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.
Graph ConvNet improves classification by leveraging label graph structure.
The relation between time series irreversibility and entropy production has been recently investigated in thermodynamic systems operating away from equilibrium. In this work we explore this concept in the context of financial time series. We make use of visibility algorithms to quantify in graph-theoretical terms time …
Metric graphs have subgraphs with entropy at least λ.
Polterovich proved a remarkable closed formula for heat kernel coefficients of the Laplace operator on compact Riemannian manifolds involving powers of Laplacians acting on the distance function. In the case of Kähler manifolds, we prove a combinatorial formula for powers of the complex Laplacian and use it to derive a…
By proving graph theoretical versions of Green-Stokes, Gauss-Bonnet and Poincare-Hopf, core ideas of undergraduate mathematics can be illustrated in a simple graph theoretical setting. In this pedagogical exposition we present the main proofs on a single page and add illustrations. While discrete Stokes is is old, the …
G1 uses RL to enhance LLMs' graph reasoning, improving performance on diverse tasks.
Graph theory connects automorphisms to cohomology.
We say that a link is an s-major of a link if any diagram of can be transformed into a diagram of by changing some crossings and smoothing some crossings. This relation is a partial ordering on the set of all prime alternating links. We determine this partial order for all prime alternating knot…
We prove a discrete Gauss-Bonnet-Chern theorem which states where summing the curvature over all vertices of a finite graph G=(V,E) gives the Euler characteristic of G.
Unified framework for OOD detection and generalization using graph theory.
Unified framework for disentangled representations using mechanistic independence.
Graph theory improves portfolio optimization for diversified investments.
We prove a graph theoretic closed formula for coefficients in the Tian-Yau-Zelditch asymptotic expansion of the Bergman kernel. The formula is expressed in terms of the characteristic polynomial of the directed graphs representing Weyl invariants. The proof relies on a combinatorial interpretation of a recursive formul…
Study algorithmic problems in RAAGs with applications to cryptography.
The equivariant cohomology ring of a GKM manifold is isomorphic to the cohomology ring of its GKM graph. In this paper we explore the implications of this fact for equivariant fiber bundles for which the total space and the base space are both GKM and derive a graph theoretical version of the Leray-Hirsch theorem. Then…
This research introduces dynamic portfolio cuts using a spectral approach for graph-theoretic diversification.
Classifies graph configuration spaces homeomorphic to manifolds.
This study explores complex structures on Lie algebras from graph perspectives.
The paper constructs graph models for n-dimensional manifolds.
We express characteristic numbers of compact hyperkähler manifolds in graph-theoretical form, considering them as a special case of the curvature invariants introduced by Rozansky and Witten. The appropriate graphs are generated by ``wheels'' and we use the recently proved Wheeling Theorem to give a formula for the L2 …
Two approaches use TDA and graph theory for tennis match prediction.
This paper continues our study, initiated in [arXiv:1108.3370], of essential state surfaces in link complements that satisfy a mild diagrammatic hypothesis (homogeneously adequate). For hyperbolic links, we show that the geometric type of these surfaces in the Thurston trichotomy is completely determined by a simple gr…
New method recovers clusters in non-convex finite metric spaces with oracle queries.
Paper formalizes a reinforcement learning model for complex information structures.
New bound for group action length without diameter restriction.
SON-NMF estimates nonnegative rank on-the-fly for NMF.
This paper tackles Gromov's filling area conjecture using discrete graph theory.
Gaussian graphical models are semi-algebraic subsets of the cone of positive definite covariance matrices. Submatrices with low rank correspond to generalizations of conditional independence constraints on collections of random variables. We give a precise graph-theoretic characterization of when submatrices of the cov…
Counting edge bicolorings of graphs on surfaces, with applications in knot theory.
By means of a slight modification of the notion of GM-complexity, the present paper performs a graph-theoretical approach to the computation of (Matveev's) complexity for closed orientable 3-manifolds. In particular, the existing crystallization catalogue C^{28}, due to Lins, is used to obtain upper bounds for the comp…
We propose a multiresolution Gaussian process to capture long-range, non-Markovian dependencies while allowing for abrupt changes. The multiresolution GP hierarchically couples a collection of smooth GPs, each defined over an element of a random nested partition. Long-range dependencies are captured by the top-level GP…
Fox coloring provides a combinatorial framework for studying dihedral representations of the knot group. The less well-known concept of Dehn coloring captures the same data. Recent work of Carter-Silver-Williams clarifies the relationship between the two focusing on how one transitions between Fox and Dehn colorings. I…
We propose graph kernels based on subgraph matchings, i.e. structure-preserving bijections between subgraphs. While recently proposed kernels based on common subgraphs (Wale et al., 2008; Shervashidze et al., 2009) in general can not be applied to attributed graphs, our approach allows to rate mappings of subgraphs by …
We introduce the index i(v) = 1 - X(S(v)) for critical points of a locally injective function f on the vertex set V of a simple graph G=(V,E). Here S(v) = {w in E | (v,w) in E, f(w)-f(v)<0} is the subgraph of the unit sphere at v in G. It is the exit set of the gradient vector field. We prove that the sum of i(v) over …
New theorem on graph curvature thresholds and uniqueness.
Optimizes network sampling for efficient community detection.
We study a class of 3-manifolds called strong L-spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. We provide evidence for the possibility that every strong L-space is the branched double cover of an alternating link in the t…
Algorithm reconstructs conserved networks from flow data.
Graph clustering uses multiscale community detection for improved performance.
We provide geometric conditions on a pair of hyperplanes of a CAT(0) cube complex that imply divergence bounds for the cube complex. As an application, we classify all right-angled Coxeter groups with quadratic divergence and show right-angled Coxeter groups cannot exhibit a divergence function between quadratic and cu…
We show how to approximate large graphs with smaller ones using spectral properties.
Consumers with low demand, like households, are generally supplied single-phase power by connecting their service mains to one of the phases of a distribution transformer. The distribution companies face the problem of keeping a record of consumer connectivity to a phase due to uninformed changes that happen. The exact…
Edge augmentation connects disconnected graphs by elevating eigenvalues.
Financial markets are a typical example of complex systems where interactions between constituents lead to many remarkable features. Here, we show that a pairwise maximum entropy model (or auto-logistic model) is able to describe switches between ordered (strongly correlated) and disordered market states. In this frame…
Quantum codes on hyperbolic lattices outperform Euclidean ones with higher rates and lower overhead.
FMI uses matching to mimic interventions for causal feature learning.
We analyze oversquashing in topological message-passing using relational structures.
Novel graph theory for neural networks improves understanding of their structure and performance.