideration of reporting errors, stage of growth, and genetic influences. Well-designed prospective studies are needed. The lack of evidence showing an association between plant-based diets and childhood obesity does not mean that such diets should not be encouraged. Plant foods are highlighted in the Dietary Guidelines for Americans, and children do not meet the current recommendations for most plant foods. Although the advice to consume a plant-based, low-energy-dense diet is sound, ethical questions arise concerning the relatively high price of these diets in the United States and the way in which such diets are perceived in other parts of the world. Reducing the burden of childhood obesity, eliminating health disparities, and preventing the further spread of the disease around the globe will require not only policy interventions to ensure that plant foods are affordable and accessible to children of all income levels but also awareness of sociocultural norms that affect consumption. 9. 发展林药间作与仿生栽培的前景和应注意的问题%The Prospects and the Matters that Should be Noticed of Expanding the Pattern Ofintercropping Trees with Medicinal Plants and Bionic Cultivation 林树坤 2016-01-01 The pattern of intercropping trees with medicinal plants and cultivation of medicinal plants in natural forest and imitating wild condition ,that can make medicinal plants back to naturally grow th ;improve the quality of medici‐nal plants;ensure safety of traditionalChinese medicinal materials .There is a problem that economic benefits and the sustainable development of ecology depend on the varieties variation in such cultivation pattern cannot be ignored .%林药间作、天然林下野生抚育和仿野生栽培中药材，让中药材回归自然生长的本性，提高中药材的产品质量，保障中医药的用药安全。还林品种的不同决定了、也局限了林下经济的与生态的可持续性发展。这是个不可忽视的问题。 10. Radiation detectors: needs and prospects Armantrout, G.A. 1981-01-01 Important applications for x- and ..gamma..-ray spectroscopy are found in prospecting, materials characterization, environmental monitoring, the life sciences, and nuclear physics. The specific requirements vary for each application with varying degrees of emphasis on either spectrometer resolution, detection efficiency, or both. Since no one spectrometer is ideally suited to this wide range of needs, compromises are usually required. Gas and scintillation spectrometers have reached a level of maturity, and recent interest has concentrated on semiconductor spectrometers. Germanium detectors are showing continuing refinement and are the spectrometers of choice for high resolution applications. The new high-Z semiconductors, such as CdTe and HgI/sub 2/, have shown steady improvement but are limited in both resolution and size and will likely be used only in applications which require their unique properties. 11. Theoretical Prospects for B Physics Fleischer, Robert 2015-01-01 The exploration of B-meson decays has reached an unprecedented level of sophistication, with a phase of even much higher precision ahead of us thanks to run 2 of the LHC and the future era of Belle II and the LHCb upgrade. For many processes, the theoretical challenge in the quest to reveal possible footprints of physics beyond the Standard Model will be the control of uncertainties from strong interactions. After a brief discussion of the global picture emerging from the LHC data, I will focus on the theoretical prospects and challenges for benchmark B decays to search for new sources of CP violation, and highlight future opportunities to probe the Standard Model with strongly suppressed rare B decays. 12. Hadron therapy: history, status, prospects Klenov, G. I.; Khoroshkov, V. S. 2016-08-01 A brief historical review is given of external radiation therapy (RT), one of the main cancer treatment methods along with surgery and chemotherapy. Cellular mechanisms of radiation damage are described. Special attention is paid to hadron (proton and ion) therapy, its history, results, problems, challenges, current trends, and prospects. Undeniably great contributions to proton therapy have been made by Russian researchers, notably at the experimental centers that have operated since the mid-20th century at the Joint Institute for Nuclear Research, the A I Alikhanov Institute for Theoretical and Experimental Physics (ITEP), and the B P Konstantinov Petersburg Institute of Nuclear Physics. A quarter of the global clinical experience was accumulated by 1990 at the world's largest ITEP-hosted multicabin proton therapy center. 13. Poinsettia plant exposure Christmas flower poisoning; Lobster plant poisoning; Painted leaf poisoning ... Leaves, stem, sap of the poinsettia plant ... Poinsettia plant exposure can affect many parts of the body. EYES (IF DIRECT CONTACT OCCURS) Burning Redness STOMACH AND ... 14. Teaching Plant Reproduction. Tolman, Marvin N., Ed.; Hardy, Garry R., Ed. 2000-01-01 Recommends using Amaryllis hippeastrum to teach young children about plant reproduction. Provides tips for growing these plants, discusses the fast growing rate of the plant, and explains the anatomy. (YDS) 15. Kansas Power Plants Kansas Data Access and Support Center — The Kansas Power Plants database depicts, as point features, the locations of the various types of power plant locations in Kansas. The locations of the power plants... 16. The impact of plant biotechnology on food allergy. Herman, Eliot M; Burks, A Wesley 2011-04-01 Concerns about food allergy and its societal growth are intertwined with the growing advances in plant biotechnology. The knowledge of plant genes and protein structures provides the key foundation to understanding biochemical processes that produce food allergy. Biotechnology offers the prospect of producing low-allergen or allergen null plants that could mitigate the allergic response. Modified low-IgE binding variants of allergens could be used as a vaccine to build immunotolerance in sensitive individuals. The potential to introduce new allergens into the food supply by biotechnology products is a regulatory concern. Copyright © 2010 Elsevier Ltd. All rights reserved. 17. Emerging Prospects for Repository Success Isaacs, T 2006-01-12 Recent events are again raising some old issues and creating new opportunities regarding the future disposition of the used, or spent, fuel from nuclear power plants. Handling these challenges well will not only help set the stage for a robust nuclear energy future, but will reflect the growing linkages among nuclear power, nuclear waste management, international security, and public and political acceptance. The emerging global nuclear regime may make spent fuel management not only more important, but improve chances of success. 18. Marine prospecting for petroleum and natural gas Katzung, G. 1982-01-01 The contribution presents a review of areas of oceans and seas, where prospecting for oil and gas is carried out. Prospecting in marine areas is characterized by advancing to growing water depths and in hospitable climatic districts. The growing expenditures, connected with these circumstances, call for a more careful preparation of drilling work. 19. Prospective Biology Teachers' Understanding of Genetics Concepts. Cakir, Mustafa; Crawford, Barbara The purpose of this study is to examine one possible source of misconceptions that are held by students of genetics--the teachers. Is there evidence to suggest that prospective biology teachers might have misconceptions about genetics and related concepts? If prospective biology teachers have misconceptions in genetics, how do these misconceptions… 20. Functional correlates of prospective memory in stroke Kant, N.\|info:eu-repo/dai/nl/357402952; Van den Berg, E.\|info:eu-repo/dai/nl/30481959X; van Zandvoort, M.J.E.\|info:eu-repo/dai/nl/229475094; Frijns, C.J.M.; Kappelle, L.J.; Postma, A.\|info:eu-repo/dai/nl/08621182X 2014-01-01 NTRODUCTION: Prospective memory is the ability to remember actions to be performed later in time or when a certain event occurs. Multiple cognitive processes are involved in prospective memory, and the degree to which automatic or effortful processes are involved may differ for different types of 1. Prospective Memory Training in older adults Schmidt, I.W.; Berg, I.J.; Deelman, B.G. 2001-01-01 This study evaluates the results of a training program for prospective remembering. The goal of the training was to improve prospective memory by associating cues from the retrieval situation with the to be remembered information. The training group consisted of 20 participants, aged between 45 and 2. Prescriptions Guiding Prospective Teachers in Teaching Mathematics Zembat, Ismail Özgür; Aslan, Mustafa 2016-01-01 This study aims to investigate the nature of different mathematics teaching modes (prescriptions) that guide prospective teachers during their instruction. The participants were 24 junior prospective middle school mathematics teachers (19 females and 5 males) who were attending a mathematics methods course at a private university in central… 3. Prospective Science Teachers' Conceptions about Astronomical Subjects Küçüközer, Hüseyin 2007-01-01 The main objective of this study was to identify prospective science teachers' conceptions on basic astronomical phenomena. A questionnaire consisting of nine open-ended questions was administered to 327 prospective science teachers. The questionnaire was constructed after extensive review of the literature and took into consideration the reported… 4. Prospective Teachers' Personal Characteristics to Multicultural Education Eskici, Menekse 2016-01-01 The aim of this paper is to determine prospective teachers' personal characteristics to multicultural education. It is also aimed to reveal whether there are meaningful differences in prospective teachers' personal characteristics to multicultural education according to their genders, age and number of siblings. The descriptive model was chosen to… 5. 青海省海北州杜鹃花科杜鹃花属植物种类形态特征及发展前景%Morphological Characteristics and Development Prospects of Plant Species of Rhododendron Genus,Ericaceae Family in Haibei State of Qinghai Province 扈晓途 2012-01-01 There are four species belonging to Rhododendron genus,Ericaceae family in Haibei State,such as Rdodendron przewalskii Maxim.,Rhododendron anthopogonlides Maxim.,Rhododendron capitatum Maxim.and Rhododendron thymifolium Maxim..The morphological characteristics,pharmacological properties,production and sales as well as development prospects of Rhododendron genus were introduced.%青海省海北州境内的杜鹃花科杜鹃花属植物有4种,即青海杜鹃、烈香杜鹃、头花杜鹃、百里香杜鹃。介绍了杜鹃花属植物的形态特征、药理性能、功效、产销情况及发展前景。 6. Prospecting sugarcane genes involved in aluminum tolerance Rodrigo D. Drummond 2001-12-01 Full Text Available Aluminum is one of the major factors that affect plant development in acid soils, causing a substantial reduction in yield in many crops. In South America, about 66% of the land surface is made up of acid soils where high aluminum saturation is one of the main limiting factors for agriculture. The biochemical and molecular basis of aluminum tolerance in plants is far from being completely understood despite a growing number of studies, and in the specific case of sugarcane there are virtually no reports on the effects of gene regulation on aluminum stress. The objective of the work presented in this paper was to prospect the sugarcane expressed sequence tag (SUCEST data bank for sugarcane genes related to several biochemical pathways known to be involved in the responses to aluminum toxicity in other plant species and yeast. Sugarcane genes similar to most of these genes were found, including those coding for enzymes that alleviate oxidative stress or combat infection by pathogens and those which code for proteins responsible for the release of organic acids and signal transducers. The role of these genes in aluminum tolerance mechanisms is reviewed. Due to the high level of genomic conservation in related grasses such as maize, barley, sorghum and sugarcane, these genes may be valuable tools which will help us to better understand and to manipulate aluminum tolerance in these species.Alumínio (Al é um dos principais fatores que afetam o desenvolvimento de plantas em solos ácidos, reduzindo substancialmente a produtividade agrícola. Na América do Sul, cerca de 66% da superfície do solo apresenta acidez, onde a alta saturação de alumínio é uma das maiores limitações à prática agrícola. Apesar do crescente número de estudos, uma compreensão completa das bases bioquímicas e moleculares da tolerância ao alumínio em plantas está longe de ser alcançada. No caso da cana-de-açúcar, não há nada publicado sobre a regulação g 7. Prospects for European labour demand. Lindley, R M 1988-07-01 The impact of economic and technological trends upon the level and structure of labor demand is examined, exploring the methods used to model the labor market and making special reference to demography and technology. Evidence on recent and prospective changes in labor demand is reviewed for France, Germany, Italy, the Netherlands, and the UK. The models used to explore future employment scenarios usually fail to incorporate the linkages required to fully analyze the various demographic-economic interactions. Further, this is not generally viewed as a limitation, given the time frame of most employment projections and their preoccupation with changes in the structure of labor demand. Medium-term multisectoral models tend to pay more attention to both demographic and technical change, but the treatment of both aspects is limited. The projections provide a framework for considering how both socioeconomic behavior and policy might change to achieve different outcomes. The greater a model's behavioral content, as expressed in its relationships between different variables, the greater the insight obtainable from simulation exercises. The 1st half of the 1970s was characterized by a reduction in German employment, representing the severest of European reactions to the oil crisis. The 2nd half of the decade recorded rapid growth in Italy and the Netherlands. The 1980s started with marked declines in Germany and the UK. Overall, the net gains of the 1970s were lost in the recession following the 2nd oil crisis. In none of the 5 countries studied does any realistic prospect emerge of achieving full employment before 2000. The most optimistic outcome is that unemployment will decline only slowly, it at all. The growth of both new forms and areas of employment will not compensate sufficiently for the loss of jobs elsewhere and the growth of labor supply. The industrial sector will continue to experience change in favor of the service sector but at a slower rate than during 8. The Present Situation and Prospect of the Study on Locoweed in China LI Jian-ke; WANG Jian-hua 2003-01-01 . Locoweed is one of main poisonous plants in the world, and also is the most important toxic plant in grassland of China. The distribution range of the locoweed is extending continuously and it has formed or is coming into dominant species gradually in some areas in recent years, which cause the retrogressive succession and grazer poisoning and died in rangeland. Locoweed seriously threatened the grassland agriculture and cure practice to the locoweed for more than ten years, this paper reviewed the present situation and prospect of the studies on the locoweed in China, which include the researches of it's biological characteristics, distribution, ecological environment, harmfulness, prevention, weeding, utilization and ecological control etc. 9. Agricultural biotechnology: Status and prospective Drinić Goran 2003-01-01 Full Text Available The development of the DNA recombinant technology has provided the transfer of a single or several genes within or among species whereby organisms with new traits were developed. Such organisms have been called genetically modified organisms. The first genetically modified varieties of cultivated plants entered the market in 1996 and since then areas sown with such crops has been increasing, amounting to 60 M ha in 2002. During the stated period, genetically modified varieties and hybrids of cultivated plants were developed with a gene introduced for tolerance to herbicides, resistance to insects, prolonged maturity period and improved quality. However, heavy disputes have arisen all over the world relating the possible gain and potential risks from the growth and utilization of modified crops. First of all, there are ethical issues related directly to gene transfer from a species to a species, then effects of the introduced gene on the environment and human health, economical justification of cultivating genetically modified crops, consumers confidence in the legislation, labeling the products encompassing a genetic modification, effects on the global market and ever increasing food requirements. The effect of products derived from genetically modified plants on human health depends on a specific content of a product itself and can potentially be useful if a product contains an increased content of vitamins, with an allergen removed, or potentially harmful, if a new allergen or a toxin were introduced by genetic modifications. Each genetically modified product is subjected to a rigorous testing of its safety prior to its introduction into a food chain. It encompasses molecular, biochemical, toxicological, nutritional and allergenic tests. Many countries apply legislation that stipulates labeling of genetically modified products, whereby the fact that the commodity encompasses products of genetic modification is clearly pointed out. . 10. Integrated Development of Chinese Herbal Medicine Planting and Tourist Commodities: A Case Study of Green Handmade Soap Development in Shandong Province Xiu; LI; Mengxuan; CHEN; Xiaoli; SONG 2015-01-01 Combining current situations of Chinese herbal medicine planting industry in Shandong,in line with existing problems of Chinese herbal medicine planting industry,this paper analyzed development prospect of tourist commodity industry in Shandong Province,and came up with actual selection and recommendations for integrated development of Chinese herbal medicine planting and tourist commodities. 11. [Prospective study in 2 hospitals]. Jiménez-Buñuales, M T; Martínez-Sáenz, M S; González-Diego, P; Vallejo-García, M; Gallardo-Anciano, J; Cestafe-Martínez, A 2016-06-01 The purpose of this study is to know the incidence rate of medication reconciliation at admission and discharge in patients of La Rioja and to improve the patient safety on medication reconciliation. An observational prospective study, part of the Joint Action PaSQ, Work Package 5, European Union Network for Patient Safety and Quality of Care. The study has taken into account the definitions of the Institute for Safe Medication Practices. Any unintended discrepancy in medication between chronic treatment and the treatment prescribed in the hospital was considered as a reconciliation error. A total of 750 patients were included, 9 (1.2%) of whom showed at least one discrepancy. The patients had a total of 3,156 mediations registered: 2,313 prescriptions (73.4%) showed no differences, while 821 prescriptions (26%) were intended discrepancies and 21 prescriptions (0.6%) unintended discrepancies were considered by the physician as reconciliation errors. A percentage of 1.2 of the patients, which represents 0.6% of the medicines (one in 166 medications registered) had reconciliation errors during their hospital stay. A proceeding has been implemented by means of the physician doing the medication reconciliation and reviewing it with the help of a medication reconciliation form. The medication reconciliation is a priority strategic objective to improve the safety of patients. Copyright © 2016 SECA. Published by Elsevier Espana. All rights reserved. 12. Dual pathways to prospective remembering McDaniel, Mark A.; Umanath, Sharda; Einstein, Gilles O.; Waldum, Emily R. 2015-01-01 According to the multiprocess framework (McDaniel and Einstein, 2000), the cognitive system can support prospective memory (PM) retrieval through two general pathways. One pathway depends on top–down attentional control processes that maintain activation of the intention and/or monitor the environment for the triggering or target cues that indicate that the intention should be executed. A second pathway depends on (bottom–up) spontaneous retrieval processes, processes that are often triggered by a PM target cue; critically, spontaneous retrieval is assumed not to require monitoring or active maintenance of the intention. Given demand characteristics associated with experimental settings, however, participants are often inclined to monitor, thereby potentially masking discovery of bottom–up spontaneous retrieval processes. In this article, we discuss parameters of laboratory PM paradigms to discourage monitoring and review recent behavioral evidence from such paradigms that implicate spontaneous retrieval in PM. We then re-examine the neuro-imaging evidence from the lens of the multiprocess framework and suggest some critical modifications to existing neuro-cognitive interpretations of the neuro-imaging results. These modifications illuminate possible directions and refinements for further neuro-imaging investigations of PM. PMID:26236213 13. Dual Pathways to Prospective Remembering Mark A Mcdaniel 2015-07-01 Full Text Available According to the multiprocess framework (McDaniel & Einstein, 2000, the cognitive system can support prospective memory (PM retrieval through two general pathways. One pathway depends on top-down attentional control processes that maintain activation of the intention and/or monitor the environment for the triggering or target cues that indicate that the intention should be executed. A second pathway depends on (bottom-up spontaneous retrieval processes, processes that are often triggered by a PM target cue; critically spontaneous retrieval is assumed to not require monitoring or active maintenance of the intention. Given demand characteristics associated with experimental settings, however, participants are often inclined to monitor, thereby potentially masking discovery of bottom-up spontaneous retrieval processes. In this article, we discuss parameters of laboratory PM paradigms to discourage monitoring and review recent behavioral evidence from such paradigms that implicate spontaneous retrieval in PM. We then re-examine the neuro-imaging evidence from the lens of the multiprocess framework and suggest some critical modifications to existing neuro-cognitive interpretations of the neuro-imaging results. These modifications illuminate possible directions and refinements for further neuro-imaging investigations of PM. 14. Prospective evaluation of myopic keratomileusis. Swinger, C A; Barker, B A 1984-07-01 The initial results of a prospective evaluation of myopic keratomileusis are reported. The procedure was attempted on 42 eyes, with an average follow-up of 10 months. The average reductions of myopia were 7.05 D and 11.59 D when measured by keratometry and refraction, respectively. Regular astigmatism increased by 0.50 D on keratometry, but there was no change in the refractive cylinder. The majority of patients had some irregular astigmatism on corneoscopy. The average percent correction, based on refraction, was 94.1 +/- 24%, and the correlation coefficient was 0.43. Visual rehabilitation was rapid. No patient followed for 1 year or more had a decrease in the best-corrected acuity, and 63% of this group had an average improvement of 1.5 lines with as much as five lines. The final refraction may take up to 6 months to stabilize. Complications consisted of epithelium and debris in the interface and focal necrosis of Bowman's membrane. The technique is difficult but may have application in the visual rehabilitation of the high myope. 15. Soap production: A green prospective. Félix, Sandra; Araújo, Joana; Pires, Ana Maria; Sousa, Ana Cláudia 2017-08-01 A green prospective based on the reuse of waste materials such as almond shells, orange peel and used cooking oil to manufacture soap is presented. In Portugal, thousands of tons of waste are generated from used cooking oil and production of nut shells' residues is growing every year. In addition, the high consumption of citrus fruits, oranges in particular, generates large amounts of citrus peel. Therefore, it is necessary to diversify reuse mechanisms of these wastes, in order to make them back into raw materials. Complying with this trend, this work was carried out by processing and grinding almond shells, treating used oil, processing orange peels and extracting limonene, formulating and producing soap, and performing an acceptance study of the final product. Results validated a high potential of the idea in the field of environmental education, so it can be replicated in practical classes. It can also be useful for waste management, and it can support the development of community projects on an ecological approach. Copyright © 2017 Elsevier Ltd. All rights reserved. 16. Plant Growth Regulators. Nickell, Louis G. 1978-01-01 Describes the effect of "plant growth regulators" on plants, such as controlling the flowering, fruit development, plant size, and increasing crop yields. Provides a list of plant growth regulators which includes their chemical, common, and trade names, as well as their different use(s). (GA) 17. Ethylene insensitive plants Ecker, Joseph R.; Nehring, Ramlah; McGrath, Robert B. 2007-05-22 Nucleic acid and polypeptide sequences are described which relate to an EIN6 gene, a gene involved in the plant ethylene response. Plant transformation vectors and transgenic plants are described which display an altered ethylene-dependent phenotype due to altered expression of EIN6 in transformed plants. 18. Plant Biology Science Projects. Hershey, David R. This book contains science projects about seed plants that deal with plant physiology, plant ecology, and plant agriculture. Each of the projects includes a step-by-step experiment followed by suggestions for further investigations. Chapters include: (1) "Bean Seed Imbibition"; (2) "Germination Percentages of Different Types of Seeds"; (3)… 19. Evolutionarilv Conserved DELLA-mediated Gibberellin Signaling in Plants Xiu-Hua Gao; Xian-Zhong Huang; Sen-Lin Xiao; Xiang-Dong Fu 2008-01-01 Gibberellins (GAs) play important roles in many essential plant growth and development processes. A family of nuclear growth-repressing DELLA proteins is the key component in GA signaling. GA perception is mediated by GID1, and the key event of GA signaling is the degradation of DELLA proteins via the 26S proteasome pathway. DELLA proteins integrating other plant hormones signaling and environmental cue modulating plant growth and development have been revealed. GA turning on the de-DELLA-repressing system is conserved, and independently establishes step-by-step recruitment of GAstimulated GID1-DELLA interaction and DELLA growth-repression functions during land plant evolution. These discoveries open new prospects for the understanding of GA action and DELLA-mediated signaling in plants. 20. Site-Specific Analysis of Geothermal Development-Data Files of Prospective Sites Williams, F.; Cohen, A.; Pfundstein, R.; Pond, S. 1977-10-01 This document presents site-specific data and sample development schedules for the first plant on line at 30 hydrothermal and 7 geopressured prospective sites (prospects) that are believed to be suited for supporting the geothermal generation of electricity. This report includes many prospects from an earlier METREK report on geothermal development scenarios. The list has been augmented with other sites chosen as development prospects by the division of Geothermal Energy (DGE) of the Energy Research and Development Administration (ERDA). The DGE additions include a general area called ''Cascade Range''. METREK has chosen the following specific Cascade Range Sites in place of that general area: Baker Hot Springs, Mount Hood, Lassen and Glass Mountain/ Diablo. All the prospects have been selected on the basis of current knowledge of hydrothermal and geopressured resources. The selection is intended for program planning purposes. Neither METREK nor the Federal government warrants that any of these sites will necessarily be developed, nor does their selection necessarily imply any commitment on the part of the Federal government to their development. [DJE-2005 1. JSTOR Plant Science 2010-01-01 JSTOR Plant Science is an online environment that brings together content, tools, and people interested in plant science. It provides access to foundational content vital to plant science – plant type specimens, taxonomic structures, scientific literature, and related materials, making them widely accessible to the plant science community as well as to researchers in other fields and to the public. It also provides an easy to use interface with powerful functionality that su... 2. Plant Research '75 1975-01-01 Research is reported on stomatal regulation of the gas exchanges between plant and environment; inhibitory effects in flower formation; plant growth and development through hormones; hormone action; development and nitrogen fixation in algae; primary cell wall glycoprotein ectensin; enzymic mechanisms and control of polysaccharide and glycoprotein synthesis; molecular studies of membrane studies; sensory transduction in plants; regulation of formation of protein complexes and enzymes in higher plant cell and mechanism of sulfur dioxide toxicity in plants. (PCS) 3. PLANT BIOPRINTING: NOVEL PERSPECTIVE FOR PLANT BIOTECHNOLOGY Adhityo WICAKSONO 2015-12-01 Full Text Available Bioprinting is a technical innovation that has revolutionized tissue engineering. Using conventional printer cartridges filled with cells as well as a suitable scaffold, major advances have been made in the biomedical field, and it is now possible to print skin, bones, blood vessels, and even organs. Unlike animal systems, the application of bioprinting in simple plant tissue cells is still in a nascent phase and has yet to be studied. One major advantage of plants is that all living parts are reprogrammable in the form of totipotent cells. Plant bioprinting may improve scientists’understanding of plant shape and morphogenesis, and could serve for the mass production of desired tissues or plants, or even the production of plant-based biomaterial for industrial uses. This perspectives paper explores these possibilities using knowledge on what is known about bioprinting in other biosystems. 4. Pathogen Phytosensing: Plants to Report Plant Pathogens C. Neal Stewart 2008-04-01 Full Text Available Real-time systems that provide evidence of pathogen contamination in crops can be an important new line of early defense in agricultural centers. Plants possess defense mechanisms to protect against pathogen attack. Inducible plant defense is controlled by signal transduction pathways, inducible promoters and cis-regulatory elements corresponding to key genes involved in defense, and pathogen-specific responses. Identified inducible promoters and cis-acting elements could be utilized in plant sentinels, or Ã¢Â€Â˜phytosensorsÃ¢Â€Â™, by fusing these to reporter genes to produce plants with altered phenotypes in response to the presence of pathogens. Here, we have employed cis-acting elements from promoter regions of pathogen inducible genes as well as those responsive to the plant defense signal molecules salicylic acid, jasmonic acid, and ethylene. Synthetic promoters were constructed by combining various regulatory elements supplemented with the enhancer elements from the Cauliflower mosaic virus (CaMV 35S promoter to increase basal level of the GUS expression. The inducibility of each synthetic promoter was first assessed in transient expression assays using Arabidopsis thaliana protoplasts and then examined for efficacy in stably transgenic Arabidopsis and tobacco plants. Histochemical and fluorometric GUS expression analyses showed that both transgenic Arabidopsis and tobacco plants responded to elicitor and phytohormone treatments with increased GUS expression when compared to untreated plants. Pathogen-inducible phytosensor studies were initiated by analyzing the sensitivity of the synthetic promoters against virus infection. Transgenic tobacco plants infected with Alfalfa mosaic virus showed an increase in GUS expression when compared to mock-inoculated control plants, whereas Tobacco mosaic virus infection caused no changes in GUS expression. Further research, using these transgenic plants against a range of different 5. Vision Trouble Can Dim Life's Prospects ... page: https://medlineplus.gov/news/fullstory_160136.html Vision Trouble Can Dim Life's Prospects But it's not ... THURSDAY, July 28, 2016 (HealthDay News) -- People with vision problems may face a higher risk of unemployment, ... 6. Hospital Outpatient Prospective Payment System (OPPS) Lim... U.S. Department of Health & Human Services — Hospital Outpatient Prospective Payment System (OPPS) Limited Data Set This file contains select claim level data and is derived from 2010 hospital outpatient PPS... 7. A prospective study of gentamicin ototoxicity Winkel, O; Hansen, M M; Kaaber-Bühler, Søren; 1978-01-01 Twenty patients were included in a prospective otoneurological study performed to assess the ototoxicity in gentamicin therapy. Gentamicin was administered intravenously, and the serum level was currently determined. Audiographic and electronystagmographic studies were carried out at the institut... 8. Nuclear radiation cleanup and uranium prospecting Mariella, Jr., Raymond P.; Dardenne, Yves M. 2017-01-03 Apparatus, systems, and methods for nuclear radiation cleanup and uranium prospecting include the steps of identifying an area; collecting samples; sample preparation; identification, assay, and analysis; and relating the samples to the area. 9. Hypnosis Attenuates Executive Cost of Prospective Memory. Demeter, Gyula; Szendi, István; Juhász, Marianna; Kovács, Zoltán Ambrus; Boncz, István; Keresztes, Attila; Pajkossy, Péter; Racsmány, Mihály 2016-01-01 Prospective memory is the ability to formulate and carry out actions at the appropriate time or in the appropriate context. This study aimed to identify the effect of hypnosis on prospective memory performance and to analyze the involvement of executive control processes in intention realization in a hypnotically altered state of consciousness. In 1 experiment, manipulating hypnotic instruction in a within-subject fashion, the authors explored the event-based prospective memory performance of 23 volunteers in 3 conditions: baseline, expectation, and execution. The primary result was that executing prospective memory responses, at the same accuracy rate, produced a significantly lower cost of ongoing responses in terms of response latency in the hypnotic state than in wake condition. 10. Workplace Counselling in Nigeria: Problems and Prospects ... Workplace Counselling in Nigeria: Problems and Prospects. ... mechanism, a risk management tool, and a medium of organizational change. Keywords – workplace counselling, counsellor, employee, company, employee-care, Nigeria. 11. Physics prospects at a linear + - collider Saurabh D Rindani 2006-10-01 The talk described the prospects of studying standard model parameters as well as scenarios beyond the standard model, like the minimal supersymmetric standard model, theories with extra dimensions and theories with extra neutral gauge bosons, at a future linear + - collider. 12. Prospective teachers information and communication technology metaphors Ömür Akdemir 2015-04-01 Full Text Available Determination of the perceptions of the prospective teachers for the Information and Communications Technology (ICT terms have a remarkable potential to provide input for technology integration plans and ICT trainings. Within this context, the purpose of this study is to discover the metaphors constructed by prospective teachers for the ICT terms. Data were gathered from 180 prospective teachers through survey. 977 valid metaphors constructed by the participants were grouped into conceptual categories for the six ICT terms. The most common conceptual categories are “developing and changing” for technology, “making life easy” for computers and search engines, “limitless and endless” for the Internet, “means of communication” for social networks, and “addictive items” for video games. Future research should concentrate on investigating the match and mismatches between intended use of the ICT tools and the perception of the prospective teachers. 13. Prospective Coding by Spiking Neurons. Johanni Brea 2016-06-01 Full Text Available Animals learn to make predictions, such as associating the sound of a bell with upcoming feeding or predicting a movement that a motor command is eliciting. How predictions are realized on the neuronal level and what plasticity rule underlies their learning is not well understood. Here we propose a biologically plausible synaptic plasticity rule to learn predictions on a single neuron level on a timescale of seconds. The learning rule allows a spiking two-compartment neuron to match its current firing rate to its own expected future discounted firing rate. For instance, if an originally neutral event is repeatedly followed by an event that elevates the firing rate of a neuron, the originally neutral event will eventually also elevate the neuron's firing rate. The plasticity rule is a form of spike timing dependent plasticity in which a presynaptic spike followed by a postsynaptic spike leads to potentiation. Even if the plasticity window has a width of 20 milliseconds, associations on the time scale of seconds can be learned. We illustrate prospective coding with three examples: learning to predict a time varying input, learning to predict the next stimulus in a delayed paired-associate task and learning with a recurrent network to reproduce a temporally compressed version of a sequence. We discuss the potential role of the learning mechanism in classical trace conditioning. In the special case that the signal to be predicted encodes reward, the neuron learns to predict the discounted future reward and learning is closely related to the temporal difference learning algorithm TD(λ. 14. Prospective Optimization with Limited Resources. Snider, Joseph; Lee, Dongpyo; Poizner, Howard; Gepshtein, Sergei 2015-09-01 The future is uncertain because some forthcoming events are unpredictable and also because our ability to foresee the myriad consequences of our own actions is limited. Here we studied how humans select actions under such extrinsic and intrinsic uncertainty, in view of an exponentially expanding number of prospects on a branching multivalued visual stimulus. A triangular grid of disks of different sizes scrolled down a touchscreen at a variable speed. The larger disks represented larger rewards. The task was to maximize the cumulative reward by touching one disk at a time in a rapid sequence, forming an upward path across the grid, while every step along the path constrained the part of the grid accessible in the future. This task captured some of the complexity of natural behavior in the risky and dynamic world, where ongoing decisions alter the landscape of future rewards. By comparing human behavior with behavior of ideal actors, we identified the strategies used by humans in terms of how far into the future they looked (their "depth of computation") and how often they attempted to incorporate new information about the future rewards (their "recalculation period"). We found that, for a given task difficulty, humans traded off their depth of computation for the recalculation period. The form of this tradeoff was consistent with a complete, brute-force exploration of all possible paths up to a resource-limited finite depth. A step-by-step analysis of the human behavior revealed that participants took into account very fine distinctions between the future rewards and that they abstained from some simple heuristics in assessment of the alternative paths, such as seeking only the largest disks or avoiding the smaller disks. The participants preferred to reduce their depth of computation or increase the recalculation period rather than sacrifice the precision of computation. 15. Prospective Optimization with Limited Resources. Joseph Snider 2015-09-01 Full Text Available The future is uncertain because some forthcoming events are unpredictable and also because our ability to foresee the myriad consequences of our own actions is limited. Here we studied how humans select actions under such extrinsic and intrinsic uncertainty, in view of an exponentially expanding number of prospects on a branching multivalued visual stimulus. A triangular grid of disks of different sizes scrolled down a touchscreen at a variable speed. The larger disks represented larger rewards. The task was to maximize the cumulative reward by touching one disk at a time in a rapid sequence, forming an upward path across the grid, while every step along the path constrained the part of the grid accessible in the future. This task captured some of the complexity of natural behavior in the risky and dynamic world, where ongoing decisions alter the landscape of future rewards. By comparing human behavior with behavior of ideal actors, we identified the strategies used by humans in terms of how far into the future they looked (their "depth of computation" and how often they attempted to incorporate new information about the future rewards (their "recalculation period". We found that, for a given task difficulty, humans traded off their depth of computation for the recalculation period. The form of this tradeoff was consistent with a complete, brute-force exploration of all possible paths up to a resource-limited finite depth. A step-by-step analysis of the human behavior revealed that participants took into account very fine distinctions between the future rewards and that they abstained from some simple heuristics in assessment of the alternative paths, such as seeking only the largest disks or avoiding the smaller disks. The participants preferred to reduce their depth of computation or increase the recalculation period rather than sacrifice the precision of computation. 16. Cosmic Humanity: Utopia, Realities, Prospects Sergey Krichevsky 2017-07-01 Full Text Available The philosophical foundations of the theory and practice of the creation of cosmic humanity as a process of the evolution of human civilization, the emergence into space, with the prospect of resettlement outside the Earth are considered. There is a connection between myths, fantasies, ideas, concepts and projects aimed at the exploration of outer space, the creation of cosmic humanity. A new and voluminous definition of cosmic humanity in the evolutionary paradigm is given. Cosmic humanity is (essence and 4 stages of evolution: 1. Humanity living on Earth, sensing, knowing, understanding its cosmic origin, relationship with the cosmos and cosmic destiny. 2. Humanity living on Earth, leading aerospace activity for the purposes of exploration and use of aerospace space (Heaven, Space for survival and development. 3. Humanity living on Earth and outside the Earth — in the solar system, preserving the Earth and mastering the Cosmos for survival and development. 4. Humanity, settled and living in the Cosmos. Now humanity is in the process of transition from the second to the third stage. In the process of this evolution, a complex transformation of man and society takes place. The problem-semantic field of cosmic humanity is described and its general model is presented. The meta-goal-setting is the justification of cosmic humanity with the application of the anthropic principle and its “active” super (post anthropic supplement: “Cosmic humanity has an evolutionary purpose to actively manage evolution: change man, humanity and the universe.” The evolution of the “cosmic dream”, goals and technologies of space activities is formalized in the form of a conceptual model. Challenges and negative trends are considered in connection with the crisis of space activity, criticism and attempts to limit the flights of people into space. The prototype of cosmic humanity, its basis and acting model is the cosmonauts’ community. The main 17. Russia’s Prospects in Asia 2010-12-01 culture, including cuisine and cinema , are in vogue among Russian elites. Russian energy resources in Si- beria and the RFE and Japan’s dependence on...they credit him with prag- matism and realism in the face of George W. Bush’s misguided attempts to achieve full global hegemony. By assigning a...prospects, more realism toward the destabilizing impact of weapons of mass destruction (WMD) in North Korea as well as Iran, and new prospects for 18. Lignin peroxidase functionalities and prospective applications Falade, Ayodeji O.; Nwodo, Uchechukwu U.; Iweriebor, Benson C.; Green, Ezekiel; Leonard V. Mabinya; Okoh, Anthony I. 2016-01-01 Abstract Ligninolytic extracellular enzymes, including lignin peroxidase, are topical owing to their high redox potential and prospective industrial applications. The prospective applications of lignin peroxidase span through sectors such as biorefinery, textile, energy, bioremediation, cosmetology, and dermatology industries. The litany of potentials attributed to lignin peroxidase is occasioned by its versatility in the degradation of xenobiotics and compounds with both phenolic and non‐phe... 19. Green Plants in the Red: A Baseline Global Assessment for the IUCN Sampled Red List Index for Plants. Neil A Brummitt Full Text Available Plants provide fundamental support systems for life on Earth and are the basis for all terrestrial ecosystems; a decline in plant diversity will be detrimental to all other groups of organisms including humans. Decline in plant diversity has been hard to quantify, due to the huge numbers of known and yet to be discovered species and the lack of an adequate baseline assessment of extinction risk against which to track changes. The biodiversity of many remote parts of the world remains poorly known, and the rate of new assessments of extinction risk for individual plant species approximates the rate at which new plant species are described. Thus the question 'How threatened are plants?' is still very difficult to answer accurately. While completing assessments for each species of plant remains a distant prospect, by assessing a randomly selected sample of species the Sampled Red List Index for Plants gives, for the first time, an accurate view of how threatened plants are across the world. It represents the first key phase of ongoing efforts to monitor the status of the world's plants. More than 20% of plant species assessed are threatened with extinction, and the habitat with the most threatened species is overwhelmingly tropical rain forest, where the greatest threat to plants is anthropogenic habitat conversion, for arable and livestock agriculture, and harvesting of natural resources. Gymnosperms (e.g. conifers and cycads are the most threatened group, while a third of plant species included in this study have yet to receive an assessment or are so poorly known that we cannot yet ascertain whether they are threatened or not. This study provides a baseline assessment from which trends in the status of plant biodiversity can be measured and periodically reassessed. 20. Green Plants in the Red: A Baseline Global Assessment for the IUCN Sampled Red List Index for Plants. Brummitt, Neil A; Bachman, Steven P; Griffiths-Lee, Janine; Lutz, Maiko; Moat, Justin F; Farjon, Aljos; Donaldson, John S; Hilton-Taylor, Craig; Meagher, Thomas R; Albuquerque, Sara; Aletrari, Elina; Andrews, A Kei; Atchison, Guy; Baloch, Elisabeth; Barlozzini, Barbara; Brunazzi, Alice; Carretero, Julia; Celesti, Marco; Chadburn, Helen; Cianfoni, Eduardo; Cockel, Chris; Coldwell, Vanessa; Concetti, Benedetta; Contu, Sara; Crook, Vicki; Dyson, Philippa; Gardiner, Lauren; Ghanim, Nadia; Greene, Hannah; Groom, Alice; Harker, Ruth; Hopkins, Della; Khela, Sonia; Lakeman-Fraser, Poppy; Lindon, Heather; Lockwood, Helen; Loftus, Christine; Lombrici, Debora; Lopez-Poveda, Lucia; Lyon, James; Malcolm-Tompkins, Patricia; McGregor, Kirsty; Moreno, Laura; Murray, Linda; Nazar, Keara; Power, Emily; Quiton Tuijtelaars, Mireya; Salter, Ruth; Segrott, Robert; Thacker, Hannah; Thomas, Leighton J; Tingvoll, Sarah; Watkinson, Gemma; Wojtaszekova, Katerina; Nic Lughadha, Eimear M 2015-01-01 Plants provide fundamental support systems for life on Earth and are the basis for all terrestrial ecosystems; a decline in plant diversity will be detrimental to all other groups of organisms including humans. Decline in plant diversity has been hard to quantify, due to the huge numbers of known and yet to be discovered species and the lack of an adequate baseline assessment of extinction risk against which to track changes. The biodiversity of many remote parts of the world remains poorly known, and the rate of new assessments of extinction risk for individual plant species approximates the rate at which new plant species are described. Thus the question 'How threatened are plants?' is still very difficult to answer accurately. While completing assessments for each species of plant remains a distant prospect, by assessing a randomly selected sample of species the Sampled Red List Index for Plants gives, for the first time, an accurate view of how threatened plants are across the world. It represents the first key phase of ongoing efforts to monitor the status of the world's plants. More than 20% of plant species assessed are threatened with extinction, and the habitat with the most threatened species is overwhelmingly tropical rain forest, where the greatest threat to plants is anthropogenic habitat conversion, for arable and livestock agriculture, and harvesting of natural resources. Gymnosperms (e.g. conifers and cycads) are the most threatened group, while a third of plant species included in this study have yet to receive an assessment or are so poorly known that we cannot yet ascertain whether they are threatened or not. This study provides a baseline assessment from which trends in the status of plant biodiversity can be measured and periodically reassessed. 1. Green Plants in the Red: A Baseline Global Assessment for the IUCN Sampled Red List Index for Plants Griffiths-Lee, Janine; Lutz, Maiko; Moat, Justin F.; Farjon, Aljos; Donaldson, John S.; Hilton-Taylor, Craig; Meagher, Thomas R.; Albuquerque, Sara; Aletrari, Elina; Andrews, A. Kei; Atchison, Guy; Baloch, Elisabeth; Barlozzini, Barbara; Brunazzi, Alice; Carretero, Julia; Celesti, Marco; Chadburn, Helen; Cianfoni, Eduardo; Cockel, Chris; Coldwell, Vanessa; Concetti, Benedetta; Contu, Sara; Crook, Vicki; Dyson, Philippa; Gardiner, Lauren; Ghanim, Nadia; Greene, Hannah; Groom, Alice; Harker, Ruth; Hopkins, Della; Khela, Sonia; Lakeman-Fraser, Poppy; Lindon, Heather; Lockwood, Helen; Loftus, Christine; Lombrici, Debora; Lopez-Poveda, Lucia; Lyon, James; Malcolm-Tompkins, Patricia; McGregor, Kirsty; Moreno, Laura; Murray, Linda; Nazar, Keara; Power, Emily; Quiton Tuijtelaars, Mireya; Salter, Ruth; Segrott, Robert; Thacker, Hannah; Thomas, Leighton J.; Tingvoll, Sarah; Watkinson, Gemma; Wojtaszekova, Katerina; Nic Lughadha, Eimear M. 2015-01-01 Plants provide fundamental support systems for life on Earth and are the basis for all terrestrial ecosystems; a decline in plant diversity will be detrimental to all other groups of organisms including humans. Decline in plant diversity has been hard to quantify, due to the huge numbers of known and yet to be discovered species and the lack of an adequate baseline assessment of extinction risk against which to track changes. The biodiversity of many remote parts of the world remains poorly known, and the rate of new assessments of extinction risk for individual plant species approximates the rate at which new plant species are described. Thus the question ‘How threatened are plants?’ is still very difficult to answer accurately. While completing assessments for each species of plant remains a distant prospect, by assessing a randomly selected sample of species the Sampled Red List Index for Plants gives, for the first time, an accurate view of how threatened plants are across the world. It represents the first key phase of ongoing efforts to monitor the status of the world’s plants. More than 20% of plant species assessed are threatened with extinction, and the habitat with the most threatened species is overwhelmingly tropical rain forest, where the greatest threat to plants is anthropogenic habitat conversion, for arable and livestock agriculture, and harvesting of natural resources. Gymnosperms (e.g. conifers and cycads) are the most threatened group, while a third of plant species included in this study have yet to receive an assessment or are so poorly known that we cannot yet ascertain whether they are threatened or not. This study provides a baseline assessment from which trends in the status of plant biodiversity can be measured and periodically reassessed. PMID:26252495 2. Prospecting for marine gas hydrate resources Boswell, Ray; Shipp, Craig; Reichel, Thomas; Shelander, Dianna; Saeki, Tetsuo; Frye, Matthew; Shedd, William; Collett, Timothy S.; McConnell, Daniel R. 2016-01-01 As gas hydrate energy assessment matures worldwide, emphasis has evolved away from confirmation of the mere presence of gas hydrate to the more complex issue of prospecting for those specific accumulations that are viable resource targets. Gas hydrate exploration now integrates the unique pressure and temperature preconditions for gas hydrate occurrence with those concepts and practices that are the basis for conventional oil and gas exploration. We have aimed to assimilate the lessons learned to date in global gas hydrate exploration to outline a generalized prospecting approach as follows: (1) use existing well and geophysical data to delineate the gas hydrate stability zone (GHSZ), (2) identify and evaluate potential direct indications of hydrate occurrence through evaluation of interval of elevated acoustic velocity and/or seismic events of prospective amplitude and polarity, (3) mitigate geologic risk via regional seismic and stratigraphic facies analysis as well as seismic mapping of amplitude distribution along prospective horizons, and (4) mitigate further prospect risk through assessment of the evidence of gas presence and migration into the GHSZ. Although a wide range of occurrence types might ultimately become viable energy supply options, this approach, which has been tested in only a small number of locations worldwide, has directed prospect evaluation toward those sand-hosted, high-saturation occurrences that were presently considered to have the greatest future commercial potential. 3. Prospect Theory for Online Financial Trading Liu, Yang-Yu; Nacher, Jose C.; Ochiai, Tomoshiro; Martino, Mauro; Altshuler, Yaniv 2014-03-01 Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. According to prospect theory, people make decisions based on the potential value of losses and gains rather than the final outcome. People are risk-averse with respect to gains and risk-seeking with respect to losses, a phenomenon called loss aversion''. Despite of the fact that prospect theory has been well studied in behavioral economics at the theoretical level, there exist very few empirical research and most of them has been undertaken with micro-panel data. Here we analyze the trading activities of over 1.5 million members of an online financial trading community over 28 months, aiming to explore the large-scale empirical aspect of prospect theory. By analyzing and comparing the behaviour of winners'' and `losers'', i.e., traders with positive or negative final net profit, we find clear evidence of the loss aversion phenomenon, an essence in prospect theory. This work demonstrates an unprecedented large-scale empirical evidence of prospect theory. It has immediate implication in financial trading, e.g., developing new trading strategies by minimizing the effect of loss aversion. It also provides opportunity to augment online social trading, where users are allowed to watch and follow the trading activity of others, by predicting potential winners based on their historical trading behaviour. 4. DADOS-Prospective: an open source application for Web-based prospective data collection Nguyen Lam 2006-11-01 Full Text Available Abstract Background Randomized, prospective trials involving multi-institutional collaboration have become a central part of clinical and translational research. However, data management and coordination of multi-center studies is a complex process that involves developing systems for data collection and quality control, tracking data queries and resolutions, as well as developing communication procedures. We describe DADOS-Prospective, an open-source Web-based application for collecting and managing prospective data on human subjects for clinical and translational trials. DADOS-Prospective not only permits users to create new clinical research forms (CRF and supports electronic signatures, but also offers the advantage of containing, in a single environment, raw research data in downloadable spreadsheet format, source documentation and regulatory files stored in PDF format, and audit trails. Results Feedback from formal and field usability tests was used to guide the design and development of DADOS-Prospective. To date, DADOS-Prospective has been implemented in five prospective clinical studies at our institution. Four of these studies are still in the CRF creation phase and one study has been entirely launched. Conclusion DADOS-Prospective has significant advantages over existing Web-based data collecting programs. At our institution, it has been demonstrated to be an efficient tool for prospective clinical studies. 5. Beginning Plant Biotechnology Laboratories Using Fast Plants. Williams, Mike This set of 16 laboratory activities is designed to illustrate the life cycle of Brassicae plants from seeds in pots to pods in 40 days. At certain points along the production cycle of the central core of labs, there are related lateral labs to provide additional learning opportunities employing this family of plants, referred to as "fast… 6. Original and cumulative prospect theory: a discussion of empirical differences P.P. Wakker; H. Fennema 1997-01-01 This note discusses differences between prospect theory and cumulative prospect theory. It shows that cumulative prospect theory is not merely a formal correction of some theoretical problems in prospect theory, but it also gives different predictions. Experiments are described that favor cumulative 7. Neurocutaneous syndrome: A prospective study Radheshyam Purkait 2011-01-01 Full Text Available Background: Neurocutaneous syndromes (NCS are a group of genetic disorders that produce a variety of developmental abnormalities of the skin along with an increased risk of neurological complications. Cutaneous manifestations usually appear early in life and progress with time, but neurological features generally present at a later age. There is a paucity of data regarding the evolution of skin lesions and their correlation with the central nervous system involvement in children. Aim: The primary objective was to track the course of skin lesions in various forms of NCS in the pediatric age group. Our secondary aim was to assess whether there was any predictive value of the lesions in relation to the neurological manifestations. Materials and Methods: This prospective longitudinal study was conducted at a tertiary care pediatric dermatology referral clinic of the Institute of Child Health, Kolkata, West Bengal. Children between the age group 0 and 12 years were included in the study on the basis of standard diagnostic criteria for different NCS, during the period from March, 2000 to February, 2004, and each of the enrolled cases were followed up for a duration of six years. Results: The study population comprised of 67 children (35 boys, 32 girls.The mean age of presentation was 33.8±27.8 months (range 10 days to 111 months. The various forms of NCS observed was neurofibromatosis 1(NF1 (n=33, tuberous sclerosis complex (TSC (n=23, Sturge Weber syndrome (n=6, ataxia telangiectasia (n=2, PHACE syndrome (n=1, incontinentia pigmenti (n=1, and hypomelanosis of Ito (n=1. The presentations were varied, ranging from predominantly cutaneous to primarily neurological, depending on the disease entity and age group concerned. There was a significant increase in the number of café au lait macules (CALMs with time (P=0.0002 in NF1, unlike that of hypopigmented macules of TSC (P=0.15. Statistically, no relation was documented between the evolution of skin 8. Plant Phenotype Characterization System Daniel W McDonald; Ronald B Michaels 2005-09-09 This report is the final scientific report for the DOE Inventions and Innovations Project: Plant Phenotype Characterization System, DE-FG36-04GO14334. The period of performance was September 30, 2004 through July 15, 2005. The project objective is to demonstrate the viability of a new scientific instrument concept for the study of plant root systems. The root systems of plants are thought to be important in plant yield and thus important to DOE goals in renewable energy sources. The scientific study and understanding of plant root systems is hampered by the difficulty in observing root activity and the inadequacy of existing root study instrumentation options. We have demonstrated a high throughput, non-invasive, high resolution technique for visualizing plant root systems in-situ. Our approach is based upon low-energy x-ray radiography and the use of containers and substrates (artificial soil) which are virtually transparent to x-rays. The system allows us to germinate and grow plant specimens in our containers and substrates and to generate x-ray images of the developing root system over time. The same plant can be imaged at different times in its development. The system can be used for root studies in plant physiology, plant morphology, plant breeding, plant functional genomics and plant genotype screening. 9. Status and prospects of a deep underground laboratory in China Kang, K. J.; Cheng, J. P.; Chen, Y. H.; Li, Y. J.; Shen, M. B.; Wu, S. Y.; Yue, Q. 2010-01-01 An excellent candidate location for a deep underground laboratory with more than 2500 m of rock overburden has been identified at Sichuan Province in China. It can be accessed through a road tunnel of length 17.5 km, and is supported by services and amenities near the entrance provided by the local Ertan Hydropower Plant. The particle physics community in China is actively pursuing the construction of an underground laboratory at this location, under the leadership of Tsinghua University. Memorandum has been signed with Ertan Hydropower Plant which permits access to and construction of the underground laboratory — China JinPing Deep Underground Laboratory (CJPL). The basic features of this underground site, as well as the status and schedules of the construction of the first laboratory cavern are presented. The immediate goal is to have the first experiment operational in 2010, deploying an Ultra-Low-Energy Germanium detector for WIMP dark matter searches, with emphasis on the mass range of 1-10 GeV. The conceptual design of the experiment, as well as the future plans and prospects of the laboratory, will be surveyed. 10. Prospective surveillance of semen quality in the workplace Schenker, M.B.; Samuels, S.J.; Perkins, C.; Lewis, E.L.; Katz, D.F.; Overstreet, J.W. 1988-04-01 We performed a prospective surveillance of semen quality among workers in the plant where 1,2-dibromo-3-chloropropane was first recognized as an occupational cause of impaired semen quality and of infertility. All male employees of the Agricultural Chemical Division were required to participate. Ninety-seven workers (92% participation) provided 258 semen samples over the 4 years of the program. Most samples were analyzed at the plant with a mini-laboratory designed for the study. Motility and shape measures were made objectively. Sixty-six subjects (68%) were non-azoospermic. Generalized multiple regression showed no significant predictors for any response, with the exception of the motility measures, which were reduced with longer times between ejaculation and assay. Between- and within-person standard deviations and correlations were calculated. Comparison of this population with fertile artificial insemination donors (16 men, 498 ejaculates) revealed generally higher ejaculate-to-ejaculate standard deviations in the worker samples. This is probably due to less well controlled conditions of sperm collection in the workplace setting. For cross-sectional studies, one ejaculate per worker is recommended as sufficient; for estimating an individual worker's mean, even three ejaculates may not provide enough precision. 11. Prospects of Nanobiomaterials for Biosensing Ravindra P. Singh 2011-01-01 Full Text Available Progress and development in biosensor development will inevitably focus upon the technology of the nanomaterials that offer promise to solve the biocompatibility and biofouling problems. The biosensors using smart nanomaterials have applications for rapid, specific, sensitive, inexpensive, in-field, on-line and/or real-time detection of pesticides, antibiotics, pathogens, toxins, proteins, microbes, plants, animals, foods, soil, air, and water. Thus, biosensors are excellent analytical tools for pollution monitoring, by which implementation of legislative provisions to safeguard our biosphere could be made effectively plausible. The current trends and challenges with nanomaterials for various applications will have focus biosensor development and miniaturization. All these growing areas will have a remarkable influence on the development of new ultrasensitive biosensing devices to resolve the severe pollution problems in the future that not only challenges the human health but also affects adversely other various comforts to living entities. This review paper summarizes recent progress in the development of biosensors by integrating functional biomolecules with different types of nanomaterials, including metallic nanoparticles, semiconductor nanoparticles, magnetic nanoparticles, inorganic/organic hybrid, dendrimers, and carbon nanotubes/graphene. 12. Classification of cultivated plants. Brandenburg, W.A. 1986-01-01 Agricultural practice demands principles for classification, starting from the basal entity in cultivated plants: the cultivar. In establishing biosystematic relationships between wild, weedy and cultivated plants, the species concept needs re-examination. Combining of botanic classification, based 13. Plant tissue culture techniques Rolf Dieter Illg 1991-01-01 Full Text Available Plant cell and tissue culture in a simple fashion refers to techniques which utilize either single plant cells, groups of unorganized cells (callus or organized tissues or organs put in culture, under controlled sterile conditions. 14. Plant growth and cultivation. Podar, Dorina 2013-01-01 There is a variety of methods used for growing plants indoor for laboratory research. In most cases plant research requires germination and growth of plants. Often, people have adapted plant cultivation protocols to the conditions and materials at hand in their own laboratory and growth facilities. Here I will provide a guide for growing some of the most frequently used plant species for research, i.e., Arabidopsis thaliana, barley (Hordeum vulgare) and rice (Oryza sativa). However, the methods presented can be used for other plant species as well, especially if they are related to the above-mentioned species. The presented methods include growing plants in soil, hydroponics, and in vitro on plates. This guide is intended as a starting point for those who are just beginning to work on any of the above-mentioned plant species. Methods presented are to be taken as suggestive and modification can be made according to the conditions existing in the host laboratory. 15. Plant tissue culture techniques Rolf Dieter Illg 1991-01-01 Plant cell and tissue culture in a simple fashion refers to techniques which utilize either single plant cells, groups of unorganized cells (callus) or organized tissues or organs put in culture, under controlled sterile conditions. 16. On Plant Names. Colton, Ronald W. 1979-01-01 Discusses the scientific and common names of numerous plants and the satisfaction children derive from mastering them. Includes drawings which illustrate the connections between plant structures and their names. (MA) 17. Plant proton pumps Gaxiola, Roberto A.; Palmgren, Michael Gjedde; Schumacher, Karin 2007-01-01 Chemiosmotic circuits of plant cells are driven by proton (H+) gradients that mediate secondary active transport of compounds across plasma and endosomal membranes. Furthermore, regulation of endosomal acidification is critical for endocytic and secretory pathways. For plants to react to their co......Chemiosmotic circuits of plant cells are driven by proton (H+) gradients that mediate secondary active transport of compounds across plasma and endosomal membranes. Furthermore, regulation of endosomal acidification is critical for endocytic and secretory pathways. For plants to react... 18. The data of Lelvy and Levy , "Prospect theory: much ado about nothing??", support prospect theory P.P. Wakker 2003-01-01 Levy and Levy (Management Science, 2002) present data that, according to their claims, violate prospect theory. They suggest that prospect theoryys hypothesis of an S-shaped value function, concave for gains and convex for losses, is incorrect. However, all of the data of Levy and Levy are perfectly 19. Making Plants Break a Sweat: the Structure, Function, and Evolution of Plant Salt Glands Dassanayake, Maheshi; Larkin, John C. 2017-01-01 Salt stress is a complex trait that poses a grand challenge in developing new crops better adapted to saline environments. Some plants, called recretohalophytes, that have naturally evolved to secrete excess salts through salt glands, offer an underexplored genetic resource for examining how plant development, anatomy, and physiology integrate to prevent excess salt from building up to toxic levels in plant tissue. In this review we examine the structure and evolution of salt glands, salt gland-specific gene expression, and the possibility that all salt glands have originated via evolutionary modifications of trichomes. Salt secretion via salt glands is found in more than 50 species in 14 angiosperm families distributed in caryophyllales, asterids, rosids, and grasses. The salt glands of these distantly related clades can be grouped into four structural classes. Although salt glands appear to have originated independently at least 12 times, they share convergently evolved features that facilitate salt compartmentalization and excretion. We review the structural diversity and evolution of salt glands, major transporters and proteins associated with salt transport and secretion in halophytes, salt gland relevant gene expression regulation, and the prospect for using new genomic and transcriptomic tools in combination with information from model organisms to better understand how salt glands contribute to salt tolerance. Finally, we consider the prospects for using this knowledge to engineer salt glands to increase salt tolerance in model species, and ultimately in crops. 20. Fundaments of plant cybernetics. Zucconi, F 2001-01-01 A systemic approach is proposed for analyzing plants' physiological organization and cybernesis. To this end, the plant is inspected as a system, starting from the integration of crown and root systems, and its impact on a number of basic epigenetic events. The approach proves to be axiomatic and facilitates the definition of the principles behind the plant's autonomous control of growth and reproduction. 1. Plants of the Bayshore. Bachle, Leo; And Others This field guide gives pictures and descriptions of plants that can be found along the San Francisco Bayshore, especially along the Hayward shoreline. The plants are divided into three categories, those of the mud-flat zone, the drier zone, and the levee zone. Eighteen plants are represented in all. The guide is designed to be used alone, with an… 2. Plant Diseases & Chemicals Thompson, Sherm 2008-01-01 This course discusses the use of chemicals for plant disease control. Specifically, pesticides that can be used both in commercial or home/yard sitautions. This course also teaches how to determine plant diseases that may have caused a plant to die. 3. Designing with plants Smits, R. 2012-01-01 This "designers' manual" is made during the TIDO-course AR0531 Smart & Bioclimatic Design. Rainforests are the lungs of the earth and plants can be the lungs of a buildings. Every plant uses CO2, water and light to produce sugars and oxygen; furthermore plants provide shade, take pollutants from th 4. Plant Systems Biology (editorial) In June 2003, Plant Physiology published an Arabidopsis special issue devoted to plant systems biology. The intention of Natasha Raikhel and Gloria Coruzzi, the two editors of this first-of-its-kind issue, was ‘‘to help nucleate this new effort within the plant community’’ as they considered that ‘‘... 5. Power Plant Cycling Costs Kumar, N.; Besuner, P.; Lefton, S.; Agan, D.; Hilleman, D. 2012-07-01 This report provides a detailed review of the most up to date data available on power plant cycling costs. The primary objective of this report is to increase awareness of power plant cycling cost, the use of these costs in renewable integration studies and to stimulate debate between policymakers, system dispatchers, plant personnel and power utilities. 6. Handbook of Plant Virology Khan, J.A.; Dijkstra, J. 2006-01-01 The Handbook of Plant Virology is a comprehensive guide to the terms and expressions commonly used in the study of plant virology, complete with descriptions of plant virus families down to the generic level. Rather than simply listing terms in alphabetical order, this unique book links each term to 7. Diagnosing plant problems Cheryl A. Smith 2008-01-01 Diagnosing Christmas tree problems can be a challenge, requiring a basic knowledge of plant culture and physiology, the effect of environmental influences on plant health, and the ability to identify the possible causes of plant problems. Developing a solution or remedy to the problem depends on a proper diagnosis, a process that requires recognition of a problem and... 8. Iron stress in plants. Connolly, Erin L; Guerinot, Mary 2002-07-30 Although iron is an essential nutrient for plants, its accumulation within cells can be toxic. Plants, therefore, respond to both iron deficiency and iron excess by inducing expression of different gene sets. Here, we review recent advances in the understanding of iron homeostasis in plants gained through functional genomic approaches 9. Iron stress in plants Connolly, Erin L.; Guerinot, Mary Lou 2002-01-01 Although iron is an essential nutrient for plants, its accumulation within cells can be toxic. Plants, therefore, respond to both iron deficiency and iron excess by inducing expression of different gene sets. Here, we review recent advances in the understanding of iron homeostasis in plants gained through functional genomic approaches. 10. Recognizing plant defense priming Martinez-Medina, A.; Flors, V.; Heil, M.; Mauch-Mani, B.; Pieterse, C.M.J.; Pozo, M.J.; Ton, J.; Van Dam, N.M.; Conrath, U. 2016-01-01 Defense priming conditions diverse plant species for the superinduction of defense, often resulting in enhanced pest and disease resistance and abiotic stress tolerance. Here, we propose a guideline that might assist the plant research community in a consistent assessment of defense priming in plant 11. Full cost analysis on seawater desalination and the prospects discussion: A case study of desalination project in Tianjin Beijiang Power Plant%海水淡化全成本分析及其发展前景探讨——以天津北疆电厂海水淡化项目为例李晓琼 2012-01-01 Water shortage is a major environmental issue that attracts global concern. China is one of the countries with water scarce in the world. This study evaluated and analyzed the cost of desalination project in Tianjin Beijiang Power Plant. In accordance with the relevant theory and desalination cost evaluation methods, the study analyzed the components and calculated the full cost of seawater desalination, then made comparisons with other new ways of water resource use, including the South-to-North Water Diversion, reclaimed water use, rainwater usage, so as to explore the feasibility of desalination in alleviating the water crisis in Beijing and Tianjin areas.%水资源短缺是全球关注的重大环境问题，而中国是全球最为缺水的国家之一。选取天津北疆发电厂海水淡化项目进行成本实证评估与分析，进行全成本的构成分析和综合核算评估，进而与其他新型水资源利用方法（南水北调、中水回用与污水资源化、雨水利用）进行成本比较与分析，探讨其海水淡化模式应对京津地区水资源危机的可行性。 12. Problems and prospects concerning the phytoremediation of heavy metal polluted soils: A review Koptsik, G. N. 2014-09-01 The current state, problems, and prospects of phymoremediation of heavy metal polluted soils are analyzed. The main attention is paid to the phytoextraction and phytostabilization as the most widespread and alternative methods of soil phytoremediation. The efficiency of phymoremediation is related to the natural capability of plants for the accumulation and translocation of metals, their tolerance to a high content of metals, the plant biomass, and the amendments applied. The advantages and disadvantages of phytoremediation as compared to other methods of remediation of polluted soils in situ are considered. Examples of successful phytoextraction and phytomining for cleaning up of contaminated soils in Rasteburg (South Africa) and the phytostabilization of technogenic barrens nearby the copper-nickel plants in Sudbury (Ontario, Canada) and in the Kola Subarctic (Russia) are presented. 13. Cannabinoids and schizophrenia: therapeutic prospects. Robson, P J; Guy, G W; Di Marzo, V 2014-01-01 Approximately one third of patients diagnosed with schizophrenia do not achieve adequate symptom control with standard antipsychotic drugs (APs). Some of these may prove responsive to clozapine, but non-response to APs remains an important clinical problem and cause of increased health care costs. In a significant proportion of patients, schizophrenia is associated with natural and iatrogenic metabolic abnormalities (obesity, dyslipidaemia, impaired glucose tolerance or type 2 diabetes mellitus), hyperadrenalism and an exaggerated HPA response to stress, and chronic systemic inflammation. The endocannabinoid system (ECS) in the brain plays an important role in maintaining normal mental health. ECS modulates emotion, reward processing, sleep regulation, aversive memory extinction and HPA axis regulation. ECS overactivity contributes to visceral fat accumulation, insulin resistance and impaired energy expenditure. The cannabis plant synthesises a large number of pharmacologically active compounds unique to it known as phytocannabinoids. In contrast to the euphoric and pro-psychotic effects of delta-9-tetrahydrocannabinol (THC), certain non-intoxicating phytocannabinoids have emerged in pre-clinical and clinical models as potential APs. Since the likely mechanism of action does not rely upon dopamine D2 receptor antagonism, synergistic combinations with existing APs are plausible. The anti-inflammatory and immunomodulatory effects of the non-intoxicating phytocannabinoid cannabidiol (CBD) are well established and are summarised below. Preliminary data reviewed in this paper suggest that CBD in combination with a CB1 receptor neutral antagonist could not only augment the effects of standard APs but also target the metabolic, inflammatory and stress-related components of the schizophrenia phenotype. 14. A review of fractionations of rare earth elements in plants LIANG Tao; DING Shiming; SONG Wenchong; CHONG Zhongyi; ZHANG Chaosheng; LI Haitao 2008-01-01 Studies were carried out on several aspects of rare earth elements (REEs), such as the theory and practice of their applications in agriculture, their geochemical behaviors in natural and agricultural ecosystems, the mechanisms for the increase of crop yield using REE fertilizer, and their toxicology. However, limited knowledge was available for the transfer processes and the features and mechanisms of distribution and fractionatious of REEs inside plants. The characteristics of REE fractionations in plants can be used to "trace" the pathway of REE transportation from soils (solution) to plants. A better understanding of the mechanisms of REE fractionations was helpful to investigate the controlling factors, including both the internal and the external ones. The characteristics and mechanisms of REE fractionatious in plants and their significance were reviewed. Furthermore, the prospect for these fields was discussed, in hope of providing a new way in studying the bioavailability of REEs and heavy metals. 15. Nuclear magnetic resonance imaging of lipid in living plants. Borisjuk, Ljudmilla; Rolletschek, Hardy; Neuberger, Thomas 2013-10-01 This review highlights technological developments in magnetic resonance imaging (MRI), which are creating opportunities for the three dimensional visualization and quantification of lipids in plant materials. A major feature of MRI is that it is a non-invasive platform, and thus can be used for the analysis of living organisms. An overview of the theoretical aspects of MRI is provided, followed by a description of the various analytical modes available, and an explanation of how MRI can be applied to plant samples and what it can achieve. Various lipid maps and three dimensional models of seeds and fruits are included to demonstrate the potential of MRI and to exemplify recent cutting-edge advances in the field. The importance and prospects of the imaging of lipids in living plants, as well as the integration of lipid imaging with other emerging techniques, are outlined to provide impetus for future plant lipid research. Copyright © 2013 Elsevier Ltd. All rights reserved. 16. The Power of CRISPR-Cas9-Induced Genome Editing to Speed Up Plant Breeding Hieu X. Cao 2016-01-01 Full Text Available Genome editing with engineered nucleases enabling site-directed sequence modifications bears a great potential for advanced plant breeding and crop protection. Remarkably, the RNA-guided endonuclease technology (RGEN based on the clustered regularly interspaced short palindromic repeats (CRISPR and CRISPR-associated protein 9 (Cas9 is an extremely powerful and easy tool that revolutionizes both basic research and plant breeding. Here, we review the major technical advances and recent applications of the CRISPR-Cas9 system for manipulation of model and crop plant genomes. We also discuss the future prospects of this technology in molecular plant breeding. 17. The Power of CRISPR-Cas9-Induced Genome Editing to Speed Up Plant Breeding Wang, Wenqin; Le, Hien T. T. 2016-01-01 Genome editing with engineered nucleases enabling site-directed sequence modifications bears a great potential for advanced plant breeding and crop protection. Remarkably, the RNA-guided endonuclease technology (RGEN) based on the clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated protein 9 (Cas9) is an extremely powerful and easy tool that revolutionizes both basic research and plant breeding. Here, we review the major technical advances and recent applications of the CRISPR-Cas9 system for manipulation of model and crop plant genomes. We also discuss the future prospects of this technology in molecular plant breeding. PMID:28097123 18. Nanobiotechnology meets plant cell biology: Carbon nanotubes as organelle targeting nanocarriers Bayoumi, Maged Fouad 2013-01-01 For years, nanotechnology has shown great promise in the fields of biomedical and biotechnological sciences and medical research. In this review, we demonstrate its versatility and applicability in plant cell biology studies. Specifically, we discuss the ability of functionalized carbon nanotubes to penetrate the plant cell wall, target specific organelles, probe protein-carrier activity and induce organelle recycling in plant cells. We also, shed light on prospective applications of carbon nanomaterials in cell biology and plant cell transformation. © 2013 The Royal Society of Chemistry. 19. [Effects of soil PAHs pollution on plant ecophysiology]. Xu, Sheng; Wang, Hui; Chen, Wei; He, Xing-Yuan; Su, Dao-Yan; Li, Bo; Li, Mei 2013-05-01 Polycyclic aromatic hydrocarbons (PAHs) are the ubiquitous organic persistent pollutants in natural environments (especially in soil), giving serious potential risks to the eco-environment, plants, and human beings. At present, the remediation of PAHs-polluted soil is one of the hot topics in the research fields of soil and environment. Phytoremediation is one of the environmental restoration techniques with most potentiality. This paper reviewed the newest progress in the researches of the effects of soil PAHs pollution and its combined stress with other pollutants on the plant growth, morphological structure, photosynthesis, and antioxidant system, and prospected the important fields and hotspots of related researches in the future. 20. Thermoeconomic Analysis of Advanced Solar-Fossil Combined Power Plants Yassine Allani; Klaus Ziegler; Daniel Favrat; Malick Kane 2000-01-01 Hybrid solar thermal power plants (with parabolic trough type of solar collectors) featuring gas burners and Rankine steam cycles have been successfully demonstrated by California's Solar Electric Generating System (SEGS). This system has been proven to be one of the most efficient and economical schemes to convert solar energy into electricity. Recent technological progress opens interesting prospects for advanced cycle concepts: a) the ISCCS (Integrated Solar Combined Cycle System)... 1. Geochemical field method for determination of nickel in plants Reichen, L.E. 1951-01-01 The use of biogeochemical data in prospecting for nickel emphasizes the need for a simple, moderately accurate field method for the determination of nickel in plants. In order to follow leads provided by plants of unusual nickel content without loss of time, the plants should be analyzed and the results given to the field geologist promptly. The method reported in this paper was developed to meet this need. Speed is acquired by elimination of the customary drying and controlled ashing; the fresh vegetation is ashed in an open dish over a gasoline stove. The ash is put into solution with hydrochloric acid and the solution buffered. A chromograph is used to make a confined spot with an aliquot of the ash solution on dimethylglyoxime reagent paper. As little as 0.025% nickel in plant ash can be determined. With a simple modification, 0.003% can be detected. Data are given comparing the results obtained by an accepted laboratory procedure. Results by the field method are within 30% of the laboratory values. The field method for nickel in plants meets the requirements of biogeochemical prospecting with respect to accuracy, simplicity, speed, and ease of performance in the field. With experience, an analyst can make 30 determinations in an 8-hour work day in the field. 2. Role of RNA interference in plant improvement Jagtap, Umesh Balkrishna; Gurav, Ranjit Gajanan; Bapat, Vishwas Anant 2011-06-01 Research to alter crops for their better performance involving modern technology is underway in numerous plants, and achievements in transgenic plants are impacting crop improvements in unparalleled ways. Striking progress has been made using genetic engineering technology over the past two decades in manipulating genes from diverse and exotic sources, and inserting them into crop plants for inducing desirable characteristics. RNA interference (RNAi) has recently been identified as a natural mechanism for regulation of gene expression in all higher organisms from plants to humans and promises greater accuracy and precision to plant improvement. The expression of any gene can be down-regulated in a highly explicit manner exclusive of affecting the expression of any other gene by using RNAi technologies. Additional research in this field has been focused on a number of other areas including microRNAs, hairpin RNA, and promoter methylation. Manipulating new RNAi pathways, which generate small RNA molecules to amend gene expression in crops, can produce new quality traits and having better potentiality of protection against abiotic and biotic stresses. Nutritional improvement, change in morphology, or enhanced secondary metabolite synthesis are some of the other advantages of RNAi technology. In addition to its roles in regulating gene expression, RNAi is also used as a natural defense mechanism against molecular parasites such as jumping genes and viral genetic elements that affect genome stability. Even though much advancement has been made on the field of RNAi over the preceding few years, the full prospective of RNAi for crop improvement remains to be fully realized. The intricacy of RNAi pathway, the molecular machineries, and how it relates to plant development are still to be explained. 3. Scenarios planning: the evolution of prospective thinking Maurício Fernandes Pereira 2005-01-01 Full Text Available The world is changing even more than before. Around the world, the organizational stability is in face of threats unnoticed before, due to technologic innovations, uncontrolled financial markets, up to date customers, and an observant society and government, in order to control the organizations’ social and environmental responsibilities. To face this threats, organizations needs to worry even more, renew its long range planning systems, and use Prospective Scenaries to find out, in a better way, the dynamic forces that will preveil in the next years. This paper seeks to clarify the source of prospective thinking that has created and developed this tool. Prospective Thinking is considered, nowadays, one of most innovatives tools used by the strategic management in organizations. 4. Prospect theory for online financial trading. Yang-Yu Liu Full Text Available Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. According to prospect theory, people are typically risk-averse with respect to gains and risk-seeking with respect to losses, known as the "reflection effect". People are much more sensitive to losses than to gains of the same magnitude, a phenomenon called "loss aversion". Despite of the fact that prospect theory has been well developed in behavioral economics at the theoretical level, there exist very few large-scale empirical studies and most of the previous studies have been undertaken with micro-panel data. Here we analyze over 28.5 million trades made by 81.3 thousand traders of an online financial trading community over 28 months, aiming to explore the large-scale empirical aspect of prospect theory. By analyzing and comparing the behavior of winning and losing trades and traders, we find clear evidence of the reflection effect and the loss aversion phenomenon, which are essential in prospect theory. This work hence demonstrates an unprecedented large-scale empirical evidence of prospect theory, which has immediate implication in financial trading, e.g., developing new trading strategies by minimizing the impact of the reflection effect and the loss aversion phenomenon. Moreover, we introduce three novel behavioral metrics to differentiate winning and losing traders based on their historical trading behavior. This offers us potential opportunities to augment online social trading where traders are allowed to watch and follow the trading activities of others, by predicting potential winners based on their historical trading behavior. 5. Prospect theory for online financial trading. Liu, Yang-Yu; Nacher, Jose C; Ochiai, Tomoshiro; Martino, Mauro; Altshuler, Yaniv 2014-01-01 Prospect theory is widely viewed as the best available descriptive model of how people evaluate risk in experimental settings. According to prospect theory, people are typically risk-averse with respect to gains and risk-seeking with respect to losses, known as the "reflection effect". People are much more sensitive to losses than to gains of the same magnitude, a phenomenon called "loss aversion". Despite of the fact that prospect theory has been well developed in behavioral economics at the theoretical level, there exist very few large-scale empirical studies and most of the previous studies have been undertaken with micro-panel data. Here we analyze over 28.5 million trades made by 81.3 thousand traders of an online financial trading community over 28 months, aiming to explore the large-scale empirical aspect of prospect theory. By analyzing and comparing the behavior of winning and losing trades and traders, we find clear evidence of the reflection effect and the loss aversion phenomenon, which are essential in prospect theory. This work hence demonstrates an unprecedented large-scale empirical evidence of prospect theory, which has immediate implication in financial trading, e.g., developing new trading strategies by minimizing the impact of the reflection effect and the loss aversion phenomenon. Moreover, we introduce three novel behavioral metrics to differentiate winning and losing traders based on their historical trading behavior. This offers us potential opportunities to augment online social trading where traders are allowed to watch and follow the trading activities of others, by predicting potential winners based on their historical trading behavior. 6. Plant Physiology and Development Taiz, Lincoln; Zeiger, Eduardo; Møller, Ian Max Physiology and Development. As before, Unit III begins with updated chapters on Cell Walls and Signals and Signal Transduction. The latter chapter has been expanded to include a discussion of major signaling molecules, such as calcium ions and plant hormones. A new, unified chapter entitled Signals from......Throughout its twenty-two year history, the authors of Plant Physiology have continually updated the book to incorporate the latest advances in plant biology and implement pedagogical improvements requested by adopters. This has made Plant Physiology the most authoritative, comprehensive......, and widely used upper-division plant biology textbook. In the Sixth Edition, the Growth and Development section (Unit III) has been reorganized and expanded to present the complete life cycle of seed plants from germination to senescence. In recognition of this enhancement, the text has been renamed Plant... 7. Multinationals and plant survival Bandick, Roger 2010-01-01 The aim of this paper is twofold: first, to investigate how different ownership structures affect plant survival, and second, to analyze how the presence of foreign multinational enterprises (MNEs) affects domestic plants’ survival. Using a unique and detailed data set on the Swedish manufacturing...... sector, I am able to separate plants into those owned by foreign MNEs, domestic MNEs, exporting non-MNEs, and purely domestic firms. In line with previous findings, the result, when conditioned on other factors affecting survival, shows that foreign MNE plants have lower survival rates than non......-MNE plants. However, separating the non-MNEs into exporters and non-exporters, the result shows that foreign MNE plants have higher survival rates than non-exporting non-MNEs, while the survival rates of foreign MNE plants and exporting non-MNE plants do not seem to differ. Moreover, the simple non... 8. Collaborative Software Engineering: Challenges and Prospects Mistrík, Ivan; Grundy, John; van der Hoek, André; Whitehead, Jim Much work is presently ongoing in collaborative software engineering research. This work is beginning to make serious inroads into our ability to more effectively practice collaborative software engineering, with best practices, processes, tools, metrics, and other techniques becoming available for day-to-day use. However, we have not yet reached the point where the practice of collaborative software engineering is routine, without surprises, and generally as optimal as possible. This chapter summarizes the main findings of this book, draws some conclusions on these findings and looks at the prospects for software engineers in dealing with the challenges of collaborative software development. The chapter ends with prospects for collaborative software engineering. 9. Pharming and transgenic plants. Liénard, David; Sourrouille, Christophe; Gomord, Véronique; Faye, Loïc 2007-01-01 Plant represented the essence of pharmacopoeia until the beginning of the 19th century when plant-derived pharmaceuticals were partly supplanted by drugs produced by the industrial methods of chemical synthesis. In the last decades, genetic engineering has offered an alternative to chemical synthesis, using bacteria, yeasts and animal cells as factories for the production of therapeutic proteins. More recently, molecular farming has rapidly pushed towards plants among the major players in recombinant protein production systems. Indeed, therapeutic protein production is safe and extremely cost-effective in plants. Unlike microbial fermentation, plants are capable of carrying out post-translational modifications and, unlike production systems based on mammalian cell cultures, plants are devoid of human infective viruses and prions. Furthermore, a large panel of strategies and new plant expression systems are currently developed to improve the plant-made pharmaceutical's yields and quality. Recent advances in the control of post-translational maturations in transgenic plants will allow them, in the near future, to perform human-like maturations on recombinant proteins and, hence, make plant expression systems suitable alternatives to animal cell factories. 10. Safe genetically engineered plants Rosellini, D.; Veronesi, F. 2007-10-01 The application of genetic engineering to plants has provided genetically modified plants (GMPs, or transgenic plants) that are cultivated worldwide on increasing areas. The most widespread GMPs are herbicide-resistant soybean and canola and insect-resistant corn and cotton. New GMPs that produce vaccines, pharmaceutical or industrial proteins, and fortified food are approaching the market. The techniques employed to introduce foreign genes into plants allow a quite good degree of predictability of the results, and their genome is minimally modified. However, some aspects of GMPs have raised concern: (a) control of the insertion site of the introduced DNA sequences into the plant genome and of its mutagenic effect; (b) presence of selectable marker genes conferring resistance to an antibiotic or an herbicide, linked to the useful gene; (c) insertion of undesired bacterial plasmid sequences; and (d) gene flow from transgenic plants to non-transgenic crops or wild plants. In response to public concerns, genetic engineering techniques are continuously being improved. Techniques to direct foreign gene integration into chosen genomic sites, to avoid the use of selectable genes or to remove them from the cultivated plants, to reduce the transfer of undesired bacterial sequences, and make use of alternative, safer selectable genes, are all fields of active research. In our laboratory, some of these new techniques are applied to alfalfa, an important forage plant. These emerging methods for plant genetic engineering are briefly reviewed in this work. 11. Toxic proteins in plants. Dang, Liuyi; Van Damme, Els J M 2015-09-01 Plants have evolved to synthesize a variety of noxious compounds to cope with unfavorable circumstances, among which a large group of toxic proteins that play a critical role in plant defense against predators and microbes. Up to now, a wide range of harmful proteins have been discovered in different plants, including lectins, ribosome-inactivating proteins, protease inhibitors, ureases, arcelins, antimicrobial peptides and pore-forming toxins. To fulfill their role in plant defense, these proteins exhibit various degrees of toxicity towards animals, insects, bacteria or fungi. Numerous studies have been carried out to investigate the toxic effects and mode of action of these plant proteins in order to explore their possible applications. Indeed, because of their biological activities, toxic plant proteins are also considered as potentially useful tools in crop protection and in biomedical applications, such as cancer treatment. Genes encoding toxic plant proteins have been introduced into crop genomes using genetic engineering technology in order to increase the plant's resistance against pathogens and diseases. Despite the availability of ample information on toxic plant proteins, very few publications have attempted to summarize the research progress made during the last decades. This review focuses on the diversity of toxic plant proteins in view of their toxicity as well as their mode of action. Furthermore, an outlook towards the biological role(s) of these proteins and their potential applications is discussed. 12. Plant Communities of Rough Rock. Jacobs, Linda A unit of study on plants grown in the Navajo community of Rough Rock, Arizona, is presented in sketches providing the common Navajo name for the plant, a literal English translation, the English name of the plant, and the Latin name. A brief description of each plant includes where the plant grows, how the Navajos use the plant, and the color and… 13. Russia's Precious Metals Market: Condition and Prospects KOTLYAR A. Yu. 2012-01-01 The region of existence of phases in equilibrium with the solid solution based on palladium.Presented to analyze the current situation in the market of precious metals in Russia.Provides information about the production and processing of precious metals.Prospects for the most likely path of development of the Russian market of precious metals. 14. School Food Practices of Prospective Teachers Rossiter, Melissa; Glanville, Theresa; Taylor, Jennifer; Blum, Ilya 2007-01-01 Background: Schoolteachers can affect students' eating habits in several ways: through nutrition knowledge, positive role modeling, and avoidance of unhealthy classroom food practices. In this study, the knowledge, attitudes, and eating behaviors of prospective teachers as determinants of intended classroom food practices and the school… 15. Rural renewable energy (prospects) in Estonia Tomson, T. [Estonian Energy Research Institute, Tallinn (Estonia); Kaeaermann, L. [Estonian National Maritime Board, Tallinn (Estonia); Raesaar, P. [Tallinn Technological University, Tallinn (Estonia) 1997-12-31 Total potential share of renewables (biomass, wind, hydropower and solar) in Estonia is 35 %. Total real share (wood, wood chips) of renewables is only about 4.5 % (1995). The constrains and prospects of the development are discussed. The attention is focused on rural conditions 16. Teacher Education: Its Problems and Some Prospects Sykes, Gary; Bird, Tom; Kennedy, Mary 2010-01-01 Based on an analysis of occupational competence in teaching and teacher education, this article draws together a set of dilemmas that face the field, arguing that an occupational analysis is needed to complement the more common institutional analysis of teacher education. Then, this analysis is used to evaluate the prospects of the reforms that… 17. Prospective Educators' Knowledge of Children's Legal Rights. Mcloughlin, Caven S.; And Others 1983-01-01 Prospective educators' knowledge of children's legal rights in several areas was assessed. Results indicated limited legal knowledge and some misconceptions about the law. The need for colleges of education to adapt their curricula to include legal issues is discussed. (Author/DWH) 18. Prospective Teachers' Metaphorical Conceptualizations of Learner Saban, Ahmet 2010-01-01 This study investigated the metaphorical images that prospective teachers in Turkey formulated to describe learners. Participants (N = 2847) completed the prompt "A student is like ... because ..." to indicate their conceptualizations of learner. Data were analyzed both qualitatively and quantitatively. Altogether 98 well-articulated… 19. Voice and culture: A prospect theory approach Paddock, E.L.; Ko, Junsu; Cropanzano, R.; Bagger, J.; El Akremi, A.; Camerman, A.; Greguras, G. J.; Mladinic, A.; Moliner, C.; Nam, K.; Törnblom, K.; Van den Bos, Kees 2015-01-01 The present study examines the congruence of individuals' minimum preferred amounts of voice with the prospect theory value function across nine countries. Accounting for previously ignored minimum preferred amounts of voice and actual voice amounts integral to testing the steepness of gain and loss 20. The Japanese economy and future growth prospects Sian Fenner 2004-01-01 This paper examines Japanese growth prospects through a 3P framework - population, participation and productivity - and illustrates the importance of productivity growth in offsetting the effects of declining population and aggregate labour force participation. Without further structural reforms, particularly in the labour market and non-tradeable sectors, labour productivity growth will remain subdued and Japanese potential GDP growth constrained. 1. Metamaterial localized resonance sensors: prospects and limitations Jeppesen, Claus; Xiao, Sanshui; Mortensen, Asger; 2010-01-01 The prospects and limitations of metamaterial localized resonance sensors are investigated theoretically and experimentally. Gold split-ring resonators are employed as the model system where the light induced LC-resonance yields a figure-of-merit, sensitivity divided by linewidth, up to 54 depend... 2. Prospective associations between loneliness and emotional intelligence. Wols, A; Scholte, R H J; Qualter, P 2015-02-01 Loneliness has been linked cross-sectionally to emotional skill deficits (e.g., Zysberg, 2012), but missing from the literature is a longitudinal examination of these relationships. The present study fills that gap by examining the prospective relationships between loneliness and emotional functioning in young adolescents in England. One hundred and ninety-six adolescents aged 11-13 years (90 females) took part in the study and completed the youth version of the Mayer-Salovey-Caruso Emotional Intelligence Test (MSCEIT-YV) and the peer-related subscale of the Loneliness and Aloneness Scale for Children and Adolescents (LACA) at two time points, which were 10 months apart. Prospective associations were obtained for male and female adolescents separately using cross-lagged statistical techniques. Our results showed prospective links between understanding and managing emotions and loneliness for both females and males. Perceiving and using emotions were prospectively linked to loneliness in males only. Possible explanations and directions for future research are discussed. Copyright © 2014 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved. 3. School Food Practices of Prospective Teachers Rossiter, Melissa; Glanville, Theresa; Taylor, Jennifer; Blum, Ilya 2007-01-01 Background: Schoolteachers can affect students' eating habits in several ways: through nutrition knowledge, positive role modeling, and avoidance of unhealthy classroom food practices. In this study, the knowledge, attitudes, and eating behaviors of prospective teachers as determinants of intended classroom food practices and the school… 4. A prospective toxicology analysis in alcoholics Thomsen, Jørgen Lange; Simonsen, Kirsten Wiese; Felby, Søren 1997-01-01 A prospective and comprehensive investigation was done on 73 medico–legal autopsies in alcoholics. The results of the toxicology analyses are described. Alcohol intoxication was the cause of death in 8%, combined alcohol/drug intoxication in 15% and drugs alone in 19%. Alcoholic ketoacidosis...... than the exception in deaths in alcoholics.... 5. Prospective associations between loneliness and emotional intelligence Wols, A.C.; Scholte, R.H.J.; Qualter, P. 2015-01-01 Loneliness has been linked cross-sectionally to emotional skill deficits (e.g., Zysberg, 2012), but missing from the literature is a longitudinal examination of these relationships. The present study fills that gap by examining the prospective relationships between loneliness and emotional 6. Lignin peroxidase functionalities and prospective applications. Falade, Ayodeji O; Nwodo, Uchechukwu U; Iweriebor, Benson C; Green, Ezekiel; Mabinya, Leonard V; Okoh, Anthony I 2017-02-01 Ligninolytic extracellular enzymes, including lignin peroxidase, are topical owing to their high redox potential and prospective industrial applications. The prospective applications of lignin peroxidase span through sectors such as biorefinery, textile, energy, bioremediation, cosmetology, and dermatology industries. The litany of potentials attributed to lignin peroxidase is occasioned by its versatility in the degradation of xenobiotics and compounds with both phenolic and non-phenolic constituents. Over the years, ligninolytic enzymes have been studied however; research on lignin peroxidase seems to have been lagging when compared to other ligninolytic enzymes which are extracellular in nature including laccase and manganese peroxidase. This assertion becomes more pronounced when the application of lignin peroxidase is put into perspective. Consequently, a succinct documentation of the contemporary functionalities of lignin peroxidase and, some prospective applications of futuristic relevance has been advanced in this review. Some articulated applications include delignification of feedstock for ethanol production, textile effluent treatment and dye decolourization, coal depolymerization, treatment of hyperpigmentation, and skin-lightening through melanin oxidation. Prospective application of lignin peroxidase in skin-lightening functions through novel mechanisms, hence, it holds high value for the cosmetics sector where it may serve as suitable alternative to hydroquinone; a potent skin-lightening agent whose safety has generated lots of controversy and concern. © 2016 The Authors. MicrobiologyOpen published by John Wiley & Sons Ltd. 7. Many Rivets t0 Cross: Prospects by informal cross-border trading networks which exploit exchange rate disparities .... Obi: Many Rivets to Cross-Prospects of a Nigeria-led Common Market 63 tion and the ..... operators Huge proﬁts are made by smuggling cheap Nigerian. 8. Organic solvent nanofiltration: prospects and application Volkov, A V; Korneeva, G A; Tereshchenko, Gennadii F [A. V. Topchiev Institute of Petrochemical Synthesis, Russian Academy of Sciences, Moscow (Russian Federation) 2008-11-30 The key lines of research in a new field of the membrane science and technology, viz., organic solvent nanofiltration, are considered. The prospects for its use in chemical, petrochemical and food industries are discussed. Attention is focused on membranes developed for this method. 9. Prospects of Private Education in China Hua, Wu 2009-01-01 Private education contributes a great deal to education in China, but people are confused about the prospects of teacher development, tax problems, property rights problems, remunerations, and so forth. Legal provisions stipulate that private education and public education have the same legal status and rights, but there is still a long way to go… 10. Prospective associations between loneliness and emotional intelligence Wols, A.; Scholte, R.H.J.; Qualter, P. 2015-01-01 Loneliness has been linked cross-sectionally to emotional skill deficits (e.g., Zysberg, 2012), but missing from the literature is a longitudinal examination of these relationships. The present study fills that gap by examining the prospective relationships between loneliness and emotional functioni 11. Carbohydrate drugs: current status and development prospect. Zhang, Yan; Wang, Fengshan 2015-04-01 In recent years, there has been a great effort devoted to the investigation of the roles of carbohydrates in various essential biological processes and the development of carbohydrates to therapeutic drugs. This review summarizes the carbohydrate drugs which have been recorded in several pharmacopoeias, marketed, and under development. A prospect of the future development of carbohydrate drugs is discussed as well. 12. Science Perceptions of Prospective Class Teachers Ulucinar Sagir, Safak 2017-01-01 The perceptions of class teachers, who will deliver science education at the elementary school, of information and science are significant as these affect the quality of education received by children. The aim of this research is to determine perceptions of prospective class teachers of science. The sample group of the research consists of 120… 13. An Axiomatization of Cumulative Prospect Theory Wakker, P.P.; Tversky, A. 1993-01-01 This paper presents a method for axiomatizing a variety of models for decision making under uncertainty, including Expected Utility and Cumulative Prospect Theory. This method identifies, for each model, the situations that permit consistent inferences about the ordering of value differences. Exampl 14. CDF Status and B Physics Prospects J. Stephen Miller 2002-10-07 With extensive upgrades to the detector and electronics, CDF has started collecting data with Run II of the Tevatron. The enhanced silicon coverage and the use of silicon based tracks in the trigger, make CDF well suited for a broad program of B hadron measurements. We present the current status of the experiment and prospects for measurements in Run II. 15. Prospective Teachers' Opinions Concerning Children's Rights Faiz, Melike; Kamer, Selman Tunay 2017-01-01 Consideration of the child as a social being and his/her not having the power of self-protection have propounded the significance of children's rights. Teachers are important to educate the individual. Prospective teachers who will be teachers of the future will have a considerable amount of presidency. Thus, the main objective of this research is… 16. Strategic hospital marketing responses to prospective payment. Rosko, M D; Broyles, R W 1987-01-01 Hospitals may respond to the revenue constraints of prospective payment by altering their patient mix. This article provided a brief overview of marketing management and suggested that hospitals might change their patient mix by employing marketing strategies designed to attract patients to its services or to attract physicians who specialize in the appropriate medical disciplines. 17. Voice and culture: A prospect theory approach Paddock, E.L.; Ko, Junsu; Cropanzano, R.; Bagger, J.; El Akremi, A.; Camerman, A.; Greguras, G. J.; Mladinic, A.; Moliner, C.; Nam, K.; Törnblom, K.; Van den Bos, Kees 2015-01-01 The present study examines the congruence of individuals' minimum preferred amounts of voice with the prospect theory value function across nine countries. Accounting for previously ignored minimum preferred amounts of voice and actual voice amounts integral to testing the steepness of gain and loss 18. Do Marital Prospects Dissuade Unmarried Fertility? Kennes, John; Knowles, John is that weaker marriage-market prospects may be strong enough to explain higher unmarried birth rates. Relative to the existing literature, the essential contributions of the model are to allow for accumulation of children over the lifecycle and for the marriage of single mothers. We use the model... 19. Arsenal of plant cell wall degrading enzymes reflects host preference among plant pathogenic fungi Bergstrom Gary C 2011-02-01 Full Text Available Abstract Background The discovery and development of novel plant cell wall degrading enzymes is a key step towards more efficient depolymerization of polysaccharides to fermentable sugars for the production of liquid transportation biofuels and other bioproducts. The industrial fungus Trichoderma reesei is known to be highly cellulolytic and is a major industrial microbial source for commercial cellulases, xylanases and other cell wall degrading enzymes. However, enzyme-prospecting research continues to identify opportunities to enhance the activity of T. reesei enzyme preparations by supplementing with enzymatic diversity from other microbes. The goal of this study was to evaluate the enzymatic potential of a broad range of plant pathogenic and non-pathogenic fungi for their ability to degrade plant biomass and isolated polysaccharides. Results Large-scale screening identified a range of hydrolytic activities among 348 unique isolates representing 156 species of plant pathogenic and non-pathogenic fungi. Hierarchical clustering was used to identify groups of species with similar hydrolytic profiles. Among moderately and highly active species, plant pathogenic species were found to be more active than non-pathogens on six of eight substrates tested, with no significant difference seen on the other two substrates. Among the pathogenic fungi, greater hydrolysis was seen when they were tested on biomass and hemicellulose derived from their host plants (commelinoid monocot or dicot. Although T. reesei has a hydrolytic profile that is highly active on cellulose and pretreated biomass, it was less active than some natural isolates of fungi when tested on xylans and untreated biomass. Conclusions Several highly active isolates of plant pathogenic fungi were identified, particularly when tested on xylans and untreated biomass. There were statistically significant preferences for biomass type reflecting the monocot or dicot host preference of the 20. Site-adapted optimization of the cultivation of energy crops for biogas plants. Initial results and prospects of the FNR-subsidized multi-partner project; Standortangepasste Optimierung des Anbaus von Energieplanzen fuer Biogasanlagen. Erste Ergebnisse und Perspektiven des von der FNR gefoerderten Verbundprojektes Vetter, A.; Goedeke, K.; Nehring, A. [Thueringer Landesanstalt fuer Landwirtschaft (Germany) 2007-07-01 The use of biomass as renewable energy source is on the increase, driven by the rising price of oil, measures to reduce the emission of carbon dioxide and favorable general political conditions. In addition to wood as heat source, rapeseed and cereal crops as feedstock for power plants of the first generation, mainly so called wet line crops, i.e., silage for biogas generation and fuels of the second generation can gain in importance dramatically. The generation of biogas from liquid manure and renewable primary products has seen a virtual boom after the amendment of the Renewable Energies Act (EEG) in 2004. The technology allowance also introduced at that time is responsible for the present expansion of dry fermentation exclusively based on renewable primary products. The current favorite among feedstock substrates is corn. Cultivation, maintenance, harvest and silage are common practice for this crop, which is rich in biomass. Experience is extensive and the method proven. There is no need for changes of crop rotation, corn cultivation is established. In addition to corn, any type of biomass, except lignified types, can be used for biogas production. This makes the spectrum of potential candidates wide. The choice of crops should be guided by financial and ecological considerations. The latter is of interest in as far as weeds and grasses can be tolerated in the crop stand as long as they have no negative effect on the yields or the technological sequence of substrate preparation and fermentation. In the final instance, the farmer will pick the crop according to the net revenue he can earn from the yield per unit of area, the cost per unit of energy and the way he can fit it into the normal practice of his farm. After the reform of the EU's agrarian policy in 2005, the bonus system improved the financial rating, e.g., of perennial field forage crops, winter catch crops, etc. in comparison with corn. In addition to this, new crops, e.g., Sudan grass, sweet 1. 我国能源植物概况与能源型甘蔗斑茅后代前景展望%General Situation of Energy Plant and the Cultivation of Energy Type Sugarcane and Erianthus Arundinaceus Progeny Prospect in China 李昱; 李奇伟; 邓海华; 齐永文; 吴嘉云 2014-01-01 Erianthus arundinaceus and sugarcane as a new energy plant, may become an important breakthrough of the future development of biomass energy. 2. In-Situ Decontamination of Metal-Polluted Soils by Metal-Accumulator Plants 1993-04-01 1993). In situ biorernediation of metal -contaminated soils using crops of hyperaccumulator plants: potentials and future prospects for a developing...AD-A285 710 PUBLICITY FOR US ARMY CORPS OF ENGINEERS CONTRACT R&D 6872-EN-01, APRIL 1993 IN-SITU DECONTAMINATION OF METALPOLLUTED SOILS BY METAL ...1991). In situdecontamination of heavy metal polluted soils using crops ofmetal-accumulating plants - a feasibility study. In: In Situ Bioreclaination 3. Conditional sterility in plants Meagher, Richard B.; McKinney, Elizabeth; Kim, Tehryung 2010-02-23 The present disclosure provides methods, recombinant DNA molecules, recombinant host cells containing the DNA molecules, and transgenic plant cells, plant tissue and plants which contain and express at least one antisense or interference RNA specific for a thiamine biosynthetic coding sequence or a thiamine binding protein or a thiamine-degrading protein, wherein the RNA or thiamine binding protein is expressed under the regulatory control of a transcription regulatory sequence which directs expression in male and/or female reproductive tissue. These transgenic plants are conditionally sterile; i.e., they are fertile only in the presence of exogenous thiamine. Such plants are especially appropriate for use in the seed industry or in the environment, for example, for use in revegetation of contaminated soils or phytoremediation, especially when those transgenic plants also contain and express one or more chimeric genes which confer resistance to contaminants. 4. Plant synthetic biology. Liu, Wusheng; Stewart, C Neal 2015-05-01 Plant synthetic biology is an emerging field that combines engineering principles with plant biology toward the design and production of new devices. This emerging field should play an important role in future agriculture for traditional crop improvement, but also in enabling novel bioproduction in plants. In this review we discuss the design cycles of synthetic biology as well as key engineering principles, genetic parts, and computational tools that can be utilized in plant synthetic biology. Some pioneering examples are offered as a demonstration of how synthetic biology can be used to modify plants for specific purposes. These include synthetic sensors, synthetic metabolic pathways, and synthetic genomes. We also speculate about the future of synthetic biology of plants. 5. Risk-taking plants Sade, Nir; Gebremedhin, Alem; Moshelion, Menachem 2012-01-01 Water scarcity is a critical limitation for agricultural systems. Two different water management strategies have evolved in plants: an isohydric strategy and an anisohydric strategy. Isohydric plants maintain a constant midday leaf water potential (Ψleaf) when water is abundant, as well as under drought conditions, by reducing stomatal conductance as necessary to limit transpiration. Anisohydric plants have more variable Ψleaf and keep their stomata open and photosynthetic rates high for longer periods, even in the presence of decreasing leaf water potential. This risk-taking behavior of anisohydric plants might be beneficial when water is abundant, as well as under moderately stressful conditions. However, under conditions of intense drought, this behavior might endanger the plant. We will discuss the advantages and disadvantages of these two water-usage strategies and their effects on the plant’s ability to tolerate abiotic and biotic stress. The involvement of plant tonoplast AQPs in this process will also be discussed. PMID:22751307 6. Annual Plant Reviews , three dimensional structures and functions of each protein in a biological system. In plant science, the number of proteome studies is rapidly expanding after the completion of the Arabidopsis thaliana genome sequence, and proteome analyses of other important or emerging model systems and crop plants...... are in progress or are being initiated. Proteome analysis in plants is subject to the same obstacles and limitations as in other organisms, but the nature of plant tissues, with their rigid cell walls and complex variety of secondary metabolites, means that extra challenges are involved that may not be faced when...... analysing other organisms. This volume aims to highlight the ways in which proteome analysis has been used to probe the complexities of plant biochemistry and physiology. It is aimed at researchers in plant biochemistry, genomics, transcriptomics and metabolomics who wish to gain an up-to-date insight... 7. Scutellaria biotechnology: Achievements and future prospects Plants of the genus Scutellaria (Family Lamiaceae) constitute one of the common components of Eastern as well as traditional American medicine. Skullcap is a North American perennial plant belonging to the genus Scutellaria. The genus is widespread in Northern Hemisphere represented by close to 400 ... 8. Overview and prospects of selenium phytoremediation approaches Evidence is lacking on whether selenium (Se) is essential for vegetation growth, but plants can absorb, assimilate, and accumulate Se in leaves and roots. The capability of plants to take up substantial amount of Se is now being utilized to remove excess Se from contaminated soils. This process has ... 9. Florigen unmasked - exciting prospects for horticulture The pioneer work of Garner and Allard, who coined the term “photoperiod” to describe the dramatic effects of day length on flowering of many plants, led to the widespread commercial use of photoperiod modification to control flowering in plants, particularly ornamentals. M.K. Chailakhyan suggested t... 10. Recombinant Cytokines from Plants Patrycja Redkiewicz; Anna Góra-Sochacka; Tomas Vaněk; Agnieszka Sirko 2011-01-01 Plant-based platforms have been successfully applied for the last two decades for the efficient production of pharmaceutical proteins. The number of commercialized products biomanufactured in plants is, however, rather discouraging. Cytokines are small glycosylated polypeptides used in the treatment of cancer, immune disorders and various other related diseases. Because the clinical use of cytokines is limited by high production costs they are good candidates for plant-made pharmaceuticals. S... 11. MBS Native Plant Communities Minnesota Department of Natural Resources — This data layer contains results of the Minnesota County Biological Survey (MCBS). It includes polygons representing the highest quality native plant communities... 12. The Kuroshio power plant Chen, Falin 2013-01-01 By outlining a new design or the Kuroshio power plant, new approaches to turbine design, anchorage system planning, deep sea marine engineering and power plant operations and maintenance are explored and suggested. The impact on the local environment, particularly in the face of natural disasters, is also considered to provide a well rounded introduction to plan and build a 30MW pilot power plant. Following a literature review, the six chapters of this book propose a conceptual design by focusing on the plant's core technologies and establish the separate analysis logics for turbine design and 13. Plant Habitat (PH) Onate, Bryan 2016-01-01 The International Space Station (ISS) will soon have a platform for conducting fundamental research of Large Plants. Plant Habitat (PH) is designed to be a fully controllable environment for high-quality plant physiological research. PH will control light quality, level, and timing, temperature, CO2, relative humidity, and irrigation, while scrubbing ethylene. Additional capabilities include leaf temperature and root zone moisture and oxygen sensing. The light cap will have red (630 nm), blue (450 nm), green (525 nm), far red (730 nm) and broad spectrum white LEDs. There will be several internal cameras (visible and IR) to monitor and record plant growth and operations. 14. Plant Transporter Identification Larsen, Bo Membrane transport proteins (transporters) play a critical role for numerous biological processes, by controlling the movements of ions and molecules in and out of cells. In plants, transporters thus function as gatekeepers between the plant and its surrounding environment and between organs......, tissues, cells and intracellular compartments. Since plants are highly compartmentalized organisms with complex transportation infrastructures, they consequently have many transporters. However, the vast majority of predicted transporters have not yet been experimentally verified to have transport...... activity. This project contains a review of the implemented methods, which have led to plant transporter identification, and present our progress on creating a high-throughput functional genomics transporter identification platform.... 15. Plant intelligence and attention. Marder, Michael 2013-05-01 This article applies the phenomenological model of attention to plant monitoring of environmental stimuli and signal perception. Three complementary definitions of attention as selectivity, modulation and perdurance are explained with reference to plant signaling and behaviors, including foraging, ramet placement and abiotic stress communication. Elements of animal and human attentive attitudes are compared with plant attention at the levels of cognitive focus, context and margin. It is argued that the concept of attention holds the potential of becoming a cornerstone of plant intelligence studies. 16. Plant Transporter Identification Larsen, Bo Membrane transport proteins (transporters) play a critical role for numerous biological processes, by controlling the movements of ions and molecules in and out of cells. In plants, transporters thus function as gatekeepers between the plant and its surrounding environment and between organs......, tissues, cells and intracellular compartments. Since plants are highly compartmentalized organisms with complex transportation infrastructures, they consequently have many transporters. However, the vast majority of predicted transporters have not yet been experimentally verified to have transport...... activity. This project contains a review of the implemented methods, which have led to plant transporter identification, and present our progress on creating a high-throughput functional genomics transporter identification platform.... 17. Explosive Formulation Pilot Plant Federal Laboratory Consortium — The Pilot Plant for Explosive Formulation supports the development of new explosives that are comprised of several components. This system is particularly beneficial... 18. Phyllotactic Patterns on Plants Shipman, Patrick D.; Newell, Alan C. 2004-04-01 We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the deformation configurations seen on plant surfaces may be understood as the energy-minimizing buckling pattern of a compressed shell (the plant's tunica) on an elastic foundation. The key new idea is that the strain energy is minimized by configurations consisting of special triads of almost periodic deformations. We reproduce a wide spectrum of plant patterns, all with the divergence angles observed in nature, and show how the occurrences of Fibonacci-like sequences and the golden angle are natural consequences. 19. Oil from plants Calvin, M. 1983-01-01 As a result of the exhaustion of our supplies of ancient photosynthesis (oil and gas) it is necessary to develop renewable fuels for the future. The most immediate source of renewable fuel is, of course, the annually growing green plants, some of which produce hydrocarbon(s) directly. New plant sources can be selected for this purpose, plants which have high potential for production of chemicals and liquid fuels. Suggestions are made for modification of both the product character and the productivity of the plants. Ultimately, a totally synthetic device will be developed for the conversion of solar quanta into useful chemical form completely independent of the need for arable land. 20. Plant biotic interactions 2016-01-01 occurring after infestation by olive fly larvae. The last research article by Niu et al.(2016) describes a growth-promoting rhizobacterium that primes induced systemic resistance by suppressing a host R gene-targeting micro RNA pairs and activating host immune responses. This finding further supports the important roles of plant endogenous small RNAs in plant-pathogen interactions. Hailing Jin, Professor Special Issue Editor UC President’s Chair Director of Genetics, Genomics and Bioinformatics Graduate Program, Center for Plant Cell Biology, Institute for Integrative Genome Biology, University of California, Riverside, USA doi:10.1111/jipb.12476 ©2016 Institute of Botany, Chinese Academy of Sciences REFERENCES Alagna F, Kal enbach M, Pompa A, De Marchis F, Rao R, Baldwin IT, Bonaventure G, Baldoni L (2016) Olive fruits infested with olive fly larvae respond with an ethylene burst and the emission of specific volatiles. J Integr Plant Biol 58:413–425 Castiblanco LF, Sundin GW (2016) New insights on molecular regulation of biofilm formation in plant-associated bacteria. J Integr Plant Biol 58:362–372 da GraSca JV, Douhan GW, Halbert SE, Keremane ML, Lee RF, Vidalakis G, Zhao H (2016) Huanglongbing: An overview of a complex pathosystem ravaging the world’s citrus. J Integr Plant Biol 58:373–387 Giovino A, Martinel i F, Saia S (2016) Rhynchophorus ferrugineus attack affects a group of compounds rather than rearranging Phoenix canariensis metabolic pathways. J Integr Plant Biol 58:388–396 Huang J, Yang M, Zhang X (2016) The function of smal RNAs in plant biotic stress response. J Integr Plant Biol 58:312–327 Kaloshian I, Wal ing LL (2016) Hemipteran and dipteran pests: Effectors and plant host immune regulators. J Integr Plant Biol 58:350–361 Mermigka G, Verret F, Kalantidis K (2016) RNA silencing movement in plants. J Integr Plant Biol 58:328–342 Niu D, Xia J, Jiang C, Qi B, Ling X, Lin S, Zhang W, Guo J, Jin H, Zhao H (2016) Bacil us cereus AR156 1. Prospects and challenges of ecotourism development in Nigeria ... Prospects and challenges of ecotourism development in Nigeria. ... Journal of Environmental Extension ... This paper highlights the prospects and challenges of ecotourism as a veritable tool for sustainable economic development and the ... 2. Attitude level of prospective science teachers towards assessment Efendi, Ridwan; Rustaman, Nuryani Y. 2016-02-01 A descriptive study about attitude level of prospective science teachers towards assessment was conducted with the involvement of 67 prospective science teachers from four state universities in western part of the Indonesian region and middle part of Indonesia region. Data collected by using the questionnaire consisted of four aspects, id est. prospective science teachers attitude towards assessment (cognitive level of assessment, type of assessment, and criterion of evaluation), prospective science teachers instructional practice, internal difficulties that prospective science teachers experienced related to their assessment skills, and the use of assessment process of prospective science teachers. Determination of attitude level detected from prospective science teachers was carried out in descriptive statistics, in the form of respondent average values. Research finding shows that attitude level of prospective science teachers towards assessment can be categorized as "close to constructivist". 3. Stable isotope techniques in plant water sources:a review 2010-01-01 The stable hydrogen and oxygen isotopes widely exist in various kinds of natural water.Plants have to cope with various water sources:rainwater,soil water,groundwater,sea water,and mixtures.These are usually characterized by different isotopic signatures (18O/16O and D/H ratios).Because there are relative abundance variations in water,and plant roots do not discriminate against specific water isotopes during water uptake,hydrogen and oxygen stable isotope ratios of water within plants provide new information on water sources,interactions between plant species and water use patterns under natural conditions.At present,the measurement of δD,δ18O composition of various potential water sources and stem water has become significant means to identify plant water sources.Based on previous studies,this review highlights recent advances such as theory basis,methodology,as well as different spatial and temporal scales,and existed questions and prospects.Stable isotope techniques for estimating plant water sources have provided valuable tools for conducting basic and applied research.Future studies emphasize the modification of preparing methods,isotope technique combined with other measurements,and aerial organs of plant water source should be en-couraged. 4. Nuclear Power Plant Maintenance Optimization with Heuristic Algorithm Andrija Volkanovski 2014-01-01 Full Text Available The test and maintenance activities are conducted in the nuclear power plants in order to prevent or limit failures resulting from the ageing or deterioration. The components and systems are partially or fully unavailable during the maintenance activities. This is especially important for the safety systems and corresponding equipment because they are important contributors to the overall nuclear power plant safety. A novel method for optimization of the maintenance activities in the nuclear power plant considering the plant safety is developed and presented. The objective function of the optimization is the mean value of the selected risk measure. The risk measure is assessed from the minimal cut sets identified in the Probabilistic Safety Assessment. The optimal solution of the objective function is estimated with genetic algorithm. The proposed method is applied on probabilistic safety analysis model of the selected safety system of the reference nuclear power plant. Obtained results show that optimization of maintenance decreases the risk and thus improves the plant safety. The implications of the consideration of different constraints on the obtained results are investigated and presented. The future prospects for the optimization of the maintenance activities in the nuclear power plants with the presented method are discussed. 5. Liposome-Based Delivery Systems in Plant Polysaccharides Meiwan Chen 2012-01-01 Full Text Available Plant polysaccharides consist of many monosaccharide by α- or β-glycosidic bond which can be extracted by the water, alcohol, lipophile liquid from a variety of plants including Cordyceps sinensis, astragalus, and mushrooms. Recently, many evidences illustrate that natural plant polysaccharides possess various biological activities including strengthening immunity, lowering blood sugar, regulating lipid metabolism, antioxidation, antiaging, and antitumour. Plant polysaccharides have been widely used in the medical field due to their special features and low toxicity. As an important drug delivery system, liposomes can not only encapsulate small-molecule compound but also big-molecule drug; therefore, they present great promise for the application of plant polysaccharides with unique physical and chemical properties and make remarkable successes. This paper summarized the current progress in plant polysaccharides liposomes, gave an overview on their experiment design method, preparation, and formulation, characterization and quality control, as well as in vivo and in vitro studies. Moreover, the potential application of plant polysaccharides liposomes was prospected as well. 6. Increased plant productivity and decreased microbial respiratory C loss by plant growth-promoting rhizobacteria under elevated CO₂. Nie, Ming; Bell, Colin; Wallenstein, Matthew D; Pendall, Elise 2015-03-18 Increased plant productivity and decreased microbial respiratory C loss can potentially mitigate increasing atmospheric CO₂, but we currently lack effective means to achieve these goals. Soil microbes may play critical roles in mediating plant productivity and soil C/N dynamics under future climate scenarios of elevated CO₂ (eCO₂) through optimizing functioning of the root-soil interface. By using a labeling technique with (13)C and (15)N, we examined the effects of plant growth-promoting Pseudomonas fluorescens on C and N cycling in the rhizosphere of a common grass species under eCO₂. These microbial inoculants were shown to increase plant productivity. Although strong competition for N between the plant and soil microbes was observed, the plant can increase its capacity to store more biomass C per unit of N under P. fluorescens addition. Unlike eCO₂ effects, P. fluorescens inoculants did not change mass-specific microbial respiration and accelerate soil decomposition related to N cycling, suggesting these microbial inoculants mitigated positive feedbacks of soil microbial decomposition to eCO₂. The potential to mitigate climate change by optimizing soil microbial functioning by plant growth-promoting Pseudomonas fluorescens is a prospect for ecosystem management. 7. 42 CFR 412.340 - Fully prospective payment methodology. 2010-10-01 ... 42 Public Health 2 2010-10-01 2010-10-01 false Fully prospective payment methodology. 412.340...-Related Costs § 412.340 Fully prospective payment methodology. A hospital paid under the fully prospective payment methodology receives a payment per discharge based on a proportion of the hospital-specific rate... 8. 50 CFR 27.64 - Prospecting and mining. 2010-10-01 ... 50 Wildlife and Fisheries 6 2010-10-01 2010-10-01 false Prospecting and mining. 27.64 Section 27.64 Wildlife and Fisheries UNITED STATES FISH AND WILDLIFE SERVICE, DEPARTMENT OF THE INTERIOR... Property § 27.64 Prospecting and mining. Prospecting, locating, or filing mining claims on national... 9. Reversal in China’s Mineral Risk Prospecting Investment Pattern 2013-01-01 <正>The total size of China’s central and provincial level geological prospecting funds has reached 39.9 billion yuan,which effectively propelled social capital to make investment in mineral resources risk prospecting through cooperation,and reversed the previous pattern that China’s mining risk prospecting totally relied on investment by the state government. 10. Turkish Prospective Teachers' Understanding and Misunderstanding on Global Warming Ocal, A.; Kisoglu, M.; Alas, A.; Gurbuz, H. 2011-01-01 The key objective of this study is to determine the Turkish elementary prospective teachers' opinions on global warming. It is also aimed to establish prospective teachers' views about the environmental education in Turkish universities. A true-false type scale was administered to 564 prospective teachers from science education, social studies… 11. Effects of Learned Episodic Event Structure on Prospective Duration Judgments Faber, Myrthe; Gennari, Silvia P. 2017-01-01 The field of psychology of time has typically distinguished between prospective timing and retrospective duration estimation: in prospective timing, participants attend to and encode time, whereas in retrospective estimation, estimates are based on the memory of what happened. Prior research on prospective timing has primarily focused on… 12. Turkish Prospective Chemistry Teachers' Beliefs about Chemistry Teaching Boz, Yezdan; Uzuntiryaki, Esen 2006-01-01 In order to study the beliefs of Turkish prospective chemistry teachers about teaching chemistry, semi-structured interviews were conducted with 12 prospective teachers. Analysis of the interviews revealed that most of the prospective teachers held intermediate (transition between constructivist and traditional) beliefs about chemistry teaching.… 13. Turkish Prospective Chemistry Teachers' Alternative Conceptions about Acids and Bases Boz, Yezdan 2009-01-01 The purpose of this study was to obtain prospective chemistry teachers' conceptions about acids and bases concepts. Thirty-eight prospective chemistry teachers were the participants. Data were collected by means of an open-ended questionnaire and semi-structured interviews. Analysis of data indicated that most prospective teachers did not have… 14. Turkish Prospective Teachers' Understanding and Misunderstanding on Global Warming Ocal, A.; Kisoglu, M.; Alas, A.; Gurbuz, H. 2011-01-01 The key objective of this study is to determine the Turkish elementary prospective teachers' opinions on global warming. It is also aimed to establish prospective teachers' views about the environmental education in Turkish universities. A true-false type scale was administered to 564 prospective teachers from science education, social studies… 15. Turkish Prospective Chemistry Teachers' Alternative Conceptions about Acids and Bases Boz, Yezdan 2009-01-01 The purpose of this study was to obtain prospective chemistry teachers' conceptions about acids and bases concepts. Thirty-eight prospective chemistry teachers were the participants. Data were collected by means of an open-ended questionnaire and semi-structured interviews. Analysis of data indicated that most prospective teachers did not have… 16. AROMATIC PLANT OF LAMIACEAE FAMILY FOR USE IN PHYTOTHERAPY L. A. Logvinenko 2016-01-01 Full Text Available Introduction. Therapeutic action of terpenoids of essential oil in uncommon plants like Elsholtzia stauntonii, Agastache foenic-ulum, Monarda fistulosa, Perovskia atri-plicifolia, Majorana hortensis, therefore the study for these plants application in phyto-therapy is timely. The study for componen-tial content of essential oil of 18 uncommon species from Lamiaceae family from the collection of Nikitsky Botanical Garden to increase therapeutic possibilities and their practical use in phytotherapy was the purpose of this paper. The plant species under study were introduced to the South Coast of Crimea from different ecological and geographic zones in seeds from botanical gardens of Europe. Methods. Every species was represented by 3-20 samples, which were studied by biomorpholofical and principal economically valuable features. The article presents the generalization and analysis of long-time studies for biologically active substances from 18 species of aromatic plants from Lamiaceae family. The content of essential oil was determined in a phase of mass blossom, from freshly harvested raw materials by means of hydro distillation at Ginsberg apparatuses. Componential content of essential oil was studied by the method of gas liquid chromatography. Results. Identification of the essential oils components allowed isolation of plant chemotypes with high content of valuable substances (methyl chavicol, carvacrol, pinen, thymol, and others. Highproductive samples (forms, prospective for industrial cultivation were isolated by the features complex. Based on the classification of A.D. Turova in phytotherapeutic action of plants and results of our studies, the isolated plant forms were distributed in 10 groups of usage in phytotherapy. On the example of Agastache foeniculum we showed that one and the same plant species may have different chemotypes, which have treatment and toxic action. Conclusion. The data obtained broaden and add the information about a 17. Natural Gas Prospecting by Using Satellite MT Data in Chishui Area,Guizhou 杨柏林 1997-01-01 Oil-gas remote sensing information is obtained from satellite TM data through graphic treatment in the light of the hydrocarbon-microseepage theory.The nine target areas (of three types)selected on this basis concide well with the occurrence of natural gases and have been proved by subsequent prospecting .Plants in the target greas are characterized.as a result of hydrocarbon-microseepage,by abnormal spectral features with the absorption peaks of chlorophyll shifting toward blue light,reflectivity in the range of visible light increasing and reflectivity in the near infrared region decreasing. 18. Iris glaucescens Bunge (Iridaceae, the rare flag of the Siberian plant kingdom Alexeeva Nina Borisovna 2015-12-01 The work was performed in the framework of an institutional research project of the Komarov Botanical Institute of the Russian Academy of Sciences, topic 52.5. Collection of live plants of the Komarov Botanical Institute of the Russian Academy of Sciences (history, present condition, development and use prospects. 19. MRI of intact plants. As, H. van; Scheenen, T.W.J.; Vergeldt, F.J. 2009-01-01 Nuclear magnetic resonance imaging (MRI) is a non-destructive and non-invasive technique that can be used to acquire two- or even three-dimensional images of intact plants. The information within the images can be manipulated and used to study the dynamics of plant water relations and water transpor 20. MRI of intact plants As, van H.; Scheenen, T.; Vergeldt, F.J. 2009-01-01 Nuclear magnetic resonance imaging (MRI) is a non-destructive and non-invasive technique that can be used to acquire two- or even three-dimensional images of intact plants. The information within the images can be manipulated and used to study the dynamics of plant water relations and water transpor 1. Modulating lignin in plants Apuya, Nestor; Bobzin, Steven Craig; Okamuro, Jack; Zhang, Ke 2013-01-29 Materials and methods for modulating (e.g., increasing or decreasing) lignin content in plants are disclosed. For example, nucleic acids encoding lignin-modulating polypeptides are disclosed as well as methods for using such nucleic acids to generate transgenic plants having a modulated lignin content. 2. Plant vascular development Rybel, De Bert; Mähönen, Ari Pekka; Helariutta, Yrjö; Weijers, Dolf 2016-01-01 Vascular tissues in plants are crucial to provide physical support and to transport water, sugars and hormones and other small signalling molecules throughout the plant. Recent genetic and molecular studies have identified interconnections among some of the major signalling networks that regulate 3. Nuclear Power Plants. Revised. Lyerly, Ray L.; Mitchell, Walter, III This publication is one of a series of information booklets for the general public published by the United States Atomic Energy Commission. Among the topics discussed are: Why Use Nuclear Power?; From Atoms to Electricity; Reactor Types; Typical Plant Design Features; The Cost of Nuclear Power; Plants in the United States; Developments in Foreign… 4. NMR, Water and Plants As, van H. 1982-01-01 This Thesis describes the application of a non-destructive pulsed proton NMR method mainly to measure water transport in the xylem vessels of plant stems and in some model systems. The results are equally well applicable to liquid flow in other biological objects than plants, e.g. flow of blood and 5. Terrestrial plant methane production Mikkelsen, Teis Nørgaard; Bruhn, Dan; Møller, Ian M. We evaluate all experimental work published on the phenomenon of aerobic methane (CH4) generation in terrestrial plants. We conclude that the phenomenon is true. Four stimulating factors have been observed to induce aerobic plant CH4 production, i.e. cutting injuries, increasing temperature... 6. Slavery in plants Kabiri, S.; Rodenburg, J.; Ast, van A.; Bastiaans, L. 2017-01-01 The rain-fed lowland rice weed Rhamphicarpa fistulosa (Rice Vampireweed) is a facultative root parasitic plant. Growth and reproduction of R. fistulosa benefit considerably from parasitism, but how this affects the host plant is not well established. We determined accumulation and partitioning of 7. Carotenoid metabolism in plants Carotenoids are mostly C40 terpenoids, a class of hydrocarbons that participate in various biological processes in plants, such as photosynthesis, photomorphogenesis, photoprotection, and development. Carotenoids also serve as precursors for two plant hormones and a diverse set of apocarotenoids. Th... 8. Overview of plant pigments Chlorophylls, carotenoids, flavonoids and betalains are four major classes of biological pigments produced in plants. Chlorophylls are the primary pigments responsible for plant green and photosynthesis. The other three are accessary pigments and secondary metabolites that yield non-green colors and... 9. Plant pathogen resistance Greenberg, Jean T; Jung, Ho Won; Tschaplinski, Timothy 2012-11-27 Azelaic acid or its derivatives or analogs induce a robust and a speedier defense response against pathogens in plants. Azelaic acid treatment alone does not induce many of the known defense-related genes but activates a plant's defense signaling upon pathogen exposure. 10. [Neotropical plant morphology]. Pérez-García, Blanca; Mendoza, Aniceto 2002-01-01 An analysis on plant morphology and the sources that are important to the morphologic interpretations is done. An additional analysis is presented on all published papers in this subject by the Revista de Biología Tropical since its foundation, as well as its contribution to the plant morphology development in the neotropics. 11. The Plant Cell Surface Anne-Mie C.Emons; Kurt V.Fagerstedt 2010-01-01 @@ Multicellular organization and tissue construction has evolved along essentially different lines in plants and animals. Since plants do not run away, but are anchored in the soil, their tissues are more or less firm and stiff. This strength stems from the cell walls, which encase the fragile cytoplasm, and protect it. 12. Plant development models Chuine, I.; Garcia de Cortazar-Atauri, I.; Kramer, K.; Hänninen, H. 2013-01-01 In this chapter we provide a brief overview of plant phenology modeling, focusing on mechanistic phenological models. After a brief history of plant phenology modeling, we present the different models which have been described in the literature so far and highlight the main differences between them, 13. Plant growth promoting rhizobacterium Doktycz, Mitchel John; Pelletier, Dale A.; Schadt, Christopher Warren; Tuskan, Gerald A.; Weston, David 2015-08-11 The present invention is directed to the Pseudomonas fluorescens strain GM30 deposited under ATCC Accession No. PTA-13340, compositions containing the GM30 strain, and methods of using the GM30 strain to enhance plant growth and/or enhance plant resistance to pathogens. 14. Evolution & Diversity in Plants. Pearson, Lorentz C. 1988-01-01 Summarizes recent findings that help in understanding how evolution has brought about the diversity of plant life that presently exists. Discusses basic concepts of evolution, diversity and classification, the three-line hypothesis of plant evolution, the origin of fungi, and the geologic time table. Included are 31 references. (CW) 15. Methylome evolution in plants Vidalis, Amaryllis; Živković, Daniel; Wardenaar, René; Roquis, David; Tellier, Aurélien; Johannes, Frank 2016-01-01 Despite major progress in dissecting the molecular pathways that control DNA methylation patterns in plants, little is known about the mechanisms that shape plant methylomes over evolutionary time. Drawing on recent intra- and interspecific epigenomic studies, we show that methylome evolution over 16. Plants without arbuscular mycorrhizae P is second to N as the most limiting element for plant growth. Plants have evolved a number of effective strategies to acquire P and grow in a P-limited environment. Physiological, biochemical, and molecular studies of P-deficiency adaptations that occur in non-mycorrhizal species have provided str... 17. Plant pathogen resistance Greenberg, Jean T.; Jung, Ho Won; Tschaplinski, Timothy 2015-10-20 Azelaic acid or its derivatives or analogs induce a robust and a speedier defense response against pathogens in plants. Azelaic acid treatment alone does not induce many of the known defense-related genes but activates a plant's defense signaling upon pathogen exposure. 18. Plant names and classification This chapter updates one of the same title from Edition 12 of Stearn’s Introductory Biology published in 2011. It reviews binomial nomenclature, discusses three codes of plant nomenclature (the International Code of Botanical Nomenclature, the International Code of Nomenclature for Cultivated Plants... 19. Better Plants Program Overview None 2015-09-30 The U.S. Department of Energy’s (DOE’s) Better Buildings, Better Plants Program is a voluntary partnership initiative to drive significant energy efficiency improvement across energy intensive companies and organizations. 157 leading manufacturers and public water and wastewater treatment utilities are partnering with DOE through Better Plants to improve energy efficiency, slash carbon emissions, and cut energy costs. 20. Power plant chemical technology NONE 1996-12-01 17 contributions covering topies of fossil fuel combustion, flue gas cleaning, power plant materials, corrosion, water/steam cycle chemistry, monitoring and control were presented at the annual meeting devoted to Power Plant Chemical Technology 1996 at Kolding (Denmark) 4-6 September 1996. (EG) 1. Plant growth promoting rhizobacterium Doktycz, Mitchel John; Pelletier, Dale A.; Schadt, Christopher Warren; Tuskan, Gerald A.; Weston, David 2015-08-11 The present invention is directed to the Pseudomonas fluorescens strain GM30 deposited under ATCC Accession No. PTA-13340, compositions containing the GM30 strain, and methods of using the GM30 strain to enhance plant growth and/or enhance plant resistance to pathogens. 2. Plant plastid engineering. Wani, Shabir H; Haider, Nadia; Kumar, Hitesh; Singh, N B 2010-11-01 Genetic material in plants is distributed into nucleus, plastids and mitochondria. Plastid has a central role of carrying out photosynthesis in plant cells. Plastid transformation is becoming more popular and an alternative to nuclear gene transformation because of various advantages like high protein levels, the feasibility of expressing multiple proteins from polycistronic mRNAs, and gene containment through the lack of pollen transmission. Recently, much progress in plastid engineering has been made. In addition to model plant tobacco, many transplastomic crop plants have been generated which possess higher resistance to biotic and abiotic stresses and molecular pharming. In this mini review, we will discuss the features of the plastid DNA and advantages of plastid transformation. We will also present some examples of transplastomic plants developed so far through plastid engineering, and the various applications of plastid transformation. 3. Automatic micropropagation of plants Otte, Clemens; Schwanke, Joerg; Jensch, Peter F. 1996-12-01 Micropropagation is a sophisticated technique for the rapid multiplication of plants. It has a great commercial potential due to the speed of propagation, the high plant quality, and the ability to produce disease-free plants. However, micropropagation is usually done by hand which makes the process cost-intensive and tedious for the workers especially because it requires a sterile work-place. Therefore, we have developed a prototype automation system for the micropropagation of a grass species (miscanthus sinensis gigantheus). The objective of this paper is to describe the robotic system in an overview and to discuss the vision system more closely including the implemented morphological operations recognizing the cutting and gripping points of miscanthus plants. Fuzzy controllers are used to adapt the parameters of image operations on-line to each individual plant. Finally, we discuss our experiences with the developed prototype an give a preview of a possible real production line system. 4. Exploiting plant alkaloids. Schläger, Sabrina; Dräger, Birgit 2016-02-01 Alkaloid-containing plants have been used for medicine since ancient times. Modern pharmaceuticals still rely on alkaloid extraction from plants, some of which grow slowly, are difficult to cultivate and produce low alkaloid yields. Microbial cells as alternative alkaloid production systems are emerging. Before industrial application of genetically engineered bacteria and yeasts, several steps have to be taken. Original alkaloid-forming enzymes have to be elucidated from plants. Their activity in the heterologous host cells, however, may be low. The exchange of individual plant enzymes for alternative catalysts with better performance and optimal fermentation parameters appear promising. The overall aim is enhancement and stabilization of alkaloid yields from microbes in order to replace the tedious extraction of low alkaloid concentrations from intact plants. 5. Cellulose metabolism in plants. Hayashi, Takahisa; Yoshida, Kouki; Park, Yong Woo; Konishi, Teruko; Baba, Kei'ichi 2005-01-01 Many bacterial genomes contain a cellulose synthase operon together with a cellulase gene, indicating that cellulase is required for cellulose biosynthesis. In higher plants, there is evidence that cell growth is enhanced by the overexpression of cellulase and prevented by its suppression. Cellulase overexpression could modify cell walls not only by trimming off the paracrystalline sites of cellulose microfibrils, but also by releasing xyloglucan tethers between the microfibrils. Mutants for membrane-anchored cellulase (Korrigan) also show a typical phenotype of prevention of cellulose biosynthesis in tissues. All plant cellulases belong to family 9, which endohydrolyzes cellulose, but are not strong enough to cause the bulk degradation of cellulose microfibrils in a plant body. It is hypothesized that cellulase participates primarily in repairing or arranging cellulose microfibrils during cellulose biosynthesis in plants. A scheme for the roles of plant cellulose and cellulases is proposed. 6. Terrestrial plant methane production Mikkelsen, Teis Nørgaard; Bruhn, Dan; Møller, Ian M. We evaluate all experimental work published on the phenomenon of aerobic methane (CH4) generation in terrestrial plants. We conclude that the phenomenon is true. Four stimulating factors have been observed to induce aerobic plant CH4 production, i.e. cutting injuries, increasing temperature......, ultraviolet radiation and reactive oxygen species. Further, we analyze rates of measured emission of aerobically produced CH4 in pectin and in plant tissues from different studies and argue that pectin is very far from the sole contributing precursor. Hence, scaling up of aerobic CH4 emission needs to take...... the aerobic methane emission in plants. Future work is needed for establishing the relative contribution of several proven potential CH4 precursors in plant material.... 7. Alvin plant story Haas, H.J.; Jobe, H.J.; Rimel, S.F.; Hart, W.C. 1968-11-11 The Alvin plant, one of the world's largest high- ethane-recovery natural-gas-liquids-extraction plants, was designed to produce over 900,000 gal/day of natural gas liquids (NGL) and extract 50% of the contained ethane while processing 1,034 MMcfd of natural gas. The plant is a major component in a joint venture owned by Phillips Petroleum Co. and HNG Petrochemicals, Inc., a wholly owned subsidiary of Houston Natural Gas Corp. The joint venture also includes a products pipeline, an ethane storage cavern, and an ethylene manufacturing unit. Phillips engineering department designed the plant at the home offices in Bartlesville, Okla., and supervised its construction. Process-design features, mechanical-design features, and construction features are discussed. All products of the Alvin plant are used or marketed by Phillips for the benefit of the joint venture. 8. Living PSA program: LIPSAS development for safety management of an LMFBR plant Aizawa, Kiyoto [Power Reactor and Nuclear Fuel Development Corp., Tokyo (Japan); Nakai, Ryodai [O-arai Engineering Center, Ibaraki (Japan) 1994-12-31 During construction and subsequent operation of a nuclear power plant, many changes occur in components, systems and operating procedures, which continuously modify the configuration of the power plant. A living PSA program can assess and manage safety-related operations and plant changes by adequately reproducing plant models and structured databases corresponding to the changes in system configuration. A living PSA system, LIPSAS, has been developed for the Japanese prototype liquid metal-cooled fast-breeder reactor (LMFBR), Monju, which is in the preoperation functional test stage. In order to utilize the LIPSAS as a risk management tool, equations for the schematic time history of the plant risk level and the relative risk criteria have been developed. Experience with LIPSAS shows that this program is a prospective tool to support decisions that affect plant safety, although a continuing and significant resource commitment of the operations staff at the site is still required. (author). 9. Shaping plant architecture Thomas eTeichmann 2015-04-01 Full Text Available Plants exhibit phenotypical plasticity. Their general body plan is genetically determined, but plant architecture and branching patterns are variable and can be adjusted to the prevailing environmental conditions. The modular design of the plant facilitates such morphological adaptations. The prerequisite for the formation of a branch is the initiation of an axillary meristem. Here, we review the current knowledge about this process. After its establishment, the meristem can develop into a bud which can either become dormant or grow out and form a branch. Many endogenous factors, such as photoassimilate availability, and exogenous factors like nutrient availability or shading, have to be integrated in the decision whether a branch is formed. The underlying regulatory network is complex and involves phytohormones and transcription factors. The hormone auxin is derived from the shoot apex and inhibits bud outgrowth indirectly in a process termed apical dominance. Strigolactones appear to modulate apical dominance by modification of auxin fluxes. Furthermore, the transcription factor BRANCHED1 plays a central role. The exact interplay of all these factors still remains obscure and there are alternative models. We discuss recent findings in the field along with the major models.Plant architecture is economically significant because it affects important traits of crop and ornamental plants, as well as trees cultivated in forestry or on short rotation coppices. As a consequence, plant architecture has been modified during plant domestication. Research revealed that only few key genes have been the target of selection during plant domestication and in breeding programs. Here, we discuss such findings on the basis of various examples. Architectural ideotypes that provide advantages for crop plant management and yield are described. We also outline the potential of breeding and biotechnological approaches to further modify and improve plant architecture 10. Plant Sex Determination. Pannell, John R 2017-03-06 Sex determination is as important for the fitness of plants as it is for animals, but its mechanisms appear to vary much more among plants than among animals, and the expression of gender in plants differs in important respects from that in most animals. In this Minireview, I provide an overview of the broad variety of ways in which plants determine sex. I suggest that several important peculiarities of plant sex determination can be understood by recognising that: plants show an alternation of generations between sporophytic and gametophytic phases (either of which may take control of sex determination); plants are modular in structure and lack a germ line (allowing for a quantitative expression of gender that is not common in animals); and separate sexes in plants have ultimately evolved from hermaphroditic ancestors. Most theorising about sex determination in plants has focused on dioecious species, but we have much to learn from monecious or hermaphroditic species, where sex is determined at the level of modules, tissues or cells. Because of the fundamental modularity of plant development and potentially important evolutionary links between monoecy and dioecy, it may be useful to relax the distinction often made between 'developmental sex determination' (which underpins the development of male versus female flowers in monoecious species) and 'genetic sex determination' (which underpins the separation of males and females in dioecious species, often mediated by a genetic polymorphism and sex chromosomes). I also argue for relaxing the distinction between sex determination involving a genetic polymorphism and that involving responses to environmental or hormonal cues, because non-genetic cues might easily be converted into genetic switches. 11. Mycoplasma infections of plants. Bove, J M 1981-07-01 Plants can be infected by two types of wall-less procaryotes, spiroplasmas and mycoplasma-like organisms (MLO), both located intracellularly in the phloem tissues of affected plants. Spiroplasmas have been cultured, characterized and shown to be true members of the class Mollicutes. MLO have not yet been cultured or characterized; they are thought to be mycoplasma-like on the basis of their ultrastructure as seen in situ, their sensitivity to tetracycline and resistance to penicillin. Mycoplasmas can also be found on the surface of plants. These extracellularly located organisms are members of the following genera: Spiroplasma. Mycoplasma and Acholeplasma. The presence of such surface mycoplasmas must not be overlooked when attempts to culture MLO from affected plants are undertaken. Sensitive serological techniques such as the enzyme-linked immunosorbent assay (ELISA) can successfully be used to compare the MLO located in the phloem of affected plants with those eventually cultured from the same plants. In California and Morocco periwinkles naturally infected with both Spiroplasma citri and MLO have been reported. With such doubly infected plants, the symptom expression has been that characteristic of the MLO disease (phyllody or stolbur), not that given by S. citri. Only S. citri can be cultured from such plants, but this does not indicate that S. citri is the causal agent of the disease expressed by the plant. In California many nonrutaceous plants have been found to be infected with S. citri. Stubborn affected citrus trees represent an important reservoir of S. citri, and Circulifer tenellus is an active leafhopper vector of S. citri. Hence, it is not surprising that in California MLO-infected fruit trees could also become infected with S. citri but it would not mean that S. citri is the causal agent of the disease. Criteria are discussed that are helpful in distinguishing between MLO infections and S. citri infections. 12. Plant nuclear envelope proteins. Rose, Annkatrin; Patel, Shalaka; Meier, Iris 2004-01-01 Compared to research in the animal field, the plant NE has been clearly under-investigated. The available data so far indicate similarities as well as striking differences that raise interesting questions about the function and evolution of the NE in different kingdoms. Despite a seemingly similar structure and organization of the NE, many of the proteins that are integral components of the animal NE appear to lack homologues in plant cells. The sequencing of the Arabidopsis genome has not led to the identification of homologues of animal NE components, but has indicated that the plant NE must have a distinct protein composition different from that found in metazoan cells. Besides providing a selective barrier between the nucleoplasm and the cytoplasm, the plant NE functions as a scaffold for chromatin but the scaffolding components are not identical to those found in animal cells. The NE comprises an MTOC in higher plant cells, a striking difference to the organization of microtubule nucleation in other eukaryotic cells. Nuclear pores are present in the plant NE, but identifiable orthologues of most animal and yeast nucleoporins are presently lacking. The transport pathway through the nuclear pores via the action of karyopherins and the Ran cycle is conserved in plant cells. Interestingly, RanGAP is sequestered to the NE in plant cells and animal cells, yet the targeting domains and mechanisms of attachment are different between the two kingdoms. At present, only a few proteins localized at the plant NE have been identified molecularly. Future research will have to expand the list of known protein components involved in building a functional plant NE. 13. Apathy and Prospective Memory in Aging Fabienne Esposito 2012-11-01 Full Text Available Background: Apathy is common in aging, but the processes underlying its different components are still unclear. The aim of this study was to examine the relationships between apathy and prospective memory (PM, a process involved in the execution of delayed intentions. Methods: Fifty elderly participants completed a PM task and a working memory task. Close relatives of the participants were given the Apathy Inventory, which assesses three dimensions of apathy (lack of initiative, lack of interest, emotional blunting, and a negative mood scale. Results: Correlation analyses showed strong relationships between PM and lack of initiative and interest. These relations remain significant even after controlling for global cognitive functioning, working memory, processing speed and negative mood. Conclusion: This study sheds new light on the cognitive mechanisms associated with apathy in aging and opens up interesting prospects for psychological intervention. 14. M-Commerce In Indonesia: Problems & Prospects Suyoto Indonesia 2012-08-01 Full Text Available This paper presents a preliminary observation of the latest m-Commerce problems and prospects in Indonesia. Every year the Indonesian mobile market has grown, from 175.1 million subscribers in 2009 to 222.7 million in 2010 and then to more than 240 million subscribers by 2011. However, the fact is that the m-Commerce adoption in Indonesia has still been low and slow. Mobile commerce or commonly abbreviated as m-Commerce is still considered as something new in Indonesia. The purposes of this paper are to describe the m-Commerce development trends in Indonesia, to identify problems faced by Indonesia, to identify its prospects in Indonesia, and to propose alternative solutions to the problems that have been identified. This paper attempts to help business managers to understand the problems of m-Commerce and to be capitalize on the advantages of m-Commerce. 15. Detection prospects of singlet fermionic dark matter Esch, Sonja; Yaguna, Carlos E 2013-01-01 A singlet fermion which interacts only with a new singlet scalar provides a viable and minimal scenario that can explain the dark matter. The singlet fermion is the dark matter particle whereas the new scalar mixes with the Higgs boson providing a link between the dark matter sector and the Standard Model. In this paper, we present an updated analysis of this model focused on its detection prospects. Both, the parity-conserving case and the most general case are considered. First, the full parameter space of the model is analyzed, and the regions compatible with the dark matter constraint are obtained and characterized. Then, the implications of current and future direct detection experiments are taken into account. Specifically, we determine the regions of the multidimensional parameter space that are currently excluded and those that are going to be probed by next generation experiments. Finally, indirect detection prospects are discussed and the expected signal at neutrino telescopes is calculated. 16. Detection prospects of singlet fermionic dark matter Esch, Sonja; Klasen, Michael; Yaguna, Carlos E. 2013-10-01 A singlet fermion which interacts only with a new singlet scalar provides a viable and minimal scenario that can explain the dark matter. The singlet fermion is the dark matter particle whereas the new scalar mixes with the Higgs boson providing a link between the dark matter sector and the standard model. In this paper, we present an updated analysis of this model focused on its detection prospects. Both the parity-conserving case and the most general case are considered. First, the full parameter space of the model is analyzed, and the regions compatible with the dark matter constraint are obtained and characterized. Then, the implications of current and future direct detection experiments are taken into account. Specifically, we determine the regions of the multidimensional parameter space that are currently excluded and those that are going to be probed by next generation experiments. Finally, indirect detection prospects are discussed and the expected signal at neutrino telescopes is calculated. 17. Renewable Energy: Markets and Prospects by Technology NONE 2011-07-01 This information paper accompanies the IEA publication Deploying Renewables 2011: Best and Future Policy Practice (IEA, 2011a). It provides more detailed data and analysis, and explores the markets, policies and prospects for a number of renewable energy technologies. This paper provides a discussion of ten technology areas: bioenergy for electricity and heat, biofuels, geothermal energy, hydro energy, ocean energy, solar energy (solar photovoltaics, concentrating solar power, and solar heating), and wind energy (onshore and offshore). Each technology discussion includes: the current technical and market status; the current costs of energy production and cost trends; the policy environment; the potential and projections for the future; and an analysis of the prospects and key hurdles to future expansion. 18. Future prospects for secondary-beam production Schmidt, K H; Enqvist, T; Junghans, A R; Rejmund, F; Ricciardi, M V 2002-01-01 This contribution discusses the characteristics of different types of nuclear reactions and the influence of the beam energy in view of future prospects for secondary-beam production. First, electronic interactions in the target are considered because they define the usable target thickness. Rather high beam energies are advantageous. Secondly, the nuclear-reaction aspects are discussed. Three reaction mechanisms provide the most promising prospects for the production of secondary beams. Fusion is best suited for the production of nuclei near the proton drip line and for the heaviest elements. Fission specifically populates mid-mass neutron-rich isotopes. Fragmentation and spallation reactions represent rather universal production mechanisms for both neutron-deficient and neutron-rich exotic nuclei, since the fluctuations in the N-over-Z ratio are very important. Due to these large fluctuations, this is the most promising reaction mechanism to reach extremely exotic nuclei over the whole mass range, if suffic... 19. Prospect of MH-Ni Batteries Development Xu Shaoping; Xing Zhiqiang; Liang Wanlong; Ma Yijun 2004-01-01 The development trend and promising application prospects of high-power MH-Ni battery were reviewed by studying and comparing the current high-power batteries research area.High-power MH-Ni batiery has good performlife with 500 ～ 1000 times, abundant material resource, especially abundant rare earth resource in China, high-rate discharging, rapid charging, good safety as well as no pollution, etc., which is regarded as the most promising storage battery for electric vehicles.The performance of high power MH-Ni battery can be brought into play fully and ensure electric vehicles performance if it is equipped with appropriate chargers, controlling system and electric motors.Facing opportunities and challenges, MH-Ni battery has promising application prospects on hybrid electric automobile, electric bicycle and a variety of small sized electric vehicles by improving its technology constantly and developing market actively. 20. Global Activities and Plant Survival Bandick, Roger 2014-01-01 This chapter provides an extensive review of the empirical evidence found for Sweden concerning plant survival. The result reveals that foreign MNE plants and exporting non-MNE plants have the lowest exit rates, followed by purely domestic-oriented plants, and that domestic MNE plants have...... the highest exit rates. Moreover, the exit rates of globally engaged plants seem to be unaffected by increased foreign presence, whereas there appears to be a negative impact on the survival rates of non-exporting non-MNE plants. Finally, the result reveals that the survival ratio of plants of acquired...... exporters, but not other types of plants, improves post acquisition.... 1. Prospects of Organic Farming in Bhutan: A SWOT Analysis Sonam Tashi 2016-01-01 Full Text Available A study was conducted to investigate the prospects of organic agriculture (OA in Bhutan from the experts’ perspective, particularly the SWOT (strength, weakness, opportunity, and threat aspect. Thirty-five Bhutanese experts were interviewed. The strengths of OA were (i good alignment of the principles of OA with Bhutan’s development philosophy, (ii strong policy and political support, (iii pristine environment, (iv OA practices similar to traditional farming, and (v compatibility of OA with the local farming knowledge. The major weaknesses were (i a lack of awareness of the benefits of OA, (ii lack of incentives, (iii shortage of farm labor, (iv small and irregular supply of organic product, (v lack of clarity in policy, (vi limited plant protection materials, and (vii a lack of coordination between agencies. Opportunities were (i a huge regional and global organic market, (ii promoting healthy lifestyle, (iii sustainable use of resources, (iv lowering dependence on food and input imports, (v development of local organic manure suppliers, (vi creating seed sovereignty, (vii conserving local crops, (viii building soil fertility, (ix introducing premium price for organic products, and (x addressing unemployment. Threats included (i increasing incidences of pests and diseases, (ii decline in sources of organic manure, and (iii limited sources of organic manures and fertilizers. 2. PROSPECTIVE EVALUATION FOR THE SUGAR CANE FACTORY TRANSFORMATION IN BIOREFINERY Rocío Rodríguez Plaza 2015-10-01 Full Text Available The present work has as goal to evaluate prospectively alternative of transformation in the "5 de Septiembre" sugar industry, located in Cienfuegos, for a superfine alcohol biorefinery. Two alternatives were taking into account; the first one was the installation of a distillery for a capacity of 500 hl/d of superfine alcohol, using the molasses and 10% of the filters juice coming from the sugar mill, as complement of the stage of fermentation, and also a plant of biodiesel production starting from microalgae biomass and of mud separated in the sugar mill and another installation of a distillery for a similar capacity of 500 Hl/d of superfine ethanol using molasses, the filters juices and microalgae hydrolysate. For the second alternative, it intends a distillery where saving of 67 % for the molasses, and 22.73 % for the water, these results are experimentally obtained. The most feasible alternative obtain 5 years of payback period, 21 % of an IRR and UD 37104 419.21 of NPV. 3. Yeast Acid Phosphatases and Phytases: Production, Characterization and Commercial Prospects Kaur, Parvinder; Satyanarayana, T. The element phosphorus is critical to all life forms as it forms the basic component of nucleic acids and ATP and has a number of indispensable biochemical roles. Unlike C or N, the biogeochemical cycling of phosphorus is very slow, and thus making it the growth-limiting element in most soils and aquatic systems. Phosphohydrolases (e.g. acid phosphatases and phytases) are enzymes that break the C-O-P ester bonds and provide available inorganic phosphorus from various inassimilable organic forms of phosphorus like phytates. These enzymes are of significant value in effectively combating phosphorus pollution. Although phytases and acid phosphatases are produced by various plants, animals and micro organisms, microbial sources are more promising for the production on a commercial scale. Yeasts being the simplest eukaryotes are ideal candidates for phytase and phos-phatase research due to their mostly non-pathogenic and GRAS status. They have not, however, been utilized to their full potential. This chapter focuses attention on the present state of knowledge on the production, characterization and potential commercial prospects of yeast phytases and acid phosphatases. 4. Major Achievements and Prospect of the ATLAS Integral Effect Tests Ki-Yong Choi 2012-01-01 Full Text Available A large-scale thermal-hydraulic integral effect test facility, ATLAS (Advanced Thermal-hydraulic Test Loop for Accident Simulation, has been operated by KAERI. The reference plant of ATLAS is the APR1400 (Advanced Power Reactor, 1400 MWe. Since 2007, an extensive series of experimental works were successfully carried out, including large break loss of coolant accident tests, small break loss of coolant accident tests at various break locations, steam generator tube rupture tests, feed line break tests, and steam line break tests. These tests contributed toward an understanding of the unique thermal-hydraulic behavior, resolving the safety-related concerns and providing validation data for evaluation of the safety analysis codes and methodology for the advanced pressurized water reactor, APR1400. Major discoveries and lessons found in the past integral effect tests are summarized in this paper. As the demand for integral effect tests is on the rise due to the active national nuclear R&D program in Korea, the future prospects of the application of the ATLAS facility are also discussed. 5. Status and prospects of maize research in Nepal Govind KC 2015-12-01 Full Text Available Food and nutritional securities are the major threats coupled with declining factor productivity and climate change effects in Nepal. Maize being the principal food crops of the majority of the hill people and source of animal feed for ever growing livestock industries in Terai of Nepal. Despite the many efforts made to increase the maize productivity in the country, the results are not much encouraging. Many of the maize based technologies developed and recommended for the farmers to date are not fully adopted. Therefore, problem is either on technology development or on dissemination or on both. Considering the above facts, some of the innovative and modern approaches of plant breeding and crop management technologies to increase the maize yield need to be developed and disseminated. There is a need for location-specific maize production technologies, especially for lowland winter maize, marginal upland maize production system, and resource poor farmers. Research efforts can be targeted to address both yield potential and on-farm yields by reducing the impacts of abiotic and biotic constraints. Therefore, in order to streamline the future direction of maize research in Nepal, an attempt has been made in this article to highlight the present status and future prospects with few key pathways. 6. World food trends and prospects to 2025 Dyson, Tim 1999-01-01 This paper reviews food (especially cereal) production trends and prospects for the world and its main regions. Despite fears to the contrary, in recent years we have seen continued progress toward better methods of feeding humanity. Sub-Saharan Africa is the sole major exception. Looking to the future, this paper argues that the continuation of recent cereal yield trends should be sufficient to cope with most of the demographically driven expansion of cereal demand th... 7. A Review and Prospect on Herbicide Adjuvants 2005-01-01 The history, present status and future prospects of adjuvants application in herbicides were briefly reviewed. Adjuvants can be separated into two groups, activator adjuvants and utility adjuvants. The former directly enhances the efficacy of a herbicide through increasement of herbicide absorption, spreading, cuticular penetration, rainfastness and retention enhancement, and photodegradation of the herbicide can also be decreased. And the latter is utilized for improving application characteristics, behaviors and physical properties of herbicides and reducing or minimizing unwanted side effects on application. 8. Monograph on prospective developments in oceanology Monin, A. S. 1986-01-01 Excerpts from a chapter of a monograph, Oceanology in the Year 2000, which has been prepared for publication at the USSR Academy of Sciences' Institute of Oceanology, is presented. The author of this chapter is A. S. Morin, corresponding member of the USSR Academy of Sciences and director of the oceanology institute. The monograph is said to be the collective work of a group of specialists. Monin views prospective developments of oceanology and oceanology related research and development, technology and expedition research. 9. Prospects for Inflationary B-Mode Detection Kogut, Alan J. 2011-01-01 Measurements of the linear polarization of the cosmic microwave background provide a direct window into the physics of inflation. The experimental challenges are daunting: not only is the predicted signal faint compared to the photon noise limit, but it is hidden behind competing foregrounds from both local and cosmic sources. I will discuss the experimental response to these challenges and the prospects for eventual detection and characterization of the inflationary signal. 10. GEOMAGNETIC PROSPECTING FOR DEPOSITS OF BUILDING MATERIALS Željko Zagorac; Franjo Šumanovac 1990-01-01 Some characteristic examples are given of the magnetic prospecting for the rocks used as building materials. Conclusions are drawn about the applicability of the magnetic method for this purpose. Method proved to be very speedy and inexpensive, it gives important informations on the extension, position and depth of the magnetic rock. The quality of the rock is better determined by other methods (the paper is published in Croatian). 11. Plant PRMTs Broaden the Scope of Arginine Methylation 2012-01-01 Post-translational methylation at arginine residues is one of the most important covalent modifications of proteins,involved in a myriad of essential cellular processes in eukaryotes,such as transcriptional regulation,RNA processing,signal transduction,and DNA repair.Methylation at arginine residues is catalyzed by a family of enzymes called protein arginine methyltransferases (PRMTs).PRMTs have been extensively studied in various taxa and there is a growing tendency to unveil their functional importance in plants.Recent studies in plants revealed that this evolutionarily conserved family of enzymes regulates essential traits including vegetative growth,flowering time,circadian cycle,and response to high medium salinity and ABA.In this review,we highlight recent advances in the field of posttranslational arginine methylation with special emphasis on the roles and future prospects of this modification in plants. 12. The Development of Plant Biotechnology. Torrey, John G. 1985-01-01 Examines major lines of thought leading to what is meant by plant biotechnology, namely, the application of existing techniques of plant organ, tissue, and cell culture, plant molecular biology, and genetic engineering to the improvement of plants and of plant productivity for the benefit of man. (JN) 13. Prospective Teachers’ Views about Critical Pedagogy 2011-08-01 Full Text Available The main aim of the research is to examine prospective teachers’ views about critical pedagogy according to various variables. The participants’ views are compared according to gender, the current university program and grade. The sample of the survey model study consists of 567 randomly chosen teachers. Data is gathered by Principles of Critical Pedagogy Scale. The scale consists of three sub-dimensions: “Education System, Functions of School and Emancipator School”. Descriptive statistics, t-test and ANOVA are used for data analysis. According to the research findings, prospective teachers most agree with Emancipator School, Functions of School and Education System respectively. Prospective teachers agree with the following item the most: “Teachers must question themselves when students criticize” and with the following item the least: “Schools waste individuals and societies”. The participants’ views vary according to gender, the current university program and grade. There is a significant difference between the views ofprospective teachers from Thesis and Non-thesis Master’s Programs. 14. Examining Media Literacy Levels of Prospective Teachers 2012-04-01 Full Text Available As in many other countries, following the 2007-2008 education year when media literacy courses began to be included in the curricula, media literacy has become one of the discussion topics among educators and decision makers in Turkey. Discussion topics related to media literacy have included who is going to give the media literacy courses, what qualifications will be sought out in media literacy education teachers, what will be included in the media literacy curriculum in terms of its content, and at what level the media literacy course will be given. The current study which aims to examine media literacy levels of prospective teachers utilized thesurvey method. The sample of the study included prospective teachers (480 attending Elementary School Education, Social Studies Education and Turkish Language Education departments in the Education Faculty at the Dumlupinar University in the 2008-2009 education year. The results of the study showed that prospective teachers have a low level of reaction to media messages, do not educate people around enough about the effects of media, but make use of different sources of media to gain information, and are cognizant of media literacy. 15. A prospective study of gentamicin ototoxicity Winkel, O; Hansen, M M; Kaaber-Bühler, Søren 2010-01-01 Twenty patients were included in a prospective otoneurological study performed to assess the ototoxicity in gentamicin therapy. Gentamicin was administered intravenously, and the serum level was currently determined. Audiographic and electronystagmographic studies were carried out at the institut......Twenty patients were included in a prospective otoneurological study performed to assess the ototoxicity in gentamicin therapy. Gentamicin was administered intravenously, and the serum level was currently determined. Audiographic and electronystagmographic studies were carried out...... at the institution and discontinuation of the treatment and again a few weeks later. Ten patients exhibited ototoxic actions, predominantly cochlear, 4 of the cases being fully reversible. Two patients developed severe hearing loss, associated in one with bilateral extinction of vestibular function. Low serum levels...... of gentamicin did not rule out the possiblity of ototoxicity. These results urge the continuing of prospective studies and indicate that gentamicin should be used only as a link in the primary treatment of severe infection or in cases in which other, less toxic agents have failed.... 16. Asteroids. Prospective energy and material resources Badescu, Viorel (ed.) [Bucharest Polytechnic Univ. (Romania). Candida Oancea Institute 2013-11-01 Recent research on Prospective Energy and Material Resources on Asteroids. Carefully edited book dedicated to Asteroids prospective energy and material resources. Written by leading experts in the field. The Earth has limited material and energy resources while these resources in space are virtually unlimited. Further development of humanity will require going beyond our planet and exploring of extraterrestrial resources and sources of unlimited power. Thus far, all missions to asteroids have been motivated by scientific exploration. However, given recent advancements in various space technologies, mining asteroids for resources is becoming ever more feasible. A significant portion of asteroids value is derived from their location; the required resources do not need to be lifted at a great expense from the surface of the Earth. Resources derived from Asteroid not only can be brought back to Earth but could also be used to sustain human exploration of space and permanent settlements in space. This book investigates asteroids' prospective energy and material resources. It is a collection of topics related to asteroid exploration, and utilization. It presents past and future technologies and solutions to old problems that could become reality in our life time. The book therefore is a great source of condensed information for specialists involved in current and impending asteroid-related activities and a good starting point for space researchers, inventors, technologists and potential investors. Written for researchers, engineers, and businessmen interested in asteroids' exploration and exploitation. 17. 香樟在徐州地区的引种及前景%Prospect of Growing Camphor Tree in Xuzhou Region 何树川 2009-01-01 Camphor tree has been widely used due to its unique characteritics of large and tall trunk, dense branches and leaves, large and shady canopy,magnificent tree form, long life cycle and evergreen. With global warming,scientific and technological progress and the improvement of plant cultivation techniques, the scope of planting Camphor tree is expanded. In this paper,the conditions and prospect of growing Camphor tree in Xuzhou were illustrated from aspects of biological characteristics,feasibility of growing the trees in Xuzhou, critical techniques of planting and tending.. 18. Prospects for Corn Ethanol in Argentina Bruce A. Babcock; Miguel Carriquiry 2012-01-01 Countries that export biofuel feedstocks such as grain or sugar and that are also importers of motor fuels will have a natural competitive advantage over other countries in the production of biofuels. Argentina is one of a very few countries that both export potential feedstocks and import gasoline and diesel. This combination means that an Argentine ethanol plant will pay less for feedstock and receive a higher price for ethanol than an ethanol plant located in a country that imports feedsto... 19. Prospecting sugarcane genes involved in aluminum tolerance. Drummond Rodrigo D.; Guimarães Claudia T.; Felix Juliana; Ninamango-Cárdenas Fernando E.; Carneiro Newton P.; Paiva Edilson; Menossi Marcelo 2006-01-01 Aluminum is one of the major factors that affect plant development in acid soils, causing a substantial reduction in yield in many crops. In South America, about 66% of the land surface is made up of acid soils where high aluminum saturation is one of the main limiting factors for agriculture. The biochemical and molecular basis of aluminum tolerance in plants is far from being completely understood despite a growing number of studies, and in the specific case of sugarcane there are virtually... 20. Prospects for investment in large-scale, grid-connected solar power in Africa Hansen, Ulrich Elmer; Nygaard, Ivan; Pedersen, Mathilde Brix Solar power in Africa is on its way to becoming a market-based commodity, thus escaping the niche for individual electricity supply that is mainly supported by international donor organisations. Significant reductions in the cost of photovoltaic (PV) panels and a 400 percent increase in oil prices......-scale investments in grid-connected solar power plants and local assembly facilities for PV panels, have exceeded even optimistic scenarios. Finally, therefore, there seem to be bright prospects for investment in large-scale grid-connected solar power in Africa....... since the 1990s have changed the competiveness of solar PV in all markets, ranging from individual households via institutions to mini-grids and grid-connected installations. In volume and investment, the market for large-scale grid-connected solar power plants is by far the most important... 1. FBC utilization prospects in decentralized cogeneration units in Caucasus region countries Skodras George 2003-01-01 Full Text Available Great differences are encountered among Caucasus region countries with respect to energy resources reserves and economic conditions. Thermal power plants consist of obsolete and inefficient units, while the Soviet-type large heating systems in the area collapsed after 1992 and their reconstruction is considered uneconomic. Renovation needs of the power and heat sector, and the potential of Fluidised Bed Combustion implementations in decentralized cogeneration units were investigated, since operating oil and gas power plants exhibit high fuel consumption, low efficiency and poor environmental performance. Results showed significant prospects of Fluidised Bed Combustion utilization in decentralized cogeneration units in the Caucausus region heat and power sector. Their introduction constitutes an economically attractive way to cover power and heat demands and promotes utilization of domestic energy resources in all of three countries, provided that financial difficulties could be confronted. 2. Prospects for development of an innovative water-cooled nuclear reactor for supercritical parameters of coolant Kalyakin, S. G.; Kirillov, P. L.; Baranaev, Yu. D.; Glebov, A. P.; Bogoslovskaya, G. P.; Nikitenko, M. P.; Makhin, V. M.; Churkin, A. N. 2014-08-01 The state of nuclear power engineering as of February 1, 2014 and the accomplished elaborations of a supercritical-pressure water-cooled reactor are briefly reviewed, and the prospects of this new project are discussed based on this review. The new project rests on the experience gained from the development and operation of stationary water-cooled reactor plants, including VVERs, PWRs, BWRs, and RBMKs (their combined service life totals more than 15 000 reactor-years), and long-term experience gained around the world with operation of thermal power plants the turbines of which are driven by steam with supercritical and ultrasupercritical parameters. The advantages of such reactor are pointed out together with the scientific-technical problems that need to be solved during further development of such installations. The knowledge gained for the last decade makes it possible to refine the concept and to commence the work on designing an experimental small-capacity reactor. 3. Transparent meta-analysis of prospective memory and aging. Bob Uttl Full Text Available Prospective memory (ProM refers to our ability to become aware of a previously formed plan at the right time and place. After two decades of research on prospective memory and aging, narrative reviews and summaries have arrived at widely different conclusions. One view is that prospective memory shows large age declines, larger than age declines on retrospective memory (RetM. Another view is that prospective memory is an exception to age declines and remains invariant across the adult lifespan. The present meta-analysis of over twenty years of research settles this controversy. It shows that prospective memory declines with aging and that the magnitude of age decline varies by prospective memory subdomain (vigilance, prospective memory proper, habitual prospective memory as well as test setting (laboratory, natural. Moreover, this meta-analysis demonstrates that previous claims of no age declines in prospective memory are artifacts of methodological and conceptual issues afflicting prior research including widespread ceiling effects, low statistical power, age confounds, and failure to distinguish between various subdomains of prospective memory (e.g., vigilance and prospective memory proper. 4. International safeguards for reprocessing plants. Final report Kratzer, M.; Scheinman, L.; Sievering, N.; Wonder, E.; Lipman, D.; Immerman, W.; Elliott, J.M.; Crane, F. 1981-04-01 Proliferation risks inherent in reprocessing show the need to employ technically effective safeguards which can detect, with a high degree of assurance and on a timely basis, the diversion of significant quantities of fissionable material. A balance must be struck between what is technically feasible and effective and what is institutionally acceptable. Purpose of this report is to examine the several technical approaches to safeguards in light of their prospective acceptability. This study defines the economic, political and institutional nature of the safeguards problem; surveys generically alternative technical approaches to international safeguards including their effectiveness and relative development; characterizes the institutional implications and uncertainties associated with the acceptance and implementation of each technical alternative; and integrates these assessments into a set of overall judgments on feasible directions for reprocessing plant safeguards systems. 5. Magnetometry and archaeological prospection in Mexico Barba Pingarron, L.; Laboratorio de Prospeccion Arqueologica 2013-05-01 Luis Barba Laboratorio de Prospección Arqueológica Instituto de Investigaciones Antropológicas Universidad Nacional Autonoma de México The first magnetic survey in archaeological prospection was published in 1958 in the first number of Archaeometry, in Oxford. That article marked the beginning of this applications to archaeology. After that, magnetic field measurements have become one of the most important and popular prospection tools. Its most outstanding characteristic is the speed of survey that allows to cover large areas in short time. As a consequence, it is usually the first approach to study a buried archaeological site. The first attempts in Mexico were carried out in 196. Castillo and Urrutia, among other geophysical techniques, used a magnetometer to study the northern part of the main plaza, zocalo, in Mexico City to locate some stone Aztec sculptures. About the same time Morrison et al. in La Venta pyramid used a magnetometer to measure total magnetic field trying to find a substructure. Some years later Brainer and Coe made a magnetic survey to locate large stone Olmec heads in San Lorenzo Tenochtitlan, Veracruz. Technology development has provided everyday more portable and accurate instruments to measure the magnetic field. The first total magnetic field proton magnetometers were followed by differential magnetometers and more recently gradiometers. Presently, multiple sensor magnetometers are widely used in European archaeology. The trend has been to remove the environmental and modern interference and to make more sensitive the instruments to the superficial anomalies related to most of the archaeological sites. There is a close relationship between the geology of the region and the way magnetometry works in archaeological sites. Archaeological prospection in Europe usually needs very sensitive instruments to detect slight magnetic contrast of ditches in old sediments. In contrast, volcanic conditions in Mexico produce large magnetic contrast 6. Plant-soil feedbacks: role of plant functional group and plant traits Cortois, R.; Schröder-Georgi, T.; Weigelt, A.; van der Putten, W.H.; De Deyn, G.B. 2016-01-01 Plant-soil feedback (PSF), plant trait and functional group concepts advanced our understanding of plant community dynamics, but how they are interlinked is poorly known. To test how plant functional groups (FGs: graminoids, small herbs, tall herbs, legumes) and plant traits relate to PSF, we grew 4 7. TOR signalling in plants. Rexin, Daniel; Meyer, Christian; Robaglia, Christophe; Veit, Bruce 2015-08-15 Although the eukaryotic TOR (target of rapamycin) kinase signalling pathway has emerged as a key player for integrating nutrient-, energy- and stress-related cues with growth and metabolic outputs, relatively little is known of how this ancient regulatory mechanism has been adapted in higher plants. Drawing comparisons with the substantial knowledge base around TOR kinase signalling in fungal and animal systems, functional aspects of this pathway in plants are reviewed. Both conserved and divergent elements are discussed in relation to unique aspects associated with an autotrophic mode of nutrition and adaptive strategies for multicellular development exhibited by plants. Kim, Jae Sung; Song, Hi Sup; Lee, Young Keun; Lee, Byung Hun; Shin, In Chul; Lim, Young Taek 2000-04-01 This research was performed to investigate the effects of low dose {gamma}-ray radiation on the seed germination and the following physiological responses in vegetable crops. Special attention was focused on whether the resistance of vegetables against the unfavorable conditions of environment such as subsequent high doses of radiation or Phytophthora blight of pepper could be enhanced as an aspect of radiation hormesis. Analysis and characterization of antioxidant enzyme from plant culture cells and radiation tolerant of transformed plants from antioxidant (POD) were accomplished in the plant irradiated with different dose of {gamma}-ray. (author) 9. FRIB Cryogenic Plant Status Dixon, Kelly D. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Ganni, Venkatarao [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Knudsen, Peter N. [Thomas Jefferson National Accelerator Facility (TJNAF), Newport News, VA (United States); Casagranda, Fabio [Michigan State Univ., East Lansing, MI (United States) 2015-12-01 After practical changes were approved to the initial conceptual design of the cryogenic system for MSU FRIB and an agreement was made with JLab in 2012 to lead the design effort of the cryogenic plant, many activities are in place leading toward a cool-down of the linacs prior to 2018. This is mostly due to using similar equipment used at CHLII for the 12 GeV upgrade at JLab and an aggressive schedule maintained by the MSU Conventional Facilities department. Reported here is an updated status of the cryogenic plant, including the equipment procurement status, plant layout, facility equipment and project schedule. Kim, Jae Sung; Song, Hi Sup; Lee, Young Keun; Cun, Ki Jung; Shin, In Chul; Lim, Young Taek 1999-04-01 This research was performed to investigate the effects of low dose {gamma}-ray radiation on the seed germination and the following physiological responses in vegetable crops. Special attention was focused on whether the resistance of vegetables against the unfavorable conditions of environment such as acid rain or soil types could be enhanced as an aspect of radiation hormesis. Analysis and characterization of antioxidant enzyme from plant culture cells and radiation tolerant of transformed plants from antioxidant enzyme (POD) were accomplished in the plant irradiated with difference dosage of {gamma}-ray. 11. Optofluidics of plants Psaltis, Demetri; Vasdekis, Andreas E.; Choi, Jae-Woo 2016-05-01 Optofluidics is a tool for synthesizing optical systems, making use of the interaction of light with fluids. In this paper we explore optofluidic mechanisms that have evolved in plants where sunlight and fluidic control combine to define most of the functionality of the plan. We hope that the presentation of how plants function, from an optofluidics point of view, will open a window for the optics community to the vast literature of plant physiology and provide inspiration for new ideas for the design of bio-mimetic optofluidic devices. 12. Plant Genome Duplication Database. Lee, Tae-Ho; Kim, Junah; Robertson, Jon S; Paterson, Andrew H 2017-01-01 Genome duplication, widespread in flowering plants, is a driving force in evolution. Genome alignments between/within genomes facilitate identification of homologous regions and individual genes to investigate evolutionary consequences of genome duplication. PGDD (the Plant Genome Duplication Database), a public web service database, provides intra- or interplant genome alignment information. At present, PGDD contains information for 47 plants whose genome sequences have been released. Here, we describe methods for identification and estimation of dates of genome duplication and speciation by functions of PGDD.The database is freely available at http://chibba.agtec.uga.edu/duplication/. 13. BOILER MATERIALS FOR ULTRASUPERCRITICAL COAL POWER PLANTS R. Viswanathan; K. Coleman 2002-10-15 The principal objective of this project is to develop materials technology for use in ultrasupercritical (USC) plant boilers capable of operating with 760 C (1400 F), 35 MPa (5000 psi) steam. In the 21st century, the world faces the critical challenge of providing abundant, cheap electricity to meet the needs of a growing global population while at the same time preserving environmental values. Most studies of this issue conclude that a robust portfolio of generation technologies and fuels should be developed to assure that the United States will have adequate electricity supplies in a variety of possible future scenarios. The use of coal for electricity generation poses a unique set of challenges. On the one hand, coal is plentiful and available at low cost in much of the world, notably in the U.S., China, and India. Countries with large coal reserves will want to develop them to foster economic growth and energy security. On the other hand, traditional methods of coal combustion emit pollutants and CO{sub 2} at high levels relative to other generation options. Maintaining coal as a generation option in the 21st century will require methods for addressing these environmental issues. This project has established a government/industry consortium to undertake a five-year effort to evaluate and develop of advanced materials that allow the use of advanced steam cycles in coal-based power plants. These advanced cycles, with steam temperatures up to 760 C, will increase the efficiency of coal-fired boilers from an average of 35% efficiency (current domestic fleet) to 47% (HHV). This efficiency increase will enable coal-fired power plants to generate electricity at competitive rates (irrespective of fuel costs) while reducing CO{sub 2} and other fuel-related emissions by as much as 29%. Success in achieving these objectives will support a number of broader goals. First, from a national prospective, the program will identify advanced materials that will make it possible to 14. BOILER MATERIALS FOR ULTRASUPERCRITICAL COAL POWER PLANTS R. Viswanathan; K. Coleman 2003-01-20 The principal objective of this project is to develop materials technology for use in ultrasupercritical (USC) plant boilers capable of operating with 760 C (1400 F), 35 MPa (5000 psi) steam. In the 21st century, the world faces the critical challenge of providing abundant, cheap electricity to meet the needs of a growing global population while at the same time preserving environmental values. Most studies of this issue conclude that a robust portfolio of generation technologies and fuels should be developed to assure that the United States will have adequate electricity supplies in a variety of possible future scenarios. The use of coal for electricity generation poses a unique set of challenges. On the one hand, coal is plentiful and available at low cost in much of the world, notably in the U.S., China, and India. Countries with large coal reserves will want to develop them to foster economic growth and energy security. On the other hand, traditional methods of coal combustion emit pollutants and CO{sub 2} at high levels relative to other generation options. Maintaining coal as a generation option in the 21st century will require methods for addressing these environmental issues. This project has established a government/industry consortium to undertake a five-year effort to evaluate and develop of advanced materials that allow the use of advanced steam cycles in coal-based power plants. These advanced cycles, with steam temperatures up to 760 C, will increase the efficiency of coal-fired boilers from an average of 35% efficiency (current domestic fleet) to 47% (HHV). This efficiency increase will enable coal-fired power plants to generate electricity at competitive rates (irrespective of fuel costs) while reducing CO{sub 2} and other fuel-related emissions by as much as 29%. Success in achieving these objectives will support a number of broader goals. First, from a national prospective, the program will identify advanced materials that will make it possible to 15. Wetland plants: biology and ecology Cronk, Julie K; Fennessy, M. Siobhan 2001-01-01 Providing a detailed account of the biology and ecology of wetland plants as well as applications of wetland plant science, this book presents a synthesis of studies and reviews from biology, plant... 16. Programmed Cell Death in Relation to Petal Senescence in Ornamental Plants Yuan ZHOU; Cai-Yun WANG; Hong GE; Frank A. HOEBERICHTS; Peter B. VISSER 2005-01-01 Cell death is a common event in all types of plant organisms. Understanding the phenomenon of programmed cell death (PCD) is an important area of research for plant scientists because of its role in senescence and the post-harvest quality of ornamentals, fruits, and vegetables. In the present paper, PCD in relation to petal senescence in ornamental plants is reviewed. Morphological, anatomical, physiological,and biochemical changes that are related to PCD in petals, such as water content, sink-source relationships,hormones, genes, and signal transduction pathways, are discussed. Several approaches to improving the quality of post-harvest ornamentals are reviewed and some prospects for future research are given. 17. Targeted Gene Manipulation in Plants Using the CRISPR/Cas Technology. Zhang, Dandan; Li, Zhenxiang; Li, Jian-Feng 2016-05-20 The CRISPR/Cas technology is emerging as a revolutionary genome editing tool in diverse organisms including plants, and has quickly evolved into a suite of versatile tools for sequence-specific gene manipulations beyond genome editing. Here, we review the most recent applications of the CRISPR/Cas toolkit in plants and also discuss key factors for improving CRISPR/Cas performance and strategies for reducing the off-target effects. Novel technical breakthroughs in mammalian research regarding the CRISPR/Cas toolkit will also be incorporated into this review in hope to stimulate prospective users from the plant research community to fully explore the potential of these technologies. 18. Antimicrobial peptide production and plant-based expression systems for medical and agricultural biotechnology. Holaskova, Edita; Galuszka, Petr; Frebort, Ivo; Oz, M Tufan 2015-11-01 Antimicrobial peptides (AMPs) are vital components of the innate immune system of nearly all living organisms. They generally act in the first line of defense against various pathogenic bacteria, parasites, enveloped viruses and fungi. These low molecular mass peptides are considered prospective therapeutic agents due to their broad-spectrum rapid activity, low cytotoxicity to mammalian cells and unique mode of action which hinders emergence of pathogen resistance. In addition to medical use, AMPs can also be employed for development of innovative approaches for plant protection in agriculture. Conferred disease resistance by AMPs might help us surmount losses in yield, quality and safety of agricultural products due to plant pathogens. Heterologous expression in plant-based systems, also called plant molecular farming, offers cost-effective large-scale production which is regarded as one of the most important factors for clinical or agricultural use of AMPs. This review presents various types of AMPs as well as plant-based platforms ranging from cell suspensions to whole plants employed for peptide production. Although AMP production in plants holds great promises for medicine and agriculture, specific technical limitations regarding product yield, function and stability still remain. Additionally, establishment of particular stable expression systems employing plants or plant tissues generally requires extended time scale for platform development compared to certain other heterologous systems. Therefore, fast and promising tools for evaluation of plant-based expression strategies and assessment of function and stability of the heterologously produced AMPs are critical for molecular farming and plant protection. 19. [Progress in research and application of gene engineering on medicinal plants]. Wang, Min; Huang, Lu-qi; Li, Meng-meng 2008-06-01 China is the country possessing the largest amount of trade and consumption of medicinal plants in the world. Research and application of gene engineering on medicinal plants are the one of the most promising ways to increase the productivity and quality of medicinal plants, reduce the resource stress, and enhance the competitive power and sustainable development ability of the medicinal plants industry. In spite of the great progress in research and application of plant gene engineering worldwide, the research of gene transformation has mostly been conducted on some model plants, and the application of transgenic plant has been limited to a few staple and important crop species. For medicinal plants, recently the researches of gene transformation has emerged, however, compared with other crop and economic plants, it is still a very limited amount. On the basis of a general introduction of application of transgenic plants, this paper focuses on the present situation of the research and application of gene engineering on medicinal plants, to put forward the problems in this field, and give a prospect for its development. 20. Belowground microbes mitigate plant-plant competition. Fonseca, Márcia Bacelar; Dias, Teresa; Carolino, Maria Manuela; França, Marcel Giovanni Costa; Cruz, Cristina 2017-09-01 Dimorphandra wilsonii, a Cerrado endemic Fabaceae tree, is threatened by land-use changes. The few remaining individuals occur in areas dominated by alien grasses like Urochloa decumbens. We tested the impact of nitrogen (N) availability and symbionts' presence on mitigating the effects of competition from U. decumbens. Dimorphandra wilsonii seedlings were 50-week pot-cultivated under limiting (3mM) or non-limiting (10mM) N, with or without U. decumbens, and inoculated or not with a N-fixer (Bradyrhizobium sp.) and an arbuscular mycorrhizal fungus (AMF - Glomus etunicatum), both forming symbioses in the field. Since D. wilsonii seedlings grew more and 'lost' fewer nutrients under the symbionts' presence, symbionts mitigated plant-plant competition. Under limiting N, inoculated D. wilsonii seedlings grew more (despite no nodulation), but N fixation was only suggested when inoculated D. wilsonii seedlings competed with U. decumbens. D. wilsonii(13)C, and substrate's carbon and respiration suggest that only the microbes performing key functions received plant carbon. Under non-limiting N, inoculated D. wilsonii seedlings became enriched in (13)C, substrate accumulated carbon and microbial respiration increased, suggesting a more generalist microbial community. Data suggest inoculating D. wilsonii seeds/seedlings with AMF and N-fixers as a conservation measure. However, long-term field-studies need to confirm these conclusions. Copyright © 2017 Elsevier B.V. All rights reserved. 1. Extraction and downstream processing of plant-derived recombinant proteins. Buyel, J F; Twyman, R M; Fischer, R 2015-11-01 Plants offer the tantalizing prospect of low-cost automated manufacturing processes for biopharmaceutical proteins, but several challenges must be addressed before such goals are realized and the most significant hurdles are found during downstream processing (DSP). In contrast to the standardized microbial and mammalian cell platforms embraced by the biopharmaceutical industry, there are many different plant-based expression systems vying for attention, and those with the greatest potential to provide inexpensive biopharmaceuticals are also the ones with the most significant drawbacks in terms of DSP. This is because the most scalable plant systems are based on the expression of intracellular proteins in whole plants. The plant tissue must therefore be disrupted to extract the product, challenging the initial DSP steps with an unusually high load of both particulate and soluble contaminants. DSP platform technologies can accelerate and simplify process development, including centrifugation, filtration, flocculation, and integrated methods that combine solid-liquid separation, purification and concentration, such as aqueous two-phase separation systems. Protein tags can also facilitate these DSP steps, but they are difficult to transfer to a commercial environment and more generic, flexible and scalable strategies to separate target and host cell proteins are preferable, such as membrane technologies and heat/pH precipitation. In this context, clarified plant extracts behave similarly to the feed stream from microbes or mammalian cells and the corresponding purification methods can be applied, as long as they are adapted for plant-specific soluble contaminants such as the superabundant protein RuBisCO. Plant-derived pharmaceutical proteins cannot yet compete directly with established platforms but they are beginning to penetrate niche markets that allow the beneficial properties of plants to be exploited, such as the ability to produce 'biobetters' with tailored 2. Plutonium Finishing Plant Federal Laboratory Consortium — The Plutonium Finishing Plant, also known as PFP, represented the end of the line (the final procedure) associated with plutonium production at Hanford.PFP was also... 3. Plant Stem Cells Greb, Thomas; Lohmann, Jan U 2016-01-01 .... While the promise of organ regeneration and the end of cancer have captured our imagination, it has gone almost unnoticed that plant stem cells represent the ultimate origin of much of the food we... Miller, R.L. 1994-07-01 The stellarator is a class of helical/toroidal magnetic fusion devices. Recent international progress in stellarator power plant conceptual design is reviewed and comparisons in the areas of physics, engineering, and economics are made with recent tokamak design studies. Miller, R.L. 1994-07-01 The stellarator is a class of helical/toroidal magnetic fusion devices. Recent international progress in stellarator power plant conceptual design is reviewed and comparisons in the areas of physics, engineering, and economics are made with recent tokamak design studies. 6. Poison plants (image) ... by poor circulation, even stress. An example of contact dermatitis is the reaction of a sensitive person's skin to poison ivy, oak or sumac. Contact with these plants, which contain a chemical called ... 7. Plant Vascular Biology 2010 Ding, Biao 2014-11-17 This grant supported the Second International Conference on Plant Vascular Biology (PVB 2010) held July 24-28, 2010 on the campus of Ohio State University, Columbus, Ohio. Biao Ding (Ohio State University; OSU) and David Hannapel (Iowa State University; ISU) served as co-chairs of this conference. Biao Ding served as the local organizer. PVB is defined broadly here to include studies on the biogenesis, structure and function of transport systems in plants, under conditions of normal plant growth and development as well as of plant interactions with pathogens. The transport systems cover broadly the xylem, phloem, plasmodesmata and vascular cell membranes. The PVB concept has emerged in recent years to emphasize the integrative nature of the transport systems and approaches to investigate them. 8. Plant stem cell niches. Aichinger, Ernst; Kornet, Noortje; Friedrich, Thomas; Laux, Thomas 2012-01-01 Multicellular organisms possess pluripotent stem cells to form new organs, replenish the daily loss of cells, or regenerate organs after injury. Stem cells are maintained in specific environments, the stem cell niches, that provide signals to block differentiation. In plants, stem cell niches are situated in the shoot, root, and vascular meristems-self-perpetuating units of organ formation. Plants' lifelong activity-which, as in the case of trees, can extend over more than a thousand years-requires that a robust regulatory network keep the balance between pluripotent stem cells and differentiating descendants. In this review, we focus on current models in plant stem cell research elaborated during the past two decades, mainly in the model plant Arabidopsis thaliana. We address the roles of mobile signals on transcriptional modules involved in balancing cell fates. In addition, we discuss shared features of and differences between the distinct stem cell niches of Arabidopsis. 9. Lipid signaling in plants Munnik, T. 2010-01-01 This book highlights the current status of plant lipid signaling. Written by leading researchers in the field, the chapters include detailed information on the measurement, regulation and function of phospholipases, lipid kinases, lipid phosphatases, inositolpolyphosphates, polyphosphoinositides, ph 10. Registration of Plant Varieties Ethiopia, forest soils that are either red or chocolate in color classified as Dystric. Nitisol with loam ... Ethiopia has significant benefit from export of ... Animal and Plant Health Inspection Directorate and are being maintained, multiplied, and ... 11. Plant protein glycosylation Strasser, Richard 2016-01-01 Protein glycosylation is an essential co- and post-translational modification of secretory and membrane proteins in all eukaryotes. The initial steps of N-glycosylation and N-glycan processing are highly conserved between plants, mammals and yeast. In contrast, late N-glycan maturation steps in the Golgi differ significantly in plants giving rise to complex N-glycans with β1,2-linked xylose, core α1,3-linked fucose and Lewis A-type structures. While the essential role of N-glycan modifications on distinct mammalian glycoproteins is already well documented, we have only begun to decipher the biological function of this ubiquitous protein modification in different plant species. In this review, I focus on the biosynthesis and function of different protein N-linked glycans in plants. Special emphasis is given on glycan-mediated quality control processes in the ER and on the biological role of characteristic complex N-glycan structures. PMID:26911286 12. Nonferrous Metal Processing Plants Department of Homeland Security — This map layer includes nonferrous metal processing plants in the United States. The data represent commodities covered by the Minerals Information Team (MIT) of the... 13. Nuclear power plant maintainability. Seminara, J L; Parsons, S O 1982-09-01 In the mid-1970s a general awareness of human factors engineering deficiencies associated with power plant control rooms took shape and the Electric Power Research Institute (EPRI) awarded the Lockheed Corporation a contract to review the human factors aspects of five representative operational control rooms and their associated simulators. This investigation revealed a host of major and minor deficiencies that assumed unforeseen dimensions in the post- Three Mile Island accident period. In the course of examining operational problems (Seminara et al, 1976) and subsequently the methods for overcoming such problems (Seminara et al, 1979, 1980) indications surfaced that power plants were far from ideal in meeting the needs of maintenance personnel. Accordingly, EPRI sponsored an investigation of the human factors aspects of power plant maintainability (Seminara, 1981). This paper provides an overview of the maintainability problems and issues encountered in the course of reviewing five nuclear power plants. 14. Nuclear Power Plants (Rev.) Lyerly, Ray L.; Mitchell III, Walter [Southern Nuclear Engineering, Inc. 1973-01-01 Projected energy requirements for the future suggest that we must employ atomic energy to generate electric power or face depletion of our fossil-fuel resources—coal, oil, and gas. In short, both conservation and economic considerations will require us to use nuclear energy to generate the electricity that supports our civilization. Until we reach the time when nuclear power plants are as common as fossil-fueled or hydroelectric plants, many people will wonder how the nuclear plants work, how much they cost, where they are located, and what kinds of reactors they use. The purpose of this booklet is to answer these questions. In doing so, it will consider only central station plants, which are those that provide electric power for established utility systems. 15. Memristors in plants. Volkov, Alexander G; Tucket, Clayton; Reedus, Jada; Volkova, Maya I; Markin, Vladislav S; Chua, Leon 2014-01-01 We investigated electrical circuitry of the Venus flytrap, Mimosa pudica and Aloe vera. The goal was to discover if these plants might have a new electrical component--a resistor with memory. This element was postulated recently and the researchers were looking for its presence in different systems. The analysis was based on cyclic current-voltage characteristic where the resistor with memory should manifest itself. We found that the electrostimulation of plants by bipolar sinusoidal or triangle periodic waves induces electrical responses in the Venus flytrap, Mimosa pudica and Aloe vera with fingerprints of memristors. Tetraethylammonium chloride, an inhibitor of voltage gated K(+) channels, transforms a memristor to a resistor in plant tissue. Our results demonstrate that a voltage gated K(+) channel in the excitable tissue of plants has properties of a memristor. This study can be a starting point for understanding mechanisms of memory, learning, circadian rhythms, and biological clocks. 16. Ferrous Metal Processing Plants Department of Homeland Security — This map layer includes ferrous metal processing plants in the United States. The data represent commodities covered by the Minerals Information Team (MIT) of the... 17. Plant Mobile Small RNAs Dunoyer, Patrice; Melnyk, Charles; Molnar, Attila; Slotkin, R Keith 2013-01-01 In plants, RNA silencing is a fundamental regulator of gene expression, heterochromatin formation, suppression of transposable elements, and defense against viruses. The sequence specificity of these processes relies on small noncoding RNA (sRNA) molecules. Although the spreading of RNA silencing across the plant has been recognized for nearly two decades, only recently have sRNAs been formally demonstrated as the mobile silencing signals. Here, we discuss the various types of mobile sRNA mol... 18. Wet hydrate dissolution plant Stanković Mirjana S.; Kovačević Branimir T.; Pezo Lato L. 2003-01-01 The IGPC Engineering Department designed basic projects for a wet hydrate dissolution plant, using technology developed in the IGPC laboratories. Several projects were completed: technological, machine, electrical, automation. On the basis of these projects, a production plant with capacity of 50,000 t/y was manufactured, at "Zeolite Mira", Mira (VE), Italy, in 1997, for increasing detergent zeolite production from 50,000 to 100,000 t/y. Several goals were realized by designing a wet hydrate ... 19. Synthetic Plant Defense Elicitors Yasemin eBektas 2015-01-01 Full Text Available To defend themselves against invading pathogens plants utilize a complex regulatory network that coordinates extensive transcriptional and metabolic reprogramming. Although many of the key players of this immunity-associated network are known, the details of its topology and dynamics are still poorly understood. As an alternative to forward and reverse genetic studies, chemical genetics-related approaches based on bioactive small molecules have gained substantial popularity in the analysis of biological pathways and networks. Use of such molecular probes can allow researchers to access biological space that was previously inaccessible to genetic analyses due to gene redundancy or lethality of mutations. Synthetic elicitors are small drug like molecules that induce plant defense responses, but are distinct from known natural elicitors of plant immunity. While the discovery of the some synthetic elicitors had already been reported in the 1970s, recent breakthroughs in combinatorial chemical synthesis now allow for inexpensive high-throughput screens for bioactive plant defense-inducing compounds. Along with powerful reverse genetics tools and resources available for model plants and crop systems, comprehensive collections of new synthetic elicitors will likely allow plant scientists to study the intricacies of plant defense signaling pathways and networks in an unparalleled fashion. As synthetic elicitors can protect crops from diseases, without the need to be directly toxic for pathogenic organisms, they may also serve as promising alternatives to conventional biocidal pesticides, which often are harmful for the environment, farmers and consumers. Here we are discussing various types of synthetic elicitors that have been used for studies on the plant immune system, their modes-of-action as well as their application in crop protection. 20. Plant Transgenerational Epigenetics	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3486354351043701, "perplexity": 7664.351213773771}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257646914.32/warc/CC-MAIN-20180319120712-20180319140712-00512.warc.gz"}
http://aas.org/archives/BAAS/v28n4/aas189/abs/S077009.html	Session 77 - Binary Stars. Display session, Wednesday, January 15 Metropolitan Ballroom, ## [77.09] BD+33 1646, a dMe Triple K. W. Kamper, J. R. Thomson (David Dunlap Obs.), L. Kiss (JATE Univ., Hungary) The fainter component of the visual binary BD+33 1646 (Vys 250) has been found to be a double-lined spectroscopic binary. All three components of the system show strong and variable emission at H\alpha, with the equivalent width of the line increasing with decreasing brightness of the component. For all three stars the H\alpha emission profile shows central absorption. The brighter visual component flared strongly on JD2450210.61 with a tripling of the H\alpha equivalent width. Magnitude differences for the visual pair taken from CCD guider frames show probably real variations of a few tenths of a magnitude on other nights. The orbital elements for the fainter component are: P 6.2096 \pm 0.006 days e 0.043 \pm 0.16 T 2449619.8 \pm 0.4 ømega 79 \pm 20 degrees K1 40.2 \pm 0.5 km/sec K2 62.4 \pm 0.8 km/sec The large mass functions for the components, 0.42 and 0.27 solar masses, with spectral types of roughly M2 and M3, may indicate that eclipses are possible. They have not yet been observed by us.	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8812028765678406, "perplexity": 8554.273376913248}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510275463.39/warc/CC-MAIN-20140728011755-00233-ip-10-146-231-18.ec2.internal.warc.gz"}
https://www.cymath.com/blog/2021-05-31	# Problem of the Week ## Updated at May 31, 2021 5:46 PM For this week we've brought you this equation problem. How would you solve the equation $$\frac{{(4(z+2))}^{2}}{6}=96$$? Here are the steps: $\frac{{(4(z+2))}^{2}}{6}=96$ 1 Use Multiplication Distributive Property: $${(xy)}^{a}={x}^{a}{y}^{a}$$.$\frac{{4}^{2}{(z+2)}^{2}}{6}=96$2 Simplify $${4}^{2}$$ to $$16$$.$\frac{16{(z+2)}^{2}}{6}=96$3 Simplify $$\frac{16{(z+2)}^{2}}{6}$$ to $$\frac{8{(z+2)}^{2}}{3}$$.$\frac{8{(z+2)}^{2}}{3}=96$4 Multiply both sides by $$3$$.$8{(z+2)}^{2}=96\times 3$5 Simplify $$96\times 3$$ to $$288$$.$8{(z+2)}^{2}=288$6 Divide both sides by $$8$$.${(z+2)}^{2}=\frac{288}{8}$7 Simplify $$\frac{288}{8}$$ to $$36$$.${(z+2)}^{2}=36$8 Take the square root of both sides.$z+2=\pm \sqrt{36}$9 Since $$6\times 6=36$$, the square root of $$36$$ is $$6$$.$z+2=\pm 6$10 Break down the problem into these 2 equations.$z+2=6$$z+2=-6$11 Solve the 1st equation: $$z+2=6$$.1 Subtract $$2$$ from both sides.$z=6-2$2 Simplify $$6-2$$ to $$4$$.$z=4$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$z=4$12 Solve the 2nd equation: $$z+2=-6$$.1 Subtract $$2$$ from both sides.$z=-6-2$2 Simplify $$-6-2$$ to $$-8$$.$z=-8$To get access to all 'How?' and 'Why?' steps, join Cymath Plus!$z=-8$13 Collect all solutions.$z=4,-8$Donez=4,-8	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9889394640922546, "perplexity": 4863.033271782175}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057427.71/warc/CC-MAIN-20210923165408-20210923195408-00540.warc.gz"}
https://ask.libreoffice.org/en/question/166273/formula-to-find-a-row-that-uniquely-matches-multiple-criteria-including-a-regular-expression/	# Formula to find a row that uniquely matches multiple criteria, including a regular expression edit C:\fakepath\MatchCriteria.ods The following formula counts the number of rows that match certain criteria. Is there a formula that will find the row that matches those same criteria when there is exactly one such row? =IF(LEN(A2), COUNTIFS( $Sheet2.$A:$Sheet2.$A, "=" & A2, $Sheet2.$C:$Sheet2.$C, "=" & COUNTIF($A:$A,"=" & A2), $Sheet2.$D:$Sheet2.$D, ">" & SUMIF($A:$A,"=" & A2,$B:$B) - 0.5, $Sheet2.$D:$Sheet2.$D, "<" & SUMIF($A:$A,"=" & A2,$B:$B) + 0.5 ) ,"") I'd also like to be able to replace references to A2 in the formula with a regular expression string, which I can do in the formula above because COUNTIFS, COUNTIF and SUMIF all accept regular expressions. ## The rest of this post is context for the above question I have two spreadsheets (one sheet in each) both with data relating to the same list of people. The data relating to each person can be used to find which person matches which between the two spreadsheets. Only of the spreadsheets has an ID for each person. I need to add the each person's ID to the spreadsheet that doesn't have them. To do this I've written a macro that 1) Imports both spreadsheets into a new spreadsheet. The first sheet (Sheet1) in the new spreadsheet is the one without IDs, the second sheet (Sheet2) has the IDs 2) Adds a column to Sheet1 ("Match Count") with a formula for each person which counts the number of rows in Sheet2 that the matches the person's name and other criteria (See below) 3) Adds a column to Sheet1 ("ID") with a formula that shows the ID from Sheet2 when the "Match Count" value is 1. In Sheet1 there are one or more rows for each person, grouped together. Sheet1 has an "Amounts" field which has a numeric value in each row. Sheet2 has one row for each person, and has the columns "Number of Amounts", which corresponds to the number of rows for the corresponding person in Sheet1, and "Total Amount" which corresponds to the sum of the "Amounts" values for the same person in Sheet1. For the purposes of matching people between the two sheets "Total Amount" can be up to 0.5 more or less than the sum of the corresponding "Amount" values in Sheet1. There can be different people with the identical names but they will have different "Amounts". This is the "Match Count" formula (without the nested SUBSTITUTEs for readability) A is "Name" in both sheets Sheet2: B = "ID", C = "Number of Amounts", D = "Total Amount" =IF(LEN(A2), COUNTIFS( $Sheet2.$A:$Sheet2.$A, "=" & A2, $Sheet2.$C:$Sheet2.$C, "=" & COUNTIF($A:$A,"=" & A2), $Sheet2.$D:$Sheet2.$D, ">" & SUMIF($A:$A,"=" & A2,$B:$B) - 0.5, $Sheet2.$D:$Sheet2.$D, "<" & SUMIF($A:$A,"=" & A2,$B:$B) + 0.5 ) ,"") That works great, but I want is a formula that gets data ... edit retag close merge delete	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34852665662765503, "perplexity": 1884.3911776539912}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347435987.85/warc/CC-MAIN-20200603175139-20200603205139-00449.warc.gz"}
https://chemistry.stackexchange.com/questions/18441/how-does-bombarding-a-molecule-with-electrons-cause-ionization	# How does bombarding a molecule with electrons cause ionization? I am a chemistry student, and my current are of study is mass spectrometry. In the ionization process, atoms are bombarded with electrons, but how does this work? I assume the flow of electrons attract the electrons of the atom, thereby removing them, but where do the atom's electrons go? • Electrons do not attract electrons, they would repel each other as they have like charge. – Sherlock Holmes Oct 15 '14 at 1:28 • Imagine the analogy of you holding on to an object (let's say your groceries) then someone chucks stuff at you. You might accidentally drop the groceries. While this is obviously not an accurate analogy on an atomic level, it might help to visualise what is going on. – surelyourejoking Oct 15 '14 at 11:01 This type of ionization is known as electron ionization (there are many types of ionization methods used for MS). One possible reaction for EI is: $$\ce{M +e- ->M^{•+} +2e-}$$ source	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3268619179725647, "perplexity": 1008.7369388977033}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195526536.46/warc/CC-MAIN-20190720153215-20190720175215-00431.warc.gz"}
https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/	Better beware of notions like genius and inspiration; they are a sort of magic wand and should be used sparingly by anybody who wants to see things clearly. (José Ortega y Gasset, “Notes on the novel”) Does one have to be a genius to do mathematics? The answer is an emphatic NO. In order to make good and useful contributions to mathematics, one does need to work hard, learn one’s field well, learn other fields and tools, ask questions, talk to other mathematicians, and think about the “big picture”. And yes, a reasonable amount of intelligence, patience, and maturity is also required. But one does not need some sort of magic “genius gene” that spontaneously generates ex nihilo deep insights, unexpected solutions to problems, or other supernatural abilities. The popular image of the lone (and possibly slightly mad) genius – who ignores the literature and other conventional wisdom and manages by some inexplicable inspiration (enhanced, perhaps, with a liberal dash of suffering) to come up with a breathtakingly original solution to a problem that confounded all the experts – is a charming and romantic image, but also a wildly inaccurate one, at least in the world of modern mathematics. We do have spectacular, deep and remarkable results and insights in this subject, of course, but they are the hard-won and cumulative achievement of years, decades, or even centuries of steady work and progress of many good and great mathematicians; the advance from one stage of understanding to the next can be highly non-trivial, and sometimes rather unexpected, but still builds upon the foundation of earlier work rather than starting totally anew. (This is for instance the case with Wiles‘ work on Fermat’s last theorem, or Perelman‘s work on the Poincaré conjecture.) Actually, I find the reality of mathematical research today – in which progress is obtained naturally and cumulatively as a consequence of hard work, directed by intuition, literature, and a bit of luck – to be far more satisfying than the romantic image that I had as a student of mathematics being advanced primarily by the mystic inspirations of some rare breed of “geniuses”. This “cult of genius” in fact causes a number of problems, since nobody is able to produce these (very rare) inspirations on anything approaching a regular basis, and with reliably consistent correctness. (If someone affects to do so, I advise you to be very sceptical of their claims.) The pressure to try to behave in this impossible manner can cause some to become overly obsessed with “big problems” or “big theories”, others to lose any healthy scepticism in their own work or in their tools, and yet others still to become too discouraged to continue working in mathematics. Also, attributing success to innate talent (which is beyond one’s control) rather than effort, planning, and education (which are within one’s control) can lead to some other problems as well. Of course, even if one dismisses the notion of genius, it is still the case that at any given point in time, some mathematicians are faster, more experienced, more knowledgeable, more efficient, more careful, or more creative than others. This does not imply, though, that only the “best” mathematicians should do mathematics; this is the common error of mistaking absolute advantage for comparative advantage. The number of interesting mathematical research areas and problems to work on is vast – far more than can be covered in detail just by the “best” mathematicians, and sometimes the set of tools or ideas that you have will find something that other good mathematicians have overlooked, especially given that even the greatest mathematicians still have weaknesses in some aspects of mathematical research. As long as you have education, interest, and a reasonable amount of talent, there will be some part of mathematics where you can make a solid and useful contribution. It might not be the most glamorous part of mathematics, but actually this tends to be a healthy thing; in many cases the mundane nuts-and-bolts of a subject turn out to actually be more important than any fancy applications. Also, it is necessary to “cut one’s teeth” on the non-glamorous parts of a field before one really has any chance at all to tackle the famous problems in the area; take a look at the early publications of any of today’s great mathematicians to see what I mean by this. In some cases, an abundance of raw talent may end up (somewhat perversely) to actually be harmful for one’s long-term mathematical development; if solutions to problems come too easily, for instance, one may not put as much energy into working hard, asking dumb questions, or increasing one’s range, and thus may eventually cause one’s skills to stagnate. Also, if one is accustomed to easy success, one may not develop the patience necessary to deal with truly difficult problems (see also this talk by Peter Norvig for an analogous phenomenon in software engineering). Talent is important, of course; but how one develops and nurtures it is even more so. It’s also good to remember that professional mathematics is not a sport (in sharp contrast to mathematics competitions). The objective in mathematics is not to obtain the highest ranking, the highest “score”, or the highest number of prizes and awards; instead, it is to increase understanding of mathematics (both for yourself, and for your colleagues and students), and to contribute to its development and applications. For these tasks, mathematics needs all the good people it can get. Further reading: • How to be a genius“, David Dobbs, New Scientist, 15 September 2006. [Thanks to Samir Chomsky for this link.] • The mundanity of excellence“, Daniel Chambliss, Sociological Theory, Vol. 7, No. 1, (Spring, 1989), 70-86. [Thanks to John Baez for this link.]	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 4, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5811087489128113, "perplexity": 1147.1383522247522}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128323842.29/warc/CC-MAIN-20170629015021-20170629035021-00205.warc.gz"}
http://mathhelpforum.com/discrete-math/125546-set-confusion.html	# Math Help - Set confusion 1. ## Set confusion Let $S$ = {1,{2},{1,2}}. My book says the following are subsets of $S$: {1}, {1,{2}}, {{1,2}} I know that 1 , {2}, {1,2} are elements of S and that {2} and {1,2} are subsets of $S$, but I have trouble undestanding why {1}, {1,{2}}, and {{1,2}} are being subsets of $S$. The sets {1}, {1,{2}}, and {{1,2}} seem to me are the subsets of the power set of $S$, $P(S)$. I am so confused. 2. ## elements of sets can be sets Set S has three elements. If you re-label {2} as A and {1,2} as B, then S={1,A,B} Form the subsets of S from these symbols. Then ... replace A and B with {2} and {1,2} respectively. What do you have? 3. Originally Posted by novice Let $S$ = {1,{2},{1,2}}. My book says the following are subsets of $S$: {1}, {1,{2}}, {{1,2}} I know that 1 , {2}, {1,2} are elements of S and that {2} and {1,2} are subsets of $\color{red}S$, but I have trouble undestanding why {1}, {1,{2}}, and {{1,2}} are being subsets of $S$. The sets {1}, {1,{2}}, and {{1,2}} seem to me are the subsets of the power set of $S$, $P(S)$. The part in red is false. $2\notin S$ therefore neither $\{2\}\text{ nor }\{1,2\}$ could be a subset of $S$. The both contain an element not in $S$. 4. Originally Posted by Manx Set S has three elements. If you re-label {2} as A and {1,2} as B, then S={1,A,B} Form the subsets of S from these symbols. Then ... replace A and B with {2} and {1,2} respectively. What do you have? I could only see $A\subset B\subset C$ Using your notation for the answer in my book I got these: {1} $\subset S$ , $A\subset$ {1, A} $\subset S$, and ${{B}} \subset S$. Still can't picture what you are trying to say. 5. ## subset list S={1,A,B} 3 elements, 8 subsets { } {1}, {A}, {B} {1,A}, {1,B}, {A,B} {1,A,B} replace A and B (extra spaces added for emphasis -- look carefully at brackets.) { } {1}, ( {2} }, { (1,2} } {1, {2} }, {1, {1,2} } , { {2} , {1,2} } { 1, {2}, {1,2} } Do you see the sets you are looking for? 6. Originally Posted by Plato The part in red is false. $2\notin S$ therefore neither $\{2\}\text{ nor }\{1,2\}$ could be a subset of $S$. The both contain an element not in $S$. I understand it fully now. My problem being that I did not look at the definition carefully. Following the definition, I piece them together as follows: {1} $\subseteq S$, since 1 $\in$ {1} and 1 $\in S$, Next, {1,{2}} $\subseteq S$, since 1, {2} $\in${1,{2}} and 1, {2} $\in S$, Last, {{1,2}} $\subseteq S$ , since {1,2} $\in${{1,2}} and {1,2} $\in S$. I realized that the above is not exhaustive, since I can come up with more subsets, such as $S \subset S$ {{2}{1,2}} $\subseteq S$. Thanks you, Plato. Nice to know that you are not too far to reach. 7. Originally Posted by Manx S={1,A,B} 3 elements, 8 subsets { } {1}, {A}, {B} {1,A}, {1,B}, {A,B} {1,A,B} replace A and B (extra spaces added for emphasis -- look carefully at brackets.) { } {1}, ( {2} }, { (1,2} } {1, {2} }, {1, {1,2} } , { {2} , {1,2} } { 1, {2}, {1,2} } Do you see the sets you are looking for? I assume {1} is a typo. Yah? 8. not sure what you mean. I used ( in place of { in one set. 9. Originally Posted by Manx not sure what you mean. I used ( in place of { in one set. 1 is an element in $S$; it's not a subset of $S$. Here is the definition I read and reread till it sunk in: Definition of subset: For sets $A$ and $B$, if every element in $A$ belongs to $B$, then $A \subseteq B$. 10. ## are we communicating? 1 is an element of S so {1} is one of several subsets of S. 11. Originally Posted by Manx 1 is an element of S so {1} is one of several subsets of S. Since $S$={1,{2},{1,2}}, 1 $\in S$. $S$ contains there elements: 1, {2}, {1,2}, two of which are sets, namely {2}, {1,2}. So we know {1} is not one of them. Yah? 12. ## no If 1 is an element of S, then {1} is one subset of S. 13. Originally Posted by Manx If 1 is an element of S, then {1} is one subset of S. Got it now after plenty of sleep. 1 $\in S$ and {1} $\in S$ imply {1} $\subset S$ Manx, you are a good friend because you put up with me. 14. Originally Posted by novice Got it now after plenty of sleep. 1 $\in S$ and {1} $\in S$ imply {1} $\subset S$ Manx, you are a good friend because you put up with me. I don't think what you are saying is correct. If $a\in S$ THEN $\{a\}\subseteq S$. You seem to be having an awful lot of confusion. Have you tried looking at what subset means abstractly? $E\subseteq S \text{ iff }x\in E\implies x\in S$. 15. ## correction [quote=novice;446392]Got it now after plenty of sleep. 1 $\in S$ and {1} $\in S$ imply {1} $\subset S$ Manx, you are a good friend because you put up with me.[/quote technically saying {1} E S is wrong. 1 E S given S {1,{2}, {1,2}}. {1} isnt an element of S. but i think i know where your confusion comes from. a subset gets {} regardless so {1} represents the 1 in S. {{2}} represents the {2} in S and {1,{2}} represents the 1,{2} in S. on a test if you say {1} E S that would be wrong because there is no element {1} in S there IS an element of 1 in S. Saying that there is a {1} E S means that this would be S {{1},{2},{1,2}} saying 1 E S is saying there is a 1 in S which there is {1,{2},{1,2}} Page 1 of 2 12 Last	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 58, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9003838300704956, "perplexity": 1633.4697130926838}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-22/segments/1464049281363.50/warc/CC-MAIN-20160524002121-00211-ip-10-185-217-139.ec2.internal.warc.gz"}
https://slideplayer.com/slide/4611902/	# Probability Theory STAT 312 STAT 312 Dr. Zakeia AlSaiary. ## Presentation on theme: "Probability Theory STAT 312 STAT 312 Dr. Zakeia AlSaiary."— Presentation transcript: Probability Theory STAT 312 STAT 312 Dr. Zakeia AlSaiary Theorem: 7.1. p 191 A real valued function f of two variables is joint probability density function of a pair of discrete random variables X and Y if and only if : Example:7.1 page 191 For what value of the constant k the function given by Is a joint probability density function of some random variables X , Y ? Marginal probability density function Example: 7.2. Bivariate Continuous Random Variables الإثنين 10/4/1435 المحاضرة الثالثة: 7.2. Bivariate Continuous Random Variables 7.2. Bivariate Continuous Random Variables In this section, we shall extend the idea of probability density functions of one random variable to that of two random variables. Definition 7.5. The joint probability density function of the random variables X and Y is an integrable function f(x, y) such that 7.2. Bivariate Continuous Random Variables Example 7.6. Let the joint density function of X and Y be given by What is the value of the constant k ? REMARK: If we know the joint probability density function f of the random variables X and Y , then we can compute the probability of the event A from: Bivariate Continuous Random Variables Example 7.7. Let the joint density of the ontinuous random variables X and Y be What is the probability of the event Marginal probability density function: Definition 7.6. Let (X, Y ) be a continuous bivariate random variable. Let f(x, y) be the joint probability density function of X and Y . The function is called the marginal probability density function of X. Similarly, the function Marginal probability density function: Similarly, the function is called the marginal probability density function of Y. Marginal probability density function: Example 7.9. If the joint density function for X and Y is given by: What is the marginal density of X where nonzero? Definition 7.7. Let X and Y be the continuous random variables with joint probability density function f(x, y). The joint cumulative distribution function F(x, y) of X and Y is defined as The joint cumulative distribution function F(x, y): From the fundamental theorem of calculus, we again: obtain The joint cumulative distribution function F(x, y): Example If the joint cumulative distribution function of X and Y is given by then what is the joint density of X and Y ? EXERCISES: Page , 2 , 3 , 4 , 7 , 8 , 10 , 11 7.3. Conditional Distributions First, we motivate the definition of conditional distribution using discrete random variables and then based on this motivation we give a general definition of the conditional distribution. Let X and Y be two discrete random variables with joint probability density f(x, y). 7.3. Conditional Distributions Then by definition of the joint probability density, we have f(x, y) = P(X = x, Y = y). If A = {X = x}, B = {Y = y} and f (y) = P(Y = y), then from the above equation we have P ({X = x} / {Y = y}) = P (A/B) 7.3. Conditional Distributions If we write the P ({X = x} / {Y = y}) as g(x / y), then we have 7.3. Conditional Distributions Definition 7.8. Let X and Y be any two random variables with joint density f(x, y) and marginals f1(x) and f2(y). The conditional probability density function g of X, given (the event) Y = y, is defined as 7.3. Conditional Distributions Similarly, the conditional probability density function h of Y , given (the event) X = x, is defined as 7.3. Conditional Distributions Example Let X and Y be discrete random variables with joint probability function What is the conditional probability density function of Y, given X = 2 ? 7.3. Conditional Distributions Example Let X and Y be discrete random variables with joint probability function What is the conditional probability density function of Y, given X = x ? 7.3. Conditional Distributions Example Let X and Y be contiuous random variables with joint pdf What is the conditional probability density function of Y, given X = x ? 7.3. Conditional Distributions Example Let X and Y random variables such that X has pdf and the conditional density of Y given X = x is 7.3. Conditional Distributions What is the conditional density of X given Y = y over the appropriate domain? 7.4. Independence of Random Variables In this section, we define the concept of stochastic independence of two random variables X and Y . The conditional robability density function g of X given Y = y usually depends on y. If g is independent of y, then the random variables X and Y are said to be independent. This motivates the following definition. 7.4. Independence of Random Variables Definition 7.8. Let X and Y be any two random variables with joint density f(x, y) and marginals f1(x) and f2(y). The random variables X and Y are (stochastically) independent if and only if 7.4. Independence of Random Variables Example Let X and Y be discrete random variables with joint density Are X and Y stochastically independent? 7.4. Independence of Random Variables Example Let X and Y have the joint density Are X and Y stochastically independent? 7.4. Independence of Random Variables Example Let X and Y have the joint density Are X and Y stochastically independent? 7.4. Independence of Random Variables Definition 7.9. The random variables X and Y are said to be independent and identically distributed (IID) if and only if they are independent and have the same distribution. EXERCISES: Page , 16 , 21	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9814271330833435, "perplexity": 257.2005600463742}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600402128649.98/warc/CC-MAIN-20200930204041-20200930234041-00750.warc.gz"}
https://blog.mbedded.ninja/electronics/components/sensors/humidity-sensors/	SENSORS # Humidity Sensors ## Types Humidity sensors can either contain just the humidity sensing component (which means they usually just have two leads), or they may also contain signal processing circuits. The ones which also contain circuitry have an analogue (usually 3 pin) or digital output (can have many pins, 8 is a common number). ## Uses Humidity sensors are commonly used in the following equipment: • Air conditioning, heating and ventilation • Refrigerators • Industrial automation • Asset and goods tracking • Medical equipment (respiratory devices) ## Relative Humidity Relative humidity is defined as the ratio of the water vapour pressure to the saturation water vapour pressure, at the current gas temperature. It is ratio of the actual amount of water in the air to the total amount it could when saturated. $$RH = \frac{P_W}{P_{WS}}\cdot 100%$$ ## Dew Point The dew point is the point at which the atmosphere has to be cooled down too so that condensation starts to appear. The frost point is the dew point when the temperatures are below freezing. ## The Magnus Equation The Magnus equation is an approximation to calculate the dew point from the actual air temperature and relative humidity. It is a useful equation to use when you have a sensor IC which measures both temperature and relative humidity. First we find an intermediary value called gamma ($$\gamma$$): $$\gamma(T, RH) = ln(\frac{RH}{100}) + \frac{bT}{c + T}$$ where: $$RH$$ = relative humidity of the air (as a percentage from 0-100%) $$T$$ = temperature of air, in degrees Celsius $$b$$ = constant $$c$$ = constant $$\gamma$$ can then be substituted into the following equation to calculate the dew point temperature $$T_{dp}$$ (in degrees Celsius): $$T_{dp} = \frac{c\gamma(T, RH)}{b - \gamma(T, RH)}$$ The values of the constants $$a$$, $$b$$ and $$c$$ can vary depending on the data set and method used to calculate them (this is an empirical formula). Common values for them are: $$a = 6.112millibar$$ $$b = 17.67$$ $$c = 243.5^{\circ}C$$ The following is a code example in C showing a function which converts temperature and relative humidity into a dew point, using the simple Magnus equation. #include <math.h> //! @brief The B constant for the Magnus equation to calculate the dew point. #define DEW_POINT_CONSTANT_B_NO_UNIT 17.67 //! @brief The C constant for the Magnus equation to calculate the dew point. #define DEW_POINT_CONSTANT_C_DEG_C 243.5 //! @brief Calculates the dew point (in degrees Celcius) from the temperature and relative humidity. //! @details Uses the Magnus formula, given at https://en.wikipedia.org/wiki/Dew_point. //! @param temperature_DegC The temperature of the atmosphere at which the relative humidity was measured. //! @param relHumidity_Perc The relative humidity (as a percentage from 0-100) of the atmosphere measured. //! @returns The dew point (in degrees Celcius) of the atmosphere. double Humidity_CalcDewPointDegC(double temperature_DegC, double relHumidity_Perc) { // This uses the Magnus equation as explained at https://en.wikipedia.org/wiki/Dew_point // Calculate gamma, which is just a way of splitting up the equation into two operations double gamma = log(relHumidity_Perc/100.0) + (DEW_POINT_CONSTANT_B_NO_UNITtemperature_DegC)/(DEW_POINT_CONSTANT_C_DEG_C + temperature_DegC); // Finally, calculate the dew point (in degrees Celcius) double dewPoint_DegC = (DEW_POINT_CONSTANT_C_DEG_Cgamma)/(DEW_POINT_CONSTANT_B_NO_UNIT - gamma); return dewPoint_DegC; } ## Examples The Honeywell HIH-5030 (3.3V) or HIH-4030 (5.0V) analogue-output, 3-pin, SMD humidity sensors are a popular choice. They measure the full humidity range (0-100%), are easy to solder, and simple to interface too.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9064019918441772, "perplexity": 2165.788092343897}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-25/segments/1623487608702.10/warc/CC-MAIN-20210613100830-20210613130830-00409.warc.gz"}
http://mathoverflow.net/questions/53774/witten-index-letter-partition-function-and-superconformal-representations	# Witten Index, letter partition function and superconformal representations. Except in a few papers I have seen so little written about this that I am not sure I can even frame this question properly. • I would like to know of expository references and explanations on the concept of "single/multi trace letter partition function" and how it connects to Witten Index and superconformal field theory. I haven't been able to find any reference which explains the concept of letter partition function and how techniques from representation theory get used to calculate them. (especially in the context of superconformal representations) For example one can see between page 15 and 30 of this paper to see some usages of this. As said above this technology comes up often in the context of superconformal group representations. I would be happy see references which give explanations about them. In superconformal representations one often lists out "long" and "short" representations labelled by the "primaries" and then one calculates the Witten Index of them. (which apparently always vanishes for the long ones) To give an example of a case where Witten Index is calculated, So for ${\cal N} = 2$ superconformal algebra in $2+1$ dimensions the symmetry group is $SO(3,2)\times SO(2)$ and possibly the primary states of this algebra are labelled by the tuple $(\Delta, j,h)$ where $\Delta$ is the scaling dimension and $j$ is the spin and $h$ is its $R$ charge (or whatever it means to call it the $R$ charge highest weight) • I would like to know what are the precise eigenvalue equations used to do the above labeling. Now consider a primary labelled by $(\Delta, j,h)$ such that it is in the long representation and hence $\Delta >j+\vert h\vert +1$. Then I see people listing something called the “conformal content” of this representation labelled by the above state. For the above case the conformal content apparently consists of the following states, $(\Delta, j,h)$, $(\Delta+0.5, j\pm 0.5,h\pm 1)$, $(\Delta + 1 , j,h \pm 2)$, $(\Delta +1 , j+1,h)$, twice $(\Delta + 1, j,h)$, $(\Delta + 1, j-1,h)$, $(\Delta + 1.5, j\pm 0.5,h \pm 1)$ and $(\Delta + 2, j,h)$ • I would like to know what exactly is the definition of “conformal content” and how are lists like the above computed. The Witten Index of the above is supposed to be $0$ and I guess it was supposed to be obvious without explicitly enumerating the labels. Similar lists can be constructed for various kinds of short representations like those labelled by $(j+h+1,j,h)$ ($j, h \neq 0$), by $(j+1,j,0)$, by $(h,0,h)$, by $(0.5,0,\pm 0.5)$, by $(h+1,0,h)$ and $(1,0,0)$. Its not completely clear to me a priori as to why some of these states had to be taken out separately from the general case, but I guess if I am explained the above queries I would be able to understand the complete construction. -	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.920356273651123, "perplexity": 265.8196436702428}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246642012.28/warc/CC-MAIN-20150417045722-00309-ip-10-235-10-82.ec2.internal.warc.gz"}
http://math.stackexchange.com/questions/102935/universal-element-for-the-power-set-contravariant-functor?answertab=oldest	# Universal element for the power set contravariant functor I got a bit confused in MacLane's book when dealing with universals. More precisely, I don't understand the definition of the universal element of a functor. At page 57, it sais: If $D$ is a category and $H:D\rightarrow \bf{Set}$ a functor, a universal element of the functor $H$ is a pair $(r,e)$ consisting of an object $r \in D$ and an element $e \in Hr$ such that for every pair $(d,x)$ with $x \in Hd$, there is a unique arrow $f:r \rightarrow d$ of $D$, with $(Hf)e=x$. Now, I made myself a bit of a diagram, like: • $H: r \mapsto Hr \ni e$ • $H: x \mapsto Hd \ni x$ and • $Hf: Hr \mapsto Hd$, where $\exists! f: r \rightarrow d$ Sorry, I don't know how to arrange it properly... It puzzles me that it treated universals (e.g. universal arrow from and element to a functor) without elements and now we consider an element in an object. Please clarify this concept to me and consider an application: Find the universal element for the contravariant power set functor $\mathcal{P} : \bf{Set}^{op} \rightarrow \bf{Set}$. Thank you. EDIT As @Andy suggested, the definition of universal elements amounts to something like this: where the square should be commutative. I think I got it right now. - You can treat an element of a set as a map from a singleton to the set; which means that $e \in X$ is actually a map $e\colon t \to X$, where $t$ is the terminal object in set. This should clear up your doubt about using elements, I hope. – Andy Jan 27 '12 at 11:41 So we could have something like $H:D\rightarrow\bf{Set}\leftarrow\{\cdot\}:E$, where $\bf{E}$ is a kind of 'element selecting' functor'?... This could, indeed, clear up things. – AdrianM Jan 27 '12 at 11:48 Uhm, what I meant was that in the definition, you can change the "$\in$" symbol with an arrow, so that the definition is a commutative diagram (I don't know what packets the site has to make them, so I won't try, but I think you get the idea). – Andy Jan 27 '12 at 11:51 Got it! I'll try to edit the question. Thank you! – AdrianM Jan 27 '12 at 12:02 It may also help to rewrite this as saying that $\mbox{Hom}_D(r,-) \cong H$; then the universal element is just the image of $\mbox{Id}_r$! – Aaron Mazel-Gee May 18 '12 at 1:41 What the definition says is that given a functor $\mathcal F \colon \mathbf C \to \mathbf{Set}$ a universal element is an element $e$ of a $\mathcal F(r)$, for some $r \in \mathbf C$, such that every other element $x$ of another set $\mathcal F(c)$, for a $c \in \mathbf C$, it can be viewed as image of a unique function of type $\mathcal F(r) \to \mathcal F(c)$. This function must be of course the image of a morphism of $\mathbf C$ via the functor $\mathcal F$. Universal element play an important role in mathematics, primarily because $\mathbf{Set}$-based functors are really important in maths. First of all let's make a point clear: universal arrows and universal elements are essentially the same thing, I'll try to explain way. The fundamental idea is that there's a bijection between a set $X$ and the set $\mathbf{Set}(\bullet,X)$, where $\bullet$ denote the singleton set $\{\emptyset\}$: we can identify every element $e \in X$ with the (unique) morphism $\tilde e \colon \bullet \to X$ such that $\tilde e(\emptyset)=e$. Let $\mathcal F \colon \mathbf C \to \mathbf{Set}$ be a functor, then a pair $\langle r \in \mathbf C, e \in \mathcal F(r) \rangle$ is universal element if and only if the pair $\langle r\in \mathbf C, \tilde e \colon \bullet \to \mathcal F(r) \rangle$ is a universal arrow from the object $\bullet$ to the functor $\mathcal F$. Similarly given a functor $\mathcal F \colon \mathbf C \to \mathbf D$ a pair $\langle r \in \mathbf C, \tilde e \in \mathbf D(d, \mathcal F(r))\rangle$ is a universal arrow from an object $d \in \mathbf D$ to $\mathcal F$ if and only if it is also a universal element for the functor $\mathbf D(d,\mathcal F(-)) \colon \mathbf C \to \mathbf{Set}$. Remind that categories are usually considered as object living inside the category $\mathbf {Set}$ so universal elements can be thought as a way to talk about universals of a category $\mathbf C$ in $\mathbf{Set}$-terms (externally to the category $\mathbf C$) while universal arrows are the way to think universals in the term of category $\mathbf C$ itself (internally to the category $\mathbf C$). Both these point of view are actually useful: the first enables us to work in set-theoretic terms and so to work in a familiar framework, the second enable to work internally to the category we are considering, and this is really important from a logical point of view. About the request for your application what are you looking for is a pair $\langle \Omega \in \mathbf{Set}, \Theta \subseteq \Omega \rangle$ such that for every other pair $\langle X \in \mathbf {Set}, Y \subseteq X \rangle$ there exists a unique morphism $$f \in \mathbf{Set}^\text{op}(\Omega,X) = \mathbf{Set}(X,\Omega)$$ such that $$\mathcal P (f)(\Theta)=f^{-1}(\Theta)=Y\ .$$ If we take $$\Omega = \mathcal P(\{\emptyset\})=\{\emptyset,\{\emptyset\}\}=\{0,1\}$$ what we get is the $$\mathbf{Set}^\text{op}(\Omega,X)=\mathbf{Set}(X,\Omega)$$ is the set of characteristic functions of $X$. For each $Y \subseteq X$ there's a unique $f \colon X \to \Omega$ such that $f^{-1}(1) = Y$, but this means exactly that for every pair $\langle X \in \mathbf{Set}, Y \in \mathcal P(X)\rangle$ there exists always a unique $f \in \mathbf{Set}^\text{op}(\Omega,X)$ such that $\mathcal P(f)(1)=Y$, and thus $\langle \Omega,1\rangle$ is a universal element for the functor $\mathcal P$. (Edit:) I want to add something else. Universal elements of a functor $\mathcal F \colon \mathbf C^\text{op} \to \mathbf{Set}$ are important also for another reason: via yoneda-lemma universal elements are those objects corresponding to natural isomorphism from functor $\mathbf C(-,\Omega)$ to the functor $\mathcal F$. So a functor $\mathcal F$ has a universal element if and only if it is representable. This is important because representable functors actions can be represented in term of the category $\mathbf C$ itself: for instance for every morphism $f \in \mathbf C(c,c')$ we can represent the function $\mathcal F(f) \colon \mathcal F(c) \to \mathcal F(c')$ as the function $$g \in \mathbf C(c',\Omega) \mapsto g \circ f \in \mathbf C(c,\Omega)$$ identifying sets $\mathcal F(c)$ and $\mathcal F(c')$ with sets $\mathbf C(c, \Omega)$ and $\mathbf C(c',\Omega)$.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9717914462089539, "perplexity": 170.91748102694584}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-15/segments/1397609533689.29/warc/CC-MAIN-20140416005213-00655-ip-10-147-4-33.ec2.internal.warc.gz"}
https://tex.stackexchange.com/questions/407537/shading-in-bookcover	I'm trying to make a book cover using the bookcover class. The problem is that I cannot use shade (something I want to use), it always gives a black background, even with the minimal example in the user manual \documentclass[flapwidth=50mm,spinewidth=15mm]{bookcover} \begin{document} \begin{bookcover} \bookcovercomponent{color}{bg whole without flaps}{ top color=white, bottom color=blue!50!black, shading angle=60} \end{bookcover} \end{document} According to the manual it is no necessary to include tikz and xcolor packages manually, but even doing so I get the same result. Some one can see what I'm doing wrong? • Welcome to TeX SX! Works for me (albeit not very fine looking, probably due to the white \topcolor. Did you really have your problem with this very code? – Bernard Dec 24 '17 at 23:46 • The code succeeds when compiled with pdflatex or lualatex, producing a cover that is shaded from white (upper left) to blue (most of the area). The code FAILS when compiled with xelatex, producing solid black. – user139954 Dec 24 '17 at 23:53 In the manual of class bookcover I can not find that there could be a problem with XeLaTeX, but if I compile your given code code I get the following results: • PdfLaTeX: Compiles without error or warnings, shows white to blue. • luaLaTeX: compiles without error or warnings, shows white to blue. • XeLaTeX: compiles without error or warnings, but shows only a black block. My used TeX distribution is a current MiKTeX 2.9 on Windows 8. Result with PdfLaTeX: You should make a bug report ... This bug is fixed in version 2.2 If you use version 2.1, then the next code works with xelatex, lualatex and pdflatex too: \documentclass[flapwidth=50mm,spinewidth=15mm]{bookcover} \begin{document} \makeatletter\TP@absposfalse\makeatother\newgeometry{left=0em,top=-1em} % fixing code \begin{bookcover} \bookcovercomponent{color}{bg whole without flaps}{ top color=white, bottom color=blue!50!black, shading angle=60} \end{bookcover} \end{document}	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9129118323326111, "perplexity": 4484.841655631224}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998808.17/warc/CC-MAIN-20190618163443-20190618185443-00096.warc.gz"}
https://www.gradesaver.com/textbooks/math/algebra/algebra-2-common-core/chapter-7-exponential-and-logarithmic-functions-7-3-logarithmic-functions-as-inverses-practice-and-problem-solving-exercises-page-457/48	## Algebra 2 Common Core Published by Prentice Hall # Chapter 7 - Exponential and Logarithmic Functions - 7-3 Logarithmic Functions as Inverses - Practice and Problem-Solving Exercises - Page 457: 48 #### Answer $6^1=6$ #### Work Step by Step RECALL: $\log_{a}{y} = b \longleftrightarrow a^b = y$ Use the definition above to convert the equation to exponential equation and have $6^1=6.$ After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6248579025268555, "perplexity": 2117.372855097677}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376827963.70/warc/CC-MAIN-20181216165437-20181216191437-00584.warc.gz"}
https://export.arxiv.org/abs/1601.06720	physics.flu-dyn (what is this?) # Title: The Generalized Quasilinear Approximation: Application to Zonal Jets Abstract: Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. In this paper we present a generalization of quasilinear theory to include dynamic mode interactions on the large scales. This generalized quasilinear (GQL) approximation is achieved by separating the state variables into large and small zonal scales via a spectral filter rather than by a decomposition into a formal mean and fluctuations. Nonlinear interactions involving only small zonal scales are then removed. The approximation is conservative and allows for scattering of energy between small-scale modes via the large scale (through non-local spectral interactions). We evaluate GQL for the paradigmatic problems of the driving of large-scale jets on a spherical surface and on the beta-plane and show that it is accurate even for a small number of large-scale modes. As this approximation is formally linear in the small zonal scales it allows for the closure of the system and can be utilized in direct statistical simulation schemes that have proved an attractive alternative to direct numerical simulation for many geophysical and astrophysical problems. Comments: 5 pages and 5 figures Subjects: Fluid Dynamics (physics.flu-dyn); Earth and Planetary Astrophysics (astro-ph.EP); Solar and Stellar Astrophysics (astro-ph.SR); Atmospheric and Oceanic Physics (physics.ao-ph) Journal reference: Phys. Rev. Lett. 116, 214501 (2016) DOI: 10.1103/PhysRevLett.116.214501 Cite as: arXiv:1601.06720 [physics.flu-dyn] (or arXiv:1601.06720v1 [physics.flu-dyn] for this version)	{"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9655609726905823, "perplexity": 1697.4274006424127}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243988793.99/warc/CC-MAIN-20210507120655-20210507150655-00307.warc.gz"}
https://gmatclub.com/forum/a-car-traveling-at-a-certain-constant-speed-takes-2-seconds-126658.html	GMAT Question of the Day: Daily via email \| Daily via Instagram New to GMAT Club? Watch this Video It is currently 02 Jul 2020, 05:18 ### GMAT Club Daily Prep #### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email. Customized for You we will pick new questions that match your level based on your Timer History Track every week, we’ll send you an estimated GMAT score based on your performance Practice Pays we will pick new questions that match your level based on your Timer History # A car traveling at a certain constant speed takes 2 seconds Author Message TAGS: ### Hide Tags Intern Joined: 19 Nov 2011 Posts: 5 A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags Updated on: 28 Jan 2012, 03:59 5 141 00:00 Difficulty: 75% (hard) Question Stats: 62% (02:50) correct 38% (02:46) wrong based on 1463 sessions ### HideShow timer Statistics A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 Originally posted by RadhaKrishnan on 28 Jan 2012, 03:10. Last edited by Bunuel on 28 Jan 2012, 03:59, edited 1 time in total. Math Expert Joined: 02 Sep 2009 Posts: 64891 ### Show Tags 28 Jan 2012, 03:58 27 38 A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 Many approaches are possible, one of them: Let the distance be 1 kilometer. Time to cover this distance at 75 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds; Time to cover this distance at regular speed is 48+2=50 seconds = 50/3,600 hours = 1/72 hours; So, we get that to cover 1 kilometer 1/72 hours is needed --> regular speed 72 kilometers per hour (rate is a reciprocal of time or rate=distance/time). _________________ Senior Manager Joined: 23 Oct 2010 Posts: 312 Location: Azerbaijan Concentration: Finance Schools: HEC '15 (A) GMAT 1: 690 Q47 V38 Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 30 Jan 2012, 00:11 1 5 if 1 h=6060 sec, then 2 sec =2/6060=1/1800 1/1800+1/75=25/1800=1/72 since t=D/S and t=1/72 D=1 then S=72 _________________ Happy are those who dream dreams and are ready to pay the price to make them come true I am still on all gmat forums. msg me if you want to ask me smth ##### General Discussion Manager Joined: 10 Jan 2010 Posts: 132 Location: Germany Concentration: Strategy, General Management Schools: IE '15 (M) GPA: 3 WE: Consulting (Telecommunications) Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 30 Jan 2012, 02:41 1 1 B - 72 Original time in seconds: 6060/75 = 48 --> Car need 48 seconds to travel 1 km New car needs 2 more seconds to travel 1km --> 50 seconds to travel 1km Speed (new car): 50 (seconds) / 3600 (1 hour in seconds) = 1 / 72 --> in 1 Minute the car travels 1 / 72. Thus 72km/h Manager Joined: 13 Dec 2013 Posts: 58 Location: Iran (Islamic Republic of) Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 27 Jan 2015, 02:24 Bunuel wrote: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 Many approaches are possible, one of them: Let the distance be 1 kilometer. Time to cover this distance at 75 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds; Time to cover this distance at regular speed is 48+2=50 seconds = 50/3,600 hours = 1/72 hours; So, we get that to cover 1 kilometer 1/72 hours is needed --> regular speed 72 kilometers per hour (rate is a reciprocal of time or rate=distance/time). Dear BUnuel, Do you confirm this approach? 75 km is 75000 m and 1 hour is 60 min. so we have : 100060 /75000 = 4/5 min OR 4/5 60 = 48 seconds AS the promblem says take 2 seconds longer so we have 48+2 =50 seconds to cover 1 km or 1000 m as we have formula like this: Vt = d so we have v50= 1000 Or v= 1000/50 = 20 m/s NOW convert to Km/h : 20 3600 (s) /1000 m = 72000/1000 = 72 km/h Please confirm if this is true Thanks Manager Joined: 02 May 2014 Posts: 89 Schools: ESADE '16, HKU'16, SMU '16 GMAT 1: 620 Q46 V30 Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 04 Feb 2015, 05:02 Bunuel wrote: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 Many approaches are possible, one of them: Let the distance be 1 kilometer. Time to cover this distance at 75 kilometers per hour is 1/75 hours = 3,600/75 seconds = 48 seconds; Time to cover this distance at regular speed is 48+2=50 seconds = 50/3,600 hours = 1/72 hours; So, we get that to cover 1 kilometer 1/72 hours is needed --> regular speed 72 kilometers per hour (rate is a reciprocal of time or rate=distance/time). Dear BUnuel, Do you confirm this approach? 75 km is 75000 m and 1 hour is 60 min. so we have : 100060 /75000 = 4/5 min OR 4/5 60 = 48 seconds AS the promblem says take 2 seconds longer so we have 48+2 =50 seconds to cover 1 km or 1000 m as we have formula like this: Vt = d so we have v50= 1000 Or v= 1000/50 = 20 m/s NOW convert to Km/h : 20 * 3600 (s) /1000 m = 72000/1000 = 72 km/h Please confirm if this is true Thanks I'm not Bunuel but I don't see anything wrong in the approach. Board of Directors Joined: 17 Jul 2014 Posts: 2424 Location: United States (IL) Concentration: Finance, Economics GMAT 1: 650 Q49 V30 GPA: 3.92 WE: General Management (Transportation) Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 31 Oct 2015, 11:42 4 1 so the car travels 75km/hr. to cover 1 km, it would travel at 1/75 hours or 1/75 * 60 * 60 seconds. Simplify 75 and one of 60 by 15, and get 1/5 * 4 * 60 -> simplify again 5 and 60 and get 1412 = 48 seconds. We know that the car makes 1 km in 48 seconds. we know that the car spends 2 seconds more, and this is 48+2 seconds, or 50 seconds. We have the distance, and we have the time. We can solve for rate: R = Distance/Time = 1km/50sec, for the sake of getting rid of 50 sec in the denominator, divide 1km by 50 and get 0.02km/second now, 1 hour has 3600 seconds. Multiply 3,600 sec by 0.02km or 362 = 72km/h. VP Joined: 07 Dec 2014 Posts: 1256 Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 31 Oct 2015, 19:14 faster car travels 1 kilometer in 1/75 hour slower car travels 1 kilometer in 1/75+1/1800 hour 1/75+1/1800=25/1800=1/72 hour inverting time and rate, slower car travels at 72 kph Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 10623 Location: Pune, India Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 01 Nov 2015, 21:13 8 7 A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 If I had only 10 seconds to read the question and mark, I would mark it as (B) 72. The reason is the kind of numbers we are dealing with. 1 hour has 3600 seconds (which is a multiple of 2, 3 and 5, 18 etc). 75 km is again a multiple of 3 and 5. Getting 71 or 73 out of these numbers wouldn't really work out. It will be unusual to get decimals. So my best blind guess would be 72. If I did have some time, I would use the unitary method on it: Case 1: 75 kms in 3600 secs 1 km in 3600/75 = 48 secs Case 2: In (48+2) = 50 secs, it covers 1 km In 3600 secs, it will cover (1/50) 3600 = 72 km Speed = 72 km/hr _________________ Karishma Veritas Prep GMAT Instructor Director Joined: 17 Dec 2012 Posts: 628 Location: India Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 02 Nov 2015, 00:13 A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 Variables given : d1= 1 km d2=1 km s2=75 Variables expressed in terms of another:- t1 = t2+ 2/3600 To find : s1=? We need to form two equations based on the above: We know distance travelled is the same. So equate distances. s1t1=s2t2 s1(t2+2/3600)=75t2 --- (1) We also know the values of d2 and s2. So we can find t2. d2=s2t2 i.e., 1=75t2 => t2=1/75 hr Substituting the value of t2 in (1), we get s1=72 km/hr _________________ Srinivasan Vaidyaraman Magical Logicians Holistic and Holy Approach Manager Joined: 26 Dec 2015 Posts: 225 Location: United States (CA) Concentration: Finance, Strategy WE: Investment Banking (Venture Capital) A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 22 Feb 2017, 19:07 1 This is a rarity, but I like GMATPrep's solution to this problem. I'll do my best to rephrase (btw yes, this is a conversion problem): First, I like to set up the initial conversion (for the car in the 1st scenario): (75 km/1hr)(1hr/60min)(1min/60sec) --> 75 km/3600 sec. You can simplify this further into: 1 km/48 sec. Now, let's take the same car in a different scenario (2nd): 1 km/48+2 seconds --> 1 km/50 seconds. NOTE: the Q asks for speed in KM per HOUR. So we need to convert from seconds into hours. 50 seconds goes into 3600 seconds 72x. kudos always appreciated if this helps Intern Joined: 14 May 2014 Posts: 15 Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 09 Mar 2017, 20:57 With the current speed, the drive takes 2 seconds more to travel every km and 275 = 150 more seconds to travel 75 km. So it takes him 1+1/24=25/24 hours to travel 75 km It means in 1 hour, he can travel 7524/25=72 km =>> his speed = 72km/h =>> Answer B Target Test Prep Representative Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2799 Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 15 Mar 2017, 15:38 2 A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 We can let r = the speed of the car in km per hour; thus it would take the car 1/r hour to travel 1 km. If the car traveled at 75 km per hour, then it would take the car 1/75 hour to travel 1 km. We are given that the car would be 2 seconds faster traveling 1 km had it traveled at 75 km per hour. Since 2 sec = 1/1800 hour, we can create the following equation: 1/75 + 1/1800 = 1/r Multiplying the entire equation by 1800r, we have: 24r + r = 1800 25r = 1800 r = 72 _________________ # Jeffrey Miller Jeff@TargetTestPrep.com 225 Reviews 5-star rated online GMAT quant self study course See why Target Test Prep is the top rated GMAT quant course on GMAT Club. Read Our Reviews Director Status: Professional GMAT Tutor Affiliations: AB, cum laude, Harvard University (Class of '02) Joined: 10 Jul 2015 Posts: 800 Location: United States (CA) Age: 40 GMAT 1: 770 Q47 V48 GMAT 2: 730 Q44 V47 GMAT 3: 750 Q50 V42 GMAT 4: 730 Q48 V42 (Online) GRE 1: Q168 V169 WE: Education (Education) Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 16 Mar 2017, 18:05 Top Contributor Attached is a visual that should help. Attachments Screen Shot 2017-03-16 at 7.04.43 PM.png [ 136.03 KiB \| Viewed 28436 times ] VP Joined: 07 Dec 2014 Posts: 1256 A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 16 Mar 2017, 20:38 A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 75 kph=4/5 minute, or 48 seconds, per k 48+2=50 seconds=5/6 minute 60/(5/6)=72 kph Director Joined: 17 Dec 2012 Posts: 628 Location: India Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 27 May 2017, 23:43 A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 1.Since we are given that it takes 2 seconds longer to travel 1 km in the current speed, we have to find the total number of seconds to travel 1 km in the hypothetical case 2.Speed of 75 km/hr is 0.8 min or 48 seconds to travel 1 km, the car currently takes 2 seconds longer i.e. 50 seconds to travel 1 km 3.We have to convert it to km/hr i.e., 1km/50 seconds = 1km /(50/3600)hr = 72 km/hr. _________________ Srinivasan Vaidyaraman Magical Logicians Holistic and Holy Approach Manager Joined: 26 Mar 2017 Posts: 100 A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 24 Jun 2017, 05:10 t = d/r r=d/t t= 1/75 + 2/(6060) r = 1/1/75 + 2/(6060) _________________ I hate long and complicated explanations! GMAT Club Legend Joined: 11 Sep 2015 Posts: 4947 GMAT 1: 770 Q49 V46 Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 13 Dec 2017, 07:23 2 Top Contributor A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 GIVEN: A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. Let x = the car's speed We can write: (travel time at x km per hour) = (travel time at 75 km per hour) + 2 seconds Since the speeds are in km per HOUR, let's rewrite 2 seconds as 2/3600 hours (since there are 3600 second in one hour) We get: (travel time at x km per hour) = (travel time at 75 km per hour) + 2/3600 hours Or: (travel time at x km per hour) = (travel time at 75 km per hour) + 1/1800 hours Travel time = distance/speed We get: 1/x = 1/75 + 1/1800 hours The least common multiple of the denominators is 1800x, so.... Multiply both sides by 1800x to get: 1800 = 24x + x Simplify: 1800 = 25x Solve: x = 1800/25 = 72 RELATED VIDEO _________________ Test confidently with gmatprepnow.com Manager Joined: 16 Jul 2016 Posts: 52 A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 15 Dec 2017, 09:39 $$rate * time = distance$$ rate and time are inversely proportional. So assuming the distance stays the same, doubling the time will half the rate. multiplying the time by 3/2 will result in a rate 2/3 as much. 75 * (1/75) = 1 The car goes 75 km per hour for 1/75 of an hour so for (3600/75)=48 seconds. When the car takes two seconds longer it takes 50 seconds. The time increased by a factor of (25/24). The rate must therefore be multiplied by (24/25). $$75(\frac{24}{25})=72$$ Intern Joined: 23 Jun 2017 Posts: 10 Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] ### Show Tags 15 Feb 2018, 05:39 A car traveling at a certain constant speed takes 2 seconds longer to travel 1 kilometer than it would take to travel 1 kilometer at 75 kilometers per hour. At what speed, in kilometers per hour, is the car traveling? A. 71.5 B. 72 C. 72.5 D. 73 E. 73.5 ffs....... 1/x - 1/75 = 2/3600 thats it Re: A car traveling at a certain constant speed takes 2 seconds [#permalink] 15 Feb 2018, 05:39 Go to page 1 2 Next [ 25 posts ]	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5990049839019775, "perplexity": 4099.3831340108345}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593655878753.12/warc/CC-MAIN-20200702111512-20200702141512-00368.warc.gz"}
https://boredofstudies.org/threads/differential-equations-question.393873/	# Differential Equations Question (1 Viewer) #### le_420_prince ##### New Member Joined Apr 12, 2015 Messages 19 Gender Male HSC 2016 This question is giving me a headache starting from part a, I really dont even understand what theyre asking for... Thankyou! #### Attachments • 92.2 KB Views: 60 #### notme123 ##### Member Joined Apr 14, 2020 Messages 95 Gender Male HSC 2021 This question is giving me a headache starting from part a, I really dont even understand what theyre asking for... Thankyou! What is Py supposed to mean? Is it multiplication or a subscript? If it's a subscript then what's that notation? #### Qeru ##### Well-Known Member Joined Dec 30, 2020 Messages 263 Gender Male HSC 2021 Could you show what Q12 is so we actually know what the variables and constants mean? #### CM_Tutor ##### Well-Known Member Joined Mar 11, 2004 Messages 1,622 What is Py supposed to mean? Is it multiplication or a subscript? If it's a subscript then what's that notation? $\bg_white P$ is a constant and $\bg_white y$ is a function of $\bg_white t$ (time). #### CM_Tutor ##### Well-Known Member Joined Mar 11, 2004 Messages 1,622 We have a function $\bg_white N(t)$ where $\bg_white N(0)=N_0$, a constant, which satisfies the differential equation (DE) $\bg_white \frac{dN}{dt}=kN(P-N) \qquad \text{. . . . . . . . ()}$ where $\bg_white k$ and $\bg_white P$ are constants. (a) Let $\bg_white y(t)$ be a function related to $\bg_white N(t)$ by the equation $\bg_white N(t) = P \times y(t)$. It follows that $\bg_white \frac{dN}{dt}=P\times\frac{dy}{dt}$ which can be substituted into () to give: \bg_white \begin{align} \frac{dN}{dt}&=kN(P-N) \\ P\frac{dy}{dt}&=kPy(P-Py) \\ &=kP^2y(1-y) \\ \frac{dy}{dt}&=kPy(1-y) \end{align} Now, let $\bg_white r=kP$, a constant, and the DE becomes: $\bg_white \frac{dy}{dt}=ry(1-y) \qquad \text{. . . . . . . . ()}$ with the initial value of $\bg_white y$ being $\bg_white y_0 = y(0) = \frac{N(0)}{P} = \frac{N_0}{P}$. (b) Let $\bg_white x$ be a variable related to time by $\bg_white x=rt$, from which it follows that $\bg_white \frac{dx}{dt}=r \qquad \text{. . . . . . . . (1)}$. From the Chain Rule, we know that $\bg_white \frac{dy}{dx}=\frac{dy}{dt}\times\frac{dt}{dx}$ and we can substitute () and (1) into this to get \bg_white \begin{align} \frac{dy}{dx}&=\frac{dy}{dt}\times\frac{dt}{dx} \\ &=ry(1-y)\times\frac{1}{r} \\ &=y(1-y) \qquad \text{. . . . . . . . (*)} \end{align} which is a DE in two variables, $\bg_white x$ and $\bg_white y$. At $\bg_white x=0$, it has the initial value $\bg_white y = y_0 = \frac{N_0}{P} \quad \text{as} \quad t=0 \implies x=rt=r\times0=0$. (c) Let $\bg_white v$ be a variable related to $\bg_white y$ by $\bg_white v = \frac{1}{y} \implies \frac{dv}{dy} = -\frac{1}{y^2} \qquad \text{. . . . . . . . (2)$ from which it follows that \bg_white \begin{align} \frac{dv}{dx} &= \frac{dv}{dy} \times \frac{dy}{dx} \quad \text{using the Chain Rule} \\ &= -\frac{1}{y^2} \times y(1-y) \quad \text{using (2) and (*)} \\ &= \frac{y - 1}{y} \\ &= 1 - \frac{1}{y} \\ &=1-v \end{align} The problem has now been transformed into one that can be solved by integration without the need to use partial fractions: $\bg_white \frac{dv}{1-v}=dx$ I'll leave the rest for you to work on. Last edited: #### Qeru ##### Well-Known Member Joined Dec 30, 2020 Messages 263 Gender Male HSC 2021 \bg_white \begin{align}P\frac{dy}{dt}&=kPy(P-Py) \\ &=kP^2y(1-y)\end{align} Is it $\bg_white P \times y$ or $\bg_white P_y$, why can you factor out a P like that? #### CM_Tutor ##### Well-Known Member Joined Mar 11, 2004 Messages 1,622 Is it $\bg_white P \times y$ or $\bg_white P_y$, why can you factor out a P like that? It is $\bg_white P\times y$. The point is to take a DE that calls for partial fractions and get a solution without using that approach. If it was $\bg_white P_y$ then you are correct that $\bg_white P$ would not be a common factor that could be separated. Also, we would need a definition of $\bg_white P_y$. #### Qeru ##### Well-Known Member Joined Dec 30, 2020 Messages 263 Gender Male HSC 2021 It is $\bg_white P\times y$. The point is to take a DE that calls for partial fractions and get a solution without using that approach. If it was $\bg_white P_y$ then you are correct that $\bg_white P$ would not be a common factor that could be separated. Also, we would need a definition of $\bg_white P_y$. Yep thanks. I think thats where the confusion was for OP since the textbook makes it look like $\bg_white P_y$. #### le_420_prince ##### New Member Joined Apr 12, 2015 Messages 19 Gender Male HSC 2016 CM_Tutor, thankyou so much for the solution!! and thankyou everyone for the input also!!! a massive help!! i think i was quite confused by the P(subscript)y which is now agreed to be a misprint and instead P*y but now that clears it all up #### CM_Tutor ##### Well-Known Member Joined Mar 11, 2004 Messages 1,622 $\bg_white \frac{dv}{1-v}=dx \implies -\ln\|1-v\|=x+C \quad \text{for some constant C}$ At $\bg_white x=0$, we know that $\bg_white y=N_0/P$ and so $\bg_white v=\frac{P}{N_0} \implies C=-\ln\left\|1-\frac{P}{N_0}\right\| \implies x=\ln\left\|\frac{N_0-P}{N_0(1-v)}\right\|$ $\bg_white \implies v = 1-\frac{N_0-P}{N_0e^x} \implies y = \frac{N_0e^x}{N_0(e^x-1)+P}$ $\bg_white \implies N = \frac{PN_0e^{kPt}}{N_0(e^{kPt}-1)+P}=\frac{PN_0}{(P-N_0)e^{-kPt}+N_0}$ Checks When $\bg_white t=0$: $\bg_white N = \frac{PN_0}{(P-N_0)e^{0}+N_0}= \frac{PN_0}{P} = N_0$ as expected. Further, as $\bg_white t\to+\infty$: $\bg_white N \to \frac{PN_0}{(P-N_0)\times 0+N_0} \to \frac{PN_0}{N_0} \to P^{-}$ Further, as $\bg_white t\to-\infty$: $\bg_white N \to \frac{PN_0}{(P-N_0)\times e^{+\infty}+N_0} \to 0^+$ We can see that the domain is $\bg_white t\in\mathbb{R}$ and that $\bg_white N$ is bounded below by 0 and bounded above by $\bg_white P$. That is, $\bg_white N\in(0, P)$. It follows that, provided $\bg_white k>0$: $\bg_white \frac{dN}{dt}=kN(P-N)>0$ And thus $\bg_white N$ is increasing at all times. The answer to part (f) is thus: $\bg_white N = \frac{PN_0}{(P-N_0)e^{-kPt}+N_0} = \frac{PN_0}{Pe^{-kPt}+N_0(1-e^{-kPt})} = \frac{PN_0e^{kPt}}{P+N_0(e^{kPt}-1)}$ and can also be expressed as: $\bg_white N = \frac{P}{1+\left(\cfrac{P}{N_0}-1\right)e^{-kPt}} = \frac{P}{1-\left(1-\cfrac{P}{N_0}\right)e^{-kPt}}$ Last edited:	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 66, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999610185623169, "perplexity": 1086.6378308520361}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178377821.94/warc/CC-MAIN-20210307135518-20210307165518-00565.warc.gz"}
http://math.stackexchange.com/users/43495/katya-porfiryeva?tab=reputation	# Katya Porfiryeva Unregistered less info reputation 1 bio website location age member for 2 years, 3 months seen Oct 3 '12 at 14:52 profile views 2 # 11 Reputation 5 Oct 14 '12 +5 13:13 upvote Differential equation $y''=\frac{1}{y^2}$ 5 Oct 3 '12 +5 15:14 upvote Differential equation $y''=\frac{1}{y^2}$	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.23002512753009796, "perplexity": 12634.567235291408}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422122022571.56/warc/CC-MAIN-20150124175342-00053-ip-10-180-212-252.ec2.internal.warc.gz"}
https://www.eurotrib.com/story/2010/10/30/20724/383	Welcome to European Tribune. It's gone a bit quiet around here these days, but it's still going. ## KTX: of delays and ambitions by DoDo Mon Nov 1st, 2010 at 06:42:41 AM EST Korea Train eXpress (KTX) was mainland Asia's first high-speed railway (HSR), and also the first extra-European export success for European high-speed rail technology. The KTX story matches that of Taiwan's THSR in many ways: similar passenger numbers, project costs; both started with passenger numbers well below forecasts and with deficits that made them a national scandal; and in both cases, the reasons included a half-finished state, delays, and difficulties inherent in the financial construction. However, having started on 1 April 2004 already, KTX is further down the curve: it turned a profit in 2007, and it began to be seen as a success by enough people for calls for extensions to be heard. Today, on 1 November 2010, the second phase of KTX entered service, completing the HSR tracks on the more than 400 km route between the capital Seoul and second largest city Busan. A second line and several conventional line upgrades are in construction, and there is ambition in local rolling stock development. A KTX-II, a TGV clone built by domestic maker Rotem, leaves Daejeon on 5 May 2010 while a series 8200 (a Siemens Eurosprinter) approaches with an express in the background. Photo by user vvvf from Picasa Time for a closer look at this system, and, on the occasion, on the issues of national ambition as driving force and the significance of delays in mega-projects. Domesticating high-tech At its original inception in the eighties, KTX was meant to free up capacity for freight on the country's busiest traffic corridor, in a time of ever worsening traffic jams brought by rapid economic growth. This growth was created by an especially close collusion of the state and domestic Big Business: depending on how you look at it, you could call it proactive development policy, or guided capitalism, or corporatocracy, or institutionalised corruption. One specific of the South Korean model was that Big Business did not consist of big specialised companies, but the chaebol: clan-like family-owned conglomerates that rapidly built up production capacity in unrelated industries. Another speciality was that South Korea's transformation from agrarian society to industrial giant happened in a time of military dictatorship. As a result, the chaebol didn't just dominate but were almost all of the economy, public procurement was a matter of dividing up the turf between them, and the arrival of democracy didn't do much to loosen ties with politicians. While the South Korean model unquestionably brought economic prosperity and modernity, it also fostered corruption, sabotage of public oversight, and bubbles – in particular, loose loans to the chaebol to socialise the risks, which resulted in the 1997 collapse (and subsequent IMF "cure"). Under these auspices, it shouldn't be surprising that South Korea pursued high-speed rail as a state-run project, for which domestic companies were to develop and supply the technology. But this approach had its problems. First, in June 1992, construction went ahead even before the technology was fixed (more later). With suppliers lacking prior experience and getting contracts as special favour, quality problems were persistent. (Actually, they still were for the now opened section.) Second, the 1997/8 crisis hit the government budget and some of the contracted chaebol hard, forcing a re-scheduling into two phases: the tunnel-rich last third of the line was pushed back a few years. Third, it became clear that the domestic industry won't churn out a high-speed train or track any time soon, so the technology had to be imported. In 1994, GEC-Alsthom (today Alstom), the main maker of France's TGVs, won the contract to supply initial trains and equipment, and transfer the technology to local companies. A TGV in Asia: a KTX-I races towards Seoul on the longest viaduct of the line, the 6,844 m Pungse Viaduct, south of Cheonan. Photo from The World Railway Gallery Train construction itself, and with that the TGV know-how, was transferred to Hyundai's subsidiary Rotem. In parallel, a programme that was mostly state-funded and mostly run by state research institutions was started to develop an improved, wholly domestic type for Rotem. Experimental train HSR-350x in Gwangmyeong station. The commercial version took another round of development: check nose shape and bogie shrouding. Photo from Luthien's 망상공방 blog When the KTX-II was finally presented two years ago, press releases boasted about South Korea becoming the fourth country to develop a train for 300 km/h (forgetting about Made in Italy and Made in Spain, not to mention China). However, unlike its electronics and seating, the KTX-II's 305 km/h top speed and conventional trailers-between-traction-heads configuration wasn't cutting-edge any more. Thus there is already another government-pushed programme, which should result in a 350 km/h distributed-power Rotem train, in service as KTX-III by 2015. The mock-up of the HEMU-400X at an event in 2009. Photo from WHhh4nwOyo's KTX Watch pages Delays In the end, the KTX price tag, including the first trains and the completed Seoul–Busan line, grew from 5.8 to 20.7 trillion won, and the date of completion was delayed 12 years. The two aren't independent. When a mega-project is over budget, most people think of construction problems, waste and corruption. However, delays drive costs in more ways than one would think at first: • Inflation and unit costs: the simplest cost estimates are given in fixed prices (the prices at the time the estimate was made), thus even projects finished on time and without extra expenses could appear bloated. More advanced estimates (for example, Crossrail's £15.9 billion price tag) also include a future inflation forecast, however, delays mean further inflation beyond that. Note that it's not just general inflation that's relevant here: some products or services used in construction can see unit costs increase much more strongly. • Interest: if a project is financed with loans, there will be periods of maturity and interest rates to meet. Thus delays might mean paying more or before there is income, which in turn might make a refinancing with even more loans necessary. • Wages and rent: the re-scheduling of construction over a longer period of time might reduce the load on the annual budget, however, overall costs increase because wages for part of the workforce and rent for the sites and some equipment will have to be paid for longer. • Standards: over the long time a mega-project is realised, both the applied technologies and the requirements by law might change, and such changes might bring higher costs. This is especially true for HSR projects over the past few decades: tunnels dimensioned and equipped for fire safety, ballast-less track, noise protection, urban sections are all significant cost boosters. Three of the above played a significant role for KTX: • In the five years between the basic plan and the start of serious construction work, wages in the construction sector tripled; • construction of the line was separated into two phases following the 1997–1998 Asian Crisis, to please the IMF with budget cuts; • fire safety standards for tunnels were introduced only when the first phase was already built, the second phase got ballast-less track, and two city-crossing sections (and three extra stations) were (re)added to the project in 2006. A KTX-I train on a test run on the ballast-less track of the new section at Deokcheon-ri in September. Photo from Digital Kookje Disputes un/like in Europe The delay of the sections across Daejeon and Daegu was owed to long disputes with the cities over the routing: shall it be on ground, in tunnel, above ground; crossing or bypassing the city, or both? Such disputes are common in Europe. What is less common is changing plans back and forth several times while the rest of the line is already in construction. Another thing common in Europe is conflict with environmentalists and conservationists. But things get exotic with South Korea's most publicised environmental conflict: the salamanders vs. KTX case. On Mount Cheonseong, south-west of Ulsan, there are some protected mountaintop wetland areas, and in one of these, a rare kind of salamander was discovered. In the plans for the second phase of the Seoul–Busan KTX line, Wonhyo tunnel (second-longest on the line as well as in Korea at 13.27 km) was to pass right underneath, thus there was a non-zero risk of hitting and draining aquifers. The government refused to change plans. However, the protests grew and gained a nationwide, even international prominence when Buddhist nun the Venerable Ji Yul Sunim joined in, and started four hunger strikes in succession. Ji Yul & co also went to the courts, sought to make the salamanders co-plaintiffs, and hundreds turned up to testify in their stead. Salamander tapestry and live feed from Ji Yul in Seoul on the 84th day of the hunger strike that eventually achieved the halt in construction in 2005. Photos from the communist(!) Korean Action against Dispatch of Troops Ultimately, the battle ended in complete defeat for the environmentalists: the High Court did not recognise the salamanders as legal person, and construction proceeded according to original plans. Be it due to fortune or because builders paid extra attention to avoid negative publicity, no aquifer was drained. One might wonder why people were mobilised by this issue, while highways, road construction or sprawl have a much stronger effect on pristine areas than a tunnel deep below. However, at least to Ji Yul's credit, I note that currently she is documenting and protesting a massive river development project, a rather stronger intervention into nature. Traffic In Europe, a high-speed service with more than ten thousand passengers a day can be considered well-frequented, and not a single one got to more tan three times of that in its first year. In comparison, KTX's initial ridership in 2004 was astronomic – still, it was half of the final forecast, and a third of what was in the original plans. One reason is the end of 'limitless' economic growth. Another is speed: the very first plans (and ridership forecasts) foresaw 350 km/h trains covering the Seoul–Busan distance in 90 minutes, but the first phase realised only 300 km/h and 160 minutes. (The now opening second phase cuts the time to 138 minutes, KTX-III trains shall bring it down to 110 minutes.) A third reason is that the parallel improvement of urban mass transit connections to intermediate stations was put on a back-burner. A fourth reason was the policy to set ticket prices halfway between conventional express and airline tickets. The last two problems were alleviated with discounts and a selective price cut, bringing the fare on some intermediate relations almost down to conventional train level. In the end, KTX showed solid growth (until the Global Financial Crisis hit). KTX was a definite success in terms of market share. Even the new budget airlines failed to dent KTX's market share – until they got help from a railway: the new subway link to Seoul's Gimpo airport (opened a year ago) made them competitive on travel time to South Seoul. But now KTX is changing that calculation again. Responding to customer demand The loads of KTX passengers drawn from airlines and cars weren't used to seats facing backwards. Thus all seats of the KTX-II are swivelling seats which can be turned around at terminuses – something appearing in Europe only now. A funnier issue is top speed. KTX trains have video screens showing movies, and also the train's actual speed. Train speed is not constant: it reduces slightly when the train is climbing grades, entering tunnels or negotiating curves. But Korail was flooded by complaints from passengers who could only snap pictures of 29x on the screen, not the advertised 300 mark. The solution: top speed was simply raised to 305 km/h! Network expansion Back in January 2005, when KTX's failure to meet forecasts was a national scandal, the government wanted to shelve the project of a second high-speed line. However, as KTX turned into a success and a part of the "Korean way of life", the second KTX line became a matter of not being left on the sidelines for locals. Thus politicians competed with promises to bring the project back on track, and it is in the works since last year. Perhaps more significant is the KTX's effect on conventional lines. When the IMF forced the staging of the original project, and made the second line a distant dream, parts of the parallel conventional lines were upgraded so that the trains can reach their originally intended destinations. Then the experience gained led to bolder upgrades and even new lines elsewhere in the country – by early this year, practically the entire mainline network is foreseen for (or already subject to) total reconstruction. Map adapted from JoongAng Daily :: :: :: :: :: Check the Train Blogging index page for a (hopefully) complete list of ET diaries and stories related to railways and trains. Display: Threaded Minimal Nested Flat Flat UnthreadedDynamic ThreadedDynamic Minimal South Korea treats high-speed rail as an object of national prestige -- and export opportunity, trying to market it in Turkey, Brazil and the USA. However, as shown in the Salon, South Korea's plans for 2015 have already been overtaken by China. Lunatic, n. One whose delusions are out of fashion. Your really wonderful pictures of trains, and the informative, useful and well-resourced material you provide, help make ET the special place it is. Thanks, DoDo! The loads of KTX passengers drawn from airlines and cars weren't used to seats facing backwards. Thus all seats of the KTX-II are swivelling seats which can be turned around at terminuses - something appearing in Europe only now. A very low-tech version of this has been standard in New York-area commuter trains for ages.... That's interesting. I heard that there have been swivelling seats in the USA for longer; but why on commuter trains? As for why there was no significant demand for this in Europe, I can only speculate: here, speed increases weren't as dramatic in relative terms as in South Korea, that is, f.e. passengers who got used to travelling in backward facing seats at 200 km/h on the Le Capitole had not much trouble with the TGV's initial speed of 260 km/h. Lunatic, n. One whose delusions are out of fashion. They don't swivel. The whole bench has a hinge so that they can be flipped to face the other direction. Typically, the conductor flips them all at the end of the journey, but you can flip one yourself so that a group of people can travel facing each other (assuming the conductor is one who doesn't object.) As a kid in Leicester, one favourite and noisy event was 'reversing' the seats backs on trams when they got to the terminus. A slatted wooden bench seat had an upright slatted back hinged at the ends of the bench. You can't be me, I'm taken But Korail was flooded by complaints from passengers who could only snap pictures of 29x on the screen, not the advertised 300 mark. The solution: top speed was simply raised to 305 km/h! Ha ha ha. Only in Korea! The connection to Jeju Island (population 560,000, 85 km tunnel or bridge) seems a very faraway, improbable, grandiose dream. Environmental protests: Koreans have somewhat of an itch to protest and challenge the government. Student protests in the 80s against military dictatorship, labor conflicts, recent massive protests over imported beef. Much of this has a theatrical component like the physical altercations in parliament. Schengen is toast! The connection to Jeju Island (population 560,000, 85 km tunnel or bridge) seems a very faraway, improbable, grandiose dream. Yep, just one level down from madness like the daydreams about the Korea-Japan and Korea-China tunnels.In January 2009, Korea Transport Institute also proposed a 167 km (104 mi) line from Mokpo to Jeju Island, putting Jeju 2 hours 26 minutes from Seoul.[33] The line would include a 28 km (17 mi) bridge from Haenam to Bogul Island and a 73 km (45 mi) undersea tunnel from Bogil Island to Jeju Island (with a drilling station on Chuja Island), for an estimated cost of US$10 billion.[33] As the proposal was popular with lawmakers from South Jeolla province, the government is conducting a feasibility study, but the governor of Jeju expressed skepticism.[34] I'd doubt even that US$10 billion estimate. Then again, the governor expressed scepticism because he wants airport expansion instead. (BTW, I forgot to mention: for those interested in the KTX system in more detail or more in-depth, read the linked Wikipedia article and the articles on individual lines linked from it -- I wrote more than 90% of all :-) ) Lunatic, n. One whose delusions are out of fashion. Jeju Island (population 560,000 Note: the proposal had to do with the island being a popular tourist resort; extra demand comparable to the flood of vacationing Madrileans justifying the Córdoba-Málaga line. Still, even if annual demand is a few million people, it's far away from a number justifying US\$10 billion. Lunatic, n. One whose delusions are out of fashion. Even more than this: Jeju Island is the de rigueur honeymoon destination for all Korean newlyweds; this is why it is so popular. One might wonder why people were mobilised by this issue, while highways, road construction or sprawl have a much stronger effect on pristine areas than a tunnel deep below. The Greens (or at least the press coverage of them) in Italy seem to suffer from the same problem. One of them was even quoted claiming that high-speed rail makes no sense as flights are so cheap... Sigh... I'm always of two minds when such protests go on. And at least in Korea's case, environmental protests could be a very necessary means to hold construction companies responsible, whatever they build -- from what I read, shoddy work and construction accidents leading to pollution or 'civilian' casualties are a bit too common, in spite of media attention. For example, I can kind of understand when some citizens of Daegu had second thoughts about a tunnel construction after this:The explosion, caused by a leaking gas main at a subway construction site, hurled cars, trucks and buses into the air.Thousands of steel plates being used as a temporary road surface were also thrown through the air in a deadly hail, crushing and dismembering pedestrians. "I heard a loud bang and flames rose about 50 metres into the air, taking with it steel plates," a taxi driver said.The 'national humiliation' of the Seongsu Bridge collapse would, unfortunately, pale in comparison to the 101 killed and 202 injured six months later in the April 28, 1995 Daegu gas explosion... Lunatic, n. One whose delusions are out of fashion. Perhaps more significant is the KTX's effect on conventional lines. When the IMF forced the staging of the original project, and made the second line a distant dream, parts of the parallel conventional lines were upgraded so that the trains can reach their destinations. Then the experience gained led to bolder upgrades and even new lines elsewhere in the country -- by early this year, practically the entire mainline network is foreseen for (or already subject to) total reconstruction. Hong Sang-soo's film The Power of Kangwon Province (1998) has characters taking a Gyeongchun Line (I think) train as part of a journey to Seoraksan. One of the carriages is an open plan sleeping car (rather like Soviet platskartny and Chinese hard class). When the upgrade of the Gyeongchun Line is complete in December, the entire line will become part of the Seoul subway. The reduction in journey times must be pretty spectacular. From Dodopedia: :) The line is being upgraded into an electrified and double-tracked line for 180 km/h. Between Geumgok and Chuncheon, from 1997 until 2010, the line was re-laid in a straighter, 64.2 km long alignment with a budget of 2.151,931 billion won. The remaining 17.9 km of the upgraded line was built with a separate budget of 574.124 billion won. Towards Seoul, after Toegyewon Station, the new line diverges from the old alignment that ended in Seongbuk Station, and will be reconnected to the Jungang Line at Mangu Station. When the current renovations are complete in December 2010, the entire line will be added to the Seoul Metropolitan Subway system, bringing that system from Seoul all the way into Gangwon-do. Ha! Indeed I wrote all but the last sentence quoted... Incidentally, I was thinking about illustrating the line upgrades with a photo of the old and new Gyeongchun Line, but those I found appear to be copyrighted. Check them out where I found them on SkysraperCity. As for The Power of Kangwon Province, I hope I come across it sometime... Lunatic, n. One whose delusions are out of fashion. I read that thread too. :) Are you a member at SkyscraperCity? (I am, under the same name.) Nah, but I frequently go there when looking for images for my diaries. Lunatic, n. One whose delusions are out of fashion. "This growth was created by an especially close collusion of the state and domestic Big Business: depending on how you look at it, you could call it proactive development policy, or guided capitalism, or corporatocracy, or institutionalised corruption." Makes you wonder what it took for Alsthom to win the order. Hyundai/Rotem has been fairly aggressive in getting into the US market. No high speed trainsets yet (of course) but they've won a messy EMU contract for Philadelphia, double deck coaches for Boston and LA and most recently an EMU order for Denver. The Philly order was won only after a particularly bloody battle with Kawasaki. This plus lots of technical delays made delivery almost two years late. Makes you wonder what it took for Alsthom to win the order. Giving away (not the newest) technology, of course :-) There was no domestic competitor, there was tech transfer. There was, however, fierce competition between GEC-Alsthom, Siemens and Mitsubishi, thus GEC-Alsthom/Alstom had not much of a profit margin at the end of the day (just a future competitor with its own technology). That's why they teamed up with Siemens in Taiwan -- an adventure that ended badly for other reasons. Lunatic, n. One whose delusions are out of fashion. "There was no domestic competitor, there was tech transfer." I've never really understood this strategy. It seems like transferring technology to markets with large scale competitors may gain you initial entry but unless you plan on setting up long term production, it's suicidal in the long run. Of course China is taking this to the logical extreme in that they're now using this same technology to enter the European market. As you may know, in the US the carbuilders have to transfer production here to be eligible for federal funds under good old Buy America. While this policy has got its weaknesses (including higher costs, corruption and limits on technological development), it actually helps the builders who do invest here as transferring production makes technology transfer between would-be competitors straight forward: there is none! Protectionism at its best but then again we know what to look out for having done the same thing as China in building up our industrial base 100+ years ago. Alstom's tech transfer strategy was to not sell the newest technology. The KTX-I was second-generation TGV, while Alstom was already developing the third generation when it won the tender, and was developing the AGV when KTX opened. Then again, Alstom's strategy did not help it to much more contracts. China indeed demanded state-of-the-art technology with near-complete transfer, and quickly set on developing the imported technology further than the original makers -- at least in maximum speed. However, one might have doubts about the quality of production, the Chinese makers have yet to develop a non-wide-bodied export version of any CRH type, and major European railways (I'm not counting privatised British railways here BTW) tend to order from suppliers they know and trust; so eventual competition in the HSR sector can be more expected in third countries. (On all of this, also see Globalisation catches up with rail industry?) Lunatic, n. One whose delusions are out of fashion. A significant difference between the way highways are funded and railways are funded lies in the value of partial upgrades. High speed rail is generally built as a new project from scratch whereas highways are upgraded piecemeal, often creating strong pressure to complete the project: Build a dual carriageway for some section, then return to a one lane each way highway and people will talk about finishing that section of before the road is even finished. Why isn't the same strategy useful for high speed rail? Because of the differences in top speed and acceleration. High-speed rail brings a real time improvement only if trains can run at top speed continuously for a significant distance. If construction is broken into 10-20 km segments like on highways, top speed won't even be reached by the end of an isolated section. Note though that in practice, piecemeal construction for high speeds (200-250 km/h) does happen, on projects foreseeing the upgrade and limited re-alignment of existing lines. Examples: Karlsruhe-Basel in Germany, Vienna-Linz in Austria, West Coast Mainline in the UK, and Athens-Thessaloniki in Greece. This is supposed to be high-speed line construction on the cheap, however, in practice, it was the opposite in all four cases: the result was a combination of limited time savings little noticed by passengers, and high costs due to inflation and many unexpected construction problems (existing infrastructure in the way or bad geology). Lunatic, n. One whose delusions are out of fashion. I just posted about acceleration (http://www.eurotrib.com/story/2010/11/5/145342/744#16) for exactly this point. But a 50km section is workable at 300km/hour - that's the distance between stations on the TGV right? That's a different league (well, 10 actually) to a completely new line over 500km. Yes, stations on high-speed lines can be as little as 30 km apart. But it's not a typical stopping distance. Many operators run trains with different stopping patterns, giving longer distances. The fastest scheduled Seoul-Busan trains, for example, have three sections between stops that are each about 130 km (the fourth, 22 km interval is in Seoul and not high speed). An additional note on this: you can still have pretty good average travel times over 50 km if both stations are on the high-speed line. If you build piecemeal, you have to connect to conventional lines, and the connections and the conventional lines until stations will reduce the time savings. Lunatic, n. One whose delusions are out of fashion. Many operators run trains with different stopping patterns, giving longer distances. Do you mean a skip-stop system or a local-express one? Good question; both :-) To stay with the KTX example: in the current timetable, from Seoul to Busan, there are four main stops where all trains call, and 3/1/2 secondary stops between those. All trains skip at least one secondary stop, some skip all, with the full range of variation in-between. (SNCF does the same with regional trains in some rural regions -- that's pretty anti-leisure-traveller of them.) BTW, long time no see! Lunatic, n. One whose delusions are out of fashion. On the Paris-Lyons-Marseilles line, most trains never stop in Lyons but go straight to the south, for example... Un roi sans divertissement est un homme plein de misères So build the piecemeal sections such that they give good run times. I'm imagining connecting one medium town centre to the next, with 300km/hour running in between. As demand ramps up, bypasses are built (tunnelling under the town or going around). Well, in effect, that is happening in South Korea and parts of Spain. Lunatic, n. One whose delusions are out of fashion. DoDo can correct me if I am wrong, but I am under the impression that with highspeed and old running on different railways, you get to keep the advantages of the old network with its many stops. So while the high-speed increases long distance rail, old network connect the long distance stations to more population centers, giving the rail network more nodes. Sweden's finest (and perhaps only) collaborative, leftist e-newspaper Synapze.se Yep, at least when it is run that way. Again there is an interesting development to note from South Korea. While it was generally expected that Korail will simply transfer all Seoul-Busan KTX services to the high-speed line when the last third is completed, they not only kept some trains on the old route (first two-thirds on the high-speed line and last third on the conventional line), but increased the frequency of trains stopping at stations along that conventional line section -- and introduced more trains with a new route, serving a city along the conventional line on the first third and then continuing on the high-speed line. Lunatic, n. One whose delusions are out of fashion. Has it been successful? It's day 10 of the new service, methinks too early to tell. Lunatic, n. One whose delusions are out of fashion. 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https://link.springer.com/chapter/10.1007%2F978-3-642-15277-1_16	Euro-Par 2010: Euro-Par 2010 - Parallel Processing pp 157-167 # A Fast 5/2-Approximation Algorithm for Hierarchical Scheduling • Marin Bougeret • Pierre-François Dutot • Klaus Jansen • Christina Otte • Denis Trystram Conference paper Part of the Lecture Notes in Computer Science book series (LNCS, volume 6271) ## Abstract We present in this article a new approximation algorithm for scheduling a set of n independent rigid (meaning requiring a fixed number of processors) jobs on hierarchical parallel computing platform. A hierarchical parallel platform is a collection of k parallel machines of different sizes (number of processors). The jobs are submitted to a central queue and each job must be allocated to one of the k parallel machines (and then scheduled on some processors of this machine), targeting the minimization of the maximum completion time (makespan). We assume that no job require more resources than available on the smallest machine. This problem is hard and it has been previously shown that there is no polynomial approximation algorithm with a ratio lower than 2 unless P = NP. The proposed scheduling algorithm achieves a $${{5}\over{2}}$$ ratio and runs in O(log(np max )knlog(n)), where p max is the maximum processing time of the jobs. Our results also apply for the Multi Strip Packing problem where the jobs (rectangles) must be allocated on contiguous processors. ## Keywords Parallel Machine Pack Procedure Maximum Completion Time Optimal Makespan Strip Packing These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves. ## References 1. 1. Foster, I., Kesselman, C., Tuecke, S.: The anatomy of the grid: Enabling scalable virtual organizations. International Journal of High Performance Computing Applications 15(3), 200 (2001) 2. 2. Feitelson, D.G., Rudolph, L., Schwiegelshohn, U., Sevcik, K.C., Wong, P.: Theory and practice in parallel job scheduling. In: JSSPP, pp. 1–34 (1997)Google Scholar 3. 3. Zhuk, S.: Approximate algorithms to pack rectangles into several strips. Discrete Mathematics and Applications 16(1), 73–85 (2006) 4. 4. Ye, D., Han, X., Zhang, G.: On-Line Multiple-Strip Packing. In: Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications (COCOA), p. 165. Springer, Heidelberg (2009)Google Scholar 5. 5. Bougeret, M., Dutot, P.F., Jansen, K., Otte, C., Trystram, D.: Approximation algorithm for multiple strip packing. In: Bampis, E., Jansen, K. (eds.) WAOA 2010. LNCS, vol. 5893, pp. 37–48. Springer, Heidelberg (2010) 6. 6. Pascual, F., Rzadca, K., Trystram, D.: Cooperation in multi-organization scheduling. In: Kermarrec, A.-M., Bougé, L., Priol, T. (eds.) Euro-Par 2007. LNCS, vol. 4641, pp. 224–233. Springer, Heidelberg (2007) 7. 7. Schwiegelshohn, U., Tchernykh, A., Yahyapour, R.: Online scheduling in grids. In: IEEE International Symposium on Parallel and Distributed Processing, IPDPS 2008, pp. 1–10 (2008)Google Scholar 8. 8. Steinberg, A.: A strip-packing algorithm with absolute performance bound 2. SIAM Journal on Computing 26, 401 (1997) 9. 9. Hochbaum, D., Shmoys, D.: A polynomial approximation scheme for scheduling on uniform processors: Using the dual approximation approach. SIAM J. Comput. 17(3), 539–551 (1988) ## Authors and Affiliations • Marin Bougeret • 1 • Pierre-François Dutot • 1 • Klaus Jansen • 2 • Christina Otte • 2 • Denis Trystram • 1 1. 1.Grenoble UniversityMontbonnot Saint MartinFrance 2. 2.Department of Computer ScienceChristian-Albrechts-University to KielKielGermany	{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8169499635696411, "perplexity": 9893.550734848934}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202628.42/warc/CC-MAIN-20190322034516-20190322060516-00236.warc.gz"}