Relation between space-time inversion and particle-antiparticle symmetry and the microscopic essence of special relativity

After analyzing the implication of investigations on the C, P and T transformations since 1956, we propose that there is a basic symmetry in particle physics. The combined space-time inversion is equivalent to particle-antiparticle transformation, denoted by ${\cal PT=C}$. It is shown that the relativistic quantum mechanics and quantum field theory do contain this invariance explicitly or implicitly. In particular, (a) the appearance of negative energy or negative probability density in single particle theory -- corresponding to the fact of existence of antiparticle, (b) spin- statistics connection, (c) CPT theorem, (d) the Feynman propagator are linked together via this symmetry. Furthermore, we try to derive the main results of special relativity, especially, (e) the mass-energy relation, (f) the Lorentz transformation by this one ``relativistic'' postulate and some ``nonrelativistic'' knowledge.Comment: 29 pages, Latex, 1 figur

A tail-based test for differential expression analysis and pathway analysis in RNA-sequencing data

RNA sequencing data have been abundantly generated in biomedical research for biomarker discovery and pathway analysis. Such data at the exon-level are usually heavily tailed and correlated. Conventional statistical tests based on the mean or median difference for differential expression likely suffer from low power when the between-group difference occurs mostly in the upper or lower tail of the distribution of gene expression. We propose a tail-based test to make comparisons between groups in terms of a specific distribution area rather than a single location. The proposed test, which is derived from quantile regression, adjusts for covariates and accounts for within-sample dependence among the exons through a specified correlation structure. Through Monte Carlo simulation studies, we show that the proposed test is generally more powerful and robust in detecting differential expression than commonly used tests based on the mean or a single quantile. An application to TCGA lung adenocarcinoma data demonstrates the promise of the proposed method in terms of biomarker discovery. We also extend the proposed test to perform pathway analysis for a set of genes within the same pathway or share similar biological function. Genes in such sets are known to be dependent of each other and our test accounts for their pairwise correlation. Through simulation comparison with commonly used pathway analysis methods, we show the proposed test yields better results. An application on non-small cell lung cancer pathways from KEGG pathway Database also demonstrates the proposed test is a powerful method in detecting differentially expressed pathways

Parameterized Algorithmics for Computational Social Choice: Nine Research Challenges

Computational Social Choice is an interdisciplinary research area involving Economics, Political Science, and Social Science on the one side, and Mathematics and Computer Science (including Artificial Intelligence and Multiagent Systems) on the other side. Typical computational problems studied in this field include the vulnerability of voting procedures against attacks, or preference aggregation in multi-agent systems. Parameterized Algorithmics is a subfield of Theoretical Computer Science seeking to exploit meaningful problem-specific parameters in order to identify tractable special cases of in general computationally hard problems. In this paper, we propose nine of our favorite research challenges concerning the parameterized complexity of problems appearing in this context