On Quantization Errors in Approximate and Sample Entropy

Approximate and sample entropies are acclaimed tools for quantifying the regularity and unpredictability of time series. This paper analyses the causes of their inconsistencies. It is shown that the major problem is a coarse quantization of matching probabilities, causing a large error between their estimated and true values. Error distribution is symmetric, so in sample entropy, where matching probabilities are directly summed, errors cancel each other. In approximate entropy, errors are accumulating, as sums involve logarithms of matching probabilities. Increasing the time series length increases the number of quantization levels, and errors in entropy disappear both in approximate and in sample entropies. The distribution of time series also affects the errors. If it is asymmetric, the matching probabilities are asymmetric as well, so the matching probability errors cease to be mutually canceled and cause a persistent entropy error. Despite the accepted opinion, the influence of self-matching is marginal as it just shifts the error distribution along the error axis by the matching probability quant. Artificial lengthening the time series by interpolation, on the other hand, induces large error as interpolated samples are statistically dependent and destroy the level of unpredictability that is inherent to the original signal.

Genetic polymorphism and phylogenetic analysis of 15 autosomal STR markers in the Santal indigenous population of Bangladesh

Fifteen autosomal STR markers, namely D8S1179, D21S11, D7S820, CSF1PO, D3S1358, TH01, D13S317, D16S539, D2S1338, D19S433, vWA, TPOX, D18S51, D5S818, and FGA were typed using AmpFlSTR® Identifiler® Plus PCR amplification systems in 132 unrelated Santal individuals of Bangladesh. Forensic efficiency parameters like, matching probability (MP), power of discrimination (PD), polymorphism information content (PIC), power of exclusion (PE), typical paternity index (TPI), observed heterozygosity (Hobs), and expected heterozygosity (Hexp) were calculated for all the loci. No deviations from Hardy-Weinberg equilibrium were detected for the loci after Bonferroni correction. The combined matching probability (MP), combined power of discrimination (PD) and combined power of exclusion (PE) for the 15 tested STR markers were 8.38 x 10-17, 0.999999998 and 0.0.999993866, respectively. A comparison of the locus wise allele frequencies of autosomal STR data of the Santal population with the published geographically close population data based on Nei’s genetic distance revealed that the Santal population is closely related to Munda population from Jharkhand, India. Bioresearch Commu. 7(2): 1004-1009, 2021 (June)

In search of angels: the first bucket of gold for entrepreneurs

Purpose This paper aims to explore the allocation of the exit value of a start-up company in market equilibrium between an angel investor and an entrepreneur in the very early-stage financing market. Design/methodology/approach The theoretical model is established based on the two-sided random search theory and the model’s ability to match the empirical data is evaluated via simulation. Findings The model indicates that the allocation of the final investment outcome is not proportional to the initial investments by the angel investor and the entrepreneur. The simulation results show that the continued investment by the entrepreneur and the private benefit acquired by the angel investor have a more profoundly negative influence on the angel investor’s share of the exit value of the start-up company. Moreover, the market search structure represented by the matching probability of an angel investor to an entrepreneur has a more significant impact on the angel investor’s share than the other model parameters. Originality/value The importance of market search friction in the very early-stage financing market is emphasized. The concepts of continued investments and private benefits are introduced and quantified for the first time under the framework of angel investment. The impacts of such model parameters as the matching probability of an angel investor to an entrepreneur, the success rate of a start-up company, the bargaining power of an angel investor and the discount rate on the allocation of the exit value of the start-up company are investigated as well.

Use of Microsatellites in Genetic Diversity Assessment, Parentage Testing and Individual Identification of the Kangal Shepherd Dog

The Kangal Shepherd Dog is considered the most common dog breed of Turkish origin. This study investigated variations in ten autosomal microsatellite markers (PEZ01, PEZ03, PEZ05, PEZ06, PEZ08, PEZ12, PEZ20, FHC2010, FHC2054 and FHC2079) for the purposes of genetic diversity assessment of the Kangal breed. In addition, the use of markers was assessed in parentage testing and individual identification within the Kangal breed. The microsatellite markers were typed in 51 Kangal dogs. The total number of alleles in the study population was 69. The mean number of alleles per locus was 6.9, and varied from four (FHC2079) to 12 (PEZ12). The polymorphic information content (PIC) ranged from 0.52 (FHC2079) to 0.87 (PEZ12), with the mean value for all loci of 0.717. Power of exclusion (PE) in 10 microsatellites investigated varied between 0.143 (FHC2054) and 0.472 (PEZ08) per locus. In order to determine the efficiency of using microsatellites for individual identification in the Kangal breed, power of discrimination (PD) and matching probability (MP) were calculated for each microsatellite marker. The panel achieved high combined MP (6.77 × 10-10) and high combined PD value of 99.99999%. The obtained results may contribute to further recognition of the Kangal breed, and confirm that the investigated microsatellites enable a reliable parentage testing and individual identification of the breed.

Practical universal k-mer sets for minimizer schemes

Minimizer schemes have found widespread use in genomic applications as a way to quickly predict the matching probability of large sequences. Most methods for minimizer schemes use randomized (or close to randomized) ordering of k-mers when finding minimizers, but recent work has shown that not all non-lexicographic orderings perform the same. One way to find k-mer orderings for minimizer schemes is through the use of universal k-mer sets, which are subsets of k-mers that are guaranteed to cover all windows. The smaller this set the fewer false positives (where two poorly aligned sequences being identified as possible matches) are identified. Current methods for creating universal k-mer sets are limited in the length of the k-mer that can be considered, and cannot compute sets in the range of lengths currently used in practice. We take some of the first steps in creating universal k-mer sets that can be used to construct minimizer orders for large values of k that are practical. We do this using iterative extension of the k-mers in a set, and guided contraction of the set itself. We also show that this process will be guaranteed to never increase the number of distinct minimizers chosen in a sequence, and thus can only decrease the number of false positives over using the current sets on small k-mers.

The stellar content of the XMM-Newton slew survey

Aims. We present a detailed analysis of the stellar content of the current version of the XMM-Newton slew survey (XMMSL2). Methods. Since stars emit only a small fraction of their total luminosity in the X-ray band, the stellar XMMSL2 sources ought to have relatively bright optical counterparts. Therefore the stellar identifications were obtained by an automatic crossmatch of the XMMSL2 catalog with the first Gaia data release (Gaia DR1), 2MASS, and Tycho2 catalogs. The reliability of this procedure was verified by a comparison with the individually classified Einstein Observatory medium sensitivity survey X-ray sources and by a crossmatch with the Chandra Source Catalog. Results. We identify 6815 of the 23 252 unique XMMSL2 sources to be stellar sources, while 893 sources are flagged as unreliable. For every counterpart a matching probability is estimated based upon the distance between the XMMSL2 source and the counterpart. Given this matching probability the sample is expected to be reliable to 96.7 % and complete to 96.3 % . The sample contains stars of all spectral types and luminosity classes, and late-type dwarfs have the largest share. For many stellar sources the fractional contribution of the X-ray band to the total energy output is found above the saturation limit of previous studies (Lx/Lbol = 10−3), because the XMMSL2 sources are more affected by flares owing to their short exposure times of typically 6 s. A comparison with the second ROSAT all-sky survey (2RXS) source catalog shows that about 25 % of the stellar XMMSL2 sources are previously unknown X-ray sources. The results of our identification procedure can be accessed via VizieR.