arXiv research

Characterizes differential forms and vector fields with constant coefficients on manifolds.

This work studies the contraction coefficients of Schrödinger bridge problems in linear systems.

Abstract: Determines thermoelastic coefficients from boundary data.

Study optimal consumption and investment strategies with constraints in a market with random coefficients.

Develops Morse homology with DG coefficients for manifolds and spaces.

GenMod uses generative models to approximate high-dimensional PDE solutions with limited evaluations.

New cohomology theory shows compact Lie group actions are Morita invariant.

Novel method estimates complex nonlinear systems with stochastic differential equations.

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

Sequences of Levy transformations for the Darboux system of conjugates nets in multidimensions are studied. We show that after a suitable number of Levy transformations, with at least a Levy transformation in each direction, we get closed formulae in terms of multi-Wroński determinants. These formulae are for the tange…

In this article we propose a novel measure of systemic risk in the context of financial networks. To this aim, we provide a definition of systemic risk which is based on the structure, developed at different levels, of clustered neighbours around the nodes of the network. The proposed measure incorporates the generaliz…

The paper solves a complex control problem with stochastic elements and switching conditions.

The nullspace and regularization impact high-dimensional linear regression interpretability.

Develops a new method to discover stochastic systems with non-Gaussian noise.

The non-negative solution to an underdetermined linear system can be uniquely recovered sometimes, even without imposing any additional sparsity constraints. In this paper, we derive conditions under which a unique non-negative solution for such a system can exist, based on the theory of polytopes. Furthermore, we deve…

FaStR improves scalability for time-aware RS with varying coefficients.

Homological stability proved for handlebody mapping class groups.

SIP framework discovers governing equations in uncertain systems.

In this paper we propose a new identification scheme for Hammerstein systems, which are dynamic systems consisting of a static nonlinearity and a linear time-invariant dynamic system in cascade. We assume that the nonlinear function can be described as a linear combination of $p$ basis functions. We reconstruct the $p$…

Proves existence and trapped surface formation for Einstein-Vlasov system without symmetry assumptions.

Analytical results bound the approach to oligarchy in a modified asset exchange model.

Polynomial distribution can be applied to dynamical systems in certain situations. Macroeconomic systems characterized by economic variables such as income and wealth can be modelled similarly using polynomials. We extend our previous work to data regarding income from a more diversified pool of countries, which contai…

Study measures inequality in social-economic systems using Fokker-Planck equations and Lotka-Volterra dynamics.

Study bends 2D surfaces in 3D space using special equations.

Implicit schemes are popular methods for the integration of time dependent PDEs such as hyperbolic and parabolic PDEs. However the necessity to solve corresponding linear systems at each time step constitutes a complexity bottleneck in their application to PDEs with rough coefficients. We present a generalization of ga…

In this paper we consider the cohomology of a closed arithmetic hyperbolic 3-manifold with coefficients in the local system defined by the even symmetric powers of the standard representation of SL(2,C). The cohomology is defined over the integers and is a finite abelian group. We show that the order of the 2nd cohomol…

We consider coefficient bodies $\mathcal M_n$ for univalent functions. Based on the Löwner-Kufarev parametric representation we get a partially integrable Hamiltonian system in which the first integrals are Kirillov's operators for a representation of the Virasoro algebra. Then $\mathcal M_n$ are defined as sub-Riemann…

Existence of calibrated local stochastic volatility models proven for non-regular coefficients.

In the design of brain-computer interface systems, classification of Electroencephalogram (EEG) signals is the essential part and a challenging task. Recently, as the marginalized discrete wavelet transform (mDWT) representations can reveal features related to the transient nature of the EEG signals, the mDWT coefficie…

Study finds Stäckel equivalence for superintegrable systems via invariant quadrics.

Suppose $\Cal R$ is the complement of an essential arrangement of toric hyperlanes in the complex torus $(\C^*)^n$ and $π=π_1(\Cal R)$. We show that $H^*(\Cal R;A)$ vanishes except in the top degree $n$ when $A$ is one of the following systems of local coefficients: (a) a system of nonresonant coefficients in a complex…

Defines Floer homology with DG coefficients for symplectic manifolds.

Model predicts viscosity of multicomponent systems efficiently.

The purpose of this paper is applying minimality of hyperplane arrangements to local system cohomology groups. It is well known that twisted cohomology groups with coefficients in a generic rank one local system vanish except in the top degree, and bounded chambers form a basis of the remaining cohomology group. We det…

In this paper we study Morse homology and cohomology with local coefficients, i.e. "twisted" Morse homology and cohomology, on closed finite dimensional smooth manifolds. We prove a Morse theoretic version of Eilenberg's Theorem, and we prove isomorphisms between twisted Morse homology, Steenrod's CW-homology with loca…

We consider the optimal control problem for a linear conditional McKean-Vlasov equation with quadratic cost functional. The coefficients of the system and the weigh-ting matrices in the cost functional are allowed to be adapted processes with respect to the common noise filtration. Semi closed-loop strategies are intro…

In the theory of finite order knot invariants, the universal $\text{sl}_2$ weight system maps the chord diagrams to polynomials in a single variable with integer coefficients. In this paper, we define a family of polynomials that generalize the Kreweras triangle (known to refine the normalized median Genocchi numbers),…

We study systems of Brownian particles on the real line, which interact by splitting the local times of collisions among themselves in an asymmetric manner. We prove the strong existence and uniqueness of such processes and identify them with the collections of ordered processes in a Brownian particle system, in which …

Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer co…

Wilson lines generate positive Laurent polynomials in decorated triangulations.

In this paper we present some conditions for the (strong) stabilizability of an n-D Quantum MIMO system P(X). It contains two parts. The first part is to introduce the n-D Quantum MIMO systems where the coefficients vary in the algebra of Q-meromorphic functions. Then we introduce some conditions for the stabilizabilit…

EPGP priors solve linear PDEs from data.

We prove that a Pfaffian system with coefficients in the critical space $L^2_\mathrm{loc}$ on a simply connected open subset of $\mathbb{R}^2$ has a non-trivial solution in $W^{1,2}_\mathrm{loc}$ if the coefficients are antisymmetric and satisfy a compatibility condition. As an application of this result, we show that …

We show that the category of Lie triple systems is equivalent to the category of Lie algebras graded by Z/(2Z) such that the odd component generates the algbera and the second graded cohomology group coefficients in any trivial module is zero. As a corollary we obtain an analogous result for symmetric spaces and Lie gr…

Framework uses deep learning and statistical models to solve PDEs with discontinuous coefficients.

The paper solves portfolio selection for complex preferences in continuous time.

This work extracts stochastic dynamical systems with $\alpha$-stable Lévy noise.

In the present work we analyse the dynamics of indirect connections between insurance companies that result from market price channels. In our analysis we assume that the stock quotations of insurance companies reflect market sentiments which constitute a very important systemic risk factor. Interlinkages between insur…