Search results for "Number"

showing 10 items of 3939 documents

Invariant deformation theory of affine schemes with reductive group action

2015

We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we device an algorithm to compute the universal deformation of $X$ in terms of generators and relations up to a given order. In many situations, our algorithm even computes an algebraization of the universal deformation. As an application, we determine new families of examples of the invariant Hilbert scheme of Alexeev and Brion, where $G$ is a classical group acting on a classical representation, and describe their singularities.

Classical groupPure mathematicsInvariant Hilbert schemeDeformation theory01 natural sciencesMathematics - Algebraic Geometry0103 physical sciencesFOS: Mathematics0101 mathematicsInvariant (mathematics)Representation Theory (math.RT)Algebraic Geometry (math.AG)MathematicsAlgebra and Number Theory[MATH.MATH-RT]Mathematics [math]/Representation Theory [math.RT]010102 general mathematicsReductive group16. Peace & justiceObstruction theoryDeformation theoryHilbert schemeAlgebraic groupMSC: 13A50; 20G05; 14K10; 14L30; 14Q99; 14B12Gravitational singularity010307 mathematical physicsAffine transformation[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG]SingularitiesMathematics - Representation Theory
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Some contributions to the theory of transformation monoids

2019

The aim of this paper is to present some contributions to the theory of finite transformation monoids. The dominating influence that permutation groups have on transformation monoids is used to describe and characterise transitive transformation monoids and primitive transitive transformation monoids. We develop a theory that not only includes the analogs of several important theorems of the classical theory of permutation groups but also contains substantial information about the algebraic structure of the transformation monoids. Open questions naturally arising from the substantial paper of Steinberg [A theory of transformation monoids: combinatorics and representation theory. Electron. J…

Classical theoryTransitive relationPure mathematicsAlgebra and Number TheoryConjectureAlgebraic structure010102 general mathematicsPermutation group01 natural sciencesTransformation (music)Development (topology)Mathematics::Category Theory0103 physical sciencesÀlgebra010307 mathematical physics0101 mathematicsMathematicsJournal of Algebra
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Interstitial deletions of chromosome 1p: novel 1p31.3p22.2 microdeletion in a newborn with craniosynostosis, coloboma and cleft palate, and review of…

2022

Abstract Background Rearrangements of unstable DNA sequences may alter the structural integrity or the copy number of dose-sensitive genes, resulting in copy number variations. They may lead more frequently to deletions, in addition to duplications and/or inversions, which are the underlying pathogenic mechanism of a group of conditions known as genomic disorders (or also contiguous gene syndromes). Interstitial deletions of the short arm of chromosome 1 are rare, and only about 30 patients have been reported. Their clinical features are variable, in respect of the extent of the deleted region. They include global developmental delay, central nervous system (CNS) malformations, craniosynost…

Cleft PalateColobomaComparative Genomic HybridizationCraniosynostosesPhenotypeDNA Copy Number VariationsChromosomes Human Pair 1HumansFemaleGenomicsChromosome Deletion1p31.1 deletion syndrome Array-CGH Case report Chromosome 1 Contiguous gene syndrome Chromosome Deletion Chromosomes Human Pair 1 Comparative Genomic Hybridization DNA Copy Number Variations Female Genomics Humans Phenotype Cleft Palate Coloboma Craniosynostoses
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Assessing the impact of copy number variants on miRNA genes in autism by Monte Carlo simulation.

2014

Autism Spectrum Disorders (ASDs) are childhood neurodevelopmental disorders with complex genetic origins. Previous studies have investigated the role of de novo Copy Number Variants (CNVs) and microRNAs as important but distinct etiological factors in ASD. We developed a novel computational procedure to assess the potential pathogenic role of microRNA genes overlapping de novo CNVs in ASD patients. Here we show that for chromosomes # 1, 2 and 22 the actual number of miRNA loci affected by de novo CNVs in patients was found significantly higher than that estimated by Monte Carlo simulation of random CNV events. Out of 24 miRNA genes over-represented in CNVs from these three chromosomes only …

Clinical PathologyDNA Copy Number Variationsendocrine system diseasesChromosomes Human Pair 22ScienceGene regulatory networkGenomicsDevelopmental and Pediatric NeurologyBiologyPathology and Laboratory MedicinePediatricsGenomeMolecular GeneticsmiRNA Genes Monte Carlo Simulation AutismDiagnostic Medicinemental disordersGeneticsMedicine and Health SciencesmedicineHumansComputer SimulationGene Regulatory NetworksCopy-number variationAutistic DisorderGeneGeneticsMultidisciplinaryGenome HumanQRBiology and Life SciencesComputational BiologyGenomicsGenome Analysismedicine.diseaseSettore FIS/07 - Fisica Applicata(Beni Culturali Ambientali Biol.e Medicin)MicroRNAsNeurologyChromosomes Human Pair 1Genetic LociAutism spectrum disorderChromosomes Human Pair 2AutismMedicineStructural GenomicsHuman genomeMonte Carlo MethodResearch ArticlePLoS ONE
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Small-Angle Neutron Scattering from Aqueous Solutions of C12E6 and C12E8: Critical Fluctuations and Micellar Growth

1986

Static SANS measurements have been performed on 0.028 M C12E8 in D2O over the temperature range 20–74.2 °C. Little micellar growth is observed; increases in the scattered intensities in the low angle region are due to critical concentration fluctuations of correlation length g. We have also reexamined our SANS data for C12E6 in D2O, in light of other worker’s claims that a sphere-to-cylinder transition in micellar shape is occurring in these solutions. We discuss in detail the inferences about C12E6 micellar size drawn from the results of several different experimental techniques.

Cloud pointMaterials scienceAggregation numberAqueous solutionAtmospheric temperature rangeE8Molecular physicsSmall-angle neutron scattering
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Complex miscibility behaviour for polymer blends in flow

1995

Abstract Experimental observations of the effect of shear flow on the miscibility of binary polymer blends are compared to calculations based on a generalized Gibbs energy of mixing Gγ˙. This mixing free energy characterizes the steady state established at shear rateγ˙, as the sum of G z , the equilibrium Gibbs energy and E s , the energy the system stores while flowing.

Cloud pointMaterials sciencePolymers and PlasticsOrganic ChemistryBinary numberThermodynamicsMiscibilityGibbs free energyCondensed Matter::Soft Condensed MatterPhysics::Fluid Dynamicssymbols.namesakeShear (geology)Materials ChemistrysymbolsPolymer blendComposite materialShear flowPolymer
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SMART: Unique splitting-while-merging framework for gene clustering

2014

© 2014 Fa et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Successful clustering algorithms are highly dependent on parameter settings. The clustering performance degrades significantly unless parameters are properly set, and yet, it is difficult to set these parameters a priori. To address this issue, in this paper, we propose a unique splitting-while-merging clustering framework, named "splitting merging awareness tactics" (SMART), which does not require any a priori knowledge of either the number …

Clustering algorithmsMicroarrayslcsh:MedicineGene ExpressionBioinformaticscomputer.software_genreCell SignalingData MiningCluster Analysislcsh:ScienceFinite mixture modelOligonucleotide Array Sequence AnalysisPhysicsMultidisciplinarySMART frameworkConstrained clusteringCompetitive learning modelBioassays and Physiological AnalysisMultigene FamilyCanopy clustering algorithmEngineering and TechnologyData miningInformation TechnologyGenomic Signal ProcessingAlgorithmsResearch ArticleSignal TransductionComputer and Information SciencesFuzzy clusteringCorrelation clusteringResearch and Analysis MethodsClusteringMolecular GeneticsCURE data clustering algorithmGeneticsGene RegulationCluster analysista113Gene Expression Profilinglcsh:RBiology and Life SciencesComputational BiologyCell BiologyDetermining the number of clusters in a data setComputingMethodologies_PATTERNRECOGNITIONSplitting-merging awareness tactics (SMART)Signal ProcessingAffinity propagationlcsh:QGene expressionClustering frameworkcomputer
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Bayesian versus data driven model selection for microarray data

2014

Clustering is one of the most well known activities in scientific investigation and the object of research in many disciplines, ranging from Statistics to Computer Science. In this beautiful area, one of the most difficult challenges is a particular instance of the model selection problem, i.e., the identification of the correct number of clusters in a dataset. In what follows, for ease of reference, we refer to that instance still as model selection. It is an important part of any statistical analysis. The techniques used for solving it are mainly either Bayesian or data-driven, and are both based on internal knowledge. That is, they use information obtained by processing the input data. A…

Clustering Model selection Bayesian information criterion Akaike information criterion Minimum message length BioinformaticsSettore INF/01 - InformaticaComputer sciencebusiness.industryModel selectionBayesian probabilitycomputer.software_genreMachine learningComputer Science ApplicationsData-drivenDetermining the number of clusters in a data setIdentification (information)Bayesian information criterionData miningArtificial intelligenceAkaike information criterionCluster analysisbusinesscomputer
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Genomic structural diversity in local goats: Analysis of copy-number variations

2020

Copy-number variations (CNVs) are one of the widely dispersed forms of structural variations in mammalian genomes, and are present as deletions, insertions, or duplications. Only few studies have been conducted in goats on CNVs derived from SNP array data, and many local breeds still remain uncharacterized, e.g., the Sicilian goat dairy breeds. In this study, CNV detection was performed, starting from the genotypic data of 120 individuals, belonging to four local breeds (Argentata dell&rsquo

CoatSicilian goat breedBiologyGenomeArticlegenotyping arraySettore AGR/17 - Zootecnica Generale E Miglioramento Genetico03 medical and health sciencesGenotypeGenetic variationlcsh:ZoologyCopy-number variationlcsh:QL1-991Gene030304 developmental biology0303 health scienceslcsh:Veterinary medicineGeneral VeterinarySicilian goat breeds; copy number variation; genotyping array0402 animal and dairy sciencecopy number variation04 agricultural and veterinary sciencesPhenotypic trait040201 dairy & animal scienceEvolutionary biologylcsh:SF600-1100Animal Science and ZoologySicilian goat breedsSNP array
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Space counts! Brain correlates of spatial and numerical representations in synaesthesia

2018

Over-learned semantic representations, such as numbers, are strongly associated with space in normal cognition, and in the phenomenon called number-space synaesthesia. In number-space synaesthesia, numbers are linked to spatial locations in an idiosyncratic way. Synaesthetes report numbers as belonging to a specific location, or feelings that a specific location is the right location for that number. What does really differentiate synaesthetes from non-synaesthetes with respect to their number-space representation? Here we present a number-space synaesthete, MkM, whose number-space representation dramatically differs from that of controls. We examined the impact of spatial distance with res…

Cognitive Neuroscience05 social sciencesNumerical cognitionBrainExperimental and Cognitive PsychologyStimulus (physiology)Somatosensory system050105 experimental psychologyNumerical digit03 medical and health sciencesCognition0302 clinical medicineNeuropsychology and Physiological PsychologyNeuroimagingParietal LobeSpace PerceptionHumans0501 psychology and cognitive sciencesSpatial representationMental number linePsychologySynesthesia030217 neurology & neurosurgeryCognitive psychologyCoding (social sciences)Cortex
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