arXiv research

The paper characterizes potential functions whose level sets are orbits in mechanical systems.

Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.

In this study, we investigate the use of global information to speed up the learning process and increase the cumulative rewards of reinforcement learning (RL) in competition tasks. Within the actor-critic RL, we introduce multiple cooperative critics from two levels of the hierarchy and propose a reinforcement learnin…

For strong exact magnetic fields the action functional (i.e., the length plus the linear magnetic term) is not bounded from below on the space of closed contractible curves and the lower estimates for critical levels are derived by using the principle of throwing out cycles. It is proved that for almost every energy le…

Model criticism tool evaluates text coherence and structure in generated long-form text.

New Morse-Bott function defined on Stiefel manifolds, revealing complex critical structures.

We study the level sets of the distance function from a boundary point of a convex set in Euclidean space. We provide a lower bound for the range of connectivity of the level sets, in terms of the critical points of the distance function in the sense of Grove-Shiohama-Gromov-Cheeger.

A methodology is developed to identify, as units of study, each decrease in the value of a stock from a given maximum price level. A critical level in the amount of price declines is found to separate a segment operating under a random walk from a segment operating under a power law. This level is interpreted as a poin…

Paper derives trace formula for magnetic Laplacian at zero energy.

A theorem connects integral of second-order derivatives to function rise.

The paper finds infinitely many magnetic geodesics on non-compact manifolds.

Classical Morse theory proceeds by considering sublevel sets $f^{-1}(-\infty, a]$ of a Morse function $f: M \to R$, where $M$ is a smooth finite-dimensional manifold. In this paper, we study the topology of the level sets $f^{-1}(a)$ and give conditions under which the topology of $f^{-1}(a)$ changes when passing a cri…

Deep learning depends on tuning layers near critical points.

New proofs of Cheeger-like inequalities for coexact 1-forms on hyperbolic manifolds.

Families of hypersurfaces that are level-set families of harmonic functions free of critical points are characterized by a local differential-geometric condition. Harmonic functions with a specified level-set family are constructed from geometric data. As a by-product, it is shown that the evolution of the gradient of …

Paper resolves ambiguity in non-convex bilevel optimization problems.

Deep Learning can significantly benefit cancer proteomics and genomics. In this study, we attempt to determine a set of critical proteins that are associated with the FLT3-ITD mutation in newly-diagnosed acute myeloid leukemia patients. A Deep Learning network consisting of autoencoders forming a hierarchical model fro…

This paper focuses on the problem of topological equivalence of functions with isolated critical points on the boundary of a compact surface $M$ which are also isolated critical points of their restrictions to the boundary. This class of functions we denote by $Ω(M)$. Firstly, we've obtained the topological classificat…

In this paper, we present theorems specifying the critical values for series associated with debts arranged in the order of their duration.

Empirical study on trends reversion in financial markets.

New RL method MAC improves performance in sparse reward settings.

We continue the study of the variation of the $p$--modulus of a foliation initiated by the first author. We derive the formula for the second variation which allows to study $p$--stable foliations. We obtain some results concerning codimension one $p$--stable foliations. Moreover, we derive the equation for the critica…

Deep neural networks (DNNs) are vulnerable to maliciously generated adversarial examples. These examples are intentionally designed by making imperceptible perturbations and often mislead a DNN into making an incorrect prediction. This phenomenon means that there is significant risk in applying DNNs to safety-critical …

The paper analyzes how SGD visits different regions of a non-convex problem's state space.

Policy certifies inventory levels meeting service requirements.

We prove that the level sets of a real C^s function of two variables near a non-degenerate critical point are of class C^[s/2] and apply this to the study of planar sections of surfaces close to the singular section by the tangent plane at hyperbolic points or elliptic points, and in particular at umbilic points. We al…

We prove that for a uniformly convex Lagrangian system L on a compact manifold M, almost all energy levels contain a periodic orbit. We also prove that below Ma ne's critical value of the lift of the Lagrangian to the universal cover, almost all energy levels have conjugate points. We prove that if the energy level [E=…

Classification of ground state solutions to critical Dirac equation on spheres.

In this note we discuss a few properties of transnormal Finsler functions, i.e., the natural generalization of distance functions and isoparametric Finsler functions. In particular, we prove that critical level sets of an analytic transnormal function are submanifolds, and the partition of $M$ into level sets is a Fins…

In this paper we introduce two models of opinion dynamics in oligopoly markets and apply them to a situation, where a new entrant challenges two incumbents of the same size. The models differ in the way the two forces influencing consumer choice -- (local) social interactions and (global) advertising -- interact. We st…

The paper explores the structure of Reeb spaces for smooth functions on manifolds.

This paper investigates trajectory tracking problem for a class of underactuated autonomous underwater vehicles (AUVs) with unknown dynamics and constrained inputs. Different from existing policy gradient methods which employ single actor-critic but cannot realize satisfactory tracking control accuracy and stable learn…

Study critical metrics on manifolds, proving specific isometries.

We prove that the number of critical points of a Li-Tam Green's function on a complete open Riemannian surface of finite type admits a topological upper bound, given by the first Betti number of the surface. In higher dimensions, we show that there are no topological upper bounds on the number of critical points by con…

LICA learns credit assignment for cooperative agents without explicit formulation.

Parastatistic distribution of a total debt owed to a large number of creditors considered in relation to the duration of these debts. The process of debt calculation depends on the fractal dimension of economic system in which this process takes place. Two actual variants of these dimensions are investigated. Critical …

Study estimates personalized effects of maternal PM2.5 exposure on birth weight.

Bayesian CNN improves MRI stroke diagnosis accuracy and uncertainty quantification.

Single-timescale actor-critic finds globally optimal policy.

We present the complete analytical classification of the atoms arising at the critical points of rank 1 of the Kowalevski-Yehia gyrostat. To classify the Smale-Fomenko diagrams, all separating values of the gyrostatic momentum are found. We present a kind of constructor of the Fomenko graphs; its application gives the …

We introduce a new critical value $c_\infty(L)$ for Tonelli Lagrangians $L$ on the tangent bundle of the 2-sphere without minimizing measures supported on a point. We show that $c_\infty(L)$ is strictly larger than the Mañé critical value $c(L)$, and on every energy level $e\in(c(L),c_\infty(L))$ there exist infinitely…

Level set flow's singularities are type I under 2-convexity, leading to specific curvature blow-up rates.

Multilayer graphs are commonly used for representing different relations between entities and handling heterogeneous data processing tasks. New challenges arise in multilayer graph clustering for assigning clusters to a common multilayer node set and for combining information from each layer. This paper presents a theo…

For a given level of accuracy in option prices, the paper considers the problem of deciding when exactly, as one or more of the pricing parameters change, a barrier option degenerates into a simpler type of option. This problem is meaningful in the real world where option prices are always determined within a certain l…

Kirchhoff energy is a classical functional on the space of arclength-parameterized framed curves whose critical points approximate configurations of springy elastic rods. We introduce a generalized functional on the space of framed curves of arbitrary parameterization, which model rods with axial stretch or cross-secti…

New autoencoder uses goodness-of-fit tests for better model performance.

Smooth tori in S^4 are topologically unknotted.

We are going to use the Euler's vector fields in order to show that for real quasi-homogeneous singularities with isolated critical value, the Milnor's fibration in a "thin" hollowed tube involving the zero level and the fibration in the complement of "link" in sphere are equivalents, since they exist. Moreover, in ord…