Large-scale adaptive multiple testing for sequential data controlling false discovery and nondiscovery rates

In modern scientific experiments, we frequently encounter data that have large dimensions, and in some experiments, such high dimensional data arrive sequentially rather than full data being available all at a time. We develop multiple testing procedures with simultaneous control of false discovery and nondiscovery rates when $m$-variate data vectors $\mathbf{X}_1, \mathbf{X}_2, \dots$ are observed sequentially or in groups and each coordinate of these vectors leads to a hypothesis testing. Existing multiple testing methods for sequential data uses fixed stopping boundaries that do not depend on sample size, and hence, are quite conservative when the number of hypotheses $m$ is large. We propose sequential tests based on adaptive stopping boundaries that ensure shrinkage of the continue sampling region as the sample size increases. Under minimal assumptions on the data sequence, we first develop a test based on an oracle test statistic such that both false discovery rate (FDR) and false nondiscovery rate (FNR) are nearly equal to some prefixed levels with strong control. Under a two-group mixture model assumption, we propose a data-driven stopping and decision rule based on local false discovery rate statistic that mimics the oracle rule and guarantees simultaneous control of FDR and FNR asymptotically as $m$ tends to infinity. Both the oracle and the data-driven stopping times are shown to be finite (i.e., proper) with probability 1 for all finite $m$ and converge to a finite constant as $m$ grows to infinity. Further, we compare the data-driven test with the existing gap rule proposed in He and Bartroff (2021) and show that the ratio of the expected sample sizes of our method and the gap rule tends to zero as $m$ goes to infinity. Extensive analysis of simulated datasets as well as some real datasets illustrate the superiority of the proposed tests over some existing methods.Comment: 44 pages, 4 figures, 2 table

Spin-Hall effect in triplet chiral superconductors and graphene

We study spin-Hall effects in time-reversal symmetry (TRS) broken systems such as triplet chiral superconductors and TRS preserved ones such as graphene. For chiral triplet superconductors, we show that the edge states carry a quantized spin-Hall current in response to an applied Zeeman magnetic field $B$ along the ${\bf d}$ vector \cite{leggett1}, whereas the edge spin-current for ${\bf B} \perp {\bf d}$ is screened by the condensate. We also derive the bulk spin-Hall current for chiral triplet superconductors for arbitrary relative orientation of ${\bf B}$ and ${\bf d}$ and discuss its relation with the edge spin-current. For TRS invariant system graphene, we show that the bulk effective action, unlike its TRS broken counterparts, does not support a SU(2) Hopf term but allows a crossed Hopf term in the presence of an external electromagnetic field, which yields a quantized bulk spin-Hall current in response to an electric field. We also present an analytical solution of the edge problem for armchair edges of graphene and contrast the properties of these edge states with their time reversal symmetry broken counterparts in chiral superconductors. We propose possible experiments to test our results.Comment: v2; minor changes, additional ref

Anchor-Based Whole Genome Phylogeny (ABWGP): A Tool for Inferring Evolutionary Relationship among Closely Related Microorganims

Phenotypic behavior of a group of organisms can be studied using a range of molecular evolutionary tools that help to determine evolutionary relationships. Traditionally a gene or a set of gene sequences was used for generating phylogenetic trees. Incomplete evolutionary information in few selected genes causes problems in phylogenetic tree construction. Whole genomes are used as remedy. Now, the task is to identify the suitable parameters to extract the hidden information from whole genome sequences that truly represent evolutionary information. In this study we explored a random anchor (a stretch of 100 nucleotides) based approach (ABWGP) for finding distance between any two genomes, and used the distance estimates to compute evolutionary trees. A number of strains and species of Mycobacteria were used for this study. Anchor-derived parameters, such as cumulative normalized score, anchor order and indels were computed in a pair-wise manner, and the scores were used to compute distance/phylogenetic trees. The strength of branching was determined by bootstrap analysis. The terminal branches are clearly discernable using the distance estimates described here. In general, different measures gave similar trees except the trees based on indels. Overall the tree topology reflected the known biology of the organisms. This was also true for different strains of Escherichia coli. A new whole genome-based approach has been described here for studying evolutionary relationships among bacterial strains and species

Identification of Hot and Cold spots in genome of Mycobacterium tuberculosis using Shewhart Control Charts

The organization of genomic sequences is dynamic and undergoes change during the process of evolution. Many of the variations arise spontaneously and the observed genomic changes can either be distributed uniformly throughout the genome or be preferentially localized to some regions (hot spots) compared to others. Conversely cold spots may tend to accumulate very few variations or none at all. In order to identify such regions statistically, we have developed a method based on Shewhart Control Chart. The method was used for identification of hot and cold spots of single-nucleotide variations (SNVs) in Mycobacterium tuberculosis genomes. The predictions have been validated by sequencing some of these regions derived from clinical isolates. This method can be used for analysis of other genome sequences particularly infectious microbes

Identification of Genomic Regions and Sources for Wheat Blast Resistance through GWAS in Indian Wheat Genotypes

Wheat blast (WB) is a devastating fungal disease that has recently spread to Bangladesh and poses a threat to the wheat production in India, which is the second-largest wheat producing country in the world. In this study, 350 Indian wheat genotypes were evaluated for WB resistance in 12 field experiments in three different locations, namely Jashore in Bangladesh and Quirusillas and Okinawa in Bolivia. Single nucleotide polymorphisms (SNPs) across the genome were obtained using DArTseq (R) technology, and 7554 filtered SNP markers were selected for a genome-wide association study (GWAS). All the three GWAS approaches used identified the 2NS translocation as the only major source of resistance, explaining up to 32% of the phenotypic variation. Additional marker-trait associations were located on chromosomes 2B, 3B, 4D, 5A and 7A, and the combined effect of three SNPs (2B_180938790, 7A_752501634 and 5A_618682953) showed better resistance, indicating their additive effects on WB resistance. Among the 298 bread wheat genotypes, 89 (29.9%) carried the 2NS translocation, the majority of which (60 genotypes) were CIMMYT introductions, and 29 were from India. The 2NS carriers with a grand mean WB index of 6.6 showed higher blast resistance compared to the non-2NS genotypes with a mean index of 46.5. Of the 52 durum wheats, only one genotype, HI 8819, had the 2NS translocation and was the most resistant, with a grand mean WB index of 0.93. Our study suggests that the 2NS translocation is the only major resistance source in the Indian wheat panel analysed and emphasizes the urgent need to identify novel non-2NS resistance sources and genomic regions

Finding Inductive Loop Invariants using Large Language Models

Loop invariants are fundamental to reasoning about programs with loops. They establish properties about a given loop's behavior. When they additionally are inductive, they become useful for the task of formal verification that seeks to establish strong mathematical guarantees about program's runtime behavior. The inductiveness ensures that the invariants can be checked locally without consulting the entire program, thus are indispensable artifacts in a formal proof of correctness. Finding inductive loop invariants is an undecidable problem, and despite a long history of research towards practical solutions, it remains far from a solved problem. This paper investigates the capabilities of the Large Language Models (LLMs) in offering a new solution towards this old, yet important problem. To that end, we first curate a dataset of verification problems on programs with loops. Next, we design a prompt for exploiting LLMs, obtaining inductive loop invariants, that are checked for correctness using sound symbolic tools. Finally, we explore the effectiveness of using an efficient combination of a symbolic tool and an LLM on our dataset and compare it against a purely symbolic baseline. Our results demonstrate that LLMs can help improve the state-of-the-art in automated program verification

Identification of genomic regions and sources for wheat blast resistance through GWAS in indian wheat genotypes

Wheat blast (WB) is a devastating fungal disease that has recently spread to Bangladesh and poses a threat to the wheat production in India, which is the second-largest wheat producing country in the world. In this study, 350 Indian wheat genotypes were evaluated for WB resistance in 12 field experiments in three different locations, namely Jashore in Bangladesh and Quirusillas and Okinawa in Bolivia. Single nucleotide polymorphisms (SNPs) across the genome were obtained using DArTseq® technology, and 7554 filtered SNP markers were selected for a genome-wide association study (GWAS). All the three GWAS approaches used identified the 2NS translocation as the only major source of resistance, explaining up to 32% of the phenotypic variation. Additional marker-trait associations were located on chromosomes 2B, 3B, 4D, 5A and 7A, and the combined effect of three SNPs (2B_180938790, 7A_752501634 and 5A_618682953) showed better resistance, indicating their additive effects on WB resistance. Among the 298 bread wheat genotypes, 89 (29.9%) carried the 2NS translocation, the majority of which (60 genotypes) were CIMMYT introductions, and 29 were from India. The 2NS carriers with a grand mean WB index of 6.6 showed higher blast resistance compared to the non-2NS genotypes with a mean index of 46.5. Of the 52 durum wheats, only one genotype, HI 8819, had the 2NS translocation and was the most resistant, with a grand mean WB index of 0.93. Our study suggests that the 2NS translocation is the only major resistance source in the Indian wheat panel analysed and emphasizes the urgent need to identify novel non-2NS resistance sources and genomic regions

Combining the Specific Anti-MUC1 Antibody TAB004 and Lip-MSA-IL-2 Limits Pancreatic Cancer Progression in Immune Competent Murine Models of Pancreatic Ductal Adenocarcinoma

Immunotherapy regimens have shown success in subsets of cancer patients; however, their efficacy against pancreatic ductal adenocarcinoma (PDA) remain unclear. Previously, we demonstrated the potential of TAB004, a monoclonal antibody targeting the unique tumor-associated form of MUC1 (tMUC1) in the early detection of PDA. In this study, we evaluated the therapeutic benefit of combining the TAB004 antibody with Liposomal-MSA-IL-2 in immune competent and human MUC1 transgenic (MUC1.Tg) mouse models of PDA and investigated the associated immune responses. Treatment with TAB004 + Lip-MSA-IL-2 resulted in significantly improved survival and slower tumor growth compared to controls in MUC1.Tg mice bearing an orthotopic PDA.MUC1 tumor. Similarly, in the spontaneous model of PDA that expresses human MUC1, the combination treatment stalled the progression of pancreatic intraepithelial pre-neoplastic (PanIN) lesion to adenocarcinoma. Treatment with the combination elicited a robust systemic and tumor-specific immune response with (a) increased percentages of systemic and tumor infiltrated CD45+CD11b+ cells, (b) increased levels of myeloperoxidase (MPO), (c) increased antibody-dependent cellular cytotoxicity/phagocytosis (ADCC/ADCP), (d) decreased percentage of immune regulatory cells (CD8+CD69+ cells), and (e) reduced circulating levels of immunosuppressive tMUC1. We report that treatment with a novel antibody against tMUC1 in combination with a unique formulation of IL-2 can improve survival and lead to stable disease in appropriate models of PDA by reducing tumor-induced immune regulation and promoting recruitment of CD45+CD11b+ cells, thereby enhancing ADCC/ADCP