Infinite Lie groups meet continuity conditions.
problem Continuity conditions for Lie groups.
method Analyzing locally -convex Lie groups.
result Infinite dimensional Lie groups have the strong Trotter property.
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48 results for “Trotter property”
Generative Neural Samplers for the Quantum Heisenberg Chaincond-mat.stat-mech
Generative neural samplers estimate quantum spin system properties.
problem Estimating observables for quantum spin systems.
method Autoregressive models using Suzuki-Trotter transformation.
result Results for energy, specific heat, and susceptibility are in good agreement with Monte Carlo methods.
We generalize the theory of gradient flows of semi-convex functions on CAT(0)-spaces, developed by Mayer and Ambrosio--Gigli--Savaré, to CAT(1)-spaces. The key tool is the so-called "commutativity" representing a Riemannian nature of the space, and all results hold true also for metric spaces satisfying the commutativi…
The numerical integration plays a fundamental role in understanding the behaviour of many mechanical systems. In this paper some important aspects of the mechanical integrators on the dynamics of a mechanical system are studied. More specific, we have shown that if that the Lie-Trotter integrator is obtained, in case o…
A new transformer model accelerates training with optimization techniques.
problem Training deep neural networks efficiently and effectively.
method Interprets transformer layers as optimization steps, applying Nesterov acceleration.
result The new model outperforms existing models on benchmark datasets.
Hybrid QAOA approach optimizes portfolios with strict constraints, outperforming classical methods.
problem Combinatorial optimization under strict cardinality constraints in portfolio management.
method Constraint-preserving QAOA with XY-mixers and Trotterized initialization.
result QAOA achieves a Sharpe Ratio of 1.81, significantly outperforming classical methods.
We construct examples of knots that have isomorphic nth-order Alexander modules, but non-isomorphic nth-order linking forms, showing that the linking forms provide more information than the modules alone. This generalizes work of Trotter, who found examples of knots that have isomorphic classical Alexander modules, but…
Transformer is reinterpreted as a numerical ODE solver, leading to improved architectures.
problem Understanding and improving the Transformer architecture.
method Interpreted Transformer as a numerical ODE solver for a multi-particle dynamic system, proposing new architectures.
result Macaron Net outperforms Transformer on supervised and unsupervised learning tasks.
The paper proves differentiability of evolution maps in Lie groups.
problem Differentiability of evolution maps in infinite-dimensional Lie groups.
method Showed sequential continuity (Mackey k-continuity) leading to differentiability.
result Differentiability of evolution maps in -semiregular Lie groups.
Gordon-Litherland pairing connects combinatorics and topology.
problem Unifying quadratic forms in link theory.
method Picture proof using Kirby diagrams.
result Their theorem has numerous applications in low-dimensional topology.
A symmetric matrix invariant is defined for oriented link diagrams.
problem Defining an invariant for oriented link diagrams.
method Defining a symmetric map from regions of an oriented link diagram to , corrected by the writhe.
result The negative signature of , corrected by the writhe, conjecturally equals twice the Tristram-Levine signature function.
Quantum annealing is a generic solver of the optimization problem that uses fictitious quantum fluctuation. Its simulation in classical computing is often performed using the quantum Monte Carlo simulation via the Suzuki--Trotter decomposition. However, the negative sign problem sometimes emerges in the simulation of q…
We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant pseudo metric. We prove that for precompact open subsets of , thi…
We introduce a variation of the classical Ricci flow equation that modifies the unit volume constraint of that equation to a scalar curvature constraint. The resulting equations are named the Conformal Ricci Flow Equations because of the role that conformal geometry plays in constraining the scalar curvature. These equ…
High-fidelity quantum simulations demonstrated on short-coherence hardware.
problem Short coherence times limit the depth of quantum algorithms.
method Fixed State Variational Fast Forwarding (fsVFF) algorithm.
result Simulations of 600 time steps possible, 150x longer than previous methods.
The paper extends stability theorem for Navier-Stokes equations to negatively curved manifolds.
problem Stability of the three-dimensional Navier-Stokes equations on negatively curved manifolds.
method Analysis of the deformation Laplacian, overcoming obstacles with curvature pinching and spectral gap.
result Global mild solution with exponential decay for small data on negatively curved manifolds.
Groups with Property (T) have fiber products with Property (T).
problem When does the fiber product of groups with Property (T) have Property (T)?
method Analyzing fiber products of groups with Property (T).
result Fiber products of groups with Property (T) also have Property (T).
We prove recognition theorems for codimension one manifold factors of dimension . In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that i…
The study shows that several properties are not profinite invariants.
problem Determining which properties are profinite invariants.
method Combining Rips constructions and iterated group-theoretic Dehn filling on hyperbolic virtually special groups.
result Several properties (stable commutator length, quasimorphisms, property NL, property FW, property FA, and non-abelian free subgroups) are not profinite invariants.
We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note …
New complexity notion connects finite decomposition and asymptotic property C.
problem Understanding and connecting different properties in metric spaces.
method Introducing finite APC-decomposition complexity and proving its implications.
result Finite APC-decomposition complexity implies property A for metric spaces.
Extended Tetrahedral Property to non-Euclidean spaces.
problem Prove Tetrahedral Property in non-Euclidean spaces.
method Extend Tetrahedral Property to less restrictive definition and prove its properties.
result Generalized Tetrahedral Property retains original properties and leads to convergence results.
Investigates stability properties of Haezendonck-Goovaerts premium principles in Orlicz spaces.
problem Stability properties of Haezendonck-Goovaerts premium principles in various Orlicz spaces.
method Analysis of stability properties including Fatou and Lebesgue properties, and continuity with respect to -weak convergence.
result Haezendonck-Goovaerts principles satisfy the Fatou property and Lebesgue property under certain conditions.
The paper explores higher property T in lattices and its connections to geometric phenomena.
problem Understanding higher property T in lattices and related geometric phenomena.
method Operator-algebraic characterizations of higher property T and connections to lattice geometry.
result Unified framework for understanding higher property T and related geometric phenomena.
On asymptotic property Cmath.GT
Asymptotic property C was introduced by Dranishnikov to study spaces with infinite asymptotic dimension. We show that asymptotic property C is preserved by infinite products. We also show that countable restricted direct products of countable groups with finite asymptotic dimension have asymptotic property C. Then we i…
Groups of importance in group theory have flexible stability properties.
problem Stability and flexibility of groups in geometric and combinatorial group theory.
method Establishing Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for specific groups.
result Groups like -manifold groups, limit groups, and certain one-relator groups are very flexibly stable.
This paper generalizes property (QT) to a broader class of groups.
problem Proving property (QT) for a wider range of groups.
method Using projection complex machinery and hierarchical hyperbolic groups.
result Established sufficient conditions for groups to have property (QT).
Proves a vanishing property for symplectic manifold cohomology.
problem Generalizing complex geometry results to symplectic geometry.
method Based on Tseng and Zhou's vanishing property under symplectic flatness.
result Establishes necessity of symplectic flatness for certain results.
Survey shows degenerate elliptic equations have analytic properties despite low regularity.
problem Understanding analytic properties of degenerate elliptic equations.
method Explains why solutions of a specific degenerate elliptic equation are analytic.
result Solutions of a specific degenerate elliptic equation are analytic despite low regularity.
Unified approach amplifies data for distribution property estimation.
problem Estimating properties of discrete distributions efficiently.
method Unified, linear-time, competitive estimator using just 2n samples.
result Achieves performance of empirical estimator with n√log n samples using only 2n samples.
Survey on foliations and diffeomorphism groups.
problem Relationship between algebraic and homotopical properties.
method Survey and analysis of existing literature.
result Explains the connection between diffeomorphism groups and foliations.
Paper explores limits of graph property testing in Ising models.
problem Understanding information-theoretic limits of graph property testing in Ising models.
method Combinatorial constructs and correlation-based tests.
result Property testing is more challenging for general Ising models than ferromagnets.
We prove extension theorems for several geometric properties such as asymptotic property C (APC), finite decomposition complexity (FDC), strict finite decomposition complexity (sFDC) which are weakenings of Gromov's finite asymptotic dimension (FAD). The context of all theorems is a finitely generated group with a …
Study generalizes property elicitation to imprecise probabilities.
problem Minimizing risk over imprecise probability distributions.
method Maximin risk minimization over a set of imprecise probabilities.
result Conditions for elicitability of IP-properties.
Introduces bounded scale measure and generalizes property A.
problem Defining property A for large scale spaces with bounded geometry.
method Introduces bounded scale measure, shows its coarse invariance, and generalizes property A.
result Definition of property A for large scale spaces with bounded scale measure is a coarse invariant.
Model predicts price polarity of real estate properties using website information.
problem Predicting price polarity of real estate properties.
method Uses doc2vec and xgboost to learn correlations between price and text descriptions of properties.
result Text descriptions provide slightly higher accuracy than features alone.
Study cohomological and metric properties of non-Kähler complex manifolds.
problem Understanding cohomological invariants and metrics of non-Kähler complex manifolds.
method Partial account of problems through cohomological and metric properties.
result Partial insights into cohomological and metric properties of non-Kähler manifolds.
The paper explores the twisted Rokhlin property in mapping class groups of surfaces.
problem Classifying surfaces whose mapping class groups have the twisted Rokhlin property.
method Generalizing the Rokhlin property to the twisted version, the authors classify surfaces based on their mapping class groups' properties.
result The mapping class groups of connected orientable infinite-type surfaces without boundaries have the twisted Rokhlin property, while those of other surfaces do not.
Study shows space of persistence diagrams doesn't have Yu's property A.
problem Failure of property A in the space of persistence diagrams.
method Introduced k-prisms to prove failure of property A.
result Space of persistence diagrams fails to have Yu's property A in a Wasserstein metric.
The balance property is crucial for insurance pricing, ensuring total actuarial price equals loss. Maximum likelihood GLMs fulfill it, but Lindholm-Wüthrich suggests three methods, with constrained GLM being superior.
problem Ensuring the balance property in insurance pricing models
method Using constrained GLM fitting
result Constrained GLM fitting is superior to the two previously discussed balance correction methods
We prove some general results about quasi-actions on trees and define Property (QFA), which is analogous to Serre's Property (FA), but in the coarse setting. This property is shown to hold for a class of groups, including for . We also give a way of thinking about Property (QFA) by breaking it down …
Study Finsler metric measure manifolds' concentration properties.
problem Understanding concentration properties in Finsler metric measure manifolds.
method Established relationships with observable diameter, isoperimetric inequalities, and first eigenvalue.
result Derived a Cheng type upper bound estimate for the first closed eigenvalue.
Hybrid clustering combines partitional and hierarchical clustering for computational effectiveness and versatility in cluster shape. In such clustering, a dissimilarity measure plays a crucial role in the hierarchical merging. The dissimilarity measure has great impact on the final clustering, and data-independent prop…
Paper proves naturally reductive property is inaudible for certain manifolds.
problem Proving naturally reductive property is inaudible for specific manifolds.
method Using a pair of non-compact 11-dimensional generalized Heisenberg groups, the paper proves the naturally reductive property is inaudible.
result The naturally reductive property is inaudible for certain manifolds.
The paper examines curvature properties of twistor spaces.
problem None explicitly stated in the abstract.
method Review of Riemannian and almost Hermitian geometry of twistor spaces.
result Curvature properties of twistor spaces are explored.
3-manifold groups have a property that allows them to act on quasi-trees.
problem Proving property (QT) for 3-manifold groups.
method Analyzing the geometry of 3-manifolds and using quasi-trees.
result Compact, orientable 3-manifold groups have property (QT) if they don't support Sol or Nil geometry.
Unified method for estimating properties of large domain distributions efficiently.
problem Estimating properties of distributions over large domains efficiently.
method Piecewise-polynomial approximation technique for constructing sample- and time-efficient estimators.
result Near-linear-time computable estimators with optimal and highly-concentrated approximation values.
The average shadowing property is considered for set-valued dynamical systems, generated by parameterized IFS, which are uniformly contracting, or conjugacy, or products of such ones. We also prove that if a continuous surjective IFS F on a compact metric space X has the aver- age shadowing property, then every point x…