1. The performance of ectotherms integrated over time depends in part on the position and shape of the distribution of body temperatures (Tb) experienced during activity. For several complementary reasons, physiological ecologists have long expected that Tb distributions during activity should have a long left tail (left-skewed); but only infrequently have they quantified the magnitude and direction of Tb skewness in nature.
2. To evaluate whether left-skewed Tb distributions are general for diurnal desert lizards, we compiled and analyzed Tb (∑ = 9,023 temperatures) from our own prior studies of active desert lizards on three continents (25 species in Western Australia, 10 in the Kalahari Desert of Africa, and 10 species in western North America). We gathered these data over several decades, using standardized techniques.
3. Many species showed significantly left-skewed Tb distributions, even when records were restricted to summer months. However, magnitudes of skewness were always small, such that mean Tb were never more than 1°C lower than median Tb. The significance of Tb skewness was sensitive to sample size, and power tests reinforced this sensitivity.
4. The magnitude of skewness was not obviously related to phylogeny, desert, body size, or median body temperature. Moreover, formal phylogenetic analysis is inappropriate because geography and phylogeny are confounded (that is, are highly collinear).
5. Skewness might be limited if lizards pre-warm inside retreats before emerging in the morning, emerge only when operative temperatures are high enough to speed warming to activity Tb, or if cold lizards are especially wary and difficult to spot or catch. Telemetry studies may help evaluate these possibilities.

A common descriptive statistic in cluster analysis is the $R^2$ that measures the overall proportion of variance explained by the cluster means. This note highlights properties of the $R^2$ for clustering. In particular, we show that generally the $R^2$ can be artificially inflated by linearly transforming the data by ``stretching'' and by projecting. Also, the $R^2$ for clustering will often be a poor measure of clustering quality in high-dimensional settings. We also investigate the $R^2$ for clustering for misspecified models. Several simulation illustrations are provided highlighting weaknesses in the clustering $R^2$, especially in high-dimensional settings. A functional data example is given showing how that $R^2$ for clustering can vary dramatically depending on how the curves are estimated.

Supplementary Material 3: A supplementary file with examples of SAS script for all models that have been fitted in this paper.

This database includes simulated data showing the accuracy of estimated probability distributions of project durations when limited data are available for the project activities. The base project networks are taken from PSPLIB. Then, various stochastic project networks are synthesized by changing the variability and skewness of project activity durations. Number of variables: 20 Number of cases/rows: 114240 Variable List: • Experiment ID: The ID of the experiment • Experiment for network: The ID of the experiment for each of the synthesized networks • Network ID: ID of the synthesized network • #Activities: Number of activities in the network, including start and finish activities • Variability: Variance of the activities in the network (this value can be either high, low, medium or rand, where rand shows a random combination of low, high and medium variance in the network activities.) • Skewness: Skewness of the activities in the network (Skewness can be either right, left, None or rand, where rand shows a random combination of right, left, and none skewed in the network activities)
• Fitted distribution type: Distribution type used to fit on sampled data • Sample size: Number of sampled data used for the experiment resembling limited data condition • Benchmark 10th percentile: 10th percentile of project duration in the benchmark stochastic project network • Benchmark 50th percentile: 50th project duration in the benchmark stochastic project network • Benchmark 90th percentile: 90th project duration in the benchmark stochastic project network • Benchmark mean: Mean project duration in the benchmark stochastic project network • Benchmark variance: Variance project duration in the benchmark stochastic project network • Experiment 10th percentile: 10th percentile of project duration distribution for the experiment • Experiment 50th percentile: 50th percentile of project duration distribution for the experiment • Experiment 90th percentile: 90th percentile of project duration distribution for the experiment • Experiment mean: Mean of project duration distribution for the experiment • Experiment variance: Variance of project duration distribution for the experiment • K-S: Kolmogorov–Smirnov test comparing benchmark distribution and project duration • distribution of the experiment • P_value: the P-value based on the distance calculated in the K-S test

Observed phenotypic responses to selection in the wild often differ from predictions based on measurements of selection and genetic variance. An overlooked hypothesis to explain this paradox of stasis is that a skewed phenotypic distribution affects natural selection and evolution. We show through mathematical modelling that, when a trait selected for an optimum phenotype has a skewed distribution, directional selection is detected even at evolutionary equilibrium, where it causes no change in the mean phenotype. When environmental effects are skewed, Lande and Arnold’s (1983) directional gradient is in the direction opposite to the skew. In contrast, skewed breeding values can displace the mean phenotype from the optimum, causing directional selection in the direction of the skew. These effects can be partitioned out using alternative selection estimates based on average derivatives of individual relative fitness, or additive genetic covariances between relative fitness and trait (Robertson-Price identity). We assess the validity of these predictions using simulations of selection estimation under moderate samples size. Ecologically relevant traits may commonly have skewed distributions, as we here exemplify with avian laying date – repeatedly described as more evolutionarily stable than expected –, so this skewness should be accounted for when investigating evolutionary dynamics in the wild.

This paper evaluates the claim that Welch’s t-test (WT) should replace the independent-samples t-test (IT) as the default approach for comparing sample means. Simulations involving unequal and equal variances, skewed distributions, and different sample sizes were performed. For normal distributions, we confirm that the WT maintains the false positive rate close to the nominal level of 0.05 when sample sizes and standard deviations are unequal. However, the WT was found to yield inflated false positive rates under skewed distributions, even with relatively large sample sizes, whereas the IT avoids such inflation. A complementary empirical study based on gender differences in two psychological scales corroborates these findings. Finally, we contend that the null hypothesis of unequal variances together with equal means lacks plausibility, and that empirically, a difference in means typically coincides with differences in variance and skewness. An additional analysis using the Kolmogorov-Smirnov and Anderson-Darling tests demonstrates that examining entire distributions, rather than just their means, can provide a more suitable alternative when facing unequal variances or skewed distributions. Given these results, researchers should remain cautious with software defaults, such as R favoring Welch’s test.

Supplementary Material 2: A supplementary file with examples of STATA script for all models that have been fitted in this paper.

Inlcuded is the supplementary data for Smith, B. T., Mauck, W. M., Benz, B., & Andersen, M. J. (2018). Uneven missing data skews phylogenomic relationships within the lories and lorikeets. BioRxiv, 398297. The resolution of the Tree of Life has accelerated with advances in DNA sequencing technology. To achieve dense taxon sampling, it is often necessary to obtain DNA from historical museum specimens to supplement modern genetic samples. However, DNA from historical material is generally degraded, which presents various challenges. In this study, we evaluated how the coverage at variant sites and missing data among historical and modern samples impacts phylogenomic inference. We explored these patterns in the brush-tongued parrots (lories and lorikeets) of Australasia by sampling ultraconserved elements in 105 taxa. Trees estimated with low coverage characters had several clades where relationships appeared to be influenced by whether the sample came from historical or modern specimens, which were not observed when more stringent filtering was applied. To assess if the topologies were affected by missing data, we performed an outlier analysis of sites and loci, and a data reduction approach where we excluded sites based on data completeness. Depending on the outlier test, 0.15% of total sites or 38% of loci were driving the topological differences among trees, and at these sites, historical samples had 10.9x more missing data than modern ones. In contrast, 70% data completeness was necessary to avoid spurious relationships. Predictive modeling found that outlier analysis scores were correlated with parsimony informative sites in the clades whose topologies changed the most by filtering. After accounting for biased loci and understanding the stability of relationships, we inferred a more robust phylogenetic hypothesis for lories and lorikeets.

CompanyKG is a heterogeneous graph consisting of 1,169,931 nodes and 50,815,503 undirected edges, with each node representing a real-world company and each edge signifying a relationship between the connected pair of companies.

Edges: We model 15 different inter-company relations as undirected edges, each of which corresponds to a unique edge type. These edge types capture various forms of similarity between connected company pairs. Associated with each edge of a certain type, we calculate a real-numbered weight as an approximation of the similarity level of that type. It is important to note that the constructed edges do not represent an exhaustive list of all possible edges due to incomplete information. Consequently, this leads to a sparse and occasionally skewed distribution of edges for individual relation/edge types. Such characteristics pose additional challenges for downstream learning tasks. Please refer to our paper for a detailed definition of edge types and weight calculations.

Nodes: The graph includes all companies connected by edges defined previously. Each node represents a company and is associated with a descriptive text, such as "Klarna is a fintech company that provides support for direct and post-purchase payments ...". To comply with privacy and confidentiality requirements, we encoded the text into numerical embeddings using four different pre-trained text embedding models: mSBERT (multilingual Sentence BERT), ADA2, SimCSE (fine-tuned on the raw company descriptions) and PAUSE.

Evaluation Tasks. The primary goal of CompanyKG is to develop algorithms and models for quantifying the similarity between pairs of companies. In order to evaluate the effectiveness of these methods, we have carefully curated three evaluation tasks:

Similarity Prediction (SP). To assess the accuracy of pairwise company similarity, we constructed the SP evaluation set comprising 3,219 pairs of companies that are labeled either as positive (similar, denoted by "1") or negative (dissimilar, denoted by "0"). Of these pairs, 1,522 are positive and 1,697 are negative.

Competitor Retrieval (CR). Each sample contains one target company and one of its direct competitors. It contains 76 distinct target companies, each of which has 5.3 competitors annotated in average. For a given target company A with N direct competitors in this CR evaluation set, we expect a competent method to retrieve all N competitors when searching for similar companies to A.

Similarity Ranking (SR) is designed to assess the ability of any method to rank candidate companies (numbered 0 and 1) based on their similarity to a query company. Paid human annotators, with backgrounds in engineering, science, and investment, were tasked with determining which candidate company is more similar to the query company. It resulted in an evaluation set comprising 1,856 rigorously labeled ranking questions. We retained 20% (368 samples) of this set as a validation set for model development.

Edge Prediction (EP) evaluates a model's ability to predict future or missing relationships between companies, providing forward-looking insights for investment professionals. The EP dataset, derived (and sampled) from new edges collected between April 6, 2023, and May 25, 2024, includes 40,000 samples, with edges not present in the pre-existing CompanyKG (a snapshot up until April 5, 2023).

Background and Motivation

In the investment industry, it is often essential to identify similar companies for a variety of purposes, such as market/competitor mapping and Mergers & Acquisitions (M&A). Identifying comparable companies is a critical task, as it can inform investment decisions, help identify potential synergies, and reveal areas for growth and improvement. The accurate quantification of inter-company similarity, also referred to as company similarity quantification, is the cornerstone to successfully executing such tasks. However, company similarity quantification is often a challenging and time-consuming process, given the vast amount of data available on each company, and the complex and diversified relationships among them.

While there is no universally agreed definition of company similarity, researchers and practitioners in PE industry have adopted various criteria to measure similarity, typically reflecting the companies' operations and relationships. These criteria can embody one or more dimensions such as industry sectors, employee profiles, keywords/tags, customers' review, financial performance, co-appearance in news, and so on. Investment professionals usually begin with a limited number of companies of interest (a.k.a. seed companies) and require an algorithmic approach to expand their search to a larger list of companies for potential investment.

In recent years, transformer-based Language Models (LMs) have become the preferred method for encoding textual company descriptions into vector-space embeddings. Then companies that are similar to the seed companies can be searched in the embedding space using distance metrics like cosine similarity. The rapid advancements in Large LMs (LLMs), such as GPT-3/4 and LLaMA, have significantly enhanced the performance of general-purpose conversational models. These models, such as ChatGPT, can be employed to answer questions related to similar company discovery and quantification in a Q&A format.

However, graph is still the most natural choice for representing and learning diverse company relations due to its ability to model complex relationships between a large number of entities. By representing companies as nodes and their relationships as edges, we can form a Knowledge Graph (KG). Utilizing this KG allows us to efficiently capture and analyze the network structure of the business landscape. Moreover, KG-based approaches allow us to leverage powerful tools from network science, graph theory, and graph-based machine learning, such as Graph Neural Networks (GNNs), to extract insights and patterns to facilitate similar company analysis. While there are various company datasets (mostly commercial/proprietary and non-relational) and graph datasets available (mostly for single link/node/graph-level predictions), there is a scarcity of datasets and benchmarks that combine both to create a large-scale KG dataset expressing rich pairwise company relations.

Source Code and Tutorial:https://github.com/llcresearch/CompanyKG2

Paper: to be published

Supplementary Material 1: A supplementary file with examples of R script for all models that have been fitted in this paper.

We introduce a novel framework that leverages the Box-Cox transformation to address the skewed distribution of samples and incorporates additional critical predictors to enhance the accuracy of soil salinity (measured as electrical conductivity of the saturated soil extract, ECe) and sodicity (measured as exchangeable sodium percentage, ESP) estimates.

We provide high-resolution (1 km × 1 km) global maps of soil salinity and sodicity from 1980 to 2022 in GeoTIFF file format for each year.

Note: the scale factor for ECe and ESP maps is 0.001

A skewed exponential power distribution, with parameters defining kurtosis and skewness, is introduced as a way to visualize Type II error in normality tests. By varying these parameters a mosaic of distributions is built, ranging from double exponential to uniform or from positive to negative exponential; the normal distribution is a particular case located in the center of the mosaic. Using a sequential color scheme, a different color is assigned to each distribution in the mosaic depending on the probability of committing a Type II error. This graph gives a visual representation of the power of the performed test. This way of representing results facilitates the comparison of the power of various tests and the influence of sample size. A script to perform this graphical representation, programmed in the R statistical software, is available online as supplementary material.

This dataset provides information about earnings of employees who are working in an area, who are on adult rates and whose pay for the survey pay-period was not affected by absence.

Tables provided here include total gross weekly earnings, and full time weekly earnings with breakdowns by gender, and annual median, mean and lower quartile earnings by borough and UK region. These are provided both in nominal and real terms.

Real earnings figures are on sheets labelled "real", are in 2016 prices, and calculated by applying ONS’s annual CPI index series for April to ASHE data.

Annual Survey of Hours and Earnings (ASHE) is based on a sample of employee jobs taken from HM Revenue & Customs PAYE records. Information on earnings and hours is obtained in confidence from employers. ASHE does not cover the self-employed nor does it cover employees not paid during the reference period.

The earnings information presented relates to gross pay before tax, National Insurance or other deductions, and excludes payments in kind.

The confidence figure is the coefficient of variation (CV) of that estimate. The CV is the ratio of the standard error of an estimate to the estimate itself and is expressed as a percentage. The smaller the coefficient of variation the greater the accuracy of the estimate. The true value is likely to lie within +/- twice the CV.

Results for 2003 and earlier exclude supplementary surveys. In 2006 there were a number of methodological changes made. For further details goto : http://www.nomisweb.co.uk/articles/341.aspx.
The headline statistics for ASHE are based on the median rather than the mean. The median is the value below which 50 per cent of employees fall. It is ONS's preferred measure of average earnings as it is less affected by a relatively small number of very high earners and the skewed distribution of earnings. It therefore gives a better indication of typical pay than the mean.

Survey data from a sample frame, use caution if using for performance measurement and trend analysis
'#' These figures are suppressed as statistically unreliable.
! Estimate and confidence interval not available since the group sample size is zero or disclosive (0-2).

Furthermore, data from Abstract of Regional Statistics, New Earnings Survey and ASHE have been combined to create long run historical series of full-time weekly earnings data for London and Great Britain, stretching back to 1965, and is broken down by sex.

In this paper, we show that the individual skewness, defined as the average of monthly skewness across firms, performs very well at predicting the return of S&P 500 index futures. This result holds after controlling for the liquidity risk or for the current business cycle conditions. We also find that individual skewness performs very well at predicting index futures returns out-of-sample.

Proteinoids are artificial polymers that imitate certain characteristics of natural proteins, including self-organization, catalytic activity, and responsiveness to external stimuli. This paper investigates the potential of proteinoids as organic audio signal processors. We convert sounds of the English alphabet into waveforms of electrical potential, feed the waveforms into proteinoid solutions and record electrical responses of the proteinoids. We also undertake a detailed comparison of proteinoids’ electrical responses (frequencies, periods, and amplitudes) with original input signals. We found that responses of proteinoids are less regular and have lower dominant frequency, wider distribution of proteinoids and less skewed distribution of amplitudes compared with input signals. We found that letters of the English alphabet uniquely map onto a pattern of electrical activity of a proteinoid ensemble, that is the proteinoid ensembles recognise spoken letters of the English alphabet. The finding will be used in further designs of organic electronic devices, based on ensembles of proteinoids, for sound processing and speech recognition. Methods We used a high-resolution data logger, specifically the ADC-24 from Pico Technology in the UK, along with iridium-coated stainless steel sub-dermal needle electrodes from Spes Medica S.r.l. in Italy, to accurately measure the electrical activity of the proteinoids. In order to measure the potential difference, pairs of electrodes were arranged with a distance of approximately 10 mm between each electrode. All electrical activity was captured at a rate of one sample per second. The data logger captured multiple measurements, up to 600 per second, and saved their average for further study. The BK 4060B function generator, referred to as the "device" in this paper, was used to generate electrical spikes. The device is a dual-channel function/arbitrary waveform generator. The device has the ability to generate a wide range of waveforms with high accuracy. These include sine, square, triangle, pulse, and arbitrary waveforms. In real point-by-point arbitrary mode, the maximum waveform generation rate is 75 MSa/s. However, in direct digital synthesis mode, the maximum waveform generation rate increases to 300 MSa/s. A setup was designed for an experiment to analyse how proteinoids respond to audio signals. The audio signals were captured using the microphone of the laptop and then processed using Matlab. The outcome of this processing yielded CSV files that consisted of a solitary column of potential values. The audio signals consisted of the letters A to Z of the English alphabet. The letters were pronounced by a male speaker using the vocal database available at the following URL: https://freesound.org/people/dersuperanton/sounds/434730/. The database contains recordings of individual letters being spoken in isolation as well as with different tones. We proceeded by using electrodes that were connected to a BK precision 4053 B transfer function in order to apply the CSV audio files to the proteinoids. The Picoscope 4000 series oscilloscope was used to record the response of proteinoids to audio signals. The data obtained was saved as CSV files for further analysis.

Multilocus sequence data provide far greater power to resolve species limits than the single locus data typically used for broad surveys of clades. However, current statistical methods based on a multispecies coalescent framework are computationally demanding, because of the number of possible delimitations that must be compared and time-consuming likelihood calculations. New methods are therefore needed to open up the power of multilocus approaches to larger systematic surveys. Here, we present a rapid and scalable method that introduces 2 new innovations. First, the method reduces the complexity of likelihood calculations by decomposing the tree into rooted triplets. The distribution of topologies for a triplet across multiple loci has a uniform trinomial distribution when the 3 individuals belong to the same species, but a skewed distribution if they belong to separate species with a form that is specified by the multispecies coalescent. A Bayesian model comparison framework was developed and the best delimitation found by comparing the product of posterior probabilities of all triplets. The second innovation is a new dynamic programming algorithm for finding the optimum delimitation from all those compatible with a guide tree by successively analyzing subtrees defined by each node. This algorithm removes the need for heuristic searches used by current methods, and guarantees that the best solution is found and potentially could be used in other systematic applications. We assessed the performance of the method with simulated, published, and newly generated data. Analyses of simulated data demonstrate that the combined method has favorable statistical properties and scalability with increasing sample sizes. Analyses of empirical data from both eukaryotes and prokaryotes demonstrate its potential for delimiting species in real cases.

The within-host evolutionary dynamics of TB remain unclear, and underlying biological characteristics render standard population genetic approaches based upon the Wright-Fisher model largely inappropriate. In addition, the compact genome combined with an absence of recombination is expected to result in strong purifying selection effects. Thus, it is imperative to establish a biologically-relevant evolutionary framework incorporating these factors in order to enable an accurate study of this important human pathogen. Further, such a model is critical for inferring fundamental evolutionary parameters related to patient treatment, including mutation rates and the severity of infection bottlenecks. We here implement such a model and infer the underlying evolutionary parameters governing within-patient evolutionary dynamics. Results demonstrate that the progeny skew associated with the clonal nature of TB severely reduces genetic diversity and that the neglect of this parameter in previous studies has led to significant mis-inference of mutation rates. As such, our results suggest an underlying de novo mutation rate that is considerably faster than previously inferred, and a progeny distribution differing significantly from Wright-Fisher assumptions. This inference represents a more appropriate evolutionary null model, against which the periodic effects of positive selection, associated with drug-resistance for example, may be better assessed.

Sediment particle size frequency distributions from the USNL (Unites States Naval Laboratory) box cores were determined optically using a Malvern Mastersizer 2000 He-Ne LASER diffraction sizer and were used to resolve mean particle size, sorting, skewness and kurtosis.

Samples were collected on cruises JR16006 and JR17007.

Funding was provided by ''The Changing Arctic Ocean Seafloor (ChAOS) - how changing sea ice conditions impact biological communities, biogeochemical processes and ecosystems'' project (NE/N015894/1 and NE/P006426/1, 2017-2021), part of the NERC funded Changing Arctic Ocean programme.

Estimated confidence interval for Virginia ground water well yields data (in gal/min/ft).

The grain-size distribution of 223 unconsolidated sediment samples from four DSDP sites at the mouth of the Gulf of California was determined using sieve and pipette techniques. Shepard's (1954) and Inman's (1952) classification schemes were used for all samples. Most of the sediments are hemipelagic with minor turbidites of terrigenous origin. Sediment texture ranges from silty sand to silty clay. On the basis of grain-size parameters, the sediments can be divided into the following groups: (1) poorly to very poorly sorted coarse and medium sand; and (2) poorly to very poorly sorted fine to very fine sand and clay.