A Deductive Approach towards Reasoning about Algebraic Transition Systems

Algebraic transition systems are extended from labeled transition systems by allowing transitions labeled by algebraic equations for modeling more complex systems in detail. We present a deductive approach for specifying and verifying algebraic transition systems. We modify the standard dynamic logic by introducing algebraic equations into modalities. Algebraic transition systems are embedded in modalities of logic formulas which specify properties of algebraic transition systems. The semantics of modalities and formulas is defined with solutions of algebraic equations. A proof system for this logic is constructed to verify properties of algebraic transition systems. The proof system combines with inference rules decision procedures on the theory of polynomial ideals to reduce a proof-search problem to an algebraic computation problem. The proof system proves to be sound but inherently incomplete. Finally, a typical example illustrates that reasoning about algebraic transition systems with our approach is feasible

Ranking analysis of F-statistics for microarray data

<p>Abstract</p> <p>Background</p> <p>Microarray technology provides an efficient means for globally exploring physiological processes governed by the coordinated expression of multiple genes. However, identification of genes differentially expressed in microarray experiments is challenging because of their potentially high type I error rate. Methods for large-scale statistical analyses have been developed but most of them are applicable to two-sample or two-condition data.</p> <p>Results</p> <p>We developed a large-scale multiple-group <it>F</it>-test based method, named ranking analysis of <it>F</it>-statistics (RAF), which is an extension of ranking analysis of microarray data (RAM) for two-sample t-test. In this method, we proposed a novel random splitting approach to generate the null distribution instead of using permutation, which may not be appropriate for microarray data. We also implemented a two-simulation strategy to estimate the false discovery rate. Simulation results suggested that it has higher efficiency in finding differentially expressed genes among multiple classes at a lower false discovery rate than some commonly used methods. By applying our method to the experimental data, we found 107 genes having significantly differential expressions among 4 treatments at <0.7% FDR, of which 31 belong to the expressed sequence tags (ESTs), 76 are unique genes who have known functions in the brain or central nervous system and belong to six major functional groups.</p> <p>Conclusion</p> <p>Our method is suitable to identify differentially expressed genes among multiple groups, in particular, when sample size is small.</p

Optimizing the thermoelectric performance of zigzag and chiral carbon nanotubes

Using nonequilibrium molecular dynamics simulations and nonequilibrium Green's function method, we investigate the thermoelectric properties of a series of zigzag and chiral carbon nanotubes which exhibit interesting diameter and chirality dependence. Our calculated results indicate that these carbon nanotubes could have higher ZT values at appropriate carrier concentration and operating temperature. Moreover, their thermoelectric performance can be significantly enhanced via isotope substitution, isoelectronic impurities, and hydrogen adsorption. It is thus reasonable to expect that carbon nanotubes may be promising candidates for high-performance thermoelectric materials

Comparative transcriptome profiling of the fertile and sterile flower buds of a dominant genic male sterile line in sesame (Sesamum indicum L.)

Expressions and annotations of the 1502 differentially expressed unigenes in sesame. (XLSX 338 kb

Approximate Equivalence of the Hybrid Automata with Taylor Theory

Hybrid automaton is a formal model for precisely describing a hybrid system in which the computational processes interact with the physical ones. The reachability analysis of the polynomial hybrid automaton is decidable, which makes the Taylor approximation of a hybrid automaton applicable and valuable. In this paper, we studied the simulation relation among the hybrid automaton and its Taylor approximation, as well as the approximate equivalence relation. We also proved that the Taylor approximation simulates its original hybrid automaton, and similar hybrid automata could be compared quantitatively, for example, the approximate equivalence we proposed in the paper

A2A^2Nav: Action-Aware Zero-Shot Robot Navigation by Exploiting Vision-and-Language Ability of Foundation Models

We study the task of zero-shot vision-and-language navigation (ZS-VLN), a practical yet challenging problem in which an agent learns to navigate following a path described by language instructions without requiring any path-instruction annotation data. Normally, the instructions have complex grammatical structures and often contain various action descriptions (e.g., "proceed beyond", "depart from"). How to correctly understand and execute these action demands is a critical problem, and the absence of annotated data makes it even more challenging. Note that a well-educated human being can easily understand path instructions without the need for any special training. In this paper, we propose an action-aware zero-shot VLN method ($A^2$Nav) by exploiting the vision-and-language ability of foundation models. Specifically, the proposed method consists of an instruction parser and an action-aware navigation policy. The instruction parser utilizes the advanced reasoning ability of large language models (e.g., GPT-3) to decompose complex navigation instructions into a sequence of action-specific object navigation sub-tasks. Each sub-task requires the agent to localize the object and navigate to a specific goal position according to the associated action demand. To accomplish these sub-tasks, an action-aware navigation policy is learned from freely collected action-specific datasets that reveal distinct characteristics of each action demand. We use the learned navigation policy for executing sub-tasks sequentially to follow the navigation instruction. Extensive experiments show $A^2$Nav achieves promising ZS-VLN performance and even surpasses the supervised learning methods on R2R-Habitat and RxR-Habitat datasets