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.
Symmetries in shell theory lead to multiple deformation possibilities.
Paper derives formulas for surface variations in shell theory.
We discuss several issues regarding material homogeneity and strain compatibility for materially uniform thin elastic shells from the viewpoint of a 3-dimensional theory, with small thickness, as well as a 2-dimensional Cosserat theory. A relationship between inhomogeneity and incompatibility measures under the two des…
The paper analyzes thin-shell limits for viscous operators on Riemannian hypersurfaces.
Study explores kinematics of surfaces under metric restrictions.
Paper proves rigidity estimates for hyperbolic shells and applies them to \(Γ\)-limit theory.
Extends Penrose's method to null shells with pressure and energy flux.
A new functional for simplicial surfaces is suggested. It is invariant with respect to Moebius transformations and is a discrete analogue of the Willmore functional. Minima of this functional are investigated. as an application a bending energy for discrete thin-shells is derived.
We study for which polynomials a thin shell wormhole with a continuous metric (connecting two Schwarzschild spacetimes of the same mass) satisfy the null energy condition (NEC) in -gravity. We avoid junction conditions by using the mathematical framework of the Colombeau algebra which describes a generalized …
New solutions found for bending of flat surfaces and origami structures.
The paper examines rigidity of thin domains under specific boundary conditions.
Theoretical study explains grokking in neural networks.
This work presents a general unified theory for coupled nonlinear elastic and inelastic deformations of curved thin shells. The coupling is based on a multiplicative decomposition of the surface deformation gradient. The kinematics of this decomposition is examined in detail. In particular, the dependency of various ki…
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape? Motivated by this concern, we first classify, and quantify, the translational, ro…
Study finds how periodic surfaces can bend without stretching.
Characterizes neutral deformation modes of minimal surfaces.
We analyze an elastic surface energy which was recently introduced by G. Napoli and L.Vergori to model thin films of nematic liquid crystals. We show how a novel approach that takes into account also the extrinsic properties of the surfaces coated by the liquid crystal leads to considerable differences with respect to …
Shells resist three out of six possible loads if simply connected.
Discrete Morse functions induce shellings with critical tiles corresponding to function's critical faces.
Given a Lagrangian submanifold of the affine symplectic -space, one can canonically and uniquely define a center-chord and a special improper affine sphere of dimension , both of whose sets of singularities contain . Although these improper affine spheres (IAS) always present other singularities away fro…
The paper proves rigidity for shells in non-Euclidean spaces.
We introduce a notion of Morse shellings (and tilings) on finite simplicial complexes which extends the classical one and its relation to discrete Morse theory.Skeletons and barycentric subdivisions of Morse shellable (or tileable) simplicial complexes are Morse shellable (or tileable). Moreover, every triangulated clo…
The writhe polynomial is a fundamental invariant of an oriented virtual knot. We introduce a kind of local moves for oriented virtual knots called shell moves. The first aim of this paper is to prove that two oriented virtual knots have the same writhe polynomial if and only if they are related by a finite sequence of …
We introduce a method to design lightweight shell objects that are structurally robust under the external forces they may experience during use. Given an input 3D model and a general description of the external forces, our algorithm generates a structurally-sound minimum weight shell object. Our approach works by alter…
We introduce a method to learn a mixture of submodular "shells" in a large-margin setting. A submodular shell is an abstract submodular function that can be instantiated with a ground set and a set of parameters to produce a submodular function. A mixture of such shells can then also be so instantiated to produce a mor…
New concept of effective isometries for compliant shells.
We describe an end-to-end real-time S&P futures trading system. Inner-shell stochastic nonlinear dynamic models are developed, and Canonical Momenta Indicators (CMI) are derived from a fitted Lagrangian used by outer-shell trading models dependent on these indicators. Recursive and adaptive optimization using Adaptive …
Off-shell supermultiplets in 2-dimensions are formulated. These are used to construct sigma models whose target spaces are vector bundles over manifolds that are hyperkähler with torsion. The off-shell supersymmetry implies that the complex structures are simultaneously integrable and allows us to write actions…
Semichiral sigma models with a four-dimensional target space do not support extended N=(4,4) supersymmetries off-shell arXiv:0903.2376, arXiv:0912.4724. We contribute towards the understanding of the non-manifest on-shell transformations in (2,2) superspace by analyzing the extended on-shell supersymmetry of such model…
NSBI approach detects Higgs trilinear coupling with high luminosity upgrade constraints.
The paper introduces surfaces with constant solid angle for designing shell structures.
A classical result by Pachner states that two -dimensional combinatorial manifolds with boundary are PL homeomorphic if and only they can be connected by a sequence of shellings and inverse shellings. We prove that for balanced, i.e., properly -colored, manifolds such a sequence can be chosen such that bala…
The paper proves properties of Lipschitz spacetimes with bounded Ricci curvature.
FGSV defends against shell company attacks in group data valuation.
If a tangle, K, in the 3-ball has no planar, meridional, essential surfaces in its exterior then thin position for K has no thin levels.
We solve the long standing problem of finding an off-shell supersymmetric formulation for a general N = (2, 2) nonlinear two dimensional sigma model. Geometrically the problem is equivalent to proving the existence of special coordinates; these correspond to particular superfields that allow for a superspace descriptio…
We define a new notion of thin position for a graph in a 3-manifold which combines the ideas of thin position for manifolds first originated by Scharlemann and Thompson with the idea of thin position for knots first originated by Gabai. This thin position has the property that connect summing annuli and pairs-of-pants …
For curves of prescribed length embedded into the unit disc in two dimensions, we obtain scaling results for the minimal elastic energy as the length just exceeds and in the large length limit. In the small excess length case, we prove convergence to a fourth order obstacle type problem with integral constraint on…
We produce embeddings of knots in thin position that admit compressible thin levels. We also find the bridge number of tangle sums where each tangle is high distance.
New proof shows most thin knots satisfy Cabling Conjecture.
Chern-Simons gauge theories in 3 dimensions and the Poisson Sigma Model (PSM) in 2 dimensions are examples of the same theory, if their field equations are interpreted as morphisms of Lie algebroids and their symmetries (on-shell) as homotopies of such morphisms. We point out that the (off-shell) gauge symmetries of th…
We describe a natural decomposition of a normal complex surface singularity into its "thick" and "thin" parts. The former is essentially metrically conical, while the latter shrinks rapidly in thickness as it approaches the origin. The thin part is empty if and only if the singularity is metrically conical; the…
Let k be a knot in S3. In [8], H.N. Howards and J. Schultens introduced a method to construct a manifold decomposition of double branched cover of (S3, k) from a thin position of k. In this article, we will prove that if a thin position of k induces a thin decomposition of double branched cover of (S3,k) by Howards and…
Abby Thompson proved that if a link is in thin position but not in bridge position then the knot complement contains an essential meridional planar surface, and she asked whether some thin level surface must be essential. This note is to give a positive answer to this question, showing that the if a link is in thin…
New method characterizes thin links via Conway spheres and tangle decompositions.
Bistable structures associated with non-linear deformation behavior, exemplified by the Venus flytrap and slap bracelet, can switch between different functional shapes upon actuation. Despite numerous efforts in modeling such large deformation behavior of shells, the roles of mechanical and nonlinear geometric effects …
Regularized Stein thinning improves MCMC output approximations.
Thin groups found in specific lattices.