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.
Paper studies curvature of stable surfaces meeting at a common boundary.
Study proves existence of expanding solutions for multiphase surfaces with regular junctions.
The paper proves a regularity theorem for Brakke flows near triple junctions.
An undirected graphical model is a joint probability distribution defined on an undirected graph G*, where the vertices in the graph index a collection of random variables and the edges encode conditional independence relationships among random variables. The undirected graphical model selection (UGMS) problem is to es…
We consider the motion by curvature of a network of curves in the plane and we discuss existence, uniqueness, singularity formation and asymptotic behavior of the flow.
Constructs perturbations of a minimal surface with triple junctions.
Uniformizes surfaces with boundaries, focusing on triple junctions.
We study elliptic fibrations by analyzing suitable deformations of the fibrations and vanishing cycles. We introduce geometric string junctions and describe some of their properties. We show how the structure of the geometric string junctions is naturally related to the Lie algebra structures of the associated singular…
We seek to automate the design of molecules based on specific chemical properties. In computational terms, this task involves continuous embedding and generation of molecular graphs. Our primary contribution is the direct realization of molecular graphs, a task previously approached by generating linear SMILES strings …
We study junctions of Wilson lines in refined SU(N) Chern-Simons theory and their local relations. We focus on junctions of Wilson lines in antisymmetric and symmetric powers of the fundamental representation and propose a set of local relations which realize one-parameter deformations of quantum groups $\dot{U}_{q}(\m…
We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie, Nardone, Scardovelli, …
Study on network flow singularities, focusing on Type-0 singularities.
We consider the evolution by curvature of a general embedded network with two triple junctions. We classify the possible singularities and we discuss the long time existence of the evolution.
New geometric approach realizes 5D bulk theories with 4D edge modes.
We prove that on a closed surface, for any , our min-max theory for prescribing mean curvature produces a solution given by a curve of constant geodesic curvature which is almost embedded, except for finitely many points, at which the solution is a stationary junction with integer density. Moreover, each smoot…
Proves existence and uniqueness of curvature motion for regular networks.
We prove that there are no networks homeomorphic to the Greek "theta" letter (a double cell) embedded in the plane with two triple junctions with angles of degrees, such that under the motion by curvature they are self-similarly shrinking. This fact completes the classification of the self-similarly shrinking net…
Finite singular times for symmetric network curvature flow.
Energy-efficient sampling for machine learning using magnetic tunnel junctions.
Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generaliz…
We show how networks of Wilson lines realize quantum groups U_q(sl(m)), for arbitrary m, in 3d SU(N) Chern-Simons theory. Lifting this construction to foams of surface operators in 4d theory we find that rich structure of junctions is encoded in combinatorics of planar diagrams. For a particular choice of surface opera…
Chaos in cerebellar cells enhances complexity of neural patterns.
Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies predominantly on local search heuristics such as Expectation Maximization. Using te…
We view molecular optimization as a graph-to-graph translation problem. The goal is to learn to map from one molecular graph to another with better properties based on an available corpus of paired molecules. Since molecules can be optimized in different ways, there are multiple viable translations for each input graph…
Plateau's problem is to show the existence of an area minimizing surface with a given boundary, a problem posed by Lagrange in 1760. Experiments conducted by Plateau showed that an area minimizing surface can be obtained in the form of a film of oil stretched on a wire frame, and the problem came to be called Plateau's…
A new method for selecting high quality itemsets from a large collection.
The paper calculates Morse indices and nullities for embedded networks on spheres.
The goal of this project is to introduce and present a machine learning application that aims to improve the quality of life of people in Singapore. In particular, we investigate the use of machine learning solutions to tackle the problem of traffic congestion in Singapore. In layman's terms, we seek to make Singapore …
We consider the motion by mean curvature of an -dimensional graph over a time-dependent domain in , intersecting at a constant angle. In the general case, we prove local existence for the corresponding quasilinear parabolic equation with a free boundary, and derive a continuation criteri…
Study 6D localized matter spectrum on singular Calabi-Yau 3-folds.
The paper proves stability and convergence of minimal networks under curvature motion.
XIMP improves molecular property prediction by integrating multiple graph representations.
We introduce block-tree graphs as a framework for deriving efficient algorithms on graphical models. We define block-tree graphs as a tree-structured graph where each node is a cluster of nodes such that the clusters in the graph are disjoint. This differs from junction-trees, where two clusters connected by an edge al…
Mean curvature flow of clusters of n-dimensional surfaces in R^{n+k} that meet in triples at equal angles along smooth edges and higher order junctions on lower dimensional faces is a natural extension of classical mean curvature flow. We call such a flow a mean curvature flow with triple edges. We show that if a smoot…
In this paper, we prove Lorentzian positive mass theorem for spacetimes with distributional curvature. To do so, we introduce distributional curvature and generalized Arnowitt-Deser-Misner (ADM) momentum. As an application, we discuss a junction of spacetimes.
We consider planar networks of three curves that meet at two junctions with prescribed equal angles, minimizing a combination of the elastic energy and the length functional. We prove existence and regularity of minimizers, and we show some properties of the minimal configurations.
A new framework for efficient Bayesian network inference.
We minimize a linear combination of the Willmore and the length functional among networks in belonging to a given class determined by the number of curves, the order of the junctions and the angles between curves at the junctions. Since this class lacks compactness, we characterize the set of limits of s…
A new neural network model for molecular graphs that learns efficiently and accurately.
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 …
We study the curvature flow of planar nonconvex lens-shaped domains, considered as special symmetric networks with two triple junctions. We show that the evolving domain becomes convex in finite time; then it shrinks homothetically to a point. Our theorem is the analog of the result of Grayson for curvature flow of clo…
Co-PLNet combines point and line predictions to improve wireframe parsing accuracy and efficiency.
We consider the existence problem for `Steiner networks' (trivalent graphs with 120 degree angles at each junction) in strictly convex domains, with `Neumann' boundary conditions (orthogonal intersection with the domain boundary.) For each of the three possible combinatorial possibilities, sufficient conditions on the …
We propose a targeted communication architecture for multi-agent reinforcement learning, where agents learn both what messages to send and whom to address them to while performing cooperative tasks in partially-observable environments. This targeting behavior is learnt solely from downstream task-specific reward withou…
We study the stability of partitions in convex domains involving simultaneous coexistence of three phases, viz. triple junctions. We present a careful derivation of the formula for the second variation of area, written in a suitable form with particular attention to boundary and spine terms, and prove, in contrast to t…
A market-maker-based prediction market lets forecasters aggregate information by editing a consensus probability distribution either directly or by trading securities that pay off contingent on an event of interest. Combinatorial prediction markets allow trading on any event that can be specified as a combination of a …
We study D3-brane theories that are dually described as deformations of two different superconformal theories with massless monopoles and dyons. These arise at the self-intersection of a seven-brane in F-theory, which cuts out a link on a small three-sphere surrounding the self-intersection. The spectru…
We prove that the curvature flow of an embedded planar network of three curves connected through a triple junction, with fixed endpoints on the boundary of a given strictly convex domain, exists smooth until the lengths of the three curves stay far from zero. If this is the case for all times, then the evolution exists…