Browse
Submit Data
Databases
API
Help

Dataset Information

6 Views

0 Connections

0 Citations

0 Reanalyses

0 Downloads

Omics score: 0

Second-order PDEs in four dimensions with half-flat conformal structure.

ABSTRACT: We study second-order partial differential equations (PDEs) in four dimensions for which the conformal structure defined by the characteristic variety of the equation is half-flat (self-dual or anti-self-dual) on every solution. We prove that this requirement implies the Monge-Ampère property. Since half-flatness of the conformal structure is equivalent to the existence of a non-trivial dispersionless Lax pair, our result explains the observation that all known scalar second-order integrable dispersionless PDEs in dimensions four and higher are of Monge-Ampère type. Some partial classification results of Monge-Ampère equations in four dimensions with half-flat conformal structure are also obtained.

SUBMITTER: Berjawi S

PROVIDER: S-EPMC7016558 | biostudies-literature | 2020 Jan

REPOSITORIES: biostudies-literature

ACCESS DATA

Json Xml

Publications

Second-order PDEs in four dimensions with half-flat conformal structure.

Berjawi S S Ferapontov E V EV Kruglikov B B Novikov V V

Proceedings. Mathematical, physical, and engineering sciences 20200129 2233

We study second-order partial differential equations (PDEs) in four dimensions for which the conformal structure defined by the characteristic variety of the equation is half-flat (self-dual or anti-self-dual) on every solution. We prove that this requirement implies the Monge-Ampère property. Since half-flatness of the conformal structure is equivalent to the existence of a non-trivial dispersionless Lax pair, our result explains the observation that all known scalar second-order integrable dis ...[more]

PMID: 32082065

Similar Datasets

Higher-order topological insulators in synthetic dimensions.

Project description:Conventional topological insulators support boundary states with dimension one lower than that of the bulk system that hosts them, and these states are topologically protected due to quantized bulk dipole moments. Recently, higher-order topological insulators have been proposed as a way of realizing topological states with dimensions two or more lower than that of the bulk due to the quantization of bulk quadrupole or octupole moments. However, all these proposals as well as experimental realizations have been restricted to real-space dimensions. Here, we construct photonic higher-order topological insulators (PHOTIs) in synthetic dimensions. We show the emergence of a quadrupole PHOTI supporting topologically protected corner modes in an array of modulated photonic molecules with a synthetic frequency dimension, where each photonic molecule comprises two coupled rings. By changing the phase difference of the modulation between adjacent coupled photonic molecules, we predict a dynamical topological phase transition in the PHOTI. Furthermore, we show that the concept of synthetic dimensions can be exploited to realize even higher-order multipole moments such as a fourth-order hexadecapole (16-pole) insulator supporting 0D corner modes in a 4D hypercubic synthetic lattice that cannot be realized in real-space lattices.

| S-EPMC7371732 | biostudies-literature

Second-Order Footsteps Illusions.

Project description:In the "footsteps illusion", light and dark squares travel at constant speed across black and white stripes. The squares appear to move faster and slower as their contrast against the stripes varies. We now demonstrate some second-order footsteps illusions, in which all edges are defined by colors or textures-even though luminance-based neural motion detectors are blind to such edges.

| S-EPMC4975121 | biostudies-literature

Fifty-second flat-line: A dramatic case of ictal asystole.

Project description: Not available

| S-EPMC7573472 | biostudies-literature

A second-order iterated smoothing algorithm.

Project description:Simulation-based inference for partially observed stochastic dynamic models is currently receiving much attention due to the fact that direct computation of the likelihood is not possible in many practical situations. Iterated filtering methodologies enable maximization of the likelihood function using simulation-based sequential Monte Carlo filters. Doucet et al. (2013) developed an approximation for the first and second derivatives of the log likelihood via simulation-based sequential Monte Carlo smoothing and proved that the approximation has some attractive theoretical properties. We investigated an iterated smoothing algorithm carrying out likelihood maximization using these derivative approximations. Further, we developed a new iterated smoothing algorithm, using a modification of these derivative estimates, for which we establish both theoretical results and effective practical performance. On benchmark computational challenges, this method beat the first-order iterated filtering algorithm. The method's performance was comparable to a recently developed iterated filtering algorithm based on an iterated Bayes map. Our iterated smoothing algorithm and its theoretical justification provide new directions for future developments in simulation-based inference for latent variable models such as partially observed Markov process models.

| S-EPMC5573285 | biostudies-literature

Second-order induction in prediction problems.

Project description:Agents make predictions based on similar past cases, while also learning the relative importance of various attributes in judging similarity. We ask whether the resulting "empirically optimal similarity function" (EOSF) is unique and how easy it is to find it. We show that with many observations and few relevant variables, uniqueness holds. By contrast, when there are many variables relative to observations, nonuniqueness is the rule, and finding the EOSF is computationally hard. The results are interpreted as providing conditions under which rational agents who have access to the same observations are likely to converge on the same predictions and conditions under which they may entertain different probabilistic beliefs.

| S-EPMC6534984 | biostudies-literature

Higher-order dimensions of psychopathology in a neurodevelopmental transdiagnostic sample.

Project description:Hierarchical dimensional models of psychopathology derived for adult and child community populations offer more informative and efficient methods for assessing and treating symptoms of mental ill health than traditional diagnostic approaches. It is not yet clear how many dimensions should be included in models for youth with neurodevelopmental conditions. The aim of this study was to delineate the hierarchical dimensional structure of psychopathology in a transdiagnostic sample of children and adolescents with learning-related problems, and to test the concurrent predictive value of the model for clinically, socially, and educationally relevant outcomes. A sample of N = 403 participants from the Centre for Attention Learning and Memory (CALM) cohort were included. Hierarchical factor analysis delineated dimensions of psychopathology from ratings on the Conner's Parent Rating Short Form, the Revised Children's Anxiety and Depression Scale, and the Strengths and Difficulties Questionnaire. A hierarchical structure with a general p factor at the apex, broad internalizing and broad externalizing spectra below, and three more specific factors (specific internalizing, social maladjustment, and neurodevelopmental) emerged. The p factor predicted all concurrently measured social, clinical, and educational outcomes, but the other dimensions provided incremental predictive value. The neurodevelopmental dimension, which captured symptoms of inattention, hyperactivity, and executive function and emerged from the higher-order externalizing factor, was the strongest predictor of learning. This suggests that in struggling learners, cognitive and affective behaviors may interact to influence learning outcomes. (PsycInfo Database Record (c) 2021 APA, all rights reserved).

| S-EPMC8628482 | biostudies-literature

Second-order spectral lineshapes from charged interfaces.

Project description:Second-order nonlinear spectroscopy has proven to be a powerful tool in elucidating key chemical and structural characteristics at a variety of interfaces. However, the presence of interfacial potentials may lead to complications regarding the interpretation of second harmonic and vibrational sum frequency generation responses from charged interfaces due to mixing of absorptive and dispersive contributions. Here, we examine by means of mathematical modeling how this interaction influences second-order spectral lineshapes. We discuss our findings in the context of reported nonlinear optical spectra obtained from charged water/air and solid/liquid interfaces and demonstrate the importance of accounting for the interfacial potential-dependent ? (3) term in interpreting lineshapes when seeking molecular information from charged interfaces using second-order spectroscopy.

| S-EPMC5647331 | biostudies-literature

An efficient second-order poisson-boltzmann method.

Project description:Immersed interface method (IIM) is a promising high-accuracy numerical scheme for the Poisson-Boltzmann model that has been widely used to study electrostatic interactions in biomolecules. However, the IIM suffers from instability and slow convergence for typical applications. In this study, we introduced both analytical interface and surface regulation into IIM to address these issues. The analytical interface setup leads to better accuracy and its convergence closely follows a quadratic manner as predicted by theory. The surface regulation further speeds up the convergence for nontrivial biomolecules. In addition, uncertainties of the numerical energies for tested systems are also reduced by about half. More interestingly, the analytical setup significantly improves the linear solver efficiency and stability by generating more precise and better-conditioned linear systems. Finally, we implemented the bottleneck linear system solver on GPUs to further improve the efficiency of the method, so it can be widely used for practical biomolecular applications. © 2019 Wiley Periodicals, Inc.

| S-EPMC6422926 | biostudies-literature

A half-century after the molecular clock: new dimensions of molecular evolution.

Project description:The EMBO workshop on 'Evolution in the Time of Genomics' took place in May 2012 in the magnificent sixteenth century Palazzo Franchetti near Ponte dell'Accademia in Venice. The meeting focused on phenomena that are not part of the traditional narrative of molecular evolution and which might signal a paradigm shift in the field.

| S-EPMC3410383 | biostudies-other

Reliability of Scales With Second-Order Structure: Evaluation of Coefficient Alpha's Population Slippage Using Latent Variable Modeling.

Project description:A readily applicable procedure is discussed that allows evaluation of the discrepancy between the popular coefficient alpha and the reliability coefficient of a scale with second-order factorial structure that is frequently of relevance in empirical educational and psychological research. The approach is developed within the framework of the widely used latent variable modeling methodology and permits point and interval estimation of the slippage of alpha from scale reliability in a population under investigation. The method is useful when examining the consistency of complex structure measuring instruments assessing higher order latent constructs and, under its assumptions, represents a generally recommendable alternative to coefficient alpha. The outlined procedure is illustrated using data from an authoritarianism study.

| S-EPMC6293413 | biostudies-literature

OmicsDI is part of the ELIXIR infrastructure

OmicsDI is an Elixir interoperability service. Learn more ›

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