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.
The paper classifies a special family of knots in lens spaces using knot Floer homology.
This paper uses sheaf theory to constrain knot types in clean intersections.
We present new computations of tight shapes obtained using the constrained gradient descent code RIDGERUNNER for 544 composite knots with 12 and fewer crossings, expanding our dataset to 943 knots and links. We use the new data set to analyze two outstanding conjectures about tight knots, namely that the ropelengths of…
The paper studies knot densities under various constraints and degenerations.
We report on new numerical computations of the set of self-contacts in tightly knotted tubes of uniform circular cross-section. Such contact sets have been obtained before for the trefoil and figure eight knots by simulated annealing -- we use constrained gradient-descent to provide new self-contact sets for those and …
We present new computations of approximately length-minimizing polygons with fixed thickness. These curves model the centerlines of "tight" knotted tubes with minimal length and fixed circular cross-section. Our curves approximately minimize the ropelength (or quotient of length and thickness) for polygons in their kno…
Study of symmetric unions of knots with new inequality and epimorphism results.
The paper introduces new inequalities for knots in 4D cobordisms.
The Palais-Smale condition is proven for various knot energies.
A new type of knot energy is presented via real life experiments involving a thin resilient metallic tube. Knotted in different ways, the device mechanically acquires a uniquely determined (up to isometry) normal form at least when the original knot diagram has a small number of crossings, thus outperforming the famous…
We claim that HOMFLY polynomials for virtual knots, defined with the help of the matrix-model recursion relations, contain more parameters, than just the usual and . These parameters preserve topological invariance and do not show up in the case of ordinary (non-virtual) knots and links. They are most conv…
Enhanced Euler characteristic improves knot homology detection.
Method optimizes knotting pathways in constrained polymers.
Polynomial invariants classify molecular chains based on their contact arrangements.
The ropelength problem asks for the minimum-length configuration of a knotted diameter-one tube embedded in Euclidean three-space. The core curve of such a tube is called a tight knot, and its length is a knot invariant measuring complexity. In terms of the core curve, the thickness constraint has two parts: an upper b…
Proposes adaptive ridge regression for functional linear models with piecewise shapes.
Study on knot types using thickness and length constraints.
In an earlier paper (math.SG/0110169), we introduced absolute gradings on the three-manifold invariants developed in math.SG/0101206 and math.SG/0105202. Coupled with the surgery long exact sequences, we obtain a number of three- and four-dimensional applications of this absolute grading including strengthenings of the…
New algorithms for sampling in constrained domains without learning rates.
Develops a theory to make learning solutions fair and safe.
We consider the dynamics of vector fields on three-manifolds which are constrained to lie within a plane field, such as occurs in nonholonomic dynamics. On compact manifolds, such vector fields force dynamics beyond that of a gradient flow, except in cases where the underlying manifold is topologically simple. Furtherm…
This article reviews and explains HMC-based methods for sampling constrained continuous distributions.
A cardinality-constrained portfolio caps the number of stocks to be traded across and within groups or sectors. These limitations arise from real-world scenarios faced by fund managers, who are constrained by transaction costs and client preferences as they seek to maximize return and limit risk. We develop a new appro…
Tensor networks constrain kernel machines to Gaussian processes.
Extends GENO framework for GPU optimization of constrained ML problems.
Well-quasi-orders proved on embedded planar graphs.
Constrained adaptive filtering algorithms inculding constrained least mean square (CLMS), constrained affine projection (CAP) and constrained recursive least squares (CRLS) have been extensively studied in many applications. Most existing constrained adaptive filtering algorithms are developed under mean square error (…
Paper proves unique energy-minimizing curves in constrained spaces.
Algorithm tackles constrained reinforcement learning with concave-convex and knapsack constraints.
New bounds on ropelength for torus links improve previous estimates.
Energy quantization for surfaces with area, volume, and mean curvature constraints.
The class of non-rigid registration methods proposed in the framework of PDE-constrained Large Deformation Diffeomorphic Metric Mapping is a particularly interesting family of physically meaningful diffeomorphic registration methods. PDE-constrained LDDMM methods are formulated as constrained variational problems, wher…
A new method solves complex constrained minimax problems.
Proposes r2SGLD for efficient constrained exploration in non-convex learning.
The area of constrained clustering has been extensively explored by researchers and used by practitioners. Constrained clustering formulations exist for popular algorithms such as k-means, mixture models, and spectral clustering but have several limitations. A fundamental strength of deep learning is its flexibility, a…
We describe dimensionally constrained symbolic regression which has been developed for mass measurement in certain classes of events in high-energy physics (HEP). With symbolic regression, we can derive equations that are well known in HEP. However, in problems with large number of variables, we find that by constraini…
The paper optimizes policies constrained to Schur stabilizing controllers using a Newton-type algorithm.
Algorithm optimizes constrained reinforcement learning with dual variables.
We show that the homogeneous and the 2-lobe Delaunay tori in the 3-sphere provide the only isothermic constrained Willmore tori in 3-space with Willmore energy below . In particular, every constrained Willmore torus with Willmore energy below and non-rectangular conformal class is non-degenerated.
This paper tackles constrained statistical learning problems by proposing a new approach.
Constrained Willmore surfaces are critical points of the Willmore functional under conformal variations. As shown in [5] one can associate to any conformally immersed constrained Willmore torus f a compact Riemann surface Σ, such that f can be reconstructed in terms of algebraic data on Σ. Particularly interesting exam…
Study of large area-constrained Willmore surfaces in Schwarzschild-like manifolds.
New method solves constrained optimization problems efficiently.
A new method for optimizing non-decomposable metrics with constraints.
Constrained Willmore surfaces are conformal immersions of Riemann surfaces that are critical points of the Willmore energy under compactly supported infinitesimal conformal variations. Examples include all constant mean curvature surfaces in space forms. In this paper we investigate more generally the crit…
Constrained sequence codes have been widely used in modern communication and data storage systems. Sequences encoded with constrained sequence codes satisfy constraints imposed by the physical channel, hence enabling efficient and reliable transmission of coded symbols. Traditional encoding and decoding of constrained …
The paper proves geometric inequalities in sphere using locally constrained flows.
Self-distillation improves constrained language generation by aligning models with target distributions.