Related papers: Sausages
Polynomial optimization problems represent a wide class of optimization problems, with a large number of real-world applications. Current approaches for polynomial optimization, such as the sum of squares (SOS) method, rely on large-scale…
A clover is a framed trivalent graph with some additional structure, embedded in a 3-manifold. We define surgery on clovers, generalizing surgery on Y-graphs used earlier by the second author to define a new theory of finite-type invariants…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
Yannakakis' theorem relating the extension complexity of a polytope to the size of a nonnegative factorization of its slack matrix is a seminal result in the study of lifts of convex sets. Inspired by this result and the importance of lifts…
Spinor polynomials are polynomials with coefficients in the even sub-algebra of conformal geometric algebra whose norm polynomial is real. They describe rational conformal motions. Factorizations of spinor polynomial corresponds to the…
Localization principle is a powerful analytic tool in supersymmetric gauge theories which enables one to perform supersymmetric path integrals explicitly. Many important formulae have been obtained, and they led to a major breakthrough in…
The prediction of protein stability changes following single-point mutations plays a pivotal role in computational biology, particularly in areas like drug discovery, enzyme reengineering, and genetic disease analysis. Although…
We use recent extensions of the Borsuk--Ulam theorem for Stiefel manifolds to generalize the ham sandwich theorem to mass assignments. A $k$-dimensional mass assignment continuously imposes a measure on each $k$-dimensional affine subspace…
Consider polynomial maps $f:\C\to\C$ of degree $d\ge 2$, or more generally polynomial maps from a finite union of copies of $\C$ to itself. In the space of suitably normalized maps of this type, the hyperbolic maps form an open set called…
Symbolic Mathematical tasks such as integration often require multiple well-defined steps and understanding of sub-tasks to reach a solution. To understand Transformers' abilities in such tasks in a fine-grained manner, we deviate from…
Graphings are special bounded-degree graphs on probability spaces, representing limits of graph sequences that are convergent in a local or local-global sense. We describe a procedure for turning the underlying space into a compact metric…
Bayesian shrinkage methods have generated a lot of recent interest as tools for high-dimensional regression and model selection. These methods naturally facilitate tractable uncertainty quantification and incorporation of prior information.…
In this paper we present a new theory of calculus over $k$-dimensional domains in a smooth $n$-manifold, unifying the discrete, exterior, and continuum theories. The calculus begins at a single point and is extended to chains of finitely…
A basic problem in complex dynamics is to understand orbits of holomorphic maps. One problem is to understand the collection of points $S$ in an attracting basin whose forward orbits land exactly on the attracting fixed point. In the paper…
Let d\mu(t) be a probability measure on [0,+\infty) such that its moments are finite. Then the Cauchy-Stieltjes transform S of d\mu(t) is a Stieltjes function, which admits an expansion into a Stieltjes continued fraction. In the present…
In this paper, we formally define the concept of shifted contact structures on derived (Artin) stacks and study their local properties in the context of derived algebraic geometry. In this regard, for negatively shifted contact derived…
We discuss the deformation theory of special Lagrangian (SL) conifolds in complex space C^m. Conifolds are a key ingredient in the compactification problem for moduli spaces of compact SLs in Calabi-Yau manifolds. This category allows for…
Given a Nori motivic local system over a smooth, connected complex algebraic variety, we define its exceptional locus as a way to measure the variation in the motivic complexity of its stalks. The definition is given explicitly in terms of…
We apply methods from strict quantization of solvable symmetric spaces to obtain universal deformation formulae for actions of every three-dimensional solvable Lie group. We also study compatible co-products by generalizing the notion of…
We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…