A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Unified analysis of first-order methods for smooth games using IQCs.
This paper deals with conservation laws for mechanical systems with nonholonomic constraints. It uses a Lagrangian formulation of nonholonomic systems and a Cartan form approach. We present what we believe to be the most general relations between symmetries and first integrals. We discuss the so-called nonholonomic Noe…
Improved stability analysis of neural network systems using Zames-Falb multipliers.
Geometrically interprets integrability of geodesic flow using web theory.
Alt-GDA outperforms Sim-GDA in minimax games with near-optimal local convergence.
Geodesic flows with diagonalisable integrals are orthogonal.
In this paper, we consider a supervised learning setting where side knowledge is provided about the labels of unlabeled examples. The side knowledge has the effect of reducing the hypothesis space, leading to tighter generalization bounds, and thus possibly better generalization. We consider several types of side knowl…
Eigen-decomposition simplifies quadratic programming with equality constraints.
In the present paper we prove, that if the geodesic flow of a metric G on the torus T is quadratically integrable, then the torus T isometrically covers a torus with a Liouville metric on it, and describe the set of quadratically integrable geodesic flows on the Klein bottle.
Quadratic Killing tensors on Lie groups are always decomposable.
Marden and Strebel established the Heights Theorem for integrable holomorphic quadratic differentials on parabolic Riemann surfaces. We extends the validity of the Heights Theorem to all surfaces whose fundamental group is of the first kind. In fact, we establish a more general result: the {\it horizontal} map which as…
We consider a proximal operator given by a quadratic function subject to bound constraints and give an optimization algorithm using the alternating direction method of multipliers (ADMM). The algorithm is particularly efficient to solve a collection of proximal operators that share the same quadratic form, or if the qu…
Volume of unit balls defined by quadratic differentials is not proper and has integrable volume.
New conic quadratic formulations improve outlier detection in regression models.
The study characterizes infinite Riemann surfaces and their foliations using quadratic differentials.
We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem on closed surfaces and prove the nonexistence of quadratically-superintegrable metrics of nonconstant curvature on closed surfaces
The framework of Integral Quadratic Constraints (IQC) reduces the computation of upper bounds on the convergence rate of several optimization algorithms to a semi-definite program (SDP). In the case of over-relaxed Alternating Direction Method of Multipliers (ADMM), an explicit and closed form solution to this SDP was …
Novel link classification connects quadratic forms and knot theory.
Geodesic flows with specific integrals are linked to special 4-webs.
Classifies extended Abelian Chern-Simons theories using quadratic modules.
A framework integrates machine learning with robust control for safer, more reliable systems.
This paper establishes the existence of a unique nonnegative continuous viscosity solution to the HJB equation associated with a Markovian linear-quadratic control problems with singular terminal state constraint and possibly unbounded cost coefficients. The existence result is based on a novel comparison principle for…
In this note we find a 6-dimensional h-spaces of the type and then determine quadratic first integrals of the geodesic equations of these h-spaces.
We solve integrable systems to describe the motion of Kaleidocycles.
We consider an application involving a financial quadratic portfolio of options, when the joint underlying log-returns changes with multivariate elliptic distribution. This motivates the needs for methods for the approximation of multiple integrals over hyperboloids. A transformation is used to reduce the hyperboloid i…
Paper solves optimal portfolio deleveraging with cross asset impacts.
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-di…
Solves optimal control with state constraints using probabilistic methods.
Using Vovk's outer measure, which corresponds to a minimal superhedging price, the existence of quadratic variation is shown for "typical price paths" in the space of càdlàg functions possessing a mild restriction on the jumps directed downwards. In particular, this result includes the existence of quadratic variation …
Method solves complex optimization problems with high probability bounds.
Quantizes Stäckel integrable systems into self-adjoint operators.
Extends trading framework to incorporate real-world constraints.
Paper presents an ADMM-based approach to efficiently integrate quadratic programming layers into neural networks.
Simplifies neural network constraints with computationally efficient method.
We describe all pseudo-Riemannian metrics on closed surfaces whose geodesic flows admit nontrivial integrals quadratic in momenta. As an application, we solve the Beltrami problem on closed surfaces, prove the nonexistence of quadratically-superintegrable metrics of nonconstant curvature on closed surfaces, and prove t…
We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties: not on…
We study the constrained linear quadratic regulator with unknown dynamics, addressing the tension between safety and exploration in data-driven control techniques. We present a framework which allows for system identification through persistent excitation, while maintaining safety by guaranteeing the satisfaction of st…
In this paper we study a continuous-time stochastic linear quadratic control problem arising from mathematical finance. We model the asset dynamics with random market coefficients and portfolio strategies with convex constraints. Following the convex duality approach, we show that the necessary and sufficient optimalit…
Thurston's boundary to the universal Teichmüller space is the space of projective bounded measured laminations of . A geodesic ray in is of Teichmüller type if it shrinks vertical foliation of an integrable holomorphic quadratic differential. In a prio…
A scalable framework optimizes multi-asset portfolios with constraints.
We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and adaptive-gradient methods are (minimax) optimal and, conversely, when nonlinear updates -- su…
New method solves optimization problems with stochastic objectives and constraints.
New algorithm tackles stochastic optimization with inequality constraints.
We consider the problem of solving a large-scale Quadratically Constrained Quadratic Program. Such problems occur naturally in many scientific and web applications. Although there are efficient methods which tackle this problem, they are mostly not scalable. In this paper, we develop a method that transforms the quadra…
The paper proves signatures of non-geometric rough paths can approximate functionals uniformly.
Paper classifies conic submanifolds in control systems.
A new algorithm solves constrained optimization problems with stochastic gradients.
We prove that the Steinberg module of the special linear group of a quadratic imaginary number ring which is not Euclidean is not generated by integral apartments. Assuming the generalized Riemann hypothesis, this shows that the Steinberg module of a number ring is generated by integral apartments if and only if the ri…