Project description:GACAL verifies C programs by searching over the space of possible invariants, using traces of the input program to identify potential invariants. GACAL uses the ACL2s theorem prover to verify these potential invariants, using an interface provided by ACL2s for connecting with external tools. GACAL iteratively searches for and proves invariants of increasing complexity until the program is verified.
Project description:In information security, one way to keep a secret content is through encryption. The objective is to alter the content so that it is not intelligible, and therefore only the intended user can reveal the secret content. With the aim to provide examples of encrypted audio data, we applied a novel method of encryption based on the Collatz conjecture in five hundred speech recordings (50 speakers, 10 different messages), and then five hundred encrypted audio files were obtained. The main characteristics of our encrypted recordings are as follows: the spectrogram is quasi-uniform, histograms have a repetitive pattern, average of samples is around -0.4, standard deviation is around 0.55; Shannon entropy is around 7.5 (for 8-bits per sample). The novelty of the results consists in obtaining a completely different behavior than natural speech recordings, i.e.: spectrogram with higher energy in low frequencies, histogram with Gaussian behavior, average of samples around 0, standard deviation around 0.11, entropy around 5.5. A more comprehensive analysis of our encrypted signals may be obtained from the article "High-uncertainty audio signal encryption based on the Collatz conjecture" in the Journal of Information Security and Applications.
Project description:A common assumption in comparative genomics is that orthologous genes share greater functional similarity than do paralogous genes (the "ortholog conjecture"). Many methods used to computationally predict protein function are based on this assumption, even though it is largely untested. Here we present the first large-scale test of the ortholog conjecture using comparative functional genomic data from human and mouse. We use the experimentally derived functions of more than 8,900 genes, as well as an independent microarray dataset, to directly assess our ability to predict function using both orthologs and paralogs. Both datasets show that paralogs are often a much better predictor of function than are orthologs, even at lower sequence identities. Among paralogs, those found within the same species are consistently more functionally similar than those found in a different species. We also find that paralogous pairs residing on the same chromosome are more functionally similar than those on different chromosomes, perhaps due to higher levels of interlocus gene conversion between these pairs. In addition to offering implications for the computational prediction of protein function, our results shed light on the relationship between sequence divergence and functional divergence. We conclude that the most important factor in the evolution of function is not amino acid sequence, but rather the cellular context in which proteins act.
Project description:Let G be a group. Denote by π(G) the set of prime divisors of |G|. Let GK(G) be the graph with vertex set π(G) such that two primes p and q in π(G) are joined by an edge if G has an element of order p · q. We set s(G) to denote the number of connected components of the prime graph GK(G). Denote by N(G) the set of nonidentity orders of conjugacy classes of elements in G. Alavi and Daneshkhah proved that the groups, A n where n = p, p + 1, p + 2 with s(G) ≥ 2, are characterized by N(G). As a development of these topics, we will prove that if G is a finite group with trivial center and N(G) = N(A p+3) with p + 2 composite, then G is isomorphic to A p+3.
Project description:We show that weak solutions of general conservation laws in bounded domains conserve their generalized entropy, and other respective companion laws, if they possess a certain fractional differentiability of order one-third in the interior of the domain, and if the normal component of the corresponding fluxes tend to zero as one approaches the boundary. This extends various recent results of the authors.
Project description:The ortholog conjecture (OC), which is central to functional annotation of genomes, posits that orthologous genes are functionally more similar than paralogous genes at the same level of sequence divergence. However, a recent study challenged the OC by reporting a greater functional similarity, in terms of Gene Ontology (GO) annotations and expression profiles, among within-species paralogs compared with orthologs. These findings were taken to indicate that functional similarity of homologous genes is primarily determined by the cellular context of the genes, rather than evolutionary history. However, several subsequent studies suggest that GO annotations and microarray data could artificially inflate functional similarity between paralogs from the same organism. We sought to test the OC using approaches distinct from those used in previous studies. Analysis of a large RNAseq data set from multiple human and mouse tissues shows that expression similarity (correlations coefficients, rank's, or Z-scores) between orthologs is substantially greater than that for between-species paralogs with the same sequence divergence, in agreement with the OC and the results of recent detailed analyses. These findings are further corroborated by a fine-grain analysis in which expression profiles of orthologs and paralogs were compared separately for individual gene families. Expression profiles of within-species paralogs are more strongly correlated than profiles of orthologs but it is shown that this is caused by high background noise, that is, correlation between profiles of unrelated genes in the same organism. Z-scores and rank scores show a nonmonotonic dependence of expression profile similarity on sequence divergence. This complexity of gene expression evolution after duplication might be at least partially caused by selection for protein dosage rebalancing following gene duplication.
Project description:Accurate estimation of genetic correlation requires large sample sizes and access to genetically informative data, which are not always available. Accordingly, phenotypic correlations are often assumed to reflect genotypic correlations in evolutionary biology. Cheverud's conjecture asserts that the use of phenotypic correlations as proxies for genetic correlations is appropriate. Empirical evidence of the conjecture has been found across plant and animal species, with results suggesting that there is indeed a robust relationship between the two. Here, we investigate the conjecture in human populations, an analysis made possible by recent developments in availability of human genomic data and computing resources. A sample of 108,035 British European individuals from the UK Biobank was split equally into discovery and replication datasets. Seventeen traits were selected based on sample size, distribution, and heritability. Genetic correlations were calculated using linkage disequilibrium score regression applied to the genome-wide association summary statistics of pairs of traits, and compared within and across datasets. Strong and significant correlations were found for the between-dataset comparison, suggesting that the genetic correlations from one independent sample were able to predict the phenotypic correlations from another independent sample within the same population. Designating the selected traits as morphological or nonmorphological indicated little difference in correlation. The results of this study support the existence of a relationship between genetic and phenotypic correlations in humans. This finding is of specific interest in anthropological studies, which use measured phenotypic correlations to make inferences about the genetics of ancient human populations.
Project description:The Ligon-Schaaf regularization (LS mapping) was introduced in 1976 and has been used several times. However, we are not aware of any direct usage of the inverse mapping, perhaps since it appears at first sight to be quite complex, involves the use of a transcendental equation (referred to as the generalized Kepler equation) that cannot be solved in closed form, and lacks smoothness near the collision point. Here, we provide some insight into the significance of this equation, along with a very simple derivation and confirmation of the inverse LS mapping. Then we use numerical methods to investigate three applications: 1) solutions of the Kepler function, 2) calculation of orbits including time-of-flight data based on the Delaunay Hamiltonian, and 3) numerical evidence for the Birkhoff conjecture for the circular restricted 3-body problem.
Project description:Agbiotechnology uses genetic engineering to improve the output and value of crops. Altering the expression of the plant Type I Proton-pumping Pyrophosphatase (H+-PPase) has already proven to be a useful tool to enhance crop productivity. Despite the effective use of this gene in translational research, information regarding the intracellular localization and functional plasticity of the pump remain largely enigmatic. Using computer modeling several putative phosphorylation, ubiquitination and sumoylation target sites were identified that may regulate Arabidopsis H+-PPase (AVP1- Arabidopsis Vacuolar Proton-pump 1) subcellular trafficking and activity. These putative regulatory sites will direct future research that specifically addresses the partitioning and transport characteristics of this pump. We posit that fine-tuning H+-PPases activity and cellular distribution will facilitate rationale strategies for further genetic improvements in crop productivity.
Project description:The ortholog conjecture posits that orthologous genes are functionally more similar than paralogous genes. This conjecture is a cornerstone of phylogenomics and is used daily by both computational and experimental biologists in predicting, interpreting, and understanding gene functions. A recent study, however, challenged the ortholog conjecture on the basis of experimentally derived Gene Ontology (GO) annotations and microarray gene expression data in human and mouse. It instead proposed that the functional similarity of homologous genes is primarily determined by the cellular context in which the genes act, explaining why a greater functional similarity of (within-species) paralogs than (between-species) orthologs was observed. Here we show that GO-based functional similarity between human and mouse orthologs, relative to that between paralogs, has been increasing in the last five years. Further, compared with paralogs, orthologs are less likely to be included in the same study, causing an underestimation in their functional similarity. A close examination of functional studies of homologs with identical protein sequences reveals experimental biases, annotation errors, and homology-based functional inferences that are labeled in GO as experimental. These problems and the temporary nature of the GO-based finding make the current GO inappropriate for testing the ortholog conjecture. RNA sequencing (RNA-Seq) is known to be superior to microarray for comparing the expressions of different genes or in different species. Our analysis of a large RNA-Seq dataset of multiple tissues from eight mammals and the chicken shows that the expression similarity between orthologs is significantly higher than that between within-species paralogs, supporting the ortholog conjecture and refuting the cellular context hypothesis for gene expression. We conclude that the ortholog conjecture remains largely valid to the extent that it has been tested, but further scrutiny using more and better functional data is needed.