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.
The paper identifies network bottlenecks using minimax paths in stochastic networks.
The paper computes special values of combinatorial zeta functions to reveal topological properties of manifolds.
Method uses neural networks to solve combinatorial problems.
Following the work of Cano and Diaz, we consider a continuous analog of lattice path enumeration. This allows us to define a continuous version of any discrete object that counts certain types of lattice paths. We define continuous versions of binomials and multinomials, and describe some identities and partial differe…
New lattice path method for statistical inference of persistent diagrams.
In their study of fundamental groups of one-dimensional path-connected compact metric spaces, Cannon and Conner have asked: Is there a tree-like object that might be considered the topological Cayley graph? We answer this question in the positive and provide a combinatorial description of such an object.
Combinatorial transgressions are secondary invariants of a space admitting triangulations. They arise from subdivisions and are analogous to transgressive forms such as those arising in Chern-Weil theory. Unlike combinatorial characteristic classes, combinatorial transgressions have not been previously studied. First, …
Floer constructs homology from flow lines in generalized dynamical systems and combinatorial vector fields.
Constructs a path integral for fermionic SPTs, solving anomalies in 2+1D topological orders.
We propose combinatorial cascading bandits, a class of partial monitoring problems where at each step a learning agent chooses a tuple of ground items subject to constraints and receives a reward if and only if the weights of all chosen items are one. The weights of the items are binary, stochastic, and drawn independe…
We extend Jendrol' and Skupień's results about the local structure of maps on the 2-sphere: In this paper we show that if a polyhedral map on a surface $\M$ of Euler characteristic $χ(\M) \le 0$ has more than $126|χ(\M)|$ vertices, then has a vertex with "nearly" non-negative combinatorial curvature. As a corol…
The paper proves a conjecture about the dimensions of centralizer algebras related to quantum super-algebras.
It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones fun…
We introduce a number of new tools for the study of relatively hyperbolic groups. First, given a relatively hyperbolic group G, we construct a nice combinatorial Gromov hyperbolic model space acted on properly by G, which reflects the relative hyperbolicity of G in many natural ways. Second, we construct two useful bic…
New method uses hyperbolic space for faster phylogenetic tree inference.
Using techniques from the theories of convex polytopes, lattice paths, and indirect influences on directed manifolds, we construct continuous analogues for the binomial coefficients and the Catalan numbers. Our approach for constructing these analogues can be applied to a wide variety of combinatorial sequences. As an …
Single-Path NAS designs efficient ConvNets for mobile devices in hours.
Algorithm identifies best arm in combinatorial bandits with semi-bandit feedback.
Single-Path NAS designs efficient ConvNets in under 4 hours.
Researchers calculate complexity of billiard paths in regular polygons.
We consider supervised learning problems where the features are embedded in a graph, such as gene expressions in a gene network. In this context, it is of much interest to automatically select a subgraph with few connected components; by exploiting prior knowledge, one can indeed improve the prediction performance or o…
Efficient routing algorithms learn from feedback to minimize path lengths.
For a Legendrian knot L in R^3 with a chosen Morse complex sequence (MCS) we construct a differential graded algebra (DGA) whose differential counts "chord paths" in the front projection of L. The definition of the DGA is motivated by considering Morse-theoretic data from generating families. In particular, when the MC…
The paper offers efficient algorithms for combinatorial and linear bandits using empirical process theory.
We prove several combinatorial results on path algebras over discrete structures related to directed graphs. These results are motivated by Morse theory on a manifold with boundary and, more generally, by Floer theory on a configuration space with boundary. Their purpose is to organize cobordism relationships among mod…
The aim of this paper is to develop a refinement of Forman's discrete Morse theory. To an acyclic partial matching on a finite regular CW complex , Forman introduced a discrete analogue of gradient flows. Although Forman's gradient flow has been proved to be useful in practical computations of homology groups, i…
Study loop ensembles on graphs, linking group theory and topology.
Single-Path NAS reduces NAS search cost to 3 hours, achieving state-of-the-art mobile image classification.
Linear-time graph optimization using reinforcement learning.
The Ptolemy groupoid is a combinatorial groupoid generated by elementary moves on marked trivalent fatgraphs with three types of relations. Through the fatgraph decomposition of Teichmüller space, the Ptolemy groupoid is a mapping class group equivariant subgroupoid of the fundamental path groupoid of Teichmüller space…
Study transitions between tableau and spider bases for Specht modules.
Study on reward poisoning attacks on CMAB, revealing attackability depends on adversary's knowledge.
Topology of the Generic Hamiltonian Dynamical Systems on the Riemann Surfaces given by the real part of the generic holomorphic 1-forms, is studied. Our approach is based on the notion of Transversal Canonical Basis of Cycles (TCB). This approach allows us to present a convenient combinatorial model of the whole topolo…
A number of modern learning tasks involve estimation from heterogeneous information sources. This includes classification with labeled and unlabeled data as well as other problems with analogous structure such as competitive (game theoretic) problems. The associated estimation problems can be typically reduced to solvi…
We consider a nonlinear extension of the generalized network flow model, with the flow leaving an arc being an increasing concave function of the flow entering it, as proposed by Truemper and Shigeno. We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an epsi…
A new algebraic method extracts symmetry anomalies from 5D SCFTs.
The paper extends game theory using Hodge theory on graphs.
This paper tackles robust submodular minimization for image segmentation and correspondence.
We compare two important bases of an irreducible representation of the symmetric group: the web basis and the Specht basis. The web basis has its roots in the Temperley-Lieb algebra and knot-theoretic considerations. The Specht basis is a classic algebraic and combinatorial construction of symmetric group representatio…
Unified framework for robust submodular optimization with various constraints.
This study optimizes currency arbitrage using quantum computing methods.
The shape of homogeneous, generic, smooth convex bodies as described by the Euclidean distance with nondegenerate critical points, measured from the center of mass represents a rather restricted class M_C of Morse-Smale functions on S^2. Here we show that even M_C exhibits the complexity known for general Morse-Smale f…
The paper estimates Betti numbers for graphs with specific curvatures, proving bounds and characterizing rigidity.
Adapting neural networks to guide program optimization for better classifiers.
The paper studies combinatorics of injective words in the context of Temperley-Lieb algebras.
Efficiently reduces training and inference costs by dynamically selecting important channels.
GOPC algorithm finds global optimal clusters efficiently.
Knot Theory is currently a very broad field. Even a long survey can only cover a narrow area. Here we concentrate on the path from Goeritz matrices to quasi-alternating links. On the way, we often stray from the main road and tell related stories, especially if they allow as to place the main topic in a historical cont…