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.
Paper shows affine constraint is unnecessary for high-dimensional data.
The paper classifies affine hypersurfaces with symplectic structures and constraints on their curvature.
Study on relativistic nonholonomic mechanics with time-dependent constraints.
POLICE enforces linear constraints on deep neural networks efficiently.
Study rigidifies torus bundles under first Betti number constraints.
After having given the general variational formula for the functionals indicated in the title, the critical points of the integral of the equi-affine curvature under area constraint and the critical points of the full-affine arc-length are studied in greater detail.
Unified framework for hard affine SDP constraints in vRKHSs.
Study optimal policies under budget and coverage constraints.
Introduces nonlinear splittings on fibre bundles for generalizing connections.
We state and prove a simple Theorem that allows one to generate invariant quantities in Metric-Affine Geometry, under a given transformation of the affine connection. We start by a general functional of the metric and the connection and consider transformations of the affine connection possessing a certain symmetry. We…
Unified physics-informed learning method improves generalization performance.
Randomizes AD models for better option pricing.
This paper presents a geometric description of Lagrangian and Hamiltonian systems on Lie affgebroids subject to affine nonholonomic constraints. We define the notion of nonholonomically constrained system, and characterize regularity conditions that guarantee that the dynamics of the system can be obtained as a suitabl…
Optimizes portfolios with constraints and stochastic factors, deriving explicit solutions.
NucleusDiff models atomic nuclei interactions to prevent separation violations in drug design.
The study classifies certain types of incomplete surfaces with low curvature.
Many applications require recovering a matrix of minimal rank within an affine constraint set, with matrix completion a notable special case. Because the problem is NP-hard in general, it is common to replace the matrix rank with the nuclear norm, which acts as a convenient convex surrogate. While elegant theoretical c…
Non-affine aggregation rules cannot preserve monotonicity in convex learning.
Study proves existence of multiple geodesics in a specific metric space.
New proof shows affine manifolds with parallel volume are Riemannian-flat.
A broad class of convex optimization problems can be formulated as a semidefinite program (SDP), minimization of a convex function over the positive-semidefinite cone subject to some affine constraints. The majority of classical SDP solvers are designed for the deterministic setting where problem data is readily availa…
One has not any conventional energy-momentum conservation law in Lagrangian field theory, but relations involving different stress-energy-momentum tensors associated with different connections. It is not obvious how to choose the true energy-momentum tensor. This problem is solved in the framework of the multimomentum …
Estimates latent positions in 1D torus from noisy pairwise affinities.
This paper finds a metric on \(S^2 imes T^2\) with strictly positive biorthogonal curvature using an affine connection with antisymmetric torsion.
Estimates box dimension of fractal interpolation surfaces using oscillation vectors.
Recent several years have witnessed the surge of asynchronous (async-) parallel computing methods due to the extremely big data involved in many modern applications and also the advancement of multi-core machines and computer clusters. In optimization, most works about async-parallel methods are on unconstrained proble…
Paper classifies conic submanifolds in control systems.
We construct a model space $C(\gsp(\bR^{2n}))$ for the variety of Abelian simply transitive groups of affine transformations of type ${\rm Sp}(\bR^{2n})$. The model is stratified and its principal stratum is a Zariski-open subbundle of a natural vector bundle over the Grassmannian of Lagrangian subspaces in $\bR^{2n}$.…
We call a manifold with torsion and nonmetricity the metric-affine manifold. The nonmetricity leads to a difference between the auto parallel line and the extreme line, and to a change in the expression of the Frenet transport and moving basis. The torsion leads to a change in the Killing equation. We also need to add …
The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of variational calculus, we construct the Tulczyjew triple for first-order Field Theory. The important featu…
Study on friction forces for nonholonomic systems using affine connections.
Study confirms Chern's conjecture on compact Hessian manifolds and classifies their topologies.
Equations link metrics with tensors, revealing curvature constraints.
Constructs real algebraic maps with specific geometric constraints.
The geometrical structure known as Tulczyjew triple has been used with success in analytical mechanics and first order field theory to describe a wide range of physical systems including Lagrangian/Hamiltonian systems with constraints and/or sources, or with singular Lagrangian. Starting from the first principles of th…
Most existing approaches address multi-view subspace clustering problem by constructing the affinity matrix on each view separately and afterwards propose how to extend spectral clustering algorithm to handle multi-view data. This paper presents an approach to multi-view subspace clustering that learns a joint subspace…
In this paper we consider Monge-Ampère equations on compact Hessian manifolds, or equivalently Monge-Ampère equations on certain unbounded convex domains , with a periodicity constraint given by the action of an affine group. In the case where the affine group action is volume-preserving, i.e.,…
Recent years have witnessed the rapid development of block coordinate update (BCU) methods, which are particularly suitable for problems involving large-sized data and/or variables. In optimization, BCU first appears as the coordinate descent method that works well for smooth problems or those with separable nonsmooth …
Changepoint detection is a central problem in time series and genomic data. For some applications, it is natural to impose constraints on the directions of changes. One example is ChIP-seq data, for which adding an up-down constraint improves peak detection accuracy, but makes the optimization problem more complicated.…
Nonconvex and nonsmooth optimization problems are frequently encountered in much of statistics, business, science and engineering, but they are not yet widely recognized as a technology in the sense of scalability. A reason for this relatively low degree of popularity is the lack of a well developed system of theory an…
DKLM learns adaptive kernels for robust nonlinear subspace clustering.
Paper tackles hard shape constraints in kernel machines.
Minimizing the rank of a matrix subject to constraints is a challenging problem that arises in many applications in control theory, machine learning, and discrete geometry. This class of optimization problems, known as rank minimization, is NP-HARD, and for most practical problems there are no efficient algorithms that…
We present an improved Bayesian framework for performing inference of affine transformations of constrained functions. We focus on quadrature with nonnegative functions, a common task in Bayesian inference. We consider constraints on the range of the function of interest, such as nonnegativity or boundedness. Although …
Paper proposes Vertex Networks for reinforcement learning of control systems with safety guarantees.
Retrieving the most similar objects in a large-scale database for a given query is a fundamental building block in many application domains, ranging from web searches, visual, cross media, and document retrievals. State-of-the-art approaches have mainly focused on capturing the underlying geometry of the data manifolds…
Local LMO optimizes constrained problems using local linear minimization.
Heuristic algorithm for portfolio optimization reduces solve times to milliseconds.