arXiv research

We say that a graph is intrinsically knotted or completely 3-linked if every embedding of the graph into the 3-sphere contains a nontrivial knot or a 3-component link any of whose 2-component sublink is nonsplittable. We show that a graph obtained from the complete graph on seven vertices by a finite sequence of $\tria…

Conway-Gordon proved that for every spatial complete graph on 6 vertices, the sum of the linking numbers over all of the constituent 2-component links is congruent to 1 modulo 2, and for every spatial complete graph on 7 vertices, the sum of the Arf invariants over all of the Hamiltonian knots is also congruent to 1 mo…

Real bordered Floer homology computes 3-manifolds with involution.

Analyzes impermanent loss in decentralized exchanges and provides a replication formula.

We introduce an infectious default and recovery model for N obligors. Obligors are assumed to be exchangeable and their states are described by N Bernoulli random variables S_{i} (i=1,...,N). They are expressed by multiplying independent Bernoulli variables X_{i},Y_{ij},Y'_{ij}, and default and recovery infections are …

This paper investigates a multi-terminal source coding problem under a logarithmic loss fidelity which does not necessarily lead to an additive distortion measure. The problem is motivated by an extension of the Information Bottleneck method to a multi-source scenario where several encoders have to build cooperatively …

We provide a rigorous numerical computation method to validate periodic, homoclinic and heteroclinic orbits as the continuation of singular limit orbits for the fast-slow system $x' = f(x,y,ε), y' = εg(x,y,ε)$ with one-dimensional slow variable $y$. Our validation procedure is based on topological tools called isolatin…

An online framework optimizes efficiency in conformal prediction with a target miscoverage rate.

New IPL graphs identified and conditions for their projective embeddings established.

Combines CP with stability bounds for efficient continuous prediction.

This book, which is in Spanish, provides detailed descriptions, including over 550 mathematical formulas, for over 150 trading strategies across a host of asset classes (and trading styles). This includes stocks, options, fixed income, futures, ETFs, indexes, commodities, foreign exchange, convertibles, structured asse…

The paper studies symplectic operations on Stein fillings of Brieskorn singularities.

If a continuous map f: X->Q is approximable arbitrary closely by embeddings X->Q, can some embedding be taken onto f by a pseudo-isotopy? This question, called Isotopic Realization Problem, was raised by Shchepin and Akhmet'ev. We consider the case where X is a compact n-polyhedron, Q a PL m-manifold and show that the …

New simplicial complexes show unavoidable link of spheres in high dimensions.

A framework infers causal direction from symbolic sequences using compression measures.

We will give a new proof of the existence of non-compact homothetic solitons of the inverse mean curvature flow (cf. \cite{DLW}) in $\mathbb{R}^n\times \mathbb{R}$, $n\ge 2$, of the form $(r,y(r))$ or $(r(y),y)$ where $r=|x|$, $x\in\mathbb{R}^n$, is the radially symmetric coordinate and $y\in \mathbb{R}$. More precisel…

The paper solves the equivalence problem for a specific class of ODEs.

We will give a new proof of the existence of hypercylinder expander of the inverse mean curvature flow which is a radially symmetric homothetic soliton of the inverse mean curvature flow in $\mathbb{R}^n\times \mathbb{R}$, $n\ge 2$, of the form $(r,y(r))$ or $(r(y),y)$ where $r=|x|$, $x\in\mathbb{R}^n$, is the radially…

For the equations of the form $y''=P(x,y)+3 Q(x,y) y'+3 R(x,y) {y'}^2 +S(x,y) {y'}^3$ the problem of equivalence in the class of point transformations is considered. Effective procedure for determining the class of point equivalence for the given equation is suggested. This procedure is based on explicit formulas for t…

The exchange algorithm is studied for its convergence and asymptotic variance.

Study on pricing American Exchange options using Lévy processes.

This paper speeds up uncertainty quantification in inverse problems using conditional normalizing flows.

In 1883, as an early result, Sophus Lie established an explicit necessary and sufficient condition for an analytic second order ordinary differential equation y_xx = F(x,y,y_x) to be equivalent, through a point transformation (x,y) --> (X(x,y), Y(x,y)), to the Newtonian free particle equation Y_XX = 0. This result, pre…

Optimal crypto order execution using cross-exchange signals.

In this paper, we investigate the action of pseudogroup of all point transformations on the natural bundle of equations $y''=a^3(x,y)(y')^3+a^2(x,y)(y')^2+a^1(x,y)y'+a^0(x,y)$. We construct differential invariants of this action and solve the equivalence problem for some classes of these equations in particular for gen…

We prove that the presentations $\langle x,y | [x,y],1 \rangle$ and $\langle x,y | [x,[x,y^{-1}]]^2y[y^{-1},x]y^{-1},[x,[[y^{-1},x],x]] \rangle$ are not $Q^*$-equivalent even though their standard complexes have the same simple homotopy type.

In this note we prove that every metric space $(X, d)$ of asymptotic dimmension at most $n$ is coarsely equivalent to a metric space $(Y, D)$ that satisfies the following property of Nagata: For every $n+2$ points $y_1,..., y_{n+2}$ in $Y$ and for every $x$ in $Y$ there exist two different $i,j$ such that $D(y_i,y_j)\l…

For each integral homology sphere $Y$, a function $Γ_Y$ on the set of integers is constructed. It is established that $Γ_Y$ depends only on the homology cobordism of $Y$ and it recovers the Frøyshov invariant. A relation between $Γ_Y$ and Fintushel-Stern's $R$-invariant is stated. It is shown that the value of $Γ_Y$ at…

Let $G$ be a finite group and $\Y$ a $G$-gerbe over an orbifold $\B$. A disconnected orbifold $\hat{\Y}$ and a flat U(1)-gerbe $c$ on $\hat{\Y}$ is canonically constructed from $\Y$. Motivated by a proposal in physics, we study a mathematical duality between the geometry of the $G$-gerbe $\Y$ and the geometry of $\hat{…

We study here limit spaces $(M_α,g_α,p_α)\stackrel{GH}{\rightarrow} (Y,d_Y,p)$, where the $M_α$ have a lower Ricci curvature bound and are volume noncollapsed. Such limits $Y$ may be quite singular, however it is known that there is a subset of full measure $\cR(Y)\subseteq Y$, called {\it regular} points, along with c…

Study on symmetry defects of complete intersections in complex space.

In this paper, we want to discuss the topology of the non-singular hypersurface $Y^{n}$ with complex dimension $n$ in a projective toric manifold $X^{n+1}$. When $n$ is odd, our main results are a decomposition of $Y^{n}\cong Y'\sharp \ s(S^n \times S^n)$ as a connected sum of $s$ copies of $S^n \times S^n$ with a dif…

New models reduce regional inequality by adjusting exchange range and asset distribution bias.

It is the Hilbert's Fourth Problem to characterize the (not-necessarily-reversible) distance functions on a bounded convex domain in R^n such that straight lines are shortest paths. Distance functions induced by a Finsler metric are regarded as smooth ones. Finsler metrics with straight geodesics said to be projective.…

A known failing of many popular random graph models is that the Aldous-Hoover Theorem guarantees these graphs are dense with probability one; that is, the number of edges grows quadratically with the number of nodes. This behavior is considered unrealistic in observed graphs. We define a notion of edge exchangeability …

Let $M^7$ be a smooth manifold equipped with a $G_2$-structure $φ$, and $Y^3$ be an closed compact $φ$-associative submanifold. In \cite{McL}, R. McLean proved that the moduli space $\bm_{Y,φ}$ of the $φ$-associative deformations of $Y$ has vanishing virtual dimension. In this paper, we perturb $φ$ into a $G_2$-structu…

We study several questions involving relative Ricci-flat Kähler metrics for families of log Calabi-Yau manifolds. Our main result states that if $p:(X,B)\to Y$ is a Kähler fiber space such that $\displaystyle (X_y, B|_{X_y})$ is generically klt, $K_{X/Y}+B$ is relatively trivial and $p_*(m(K_{X/Y}+B))$ is Hermitian fla…

In this paper, we investigate the action of pseudogroup of all point transformations on the natural bundle of equations $y'' = u^0(x,y) + u^1(x,y)y' + u^2(x,y)(y')^2 + u^3(x,y)(y')^3$. We calculate the 1-st nontrivial differential invariant of this action. It is a horizontal differential 2-form with values in some alge…

Proposes a new Armijo's condition for general functions and provides an algorithm for its application.

On a $3$D manifold, a Weyl geometry consists of pairs $(g, A) =$ (metric, $1$-form) modulo gauge $\widehat{g} = {\rm e}^{2\varphi} g$, $\widehat{A} = A + {\rm d}\varphi$. In 1943, Cartan showed that every solution to the Einstein-Weyl equations $R_{(μν)} - \frac{1}{3} R g_{μν} = 0$ comes from an appropriate $3$D leaf s…

Infinite rank groups found in 3-manifolds with infinite fundamental groups.

Let $Y$ be a sublattice of a vector lattice $X$. We consider the problem of identifying the smallest order closed sublattice of $X$ containing $Y$. It is known that the analogy with topological closure fails. Let $\overline{Y}^o$ be the order closure of $Y$ consisting of all order limits of nets of elements from $Y$. T…

Let $f : X \lo Y$ be a map of compact metric spaces. A classical theorem of Hurewicz asserts that $\dim X \leq \dim Y +\dim f$ where $\dim f =\sup \{\dim f^{-1}(y): y \in Y \}$. The first author conjectured that {\em $\dim Y + \dim f$ in Hurewicz's theorem can be replaced by $\sup \{\dim (Y \times f^{-1}(y)): y \in Y \…

New denoisers improve signal recovery from noisy data without knowing noise distribution.

Let $\Y$ be a smooth connected manifold, $Σ\subset\C$ an open set and $(σ,y)\to\scrP_y(σ)$ a family of unbounded Fredholm operators $D\subset H_1\to H_2$ of index 0 depending smoothly on $(y,σ)\in \Y\times Σ$ and holomorphically on $σ$. We show how to associate to $\scrP$, under mild hypotheses, a smooth vector bundle …

How do individuals accumulate wealth as they interact economically? We outline the consequences of a simple microscopic model in which repeated pairwise exchanges of assets between individuals build the wealth distribution of a population. This distribution is determined for generic exchange rules --- transactions that…

Paper improves algorithms for convex-concave minimax optimization problems.

Derives a general derivative identity for conditional mean in Gaussian noise.