This paper identifies criteria for quantum confinement on non-complete Riemannian manifolds.
problem Quantum confinement on non-complete Riemannian manifolds with potential and degenerate measures.
method Identification of an effective potential Veff and formulation of criteria for quantum confinement. result Simple criteria for quantum confinement are formulated, allowing for measures with degeneracies or singularities near the metric boundary.
The paper studies submanifolds in weighted manifolds, establishing parabolicity criteria and describing bounded curvature submanifolds.
problem Characterizing submanifolds of bounded mean curvature in weighted manifolds.
method Comparisons of h-capacity, criteria for h-parabolicity, and use of geometric functions. result Established criteria for h-parabolicity and h-hyperbolicity of submanifolds. Study reveals weak knotting in confined polymers, not dominated by any single knot type.
problem Characterizing knotting in open, confined polymers.
method Modeling open curves as virtual knots, comparing lattice walks and ideal chains in confined and unconfined conditions.
result Weak knotting is a common feature in confined polymers, not dominated by any single knot type.
Study confined subgroups in groups with contracting elements, showing their growth rate is strictly greater than half of the ambient growth rate.
problem Understanding the growth rate of confined subgroups in groups with contracting elements.
method Through boundary actions, analyzing the Hopf decomposition and quotient growth.
result Confined subgroups have a growth rate strictly greater than half of the ambient growth rate.
Fast algorithm samples confined polygons efficiently.
problem Sampling confined random equilateral closed polygons efficiently.
method Uses symplectic geometry to sample moment polytope, leading to a linear-time algorithm.
result Explicit formulas for expected distances and total curvature of vertices to the origin.
CONFINE enhances neural networks' interpretability without sacrificing accuracy.
problem Lack of interpretability in deep neural networks, especially in healthcare.
method CONFINE uses conformal prediction to generate prediction sets with robust uncertainty estimates.
result CONFINE achieves correct efficiency up to 3.3% higher than original accuracy.
Study geometric quantum confinement on special incomplete Riemannian manifolds.
problem Characterize quantum confinement on Grushin-type manifolds.
method Constant-fibre direct integral scheme combined with Weyl's analysis.
result Fully characterizes essential self-adjointness of Laplace-Beltrami operator.
5D SCFTs can have confining vacua with strings and unbroken symmetries.
problem Investigating phases of 5D SCFTs by varying couplings.
method Using geometric realisation of M-theory on metrically conical Calabi-Yau threefolds.
result Many 5D SCFTs have couplings leading to massive, confining vacua with strings and unbroken symmetries.
New framework shows C∗-simplicity for groups without certain subalgebras.
problem Characterizing C∗-simplicity of groups. method Introducing confined subalgebras and Uniformly Recurrent States.
result A countable discrete group is C∗-simple if it has no non-trivial amenable confined subalgebras. Extends confining subset theory to describe hyperbolic actions of solvable groups with higher rank abelianizations.
problem Describing hyperbolic actions of solvable groups with higher rank abelianizations.
method Extends confining subset theory to apply to solvable groups with higher rank abelianizations.
result Complete description of hyperbolic actions of generalized solvable Baumslag-Solitar groups.
Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curva…
Sharp growth tightness proven for group quotients.
problem Growth behavior of group quotients by confined subgroups.
method Statistically convex-cocompact action with contracting elements.
result Sharp growth tightness proven, with applications to uniformly recurrent subgroups.
A closed equilateral random walk in 3-space is a selection of unit length vectors giving the steps of the walk conditioned on the assumption that the sum of the vectors is zero. The sample space of such walks with n edges is the (2n−3)-dimensional Riemannian manifold of equilateral closed polygons in R3…
Study on membranes under confinement, proving existence and regularity of minimizers.
problem Existence and regularity of minimizers for constrained Helfrich energy.
method Elliptic system analysis, careful study of measure-valued Lagrange multiplier.
result Optimal regularity for solutions throughout branch points, rigid behavior for unit ball minimizers.
Minimal submanifolds confined in space are highly restricted.
problem Understanding minimal submanifolds in confined spaces.
method Analyzing structural restrictions and volume growth properties.
result Proper minimal immersions with sublinear height growth must have Euclidean volume growth.
Algorithm finds safe zones in policy Markov Decision Processes to limit trajectory escape.
problem Finding safe zones in policy Markov Decision Processes to limit trajectory escape.
method Bi-criteria approximation learning algorithm with polynomial sample complexity.
result Achieves almost 2 approximation for both escape probability and safe zone size.
The study examines knot probabilities in confined lattice polygons.
problem Determining the relative knotting probabilities in confined lattice knots.
method Used Monte Carlo algorithms to enumerate conformations of lattice knots in a confined volume.
result Relative knotting probabilities are small, with the model dominated by unknots.
This work uses scientific constraints to validate neural network predictions in fusion physics.
problem Verifying the scientific plausibility of neural network predictions in fusion physics.
method Using known scientific constraints as a validation tool.
result Validated neural network predictions in fusion physics using scientific constraints.
Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
problem Neural networks' optimization dynamics are confined to a single basin despite connected basins in the loss landscape.
method Identifying entropic barriers arising from the interplay between curvature variations along low-loss paths and noise in optimization dynamics.
result Curvature-induced entropic forces bias noisy dynamics back toward the endpoints, explaining the confinement and connectivity of solutions.
Minimal submanifolds either fill space or are confined with geometric restrictions.
problem Understanding the behavior of minimal submanifolds in space.
method A dichotomy principle and volume doubling theorem.
result Quantitative restrictions on confined minimal submanifolds, including volume growth and optimal density rates.
We consider the problem of minimizing the bending or elastic energy among Jordan curves confined in a given open set Ω. We prove existence, regularity and some structural properties of minimizers. In particular, when Ω is convex we show that a minimizer is necessarily a convex curve. We also provide an example of a…
Study of bound states in quantum layers with confining potentials.
problem Investigating bound states in quantum layers with confining potentials.
method Developed a general approach using parallel coordinates based on the surface but outside its cut locus.
result Discrete eigenvalues exist for certain quantum layers with positive total Gauss curvature.
Classifies quantum particle behavior on a special cylinder.
problem Quantum confinement and transmission on a Grushin cylinder.
method Characterizes self-adjoint realizations of the Laplace-Beltrami operator.
result Identifies physically meaningful extensions of the Hamiltonian.
Hydrogen atom confined in an inverted-Gaussian potential, with detailed numerical methods and results.
problem Studying hydrogen atom in a specific potential.
method Three numerical methods: Lagrange-mesh, fourth order finite differences, and finite element method.
result Accurate numerical results for hydrogen atom energies and eigenfunctions, improving previous literature.
Geometric QCD framework establishes stable vacuum for quark confinement.
problem Quark confinement in QCD.
method Geometric construction of stable vacuum using Hodge-dual surfaces.
result Existence and stability of the Hodge-dual surface in 4D ensures quark confinement.
The study characterizes hypersurfaces in weighted cylinders and generalizes confinement properties.
problem Characterizing hypersurfaces in weighted Riemannian products.
method Analyzing parabolic hypersurfaces with boundary in weighted cylinders.
result Generalized confinement properties of hypersurfaces in weighted cylinders.
Improved neural network surrogates for ICF using manifold and cycle consistency.
problem Modeling and predicting complex physical processes in inertial confinement fusion.
method Training neural network surrogates that are consistent with the physical manifold and cyclically consistent.
result Surrogates are superior in predictive performance, more resilient to sampling artifacts, and more data efficient.
We consider an open domain with a compact boundary in an Euclidean space and a Schroedinger operator with magnetic field on this domain. We give sufficient conditions on the rate of growth of the magnetic field near the boundary which guarantees essential self-adjointness of this operator. From the physical point of vi…
We study geometric properties of complete non-compact bounded self-shrinkers and obtain natural restrictions that force these hypersurfaces to be compact. Furthermore, we observe that, to a certain extent, complete self-shrinkers intersect transversally a hyperplane through the origin. When such an intersection is comp…
Seq2seq models predict complex multi-physics systems' time evolution.
problem Predicting the time-evolution of complex multi-physics systems.
method Sequence-to-sequence models applied to multi-physics simulations.
result Seq2seq models accurately emulate complex systems and predict their evolution.
Random walks and polygons are used to model polymers. In this paper we consider the extension of writhe, self-linking number and linking number to open chains. We then study the average writhe, self-linking and linking number of random walks and polygons over the space of configurations as a function of their length. W…
Transfer learning improves fusion simulation accuracy.
problem Calibrate fusion simulation models to experimental data.
method Hierarchical transfer learning using deep neural networks.
result Calibrated models predict Omega experiments more accurately.
Modeling GDP growth rates using Lévy flights with confining potential.
problem Understanding the impact of firm size fluctuations on GDP.
method Combining microscopic firm growth rates with macroscopic GDP, using Lévy-stable fluctuations and a confining potential.
result The model accurately predicts 200 years of US GDP growth rates.
New theorem links symmetries to first integrals in plasma physics.
problem Understanding the relationship between symmetries and first integrals in divergence-free fields.
method Developed a Noether-type Theorem reformulation for three-dimensional divergence-free vector fields.
result Converse of the Noether-type Theorem holds on the toroidal region, proving the existence of flux coordinates.
We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, o…
Deep learning compares turbulence models in plasma physics.
problem Predicting edge plasma turbulence in magnetic fusion reactors.
method Physics-informed deep learning framework for comparing two-fluid and gyrokinetic models.
result Good overall agreement between two-fluid theory and gyrokinetic models in turbulent field fluctuations.
New bounds on stick number of knots found using random polygon generation.
problem Understanding the minimum number of segments needed to build a polygonal knot.
method Monte Carlo approach to generating and analyzing large ensembles of random polygons.
result Improved bounds on stick number for over 40% of knots with 10 or fewer crossings.
Criteria ensure manifold triangulation without differentiable structure.
problem Ensuring a manifold can be triangulated without differentiable structure.
method Local coordinate chart criteria for homeomorphism verification.
result Criteria guarantee triangulation of manifolds without Delaunay property.
We give some general criteria of being a homeomorphism for continuous mappings of topological manifolds, as well as criteria of being a diffeomorphism for smooth mappings of smooth manifolds. As an illustration, we apply these criteria to the problems arising in two- and three-dimensional grid generation.
The study reveals flaws in pruning criteria and proposes a new assumption for better filter selection.
problem Flaws in existing pruning criteria for CNNs.
method Empirical experiments and Convolutional Weight Distribution Assumption.
result The Convolutional Weight Distribution Assumption improves filter selection in pruning.
New method finds optimal hyperparameters for multiple tasks and criteria.
problem Finding optimal hyperparameters for multiple tasks and criteria.
method Multi-Task Multi Criteria (MTMC) method that provides Pareto-optimal solutions.
result The method selects optimal hyperparameters based on given criteria significance coefficients.
Improved recommendations using latent embeddings from user reviews.
problem Lack of consideration for latent embeddings in multi-criteria recommender systems.
method Utilized variational autoencoders to map user reviews into latent embeddings, which are then compressed into discrete vectors for multi-criteria recommendation.
result The proposed method significantly outperforms baselines across various datasets and evaluation measures.
New criteria for Heegaard splittings ensure strong irreducibility and finite Goeritz groups.
problem Determining strong irreducibility and finite Goeritz groups of Heegaard splittings.
method Two diagrammatic criteria for Heegaard splittings, accepting arbitrary disk systems.
result Criteria ensure strong irreducibility and finite Goeritz groups for Heegaard splittings.
Develops scenario theory for multi-criteria decision making.
problem Need for robustness assessment with multiple criteria and datasets.
method Collectively treats risks associated with individual criteria for multi-criteria decision problems.
result More accurate robustness certificates and sharper quantification of simultaneous criterion satisfaction.
We consider the problem of identifying patterns in a data set that exhibit anomalous behavior, often referred to as anomaly detection. In most anomaly detection algorithms, the dissimilarity between data samples is calculated by a single criterion, such as Euclidean distance. However, in many cases there may not exist …
The paper evaluates criteria for selecting cryptocurrencies based on historical data.
problem High risk of cryptocurrencies due to volatility.
method Characterized returns and risks using historical data in short time windows (7 and 15 days). Analyzed the importance of criteria using various methods.
result Importance of criteria for selecting cryptocurrencies is analyzed and evaluated.
Fairness criteria may harm over time, contrary to conventional wisdom.
problem The impact of fairness criteria on long-term population well-being.
method Study of fairness criteria in a one-step feedback model, analyzing long-term outcomes.
result Static fairness criteria do not necessarily promote improvement over time and may cause harm.
New criteria detect anomaly detection algorithms without labeled data.
problem Lack of labeled data for evaluating anomaly detection algorithms.
method Developed two new criteria based on Excess-Mass and Mass-Volume curves, and a feature sub-sampling methodology.
result Empirically validated new criteria outperform classical ROC and PR curves in non-labeled data scenarios.