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.
Designs a Cellular Automata rule for forming touching loop patterns.
This paper explores supervised techniques for continuous anomaly detection from biometric touch screen data. A capacitive sensor array used to mimic a touch screen as used to collect touch and swipe gestures from participants. The gestures are recorded over fixed segments of time, with position and force measured for e…
A successful grasp requires careful balancing of the contact forces. Deducing whether a particular grasp will be successful from indirect measurements, such as vision, is therefore quite challenging, and direct sensing of contacts through touch sensing provides an appealing avenue toward more successful and consistent …
Paper teaches robots to play piano with touch and learning.
We propose a fully automatic method for learning gestures on big touch devices in a potentially multi-user context. The goal is to learn general models capable of adapting to different gestures, user styles and hardware variations (e.g. device sizes, sampling frequencies and regularities). Based on deep neural networks…
User interfaces provide an interactive window between physical and virtual environments. A new concept in the field of human-computer interaction is a soft user interface; a compliant surface that facilitates touch interaction through deformation. Despite the potential of these interfaces, they currently lack a signal …
TACTO simulates high-resolution touch sensing for robotics.
Lipschitz equivalence of self-similar sets is an important area in the study of fractal geometry. It is known that two dust-like self-similar sets with the same contraction ratios are always Lipschitz equivalent. However, when self-similar sets have touching structures the problem of Lipschitz equivalence becomes much …
We propose a generic calibration framework to both vanilla and no-touch options for a large class of continuous semi-martingale models. The method builds upon the forward partial integro-differential equation (PIDE) derived in Hambly et al. (2016), which allows fast computation of up-and-out call prices for the complet…
After the surface theory of Möbius geometry, this study concerns a pair of conformally immersed surfaces in -sphere. Two new invariants and associated with them are introduced as well as the notion of touch and co-touch. This approach is helpful in research about transforms of certain surface classes. As an …
Ghost points affect stability in finite difference schemes for diffusion equations.
Incorrect parity-based descriptions of realizable Gauss diagrams found, but bipartite graphs provide a valid approach.
We summarize the main results of our recent investigation of bundles of real Clifford modules and briefly touch on some applications to string theory and supergravity.
Study on elastic curves pinned at the boundary, focusing on minimizers and their interaction with obstacles.
We study the strong maximum principle for horizontal (p-) mean curvature operator and p-(sub)laplacian operator on subriemannian manifolds including, in particular, Heisenberg groups and Heisenberg cylinders. Under a certain Hormander type condition on vector fields, we show the strong maximum principle holds in higher…
Non-convex optimization is ubiquitous in machine learning. Majorization-Minimization (MM) is a powerful iterative procedure for optimizing non-convex functions that works by optimizing a sequence of bounds on the function. In MM, the bound at each iteration is required to \emph{touch} the objective function at the opti…
We show that a compact embedded minimal or constant mean curvature annulus with non-vanishing Gaussian curvature which is tangent to two spheres of same radius or tangent to a sphere and meeting a plane in constant contact angle is rotational.
Study of discrete Koenigs nets and their properties.
Quantitative structuring is a rigorous framework for the design of financial products. We show how it incorporates traditional investment ideas while supporting a more accurate expression of clients' views. We touch upon adjacent topics regarding the safety of financial derivatives and the role of pricing models in pro…
Double no-touch options, contracts which pay out a fixed amount provided an underlying asset remains within a given interval, are commonly traded, particularly in FX markets. In this work, we establish model-free bounds on the price of these options based on the prices of more liquidly traded options (call and digital …
We present an axiomatic/synthetic account of the Huygens Principle of wave fronts. The primitive notions are "touching", and (a weak notion of ) metric. The paper simplifies some of the exposition of the author's "Metric spaces and SDG", Theory and Appl. of Categories 32 (2017), 803-822
We prove that an m-dimensional minimal variety in a Riemannian manifold cannot touch the boundary at a point where the sum of the smallest m principal curvatures is greater than 0. We also prove an analogous result for varieties with bounded mean curvature.
New discrete cmc surfaces defined from sphere packings and combinatorics.
We consider embedded hypersurfaces evolving by fully nonlinear flows in which the normal speed of motion is a homogeneous degree one, concave or convex function of the principal curvatures, and prove a non-collapsing estimate: Precisely, the function which gives the curvature of the largest interior sphere touching the…
This summarizes the study of the financial and economic crisis in Europe. The starting questions were: 1) Why do we have a crisis? Unde venis? 2) What will be the outcome? Quo vadis? Here is the reasoning which touches many areas, ranging from financial to politics and from psychology and economy.
Three configurations of two perpendicular disks in R^3 are examined, the first in which the disks share centers and the other two in which the disks touch at precisely one point. Volume, surface area and mean width calculations dominate the discussion. Integrated mean curvature also appears as an indirect way to comput…
A submanifold is -neighborly if for any points in there is a hyperplane, supporting and touching it at exactly these points. We prove that the minimal dimension of the Euclidean space, containing a stably -neighborly submanifold, is asymptotically not smaller than .
This is a brief review of some of the uses of nonlinear sigma models. After a short general discussion touching on point particles, strings and condensed matter systems, focus is shifted to sigma models as probes of target space geometries. The relation of supersymmetric non-linear sigma models to Kähler, hyperkähler, …
The paper proves regularity for varifolds with bounded anisotropic mean curvature.
Twenty years ago, Mumford initiated the systematic study of the cohomology ring of moduli spaces of Riemann surfaces. Around the same time, Harer proved that the homology of the mapping class groups of oriented surfaces is independent of the genus in low degrees, increasing with the genus. The (co)homology of mapping c…
We construct a completed version C(Gamma) of the configuration space of a linkage Gamma in R^3 which takes into account the ways one link can touch another. We also describe a simplified version of C(Gamma) which is a blow-up of the space of immersions of Gamma in R^3 A number of simple detailed examples are given.
Federated Learning is a distributed machine learning approach which enables model training on a large corpus of decentralized data. We have built a scalable production system for Federated Learning in the domain of mobile devices, based on TensorFlow. In this paper, we describe the resulting high-level design, sketch s…
Study smooth loops and loop bundles, relating to -structures.
New proofs and inequalities for capillarity problems quantify asymmetries.
We establish interior Lipschitz regularity for continuous viscosity solutions of fully nonlinear, conformally invariant, degenerate elliptic equations. As a by-product of our method, we also prove a weak form of the strong comparison principle, which we refer to as the principle of propagation of touching points, for o…
It is known that for each combinatorial type of convex 3-dimensional polyhedra, there is a representative with edges tangent to the unit sphere. This representative is unique up to projective transformations that fix the unit sphere. We show that there is a unique representative (up to congruence) with edges tangent to…
Our purpose is to explore, in the context of loop ensembles on finite graphs, the relations between combinatorial group theory, loops topology, loop measures, and signatures of discrete paths. We determine the distributions of the loop homotopy class, and of the first and second homologies, defined by the lower central…
We produce skew loops -- loops having no pair of parallel tangent lines -- homotopic to any loop in a flat torus or other quotient of R^n. The interesting case here is n=3. More subtly for any n, we characterize the homotopy classes that will contain a skew loop having a specified loop in the unit sphere as tangent ind…
The paper proves T-duality and Hori formulae for winding loop spaces.
Paper establishes loop space T-duality formulae and refines earlier work.
The 2-loop polynomial is a polynomial presenting the 2-loop part of the Kontsevich invariant of knots. We show a cabling formula for the 2-loop polynomial of knots. In particular, we calculate the 2-loop polynomial for torus knots.
Rational loops played a central role in Uhlenbeck's construction of harmonic maps into U(n) (chiral model in physics), and they are generated by simple elements with one pole and one zero constructed from Hermitian projections. It has been believed for long time that nilpotent loops should be added to generate rational…
These notes partly touch the topic of the talk given by the author at the XXXVIII Workshop on Geometric Methods in Physics, hold in June-July 2019 in Białowieża, Poland. They consist of a short and self-contained introduction to the isomonodromic approach to quantum cohomology, and Dubrovin's conjecture. An overview of…
Kähler manifold loop space inherits Kähler structure and is complete.
Using the relations between the theory of differentiable Bol loops and the theory of affine symmetric spaces we classify all connected differentiable Bol loops having an at most -dimensional semi-simple Lie group as the group topologically generated by their left translations. We show that all these Bol loops are is…
A skew loop is a closed curve without parallel tangent lines. We prove: The only complete surfaces in euclidean 3-space with a point of positive curvature and no skew loops are the quadrics. In particular, ellipsoids are the only closed surfaces without skew loops. We also prove results about skew loops on cylinders an…
Introduces string structures linking to loop spaces.
Study shows looping a 6-manifold over a 4-manifold results in a product of loops on spheres.