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Asymptotic Bayes’ optimality under sparsity for exchangeable dependent multivariate normal test statistics
No full textHere, we suggest a family of easy-to-implement multiple hypotheses testing rules that is asymptotically optimal for sparsely present alternatives when the tests are based on a vector of exchangeable and dependent test statistics jointly following a multivariate normal distribution
Bounds on generalized family-wise error rates for normal distributions
No full textThe Bonferroni procedure has been one of the foremost frequentist approaches for controlling the family-wise error rate (FWER) in simultaneous inference. However, many scientific disciplines often require less stringent error rates. One such measure is the generalized family-wise error rate (gFWER) proposed (Lehmann and Romano in Ann Stat 33(3):1138–1154, 2005, https://doi.org/10.1214/009053605000000084). FWER or gFWER controlling methods are considered highly conservative in problems with a moderately large number of hypotheses. Although, the existing literature lacks a theory on the extent of the conservativeness of gFWER controlling procedures under dependent frameworks. In this note, we address this gap in a unified manner by establishing upper bounds for the gFWER under arbitrarily correlated multivariate normal setups with moderate dimensions. Towards this, we derive a new probability inequality which, in turn, extends and sharpens a classical inequality. Our results also generalize a recent related work by the first author
Brain Connectivity Analysis for EEG-Based Face Perception Task
No full textFace perception is considered a highly developed visual recognition skill in human beings. Most face perception studies used functional magnetic resonance imaging to identify different brain cortices related to face perception. However, studying brain connectivity networks for face perception using electroencephalography (EEG) has not yet been done. In the proposed framework, initially, a correlation-tree traversal-based channel selection algorithm is developed to identify the \u27optimum\u27 EEG channels by removing the highly correlated EEG channels from the input channel set. Next, the effective brain connectivity network among those \u27optimum\u27 EEG channels is developed using multivariate transfer entropy (TE) while participants watched different face stimuli (i.e., famous, unfamiliar, and scrambled). We transform EEG channels into corresponding brain regions for generalization purposes and identify the active brain regions for each face stimulus. To find the stimuluswise brain dynamics, the information transfer among the identified brain regions is estimated using several graphical measures [global efficiency (GE) and transitivity]. Our model archives the mean GE of 0.800, 0.695, and 0.581 for famous, unfamiliar, and scrambled faces, respectively. Identifying face perception-specific brain regions will enhance understanding of the EEG-based face-processing system. Understanding the brain networks of famous, unfamiliar, and scrambled faces can be useful in criminal investigation applications
Brauer groups and Picard groups of the moduli of parabolic vector bundles on a nodal curve
No full textWe determine the Brauer groups and Picard groups of the moduli space UL,par′s of stable parabolic vector bundles of rank r with determinant L on a complex nodal curve Y of arithmetic genus g≥2. We also compute the Picard group of the moduli stack for parabolic SL(r)-bundles on Y and use it to give another description of the Picard group of UL,par′s. For g≥2, we determine the Brauer group of the moduli space UL′s of stable vector bundles on Y of rank r with determinant L, deduce that UL′s is simply connected and show the non-existence of the universal bundle on UL′s×Y in the non-coprime case
Coloring (P5, kite)-free graphs with small cliques
No full textLet Pn and Kn denote the induced path and complete graph on n vertices, respectively. The kite is the graph obtained from a P4 by adding a vertex and making it adjacent to all vertices in the P4 except one vertex with degree 1. A graph is (P5, kite)-free if it has no induced subgraph isomorphic to a P5 or a kite. For a graph G, the chromatic number of G (denoted by χ(G)) is the minimum number of colors needed to color the vertices of G such that no two adjacent vertices receive the same color, and the clique number of G is the size of a largest clique in G. Here, we are interested in coloring the class of (P5, kite)-free graphs with small clique number. It is known that every (P5, kite, K3)-free graph G satisfies χ(G)≤3, every (P5, kite, K4)-free graph G satisfies χ(G)≤4, and that every (P5, kite, K5)-free graph G satisfies χ(G)≤6. In this paper, we show the following: • Every (P5, kite, K6)-free graph G satisfies χ(G)≤7. • Every (P5, kite, K7)-free graph G satisfies χ(G)≤9. We also give examples to show that the above bounds are tight. Based on these partial results and some other examples, we conjecture that every (P5, kite)-free graph G satisfies [Formula presented], and that the bound is tight
CONCRETE ANALYSIS OF APPROXIMATE IDEAL-SIVP TO DECISION RING-LWE REDUCTION
No full textA seminal 2013 paper by Lyubashevsky, Peikert, and Regev proposed basing post-quantum cryptography on ideal lattices and supported this proposal by giving a polynomial-time security reduction from the approximate Shortest Independent Vectors Problem (SIVP) to the Decision Learning With Errors (DLWE) problem in ideal lattices. We give a concrete analysis of this multi-step reduction. We find that the tightness gap in the reduction is so great as to vitiate any meaningful security guarantee, and we find reasons to doubt the feasibility in the foreseeable future of the quantum part of the reduction. In addition, when we make the reduction concrete it appears that the approxi-mation factor in the SIVP problem is far larger than expected, a circumstance that causes the corresponding approximate-SIVP problem most likely not to be hard for proposed cryptosystem parameters. We also discuss implications for systems such as Kyber and SABER that are based on module-DLWE
Conflict under Incapacitation and Revenge: A Game-Theoretic Exploration
No full textIn real life, winning a conflict sometimes does not end the conflict. Revenge motivations can stay and provide momentum to the conflict, thus leading to further escalation of the conflict. This is known as the value effect or vengeance effect of revenge. However, the presence of revenge can lead to de-escalation of the conflict out of self-deterrence and sometimes retaliation out of revenge is not possible if the combatant is incapacitated. Hence, the impact of revenge on the level of violence is a priori not clear. This paper is an attempt to answer that question. Using a two-period game of conflict this paper tries to show how desire and capabilities of the combatants to exact revenge can influence the intensity of the conflict. This paper shows the following: how the strategies of the combatants are influenced by the value effect of revenge, self-deterrence and incapacitation of the combatants; how the stronger combatant is in a favourable position in the conflict and can prevent its opponent from going into second period conflict out of revenge; when the combatants are equally strong the intensity of the conflict starts falling with time. It also lays out some real-life conflicts and existing empirical work to support the results
Digital technology based game-theoretic pricing strategies in a three-tier perishable food supply chain
No full textThe purpose of this study is to examine the pricing strategies of a three-tier supply chain for perishable food products, which includes the manufacturer, distributor, and retailer. The study will examine various pricing scenarios, including single- and two-stage pricing system models that take into account the use of digital technologies. The market demand is based on retail price, freshness of product and Blockchain implementation effort. Our model is formulated under three different strategies-centralized, decentralized and revenue-cost sharing contract considering Big data technology. A Stackelberg game plan is also considered under the decentralized scheme, where the manufacturer is the leader and the retailer and distributor are the followers. The findings demonstrate that a number of variables, including the initial product quality level, the rate of deterioration, the cost optimization coefficient, and the cost of each supply chain member’s per unit of technology adoption affect each party’s profitability. Big data and Blockchain technology lead to enhanced profitability for both individual stakeholders and the overall supply chain. This adoption ensures a mutually beneficial scenario where all parties involved experience gains, resulting in a win-win situation. Further, we have explored the influence of key parameters on our model under various strategic scenarios. The outcomes of this research can be used by the academicians and practitioners to implement the best strategy in a perishable food supply chain with the help of digital technology
Enhanced bacoside synthesis in Bacopa monnieri plants using seed exudates from Tamarindus indica
No full textDiverse allelochemicals are released from different plant parts via leaching, exudation, volatilization, etc., which can induce either stimulatory or inhibitory effects depending on the target plant species. Very few reports provide details about allelopathic interaction through seed exudates. Since Tamarindus indica L. seed exudate (TSE) has been known to exhibit growth stimulatory effect on lettuce, radish, and sesame, in the present study we have evaluated its role in regulating the secondary metabolism of an over-exploited medicinal herb, Bacopa monnieri (L.) Pennel. The bacoside biosynthesis rate of B. monnieri is quite low in comparison to its increasingly high demands in the pharmaceutical industry. Currently, researches are aimed towards enhancing the biosynthesis of this secondary metabolite in planta by utilizing external stress factors. Presently, 7-day-old B. monnieri seedlings were treated with 1:16, 1:8, 1:4, 1:3, and 1:2 (seed weight: water) TSE. Maximum upregulation of secondary metabolite contents was found in the 1:4 (seed weight: water) TSE treatment set. This TSE treatment also enhanced H2O2 and salicylic acid production leading to the upregulation of the genes related to the MVA pathway (BmAACT, BmHMGR, BmMDD, BmSQS, and BmBAS) which are responsible for bacoside biosynthesis and 1.7-fold higher bacoside level was found in TSE treated set compared to control. LC-HRMS analysis of TSE confirmed the presence of alkaloid (lupanine), phenol (chlorogenic acid), and organic acid (mucic acid), which are identified as potential allelochemicals responsible for modulating the secondary metabolism of B. monnieri. Thus, this study highlights a sustainable approach towards enhancing bacoside production in planta
Enhancing Single-Cell RNA-seq Data Completeness with a Graph Learning Framework
No full textSingle cell RNA sequencing (scRNA-seq) is a powerful tool to capture gene expression snapshots in individual cells. However, a low amount of RNA in the individual cells results in dropout events, which introduce huge zero counts in the single cell expression matrix. We have developed VAImpute, a variational graph autoencoder based imputation technique that learns the inherent distribution of a large network/graph constructed from the scRNA-seq data leveraging copula correlation (Ccor) among cells/genes. The trained model is utilized to predict the dropouts events by computing the probability of all non-edges (cell-gene) in the network. We devise an algorithm to impute the missing expression values of the detected dropouts. The performance of the proposed model is assessed on both simulated and real scRNA-seq datasets, comparing it to established single-cell imputation methods. VAImpute yields significant improvements to detect dropouts, thereby achieving superior performance in cell clustering, detecting rare cells, and differential expression. All codes and datasets are given in the github link: https://github.com/sumantaray/VAImputeAvailabilit