Browse
Submit Data
Databases
API
Help

Dataset Information

0 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator.

ABSTRACT: An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into irreducibles. In the case of the ring Int(D)={f?K[x]|f(D)?D}, of integer-valued polynomials on a principal ideal domain D with quotient field K, we give an easy to verify graph-theoretic sufficient condition for an element to be absolutely irreducible and show a partial converse: the condition is necessary and sufficient for polynomials with square-free denominator.

SUBMITTER: Frisch S

PROVIDER: S-EPMC7454568 | biostudies-literature | 2020

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

A graph-theoretic criterion for absolute irreducibility of integer-valued polynomials with square-free denominator.

Frisch Sophie S Nakato Sarah S

Communications in algebra 20200403 9

An irreducible element of a commutative ring is absolutely irreducible if no power of it has more than one (essentially different) factorization into irreducibles. In the case of the ring Int(D)={f∈K[x]|f(D)⊆D}, of integer-valued polynomials on a principal ideal domain <i>D</i> with quotient field <i>K</i>, we give an easy to verify graph-theoretic sufficient condition for an element to be absolutely irreducible and show a partial converse: the condition is necessary and sufficient for polynomia ...[more]

PMID: 32939189

Similar Datasets

An Efficient Exact Quantum Algorithm for the Integer Square-free Decomposition Problem.

Project description:Quantum computers are known to be qualitatively more powerful than classical computers, but so far only a small number of different algorithms have been discovered that actually use this potential. It would therefore be highly desirable to develop other types of quantum algorithms that widen the range of possible applications. Here we propose an efficient and exact quantum algorithm for finding the square-free part of a large integer - a problem for which no efficient classical algorithm exists. The algorithm relies on properties of Gauss sums and uses the quantum Fourier transform. We give an explicit quantum network for the algorithm. Our algorithm introduces new concepts and methods that have not been used in quantum information processing so far and may be applicable to a wider class of problems.

| S-EPMC3277347 | biostudies-literature

Generalized Poisson integer-valued autoregressive processes with structural changes.

Project description:In this paper, we introduce a new first-order generalized Poisson integer-valued autoregressive process, for modeling integer-valued time series exhibiting a piecewise structure and overdispersion. Basic probabilistic and statistical properties of this model are discussed. Conditional least squares and conditional maximum likelihood estimators are derived. The asymptotic properties of the estimators are established. Moreover, two special cases of the process are discussed. Finally, some numerical results of the estimates and a real data example are presented.

| S-EPMC9336494 | biostudies-literature

GraTeLPy: graph-theoretic linear stability analysis.

Project description:BackgroundA biochemical mechanism with mass action kinetics can be represented as a directed bipartite graph (bipartite digraph), and modeled by a system of differential equations. If the differential equations (DE) model can give rise to some instability such as multistability or Turing instability, then the bipartite digraph contains a structure referred to as a critical fragment. In some cases the existence of a critical fragment indicates that the DE model can display oscillations for some parameter values. We have implemented a graph-theoretic method that identifies the critical fragments of the bipartite digraph of a biochemical mechanism.ResultsGraTeLPy lists all critical fragments of the bipartite digraph of a given biochemical mechanism, thus enabling a preliminary analysis on the potential of a biochemical mechanism for some instability based on its topological structure. The correctness of the implementation is supported by multiple examples. The code is implemented in Python, relies on open software, and is available under the GNU General Public License.ConclusionsGraTeLPy can be used by researchers to test large biochemical mechanisms with mass action kinetics for their capacity for multistability, oscillations and Turing instability.

| S-EPMC4016541 | biostudies-literature

Additive integer-valued data envelopment analysis with missing data: A multi-criteria evaluation approach.

Project description:Traditional data envelopment analysis (DEA) models assume that all the inputs and outputs data are available. However, missing data is a common problem in data analysis. Although several scholars have developed techniques to conduct DEA with missing data, these techniques have some disadvantages. A multi-criteria evaluation approach is proposed to measure the efficiency of decision making units (DMUs) with missing data. In this approach, analysts first estimate the upper and lower bounds of DMUs' efficiency using the proposed I-addIDEA-U models (interval additive integer-valued DEA models with undesirable outputs) that can be applied to address integer-valued variables and undesirable outputs. Then, DMUs' "relative" efficiency is evaluated using the proposed "Halo + Hot deck" DEA method (if there is no correlation between variables) or regression DEA techniques (if there is a correlation between variables). Finally, the multi-index comprehensive evaluation method is applied to determine which scenario (the lower bound of efficiency, the "relative" efficiency, or the upper bound of efficiency) should be selected. With a case study, it is shown that the proposed multi-criteria evaluation approach is more effective than traditional approaches such as the mean imputation DEA method, the deletion DEA method, and the dummy entries DEA method.

| S-EPMC7289371 | biostudies-literature

Graph-Theoretic Analysis of Monomethyl Phosphate Clustering in Ionic Solutions.

Project description:All-atom molecular dynamics simulations combined with graph-theoretic analysis reveal that clustering of monomethyl phosphate dianion (MMP2-) is strongly influenced by the types and combinations of cations in the aqueous solution. Although Ca2+ promotes the formation of stable and large MMP2- clusters, K+ alone does not. Nonetheless, clusters are larger and their link lifetimes are longer in mixtures of K+ and Ca2+. This "synergistic" effect depends sensitively on the Lennard-Jones interaction parameters between Ca2+ and the phosphorus oxygen and correlates with the hydration of the clusters. The pronounced MMP2- clustering effect of Ca2+ in the presence of K+ is confirmed by Fourier transform infrared spectroscopy. The characterization of the cation-dependent clustering of MMP2- provides a starting point for understanding cation-dependent clustering of phosphoinositides in cell membranes.

| S-EPMC6322214 | biostudies-literature

Reproducibility of graph-theoretic brain network metrics: a systematic review.

Project description:This systematic review aimed to assess the reproducibility of graph-theoretic brain network metrics. Primary research studies of test-retest reliability conducted on healthy human subjects were included that quantified test-retest reliability using either the intraclass correlation coefficient (ICC) or the coefficient of variance. The MEDLINE, Web of Knowledge, Google Scholar, and OpenGrey databases were searched up to February 2014. Risk of bias was assessed with 10 criteria weighted toward methodological quality. Twenty-three studies were included in the review (n=499 subjects) and evaluated for various characteristics, including sample size (5-45), retest interval (<1 h to >1 year), acquisition method, and test-retest reliability scores. For at least one metric, ICCs reached the fair range (ICC 0.40-0.59) in one study, the good range (ICC 0.60-0.74) in five studies, and the excellent range (ICC>0.74) in 16 studies. Heterogeneity of methods prevented further quantitative analysis. Reproducibility was good overall. For the metrics having three or more ICCs reported for both functional and structural networks, six of seven were higher in structural networks, indicating that structural networks may be more reliable over time. The authors were also able to highlight and discuss a number of methodological factors affecting reproducibility.

| S-EPMC4432917 | biostudies-literature

Graph-Theoretic Analysis of Belief System Dynamics under Logic Constraints.

Project description:Opinion formation cannot be modeled solely as an ideological deduction from a set of principles; rather, repeated social interactions and logic constraints among statements are consequential in the construct of belief systems. We address three basic questions in the analysis of social opinion dynamics: (i) Will a belief system converge? (ii) How long does it take to converge? (iii) Where does it converge? We provide graph-theoretic answers to these questions for a model of opinion dynamics of a belief system with logic constraints. Our results make plain the implicit dependence of the convergence properties of a belief system on the underlying social network and on the set of logic constraints that relate beliefs on different statements. Moreover, we provide an explicit analysis of a variety of commonly used large-scale network models.

| S-EPMC6586829 | biostudies-literature

Test-Retest Reliability of Graph Theoretic Metrics in Adolescent Brains.

Project description:Graph theory analysis of structural brain networks derived from diffusion tensor imaging (DTI) has become a popular analytical method in neuroscience, enabling advanced investigations of neurological and psychiatric disorders. The purpose of this study was to investigate (1) the effects of edge weighting schemes and (2) the effects of varying interscan periods on graph metrics within the adolescent brain. We compared a binary (B) network definition with three weighting schemes: fractional anisotropy (FA), streamline count, and streamline count with density and length correction (SDL). Two commonly used global and two local graph metrics were examined. The analysis was conducted with two groups of adolescent volunteers who received DTI scans either 12 weeks apart (16.62 ± 1.10 years) or within the same scanning session (30 min apart) (16.65 ± 1.14 years). The intraclass correlation coefficient was used to assess test-retest reliability and the coefficient of variation (CV) was used to assess precision. On average, each edge scheme produced reliable results at both time intervals. Weighted measures outperformed binary measures, with SDL weights producing the most reliable metrics. All edge schemes except FA displayed high CV values, leaving FA as the only edge scheme that consistently showed high precision while also producing reliable results. Overall findings suggest that FA weights are more suited for DTI connectome studies in adolescents.

| S-EPMC6444894 | biostudies-literature

Disrupted modular architecture of cerebellum in schizophrenia: a graph theoretic analysis.

Project description:Recent studies of schizophrenia have revealed cognitive and memory deficits that are accompanied by disruptions of neuronal connectivity in cortical and subcortical brain regions. More recently, alterations of topological organization of structural networks in schizophrenia are also being identified using graph theoretical analysis. However, the role of the cerebellum in this network structure remains largely unknown. In this study, global network measures obtained from diffusion tensor imaging were computed in the cerebella of 25 patients with schizophrenia and 36 healthy volunteers. While cerebellar global network characteristics were slightly altered in schizophrenia patients compared with healthy controls, the patients showed a retained small-world network organization. The modular architecture, however, was changed mainly in crus II. Furthermore, schizophrenia patients had reduced correlations between modularity and microstructural integrity, as measured by fractional anisotropy (FA) in lobules I-IV and X. Finally, FA alterations were significantly correlated with the Positive and Negative Syndrome Scale symptom scores in schizophrenia patients. Taken together, our data suggest that schizophrenia patients have altered network architecture in the cerebellum with reduced local microstructural connectivity and that cerebellar structural abnormalities are associated symptoms of the disorder.

| S-EPMC4193723 | biostudies-literature

Structural modeling and analysis of fuel cell: a graph-theoretic approach.

Project description:A fuel cell, an energy conversion system, needs analysis for its performance at the design and off-design point conditions during its real-time operation. System performance evaluation with logical methodology is helpful in decision-making while considering efficiency and cross-correlated parameters in fuel cells. This work presents an overview and categorization of different fuel cells, leading to the developing of a method combining graph theory and matrix method for analyzing fuel cell system structure to make more informed decisions. The fuel cell system is divided into four interdependent sub-systems. The methodology developed in this work consists of a series of steps comprised of digraph representation, matrix representation, and permanent function representation. A mathematical model is evaluated quantitatively to produce a performance index numerical value. With the aid of case studies, the proposed methodology is explained, and the advantages of the proposed method are corroborated.

| S-EPMC10495936 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

Tweets

OmicsDI Databases

PRIDE
PeptideAtlas
MassIVE
JPOST Repository
Physiome Model Repository

EGA
EVA
ENA
LINCS
PAXDB
Cell Collective

MetaboLights
Metabolomics Workbench
MetabolomeExpress
GNPS
BioModels
FAIRDOMHub

ArrayExpress
dbGaP
ExpressionAtlas
GEO
NODE

Information

Databases
Help
API
Contact us
Code on GitHub
Terms of use
Submit Data