Related papers: Uncapacitated Flow-based Extended Formulations
As a probabilistic modeling technique, the flow-based model has demonstrated remarkable potential in the field of lossless compression \cite{idf,idf++,lbb,ivpf,iflow},. Compared with other deep generative models (eg. Autoregressive, VAEs)…
Unbalanced optimal power flow refers to a class of optimization problems subject to the steady state physics of three-phase power grids with nonnegligible phase unbalance. Significant progress on this problem has been made on the…
In undergraduate classes, the potential flow that goes around a circular cylinder is designed for complemental understanding of mathematical technique to handle the Laplace equation with Neumann boundary conditions and the physical concept…
We develop efficient algorithms for a fundamental network design problem arising in potential-based flow models, which are central to many energy transport networks (e.g., hydrogen and electricity). In contrast to classical network flow…
We show the existence of a polynomial-size extended formulation for the base polytope of a $(k,\ell)$-sparsity matroid. For an undirected graph $G=(V,E)$, the size of the formulation is $O(|V||E|)$ when $k \geq \ell$ and $O(|V|^2 |E|)$ when…
This paper investigates the extension complexity of polytopes by exploiting the correspondence between non-negative factorizations of slack matrices and randomized communication protocols. We introduce a geometric characterization of…
Normalizing flows provide a general mechanism for defining expressive probability distributions, only requiring the specification of a (usually simple) base distribution and a series of bijective transformations. There has been much recent…
We introduce a widely applicable tensor network-based framework for developing reduced order models describing wall-bounded fluid flows. As a paradigmatic example, we consider the incompressible Navier-Stokes equations and the lid-driven…
We construct explicit combinatorial Bernoulli factories for the class of \emph{flow-based polytopes}; integral 0/1-polytopes defined by a set of network flow constraints. This generalizes the results of Niazadeh et al. (who constructed an…
This work presents mixed variational flows (MixFlows), a new variational family that consists of a mixture of repeated applications of a map to an initial reference distribution. First, we provide efficient algorithms for i.i.d. sampling,…
An extended formulation of a polyhedron $P$ is a linear description of a polyhedron $Q$ together with a linear map $\pi$ such that $\pi(Q)=P$. These objects are of fundamental importance in polyhedral combinatorics and optimization theory,…
Provided a special function of one variable and some of its derivatives can be accurately computed over a finite range, a method is presented to build a series of polynomial approximations of the function with a defined relative error over…
We propose a general algorithm of constructing an extended formulation for any given set of linear constraints with integer coefficients. Our algorithm consists of two phases: first construct a decision diagram $(V,E)$ that somehow…
We provide a complete description of the asymptotics of the gradient flow on the space of metrics on any semistable quiver representation. This involves a recursive construction of approximate solutions and the appearance of iterated…
The goal of this article is to obtain bounds on the coefficients of modular and integral flow and tension polynomials of graphs. To this end we make use of the fact that these polynomials can be realized as Ehrhart polynomials of inside-out…
It is a well-known result of T.\,Kato that given a continuous path of square matrices of a fixed dimension, the eigenvalues of the path can be chosen continuously. In this paper, we give an infinite-dimensional analogue of this result,…
We present the derivation of a new unidirectional model for We present the derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipes. We introduce a local reference frame to take into account the…
We present the method for computation of fluid flows that are characterized by the large degree of expansion/contraction and in which the fluid velocity is dominated by the bulk component associated with the expansion/contraction and/or…
Execution graphs of parallel loop programs exhibit a nested, repeating structure. We show how such graphs that are the result of nested repetition can be represented by succinct parametric structures. This parametric graph template…
Optimal Power Flow (OPF) is an important tool used to coordinate assets in electric power systems to ensure customer voltages are within pre-defined tolerances and to improve distribution system operations. While convex relaxations of…