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.
New method constructs graphs from data efficiently, suitable for large datasets.
Study on cryptocurrency market correlations at various time scales.
We study flip-graphs of triangulations on topological surfaces where distance is measured by counting the number of necessary flip operations between two triangulations. We focus on surfaces of positive genus with a single boundary curve and marked points on this curve; we consider triangulations up to homeomor…
HLOB predicts mid-price changes in L.O.Bs using deep learning.
We investigate the planar maximally filtered graphs of the portfolio of the 300 most capitalized stocks traded at the New York Stock Exchange during the time period 2001-2003. Topological properties such as the average length of shortest paths, the betweenness and the degree are computed on different planar maximally f…
Connected flip graphs for triangulations on hyperbolic surfaces.
Study on veering triangulations and their flow graphs, proving new applications.
Smooth manifolds can be triangulated with graphs of bounded twin-width.
Triangulation filters spurious circuits in multilingual models.
Method constructs hedging portfolio for carbon risk but not ESG risk.
The face pairing graph of a 3-manifold triangulation is a 4-valent graph denoting which tetrahedron faces are identified with which others. We present a series of properties that must be satisfied by the face pairing graph of a closed minimal P^2-irreducible triangulation. In addition we present constraints upon the co…
The paper bounds distances and transformations between pants decompositions and triangulations on surfaces.
Research shows finiteness in triangulations with girth constraints.
Geodesics count exponentially between triangulations of surfaces with enough topology.
Study flip graphs for surfaces of infinite type, finding uncountably many connected components.
Several algorithms have been proposed to filter information on a complete graph of correlations across stocks to build a stock-correlation network. Among them the planar maximally filtered graph (PMFG) algorithm uses edges to build a graph whose features include a high frequency of small cliques and a good clust…
Using existing technology, we prove a Masur-Minsky style distance formula for flip- graph distance between two triangulations, expressed as a sum of the distances of the projections of these triangulations into arc graphs of the suitable subsurfaces of S.
The paper finds 3-colorings of 2-sphere triangulations.
This paper focuses on spectral filters on graphs, namely filters defined as elementwise multiplication in the frequency domain of a graph. In many graph signal processing settings, it is important to transfer a filter from one graph to another. One example is in graph convolutional neural networks (ConvNets), where the…
To enumerate 3-manifold triangulations with a given property, one typically begins with a set of potential face pairing graphs (also known as dual 1-skeletons), and then attempts to flesh each graph out into full triangulations using an exponential-time enumeration. However, asymptotically most graphs do not result in …
In 1987, Kalai proved that stacked spheres of dimension are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension . In this article, we give a characterisation of stacked -spheres using what we call the {\em separatio…
Matveev and Piergallini independently showed that, with a small number of known exceptions, any triangulation of a three-manifold can be transformed into any other triangulation of the same three-manifold with the same number of vertices, via a sequence of 2-3 and 3-2 moves. We can interpret this as showing that the Pa…
Machine learning identifies 3-manifold triangulations using isomorphism signatures.
A new method uses GATs to optimise portfolios of mid-cap firms, outperforming traditional methods.
New method finds large counterexamples by selectively exploring triangulations.
We show that for a special alternating link diagram, the following three polynomials are essentially the same: a) the part of the HOMFLY polynomial that corresponds to the leading term in the Alexander polynomial; b) the -vector for a triangulation of the root polytope of the Seifert graph and c) the enumerator of p…
We study soft persistence (existence in subsequent temporal layers of motifs from the initial layer) of motif structures in Triangulated Maximally Filtered Graphs (TMFG) generated from time-varying Kendall correlation matrices computed from stock prices log-returns over rolling windows with exponential smoothing. We ob…
New findings on strong convexity in triangulations of convex polygons.
This work analyzes the stability of graph filters under large perturbations.
A is an embedding of a graph on surfaces where every face has length three. In this article, we show the existence of contractible Hamiltonian cycle in triangulated maps of which minimum degree is four.
A family of one-vertex triangulations of 3-manifolds, layered-triangulations, is defined. Layered-triangulations are first described for handlebodies and then extended to all 3-manifolds via Heegaard splittings. A complete and detailed analysis of layered-triangulations is given in the cases of the solid torus and lens…
One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions,…
It is important to have fast and effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex before we can make it smaller than its original size. Here we present experimental …
This paper is concerned with lower bounds for the connectivity of graphs (one-dimensional skeleta) of triangulations of compact manifolds. We introduce a structural invariant b_M for simplicial d-manifolds M taking values in the range 0 <= b_M <= d-1. The main result is that b_M influences connectivity in the following…
Method samples triangulations of manifolds using biased random walks.
Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more …
The paper finds and visualizes unique geometric polyhedra and tori with few vertices.
New methods learn sampling distributions for particle filters without supervision.
In graph theory, as well as in 3-manifold topology, there exist several width-type parameters to describe how "simple" or "thin" a given graph or 3-manifold is. These parameters, such as pathwidth or treewidth for graphs, or the concept of thin position for 3-manifolds, play an important role when studying algorithmic …
A guide to using low-pass graph filters for network data.
Study discrete analog of zeta-determinant maximization on triangulated surfaces.
The paper explores algorithms to transform 3-manifold triangulations while controlling sparsity.
IBPF algorithm tackles high-dimensional parameter learning for complex systems.
BankGCN improves graph convolution networks by handling multi-channel signals with adaptive filter banks.
This paper uses the technology of weighted and regular triangulations to study discrete versions of the Laplacian on piecewise Euclidean manifolds. Regular triangulations are studied in some detail, including flip algorithms. The Laplacian is then studied as an operator on functions of the vertices as a generalized wei…
It is important to have effective methods for simplifying 3-manifold triangulations without losing any topological information. In theory this is difficult: we might need to make a triangulation super-exponentially more complex before we can make it smaller than its original size. Here we present experimental work that…
Graph Kalman filters adapt classical filters to graph data.
In graph theory, Courcelle's theorem essentially states that, if an algorithmic problem can be formulated in monadic second-order logic, then it can be solved in linear time for graphs of bounded treewidth. We prove such a metatheorem for a general class of triangulations of arbitrary fixed dimension d, including all t…