arXiv research

The paper proposes a method to solve L1 regression with fewer labels using Lewis weights.

Algorithm solves robust linear regression with block Lewis weights.

Designs efficient algorithms for online and sliding window models of subspace embeddings for all p.

Defines Lewy curves in para-CR geometry and characterizes their path geometries.

RHMC improves sampling polytopes defined by inequalities with barriers.

The study compares DLS method with machine learning for cricket match result prediction.

Improved subsampling bounds for $\ell_p$ sensitivity sampling using $\ell_2$ augmentation.

LEWIS merges LLMs without training, improving performance on specific tasks.

A neural network and evolutionary algorithm framework designs nonlinear optical molecules.

New method improves sampling from logconcave distributions truncated on polytopes.

In continuing the study of harmonic mapping from 2-dimensional Riemannian simplicial complexes in order to construct minimal surfaces with singularity, we obtain an a-priori regularity result concerning the real analyticity of the free boundary curve. The free boundary is the singular set along which three disk-type mi…

We investigate local configuration controllability for mechanical control systems within the affine connection formalism. Extending the work by Lewis for the single-input case, we are able to characterize local configuration controllability for systems with $n$ degrees of freedom and $n-1$ input forces.

A free action of the direct product of two copies of the symmetric group on 3 elements on the cartesian product of two copies of the 3-sphere is constructed. This nonlinear action is constructed using surgery. The action provides a counterexample to a conjecture of Lewis made in 1968.

We prove an existence theorem for Spin(7)-instantons, which are highly concentrated near a Cayley submanifold; thus giving a partial converse to Tian's foundational compactness theorem. As an application, we show how to construct Spin(7)-instantons on Spin(7)-manifolds with suitable local K3 Cayley fibrations. This rec…

Starting from the candidate Bloch-Beilinson filtration on Chow groups of 0-cycles constructed by J. Lewis, we develop and describe geometrically a series of Hodge-theoretic invariants defined on the graded pieces. Explicit formulas (in terms of currents and membrane integrals) are given for certain quotients of the inv…

The CGMY model's ATM call-price asymptotics are derived using characteristic function.

We give a fast oblivious L2-embedding of $A\in \mathbb{R}^{n x d}$ to $B\in \mathbb{R}^{r x d}$ satisfying $(1-\varepsilon)\|A x\|_2^2 \le \|B x\|_2^2 <= (1+\varepsilon) \|Ax\|_2^2.$ Our embedding dimension $r$ equals $d$, a constant independent of the distortion $\varepsilon$. We use as a black-box any L2-embedding $Π…

In this paper, we revisit the analyses of Antonie Stern (1925) and Hans Lewy (1977) devoted to the construction of spherical harmonics with two or three nodal domains. Our method yields sharp quantitative results and a better understanding of the occurrence of bifurcations in the families of nodal sets.This paper is a …

We obtain very sharp results about the lack of validity of the Poincare lemma for the tangential Cauchy Riemann equations, acting on tangential forms, tangential to a CR manifold M of general CR dimension n, and general CR codimension k. This generalizes the classical nonsolvability example of H. Lewy. We also discuss …

The paper proves a Bonnesen-type inequality for the real projective plane.

We discuss various analytic and numerical methods that have been used to get option prices within a framework of the VG model. We show that some popular methods, for instance, Carr-Madan's FFT method could blow up for certain values of the model parameters even for an European vanilla option. Alternative methods - one …

In contrast to an infinite family of explicit examples of two-dimensional $p$-harmonic functions obtained by G.Aronsson in the late 80s, there is very little known about the higher-dimensional case. In this paper, we show how to use isoparametric polynomials to produce diverse examples of $p$-harmonic and biharmonic fu…

We examine the effects of instantiating Lewis signaling games within a population of speaker and listener agents with the aim of producing a set of general and robust representations of unstructured pixel data. Preliminary experiments suggest that the set of representations associated with languages generated within a …

Exponential Lévy processes can be used to model the evolution of various financial variables such as FX rates, stock prices, etc. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes, and the corresponding implied volatility surfaces have been analyzed in some d…

We consider the problem of finding the probability that a random triangle is obtuse, which was first raised by Lewis Caroll. Our investigation leads us to a natural correspondence between plane polygons and the Grassmann manifold of 2-planes in real $n$-space proposed by Allen Knutson and Jean-Claude Hausmann. This cor…

New method for optimization on Hadamard manifolds with curvature-independent guarantees.

The computation of Greeks for exponential Lévy models are usually approached by Malliavin Calculus and other methods, as the Likelihood Ratio and the finite difference method. In this paper we obtain exact formulas for Greeks of European options based on the Lewis formula for the option value. Therefore, it is possible…

Lewis and Mordecki have computed the Wiener-Hopf factorization of a Lévy process whose restriction on $]0,+\infty[$ of their Lévy measure has a rational Laplace transform. That allows to compute the distribution of $(X_t,\inf_{0\leq s\leq t}X_s)$. For the same class of Lévy processes, we compute the distribution of $ (…

Fourier methods fail to accurately approximate option Greeks in realistic market conditions.

This work provides efficient algorithms for approximating ℓ_p sensitivities and related statistics.

Study on isoperimetric inequalities and regularity of $A$-harmonic functions on surfaces.

New $Spin(7)$-instantons constructed on Joyce's manifold.

Active sampling algorithm for linear regression with various norms and improved query complexity.

We consider the problem of option pricing under stochastic volatility models, focusing on the linear approximation of the two processes known as exponential Ornstein-Uhlenbeck and Stein-Stein. Indeed, we show they admit the same limit dynamics in the regime of low fluctuations of the volatility process, under which we …

This paper is about randomized iterative algorithms for solving a linear system of equations $X β= y$ in different settings. Recent interest in the topic was reignited when Strohmer and Vershynin (2009) proved the linear convergence rate of a Randomized Kaczmarz (RK) algorithm that works on the rows of $X$ (data points…

New method estimates and optimizes policy differences using orthogonal learning.

For the spherical Laplacian on the sphere and for the Dirichlet Laplacian in the square}, Antonie Stern claimed in her PhD thesis (1924) the existence of an infinite sequence of eigenvalues whose corresponding eigenspaces contain an eigenfunction with exactly two nodal domains. These results were given complete proofs …

Sp(n)-instantons linked to complex Lagrangian graphs via Fourier-Mukai transform.

The paper investigates how supervised learning and self-play improve sample efficiency in teaching AI to communicate.

We prove that certain volume preserving actions of Lie groups and their lattices do not preserve rigid geometric structures in the sense of Gromov. The actions considered are the "exotic" examples obtained by Katok and Lewis and the first author, by blowing up closed orbits in the well known actions on homogeneous spac…

Pontryagin's Maximum Principle is an outstanding result for solving optimal control problems by means of optimizing a specific function on some particular variables, the so called controls. However, this is not always enough for solving all these problems. A high order maximum principle (Krener, 1977) must be used in o…

Unified model for equity option pricing and interest-rate risk assessment.

Improves disease progression prediction using auxiliary surrogate labels and health markers.

Improved pricing of vanilla options using modified Adams method and sinh-acceleration.

The ungrammatical sentence "The key to the cabinets are on the table" is known to lead to an illusion of grammaticality. As discussed in the meta-analysis by Jaeger et al., 2017, faster reading times are observed at the verb are in the agreement-attraction sentence above compared to the equally ungrammatical sentence "…

A new SINC method for fast and accurate option pricing.

Study compares methods for improving document retrieval accuracy.

In the present paper, we associate the techniques of the Lewy-Pinchuk reflection principle with the Behnke-Sommer continuity principle. Extending a so-called reflection function to a parameterized congruence of Segre varieties, we are led to studying the envelope of holomorphy of a certain domain covered by a smooth Le…