arXiv research

This paper improves online learning algorithms for unrealizable cases.

Branched covers between Riemann surfaces are associated with certain combinatorial data, and Hurwitz existence problem asks whether given data satisfying those combinatorial constraints can be realized by some branched cover. We connect recent development in spherical conic metrics to this old problem, and give a new m…

Researchers use statistical physics to model neural network learning dynamics.

Gauss diagrams' properties can change with Hamiltonian cycle choice.

Differentiable MPC improves reinforcement learning efficiency.

We develop Teichmuller theoretical methods to construct new minimal surfaces in $\BE^3$ by adding handles and planar ends to existing minimal surfaces in $\BE^3$. We exhibit this method on an interesting class of minimal surfaces which are likely to be embedded, and have a low degree Gaußmap for their genus; the (Weier…

A statistical model or a learning machine is called regular if the map taking a parameter to a probability distribution is one-to-one and if its Fisher information matrix is always positive definite. If otherwise, it is called singular. In regular statistical models, the Bayes free energy, which is defined by the minus…

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.

Qualitative behavior of Bach flow is established on compact four-dimensional locally homogeneous product manifolds. This is achieved by lifting to the homogeneous universal cover and, in most cases, capitalizing on the resultant group structure. The resulting system of ordinary differential equations is carefully analy…

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.

Case Law has a significant impact on the proceedings of legal cases. Therefore, the information that can be obtained from previous court cases is valuable to lawyers and other legal officials when performing their duties. This paper describes a methodology of applying discourse relations between sentences when processi…

In this paper the author studies the isoperimetric problem in $\re^n$ with perimeter density $|x|^p$ and volume density $1.$ We settle completely the case $n=2,$ completing a previous work by the author: we characterize the case of equality if $0\leq p\leq 1$ and deal with the case $-\infty<p<-1$ (with the additional a…

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).

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.

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 $λ_0(g_0)=0$.

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…

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…

We consider a stable Cox--Ingersoll--Ross process driven by a standard Wiener process and a spectrally positive strictly stable Lévy process, and we study asymptotic properties of the maximum likelihood estimator (MLE) for its growth rate based on continuous time observations. We distinguish three cases: subcritical, c…

Paper proves various types of varieties minimize a specific energy.

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

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…