arXiv research

Proves uniqueness of solutions for a nonlocal Liouville equation with finite Q-curvature.

This work improves density estimation by characterizing pdf complexity using NL-spectrum.

We reconsider the (rational) Calogero-Moser system from the point of view of bi-Hamiltonian geometry. By using geometrical tools of the latter, we explicitly construct set(s) of spectral canonical coordinates, that is, complete sets of Darboux coordinates defined by the eigenvalues and the eigenvectors of the Lax matri…

Simplifies NL models by approximating them as LPV systems and identifying NL subterms.

Average Oracle outperforms DCC+NLS in portfolio optimization.

The NL score optimizes speaker recognition tasks.

Introduces NL bialgebras combining Lie and Nijenhuis structures.

This paper uses a geometric approach to understand how normalization layers affect neural network optimization.

Softmax is found ineffective for NL block, leading to improved performance.

Search-oriented conversational systems rely on information needs expressed in natural language (NL). We focus here on the understanding of NL expressions for building keyword-based queries. We propose a reinforcement-learning-driven translation model framework able to 1) learn the translation from NL expressions to que…

The problem of the invariant classification of the orthogonal coordinate webs defined in Euclidean space is solved within the framework of Felix Klein's Erlangen Program. The results are applied to the problem of integrability of the Calogero-Moser model.

Non-linear shrinkage isn't optimal for portfolio optimization, especially when asset dependence is non-stationary.

The abstract describes a new manifold structure for NLS type equations.

Improved LDA using a nonlinear covariance estimator for better performance.

Recent advances in randomized incremental methods for minimizing $L$-smooth $μ$-strongly convex finite sums have culminated in tight complexity of $\tilde{O}((n+\sqrt{n L/μ})\log(1/ε))$ and $O(n+\sqrt{nL/ε})$, where $μ>0$ and $μ=0$, respectively, and $n$ denotes the number of individual functions. Unlike incremental me…

A nonlinear wave alternative for the standard Black-Scholes option-pricing model is presented. The adaptive-wave model, representing 'controlled Brownian behavior' of financial markets, is formally defined by adaptive nonlinear Schrödinger (NLS) equations, defining the option-pricing wave function in terms of the stock…

Autonomous reinforcement learning agents, like children, do not have access to predefined goals and reward functions. They must discover potential goals, learn their own reward functions and engage in their own learning trajectory. Children, however, benefit from exposure to language, helping to organize and mediate th…

We propose a new cognitive framework for option price modelling, using quantum neural computation formalism. Briefly, when we apply a classical nonlinear neural-network learning to a linear quantum Schrödinger equation, as a result we get a nonlinear Schrödinger equation (NLS), performing as a quantum stochastic filter…

A new method simplifies noisy data filtering for CNNs.

We consider the learning from noisy labels (NL) problem which emerges in many real-world applications. In addition to the widely-studied synthetic noise in the NL literature, we also consider the pseudo labels in semi-supervised learning (Semi-SL) as a special case of NL. For both types of noise, we argue that the gene…

Machine learning predicts ship performance changes over time.

Physics-Informed Neural Networks (PINNs) benchmarked against clinical estimator and reveal parameter identifiability

An important feature of successful supervised machine learning applications is to be able to explain the predictions given by the regression or classification model being used. However, most state-of-the-art models that have good predictive power lead to predictions that are hard to interpret. Thus, several model-agnos…

Program synthesis from natural language (NL) is practical for humans and, once technically feasible, would significantly facilitate software development and revolutionize end-user programming. We present SAPS, an end-to-end neural network capable of mapping relatively complex, multi-sentence NL specifications to snippe…

The aim of this paper is to investigate the relations between Seifert manifolds and (1,1)-knots. In particular, we prove that every orientable Seifert manifold with invariants {Oo,0|-1;(p,q),...,(p,q),(l, l-1)} has a cyclically presented fundamental group and, moreover, it is the n-fold strongly-cyclic covering of the …

The study shows that several properties are not profinite invariants.

This paper improves image super-resolution by integrating cross-scale non-local attention.

[Context:] Model-based testing is an instrument for automated generation of test cases. It requires identifying requirements in documents, understanding them syntactically and semantically, and then translating them into a test model. One light-weight language for these test models are Cause-Effect-Graphs (CEG) that ca…

Paper introduces efficient methods for estimating cross-partial derivatives and sensitivity indices.

Road extraction from very high resolution satellite (VHR) images is one of the most important topics in the field of remote sensing. In this paper, we propose an efficient Non-Local LinkNet with non-local blocks that can grasp relations between global features. This enables each spatial feature point to refer to all ot…

Recently, a novel adaptive wave model for financial option pricing has been proposed in the form of adaptive nonlinear Schrödinger (NLS) equation [Ivancevic a], as a high-complexity alternative to the linear Black-Scholes-Merton model [Black-Scholes-Merton]. Its quantum-mechanical basis has been elaborated in [Ivancevi…

New algorithms solve nonconvex-concave minimax problems without parameter knowledge.

The paper is devoted to quadratic Poisson structures compatible with the canonical linear Poisson structures on trivial 1-dimensional central extensions of semisimple Lie algebras. In particular, we develop the general theory of such structures and study related families of functions in involution. We also show that th…

In discrete choice modeling (DCM), model misspecifications may lead to limited predictability and biased parameter estimates. In this paper, we propose a new approach for estimating choice models in which we divide the systematic part of the utility specification into (i) a knowledge-driven part, and (ii) a data-driven…

Adaptive wave model for financial option pricing is proposed, as a high-complexity alternative to the standard Black--Scholes model. The new option-pricing model, representing a controlled Brownian motion, includes two wave-type approaches: nonlinear and quantum, both based on (adaptive form of) the Schrödinger equatio…

We establish a connection between smooth symplectic resolutions and symplectic deformations of a (possibly singular) affine Poisson variety. In particular, let V be a finite-dimensional complex symplectic vector space and G\subset Sp(V) a finite subgroup. Our main result says that the so-called Calogero-Moser deformati…

New algorithm bounds MAB regret for unknown scale and magnitude of losses.

Study scaling limits for option pricing in trinomial models.

Superintegrable systems are classical and quantum Hamiltonian systems which enjoy much symmetry and structure that permit their solubility via analytic and even, algebraic means. They include such well-known and important models as the Kepler potential, Calogero-Moser model, and harmonic oscillator, as well as its inte…

The purpose of this paper is to connect two subjects: the theory of quantum integrable systems (complete commutative rings of differential operators), and differential Galois theory. We define quantum completely integrable systems (QCIS), algebraically integrable QCIS, the differential Galois group of a QCIS. We show t…

The binormal (or vortex filament) equation provides the localized induction approximation of the 3D incompressible Euler equation. We present explicit solutions of the binormal equation in higher-dimensions that collapse in finite time. The local nature of this phenomenon suggests the appearance of singularity in nearb…

We investigate the rudiments of Riemannian geometry on orbit spaces $M/G$ for isometric proper actions of Lie groups on Riemannian manifolds. Minimal geodesic arcs are length minimising curves in the metric space $M/G$ and they can hit strata which are more singular only at the end points. This is phrased as convexity …

Background: Parkinson's disease (PD) is a prevalent long-term neurodegenerative disease. Though the diagnostic criteria of PD are relatively well defined, the current medical imaging diagnostic procedures are expertise-demanding, and thus call for a higher-integrated AI-based diagnostic algorithm. Methods: In this pape…

The paper develops methods to derive mixed superposition rules for Lie systems and applies them to various physical systems.

For a Lie-Rinehart algebra (A,L), generators for the Gerstenhaber algebra Λ_A L correspond bijectively to right (A,L)-connections on A in such a way that B-V structures correspond to right (A,L)-module structures on A. When L is projective as an A-module, given an exact generator \partial, the homology of the B-V algeb…

A large class of semi-Hamiltonian systems of hydrodynamic type is interpreted as the equations governing families of critical points of functions obeying the classical linear Darboux equations for conjugate nets.The distinguished role of the Euler-Poisson-Darboux equations and associated Lauricella-type functions is em…

Non-negative matrix factorization (NMF) is the problem of determining two non-negative low rank factors $W$ and $H$, for the given input matrix $A$, such that $A \approx W H$. NMF is a useful tool for many applications in different domains such as topic modeling in text mining, background separation in video analysis, …

The paper provides theoretical guarantees for transformation-based models in variational inference.