arXiv research

New algorithm for 2D SWDFT reduces redundant calculations.

This article examines five common misunderstandings about case-study research: (1) Theoretical knowledge is more valuable than practical knowledge; (2) One cannot generalize from a single case, therefore the single case study cannot contribute to scientific development; (3) The case study is most useful for generating …

The application of equivalence method to classify Monge-Ampère system leads to three orbits, parabolic case, hyperbolic case and elliptic case wich correspond to three types of Monge-Ampère systems. In this paper we will study the elliptic case and give a presentation of the group as a complex group.

Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be ev…

Worst-Case Sensitivity measures model sensitivity to uncertainty set size.

Proposes a CVaR-based method to learn robust options in uncertain environments.

Proposes a new framework for balancing average- and worst-case performance in machine learning.

Solves equality case in isoperimetric inequality for non-convex domains.

Paper improves worst-case regret bounds for RLSVI in reinforcement learning.

GenAI improves actuarial practices through case studies.

New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.

A method for logistic regression inference using both internal and external data.

The book explores alternatives to worst-case analysis for algorithm performance.

Expanding on a Heisenberg group case for a mathematical proposition.

Optimizes bond portfolios to avoid worst-case losses.

Study evaluates and compares numerical differentiation methods on three case studies.

Study extreme-case Value-at-Risk under IFR distributions, providing guidance for risk management.

This study identifies sentence relationships in legal transcripts.

New analysis shows halting time is predictable for large models, improving optimization efficiency.

We will compare three types of prices, namely, rational (hedging) prices, geometric (growth rate) prices, and martingale (measure) prices. We will show that rational prices in the complete market theory are sometimes contrary to common sense. In the continuous-time case, we insist that the market model should differ be…

Two-dimensional case in the theory of dynamical systems admitting the normal shift differs crucially from multidimensional case. Features of two-dimensional case are gathered and studied in this thesis.

Study examines noncompact cases of Gauss Curvature Flow on revolution surfaces.

Paper finds analytical solution for portfolio selection under worst-case model risk.

We prove a formula relating the analytic torsion and Reidemeister torsion on manifolds with boundary in the general case when the metric is not necessarily a product near the boundary. The product case has been established by W. Luck and S. M. Vishik. We find that the extra term that comes in here in the nonproduct cas…

Introduction. Case Based Reasoning (CBR) is an emerg- ing decision making paradigm in medical research where new cases are solved relying on previously solved similar cases. Usually, a database of solved cases is provided, and every case is described through a set of attributes (inputs) and a label (output). Extracting…

This paper calculates worst-case target semi-variances for uncertain losses.

Study topological properties of integrable case on Lie algebra so(4).

Painlevé analysis identifies integrable cases of Ricci solitons over specific warped products and line bundles.

We give an overview about finiteness properties of soluble S-arithmetic groups. Both, the number field case and the function field case are covered. The main result is: If B is a Borel subgroup in a Chevalley group and R is an S-arithmetic ring, then the group B(R) has finiteness length |S|-1 in the function field case…

Study pseudo-holomorphic disks in real analytic hypersurfaces using exterior differential systems.

Any generalized distance-squared mapping of equidimensional case has singularities, and their singularity types are wrapped into mystery in higher dimensional cases. Any generalized distance-squared mapping of equidimensional case is not injective. Nevertheless, in this paper, it is shown that the non-singular property…

We extend our previous results on the logarithmic Sobolev inequality along the Ricci flow in the case $λ_0(g_0)>0$ to the case $λ_0(g_0)=0$.

Bayesian model helps doctors diagnose by mixing past cases.

Bach flow studied on special product manifolds, revealing interesting behavior.

The study proves convergence of conic 4-spheres' geometry to boundary cases.

In this paper, we attach an $L_\infty$-algebra to any coisotropic submanifold in a Jacobi manifold. Our construction generalizes and unifies analogous constructions by Oh-Park (symplectic case), Cattaneo-Felder (Poisson case), Lê-Oh (locally conformal symplectic case). As a new special case, we attach an $L_\infty$-alg…

We investigate different concentration-compactness phenomena related to the Q-curvature in arbitrary even dimension. We first treat the case of an open domain in $R^{2m}$, then that of a closed manifold and, finally, the particular case of the sphere $S^{2m}$. In all cases we allow the sign of the Q-curvature to vary, …

In this article, we study complete pseudo-Riemannian manifolds whose cone admits a parallel symmetric 2-tensorfield. The situation splits in three cases: nilpotent, decomposable or complex Riemannian. In the complex Riemannian and decomposable cases we provide a classification. In the nilpotent case, we are able to des…

New framework identifies worst-case shifts for predictive resource allocation models.

Paper proves various types of varieties minimize a specific energy.

Paper simplifies and proves Bahri-Xu conjecture for various cases.

Let $A, B$ be invertible, non-commuting elements of a ring $R$. Suppose that $A-1$ is also invertible and that the equation $[B,(A-1)(A,B)]=0$ called the fundamental equation is satisfied. Then an invariant $R$-module is defined for any diagram of a (virtual) knot or link. Solutions in the classic quaternion case hav…

New algorithm tackles non-stationary combinatorial semi-bandit problems with optimal regret bounds.

A new algorithm avoids worst-case outcomes in risky contexts.

Generalized Nakano positivity for certain singular cases.

New method uses unlabeled data to estimate intercept in case-control logistic regression.

Study approximates worst-case stock trading under uncertainty, quantifying sensitivity.

We study many properties concerning weak Kählerianity on compact complex manifolds which admits a holomorphic submersion onto a Kähler or a balanced manifold. We get generalizations of some results of Harvey and Lawson (the Kähler case), Michelson (the balanced case), Popovici (the sG case) and others.