New method optimizes multiple objectives using particle dynamics and gradient flow.
problem Optimizing multiple conflicting objectives in complex scenarios.
method Interacting particle method combining Langevin and birth-death dynamics with a dominance potential.
result Method effectively relocates dominated particles, improving Pareto optimality.
We apply the potential force estimation method to artificial time series of market price produced by a deterministic dealer model. We find that dealers' feedback of linear prediction of market price based on the latest mean price changes plays the central role in the market's potential force. When markets are dominated…
Smooth dec initial data sets may not extend to smooth spacetimes.
problem Whether every dec initial data set can be extended to a smooth spacetime.
method Examined the converse of the dominant energy condition for initial data sets and spacelike hypersurfaces.
result Not all dec initial data sets can be extended to smooth spacetimes.
Continuous solutions found for complex geometry equations.
problem Finding solutions to complex geometry equations on Hermitian manifolds.
method Proving existence of continuous quasi-plurisubharmonic solutions for specific measures.
result Existence of continuous quasi-plurisubharmonic solutions for measures dominated by capacity.
In this article we discuss the distribution of asset price movements by the market potential function. From the principle of free energy minimization we analyze two different kinds of market potentials. We obtain a U-shaped potential when market reversion (i.e. contrarian investors) is dominant. On the other hand, if t…
New findings on Kähler-Einstein currents dominating Kähler forms on compact spaces.
problem Understanding Kähler-Einstein currents on singular spaces.
method Analyzing currents' properties and applying them to compact spaces with log terminal singularities.
result Kähler-Einstein currents dominate Kähler forms on compact spaces with log terminal singularities.
Characterizes causal structure dominance for latent variables.
problem Determining dominance relations between causal structures with latent variables.
method Complete characterization for three visible variables, partial for four; uses nontrivial inequality constraints.
result Equivalence classes with nontrivial inequality constraints become ubiquitous as the number of visible variables increases.
Proves spacetime positive mass theorem for spin initial data sets with arbitrary ends.
problem Proving the spacetime positive mass theorem for specific spacetime configurations.
method Solving a mixed boundary value problem for the Dirac-Witten operator with a Callias potential.
result Established spacetime positive mass theorem for asymptotically flat spin initial data sets with arbitrary ends.
New method ranks competitors from multiple types of comparisons.
problem Ranking individuals or teams from multiple conflicting comparison types.
method Combination of expectation-maximization algorithm and modified Bradley-Terry model.
result A ranking can be computed from multiple conflicting comparison types.
We describe a new approach for managing aleatoric uncertainty in the Reinforcement Learning (RL) paradigm. Instead of selecting actions according to a single statistic, we propose a distributional method based on the second-order stochastic dominance (SSD) relation. This compares the inherent dispersion of random retur…
Study finds risk sharing without convexity assumptions.
problem Finding fair risk allocations among agents with heterogeneous beliefs.
method Combines local comonotone improvement with Dieudonné-type argument.
result Existence of Pareto optima without convexity assumption.
This study attempts to analyze patterns in cryptocurrency markets using a special type of deep neural networks, namely a convolutional autoencoder. The method extracts the dominant features of market behavior and classifies the 40 studied cryptocurrencies into several classes for twelve 6-month periods starting from 15…
Investigate using LETFs to outperform benchmarks, finding them more likely to succeed.
problem The controversy and popularity of LETFs in constructing portfolios.
method Systematic investigation using IR-optimal strategies with LETFs and VETFs, including neural network-based approaches.
result IR-optimal strategies with LETFs outperform benchmarks and achieve partial stochastic dominance.
Connected domination numbers found for plane triangulations up to 13 vertices.
problem Finding connected domination numbers for plane triangulations.
method Analyzing triangulations of up to 13 vertices and proving the difference between connected and regular domination numbers can be arbitrarily large.
result Connected domination numbers for triangulations up to 13 vertices and upper bound for larger triangulations.
Study shows inflation in 3+1D cosmologies with bounded scalar potential and specific symmetry.
problem Understanding inflation in 3+1D cosmologies with specific constraints.
method Mean curvature flow and asymptotic analysis of metric variations, stress-energy tensor, and inflaton field dynamics.
result Inflation occurs in 3+1D cosmologies with specific constraints, demonstrating it is possible with inhomogeneous initial conditions.
Study improves understanding and performance of FA learning rules in neural networks.
problem Lack of theoretical understanding and limited applications of Feedback Alignment (FA) methods.
method Introduces a unified framework linking synaptic weight changes to implicit regularization, providing convergence conditions and empirical evidence.
result Better alignment can enhance FA performance on complex multi-class tasks.
Manifolds can be dominated by hypersurfaces in a sphere.
problem Dominating manifolds with hypersurfaces.
method Proving any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.
result Any smooth, closed, oriented manifold can be dominated by a codimension 1 submanifold of the sphere.
New method ranks multivariate distributions in SMOOP using q-dominance.
problem Lack of reliable methods to rank multivariate distributions in SMOOP.
method Introduces center-outward q-dominance and develops empirical test procedures.
result Proves q-dominance implies FSD and establishes a sample size threshold.
Why deep neural networks (DNNs) capable of overfitting often generalize well in practice is a mystery [#zhang2016understanding]. To find a potential mechanism, we focus on the study of implicit biases underlying the training process of DNNs. In this work, for both real and synthetic datasets, we empirically find that a…
RPN 2 improves function learning by modeling data interdependence.
problem Invalid assumption of input data independence leads to performance degradation.
method Integrates data and structural interdependence functions into RPN 2's architecture.
result Significantly improves learning performance and expands unifying potential.
New auction design uses statistical learning to reduce costs and improve fairness.
problem Designing efficient multi-item auctions with reduced implementation costs and fairness.
method Nonparametric density estimation for credible intervals, two new strategies.
result Strategies consistently outperform alternative methods in revenue maximization and cost reduction.
We show that non-domination results for targets that are not dominated by products are stable under Cartesian products.
New framework for ranking distributions using variable fractional parameters.
problem Ordering distributions with varying steepness and local non-concavities.
method Introducing a function γ:Ro[0,1] to replace the fixed parameter in fractional SD. result Enables ranking of a broader range of distributions and incorporates dynamic greediness.
Study rare-event simulation for neural networks and random forests.
problem Safety evaluation and robustness quantification of machine learning models.
method Importance sampling scheme integrating large deviations and sequential mixed integer programming.
result Efficiency guarantees and numerical demonstrations for various neural network architectures.
Research examines when 4-manifolds are dominated by geometric ones.
problem When is an orientable closed 4-manifold dominated by another?
method Focuses on geometric or fibred cases.
result Characterizes conditions for domination.
3-manifolds can virtually dominate others with positive simplicial volume.
problem Domination of 3-manifolds with positive simplicial volume.
method Proving existence of finite covers with degree-1 maps.
result Virtual domination of 3-manifolds with positive simplicial volume.
Study domination between non-Fuchsian surface group representations and anti-de Sitter geometry.
problem Domination problem between non-Fuchsian representations of closed surface groups.
method Analysis of branched harmonic immersions and construction of anti-de Sitter 3-manifolds.
result Found that representations admitting branched harmonic immersions dominate other representations, and constructed large families of branched anti-de Sitter 3-manifolds.
Paper shows local SGD outperforms mini-batch SGD under certain conditions.
problem Proving local SGD's superiority in distributed learning with heterogeneous data.
method New lower and upper bounds for local SGD under first-order heterogeneity assumptions.
result Local SGD is min-max optimal under certain conditions, resolving understanding of distributed optimization.
Dominant knots have isomorphic Seifert and Tait graphs.
problem Understanding knot dominance through graph isomorphism.
method Examined alternating knots and their Seifert and Tait graphs.
result Isomorphic Seifert and Tait graphs indicate dominant knots.
Generative classifiers show surprising human-like performance.
problem Comparing generative and discriminative models for object recognition.
method Built on recent advances in generative modeling to create classifiers and compared them to discriminative models.
result Generative classifiers outperform discriminative models in several key areas, including shape bias and out-of-distribution accuracy.
New homology theory connects graph domination to subtle algebraic structures.
problem Understanding graph domination through algebraic homology.
method Interpreting überhomology as poset homology and showing its functorial properties.
result The Euler characteristic of bold homology equals the evaluation of the connected domination polynomial.
3-manifolds can be virtually dominated by maps of degree 8.
problem Understanding virtual domination of 3-manifolds.
method Proving existence of finite covers with specific map properties.
result Virtual 8-dominance of 3-manifolds.
Odd-dimensional manifolds have contact maps of non-zero degree.
problem Contact domination in odd-dimensional manifolds.
method Proving existence of maps from tight contact manifolds.
result Existence of non-zero degree maps from Liouville-fillable but not Weinstein-fillable contact manifolds.
Unified framework for efficient Frank-Wolfe optimization of Dominant Set Clustering.
problem Optimizing Dominant Set Clustering with various Frank-Wolfe algorithms.
method Unified framework for pairwise, standard, and away-steps Frank-Wolfe algorithms, with explicit convergence rates.
result Explicit convergence rates for Frank-Wolfe methods in Dominant Set Clustering.
New EI strategies using OWA and SSD for excess return.
problem Selecting EI portfolios that stochastically dominate a benchmark.
method Proposes a new OWA-based EI model and introduces a new SSD criterion.
result OWA-based EI portfolios stochastically dominate a benchmark and generate excess return.
The Bohmian quantum approach is implemented to analyze the financial markets. In this approach, there is a wave function that leads to a quantum potential. This potential can explain the relevance and entanglements of the agent's behaviors with the past. The light is shed by considering the relevance of the market cond…
We study a generalized family of stochastic orders, semiparametrized by a distortion function H, namely H-distorted stochastic dominance, which may determine a continuum of dominance relations from the first- to the second-order stochastic dominance (and beyond). Such a family is especially suitable for representing a …
The paper analyzes how behavioral investors make portfolio decisions using Markowitz Stochastic Dominance criteria.
problem Understanding how behavioral investors make portfolio decisions.
method Developed stochastic optimization problems and MILP models to capture subjective decision weights and probability weighting functions.
result The developed models can be used to formulate computationally tractable portfolio analysis problems.
Finite simplicial complexes dominate certain manifolds with a bounded number of simplices.
problem Understanding the finite domination of manifolds by simplicial complexes.
method Proving that a manifold can be dominated by the n-skeleton of a finite simplicial complex with a bounded number of simplices. result The total number of simplices in the n-skeleton is bounded above by a constant depending only on n and the embolic volume of the manifold. New method compares classifiers using GSD-front, addressing statistical uncertainty and robustness.
problem Comparing classifiers with multiple quality metrics and statistical uncertainty.
method Proposes GSD-front and statistical tests for robust comparisons.
result Reliable method for comparing classifiers with statistical uncertainty and robustness.
Solves risk minimization problem with SSD constraints.
problem Finding SSD-minimal quantile function under mixed constraints.
method Explicitly works out SSD-minimal solution and relates to Skorokhod problem.
result Explicit solution to risk minimizing problem.
Develops a new solver for optimizing with stochastic dominance constraints.
problem Optimizing with stochastic dominance constraints is computationally expensive and impractical.
method Introduces Light Stochastic Dominance Solver (light-SD) that uses Lagrangian properties and surrogate approximation.
result The light-SD solver demonstrates superior performance on various problems.
Proposes new rule for ranking investment prospects over long horizons.
problem Ranking investment prospects over long horizons considering bounded risk aversion.
method Introduces asymptotic fractional-order stochastic dominance with bounded relative risk aversion.
result Establishes equivalent conditions for the new rule under lognormal returns without mean non-negativity constraint.
Paper extends stochastic dominance for compound binomial distributions.
problem Stochastic dominance for infinite-mean random variables.
method Investigates properties and inclusion relationships of distribution classes, extends results to compound binomial distributions.
result Establishes necessary and sufficient conditions for first-order stochastic dominance preservation.
The study shows how energy density of harmonic maps dominates in n-Fuchsian fibers, leading to unique minimal surfaces.
problem Understanding energy density and topological invariants in n-Fuchsian fibers of Higgs bundles. method Establishing an algebraic inequality generalizing a GIT theorem to prove energy density domination.
result Energy density of harmonic maps dominates in n-Fuchsian fibers, leading to unique minimal surfaces. String geometry theory connects strings to space-time and finds string vacua.
problem Identify and find the global minimum of the string vacuum.
method Identify perturbative vacua, derive path-integrals, and solve the global minimum using analytical and numerical methods.
result The global minimum of the effective potential is the string vacuum.
Unexpectedly, weighted Pareto variables are stochastically dominant.
problem Understanding stochastic dominance in Pareto distributions.
method Analyzing weighted averages of Pareto random variables with infinite mean.
result The weighted average of Pareto variables is stochastically dominant.
We consider localized deformation for initial data sets of the Einstein field equations with the dominant energy condition. Deformation results with the weak inequality need to be handled delicately. We introduce a modified constraint operator to absorb the first order change of the metric in the dominant energy condit…