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.
Proper actions on bornological spaces are characterized with compatible coarse structures.
Study equi-affine invariants for convex domains with asymptotes.
In this paper, we introduce and study various kinds of decomposition complexity. First, we give a characterization of residually finite groups having finite decomposition complexity (FDC). Secondly, we introduce equi-variant straight FDC (sFDC), and prove that a group having equi-variant sFDC if and only if its box spa…
The paper studies extremal hypersurfaces in ellipsoids using centro-affine geometry.
In this paper, the Cartan frames and the equi-affine curvatures are described with the help of the Frenet frames and the Frenet curvatures of a non-null and non-degenerate curve in a 3-dimensional pseudo-Riemannian manifold. The constancy of the Frenet curvatures of such a curve always implies the constancy of the equi…
Lorentzian distances to Cauchy surfaces fail to be locally equi-Lipschitz.
For an arbitrary nondegenerate curve in a pseudo-Riemann\-ian (including Riemannian) 2-manifold, we express the equi-affine curvature with the help of the Frenet (geodesic) curvature of this curve.
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.
Study on fractional mass for codimension-two currents, proving equi-coercivity and Γ-convergence.
The paper discusses algorithms for reconstructing curves with given Euclidean or affine curvatures.
In this article we explore some finer properties of equi-areal mirrors and introduce techniques for developing new mirror surfaces that simultaneously minimize angular and areal distortion.
New classification of complex hypersurfaces in 3D.
3D RadViz improves 3D data visualization of multidimensional datasets.
A compact Polish foliated space is considered. Part of this work studies coarsely quasi-isometric invariants of leaves in some residual saturated subset when the foliated space is transitive. In fact, we also use "equi-" versions of this kind of invariants, which means that the definition is satisfied with the same con…
Polynomial neural networks explore thresholds for maximum expressiveness.
We define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other well-known low-dimensional singularities. We also give an application to stable p…
The paper examines convergence of distances in Lipschitz structures on manifolds.
Any two equivalent discrete curves must have the same invariants at the corresponding points under an affine transformation. In this paper, we construct the moving frame and invariants for the discrete centroaffine curves, which could be used to discriminate the same discrete curves from different graphics, and estimat…
We introduce an approach based on moving frames for polygon recognition and symmetry detection. We present detailed algorithms for recognition of polygons modulo the special Euclidean, Euclidean, equi-affine, skewed-affine and similarity Lie groups, and explain the procedure for a generic Lie group. The time complexity…
In (equi-)affine differential geometry, the most important algebraic invariants are the affine (Blaschke) metric h, the affine shape operator S and the difference tensor K. A hypersurface is said to admit a pointwise symmetry if at every point there exists a linear transformation preserving the affine metric, the affin…
Self-similar solutions to geometric flows are stable under small perturbations.
The paper optimizes stock portfolios with constraints based on performance attribution.
Neuroscientific studies of drawing-like movements usually analyze neural representation of either geometric (eg. direction, shape) or temporal (eg. speed) features of trajectories rather than trajectory's representation as a whole. This work is about empirically supported mathematical ideas behind splitting and merging…
Motivated by the importance and universal character of phase singularities which are clarified recently, we study the local structure of equi-phase loci near the dislocation locus of complex valued planar and spatial waves, from the viewpoint of singularity theory of differentiable mappings, initiated by H. Whitney and…
Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces parametrized along asymptotic lines. The characterizing property of A-nets is planarity of vertex stars, so for generic A-nets the elementary quadrilaterals are skew. We classify the simply connected affine A-nets that can be ext…
Cartan's method of moving frames is briefly recalled in the context of immersed curves in the homogeneous space of a Lie group . The contact geometry of curves in low dimensional equi-affine geometry is then made explicit. This delivers the complete set of invariant data which solves the -equivalence problem via …
Yau's Affine Normal Descent optimizes smooth unconstrained problems with geometrically adapted directions.
The paper explores fully affine maximal curves and their properties.
Random Feedback Alignment helps solve low-rank matrix factorization problems.
Modern automation systems rely on closed loop control, wherein a controller interacts with a controlled process, based on observations. These systems are increasingly complex, yet most controllers are linear Proportional-Integral-Derivative (PID) controllers. PID controllers perform well on linear and near-linear syste…
Derives optimal control conditions using calculus of variations.
Framework simplifies vision-based control and goal discovery.
Paper studies constrained control games with a novel approximation method.
This work tackles force control for contact-rich manipulation tasks with rigid robots using RL.
RL applied to TCLs for power consumption control.
A framework integrates machine learning with robust control for safer, more reliable systems.
Paper uses deep reinforcement learning for better control of rocket engines during start-up phases.
Neural ODEs control graph dynamics with low energy feedback.
Just as an explicit parameterisation of system dynamics by state, i.e., a choice of coordinates, can impede the identification of general structure, so it is too with an explicit parameterisation of system dynamics by control. However, such explicit and fixed parameterisation by control is commonplace in control theory…
Unified control theory and machine learning for safety in uncertain systems.
Paper studies optimal control for a specific geometric problem.
Hybrid systems are characterized by having an interaction between continuous dynamics and discrete events. The contribution of this paper is to provide hybrid systems with a novel geometric formulation so that controls can be added. Using this framework we describe some new global controllability tests for hybrid contr…
Optimizes dividend policies in a Brownian model with controlled rates.
Paper proposes a new method to optimize robot body structure and control policy.
Non-bilinear observations make optimal control harder, showing non-convex costs and non-affine optimal controllers.
Defense strategy improves controller robustness against adversarial attacks.
This paper considers control systems defined on Lie algebroids. After deriving basic controllability tests for general control systems, we specialize our discussion to the class of mechanical control systems on Lie algebroids. This class of systems includes mechanical systems subject to holonomic and nonholonomic const…
Survey of theoretical foundations for policy optimization in control.