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 reduces spectral clustering complexity by sparsifying graphs.
Sharp bounds for spanning tree entropy in planar lattices.
The Jones polynomial can be expressed in terms of spanning trees of the graph obtained by checkerboard coloring a knot diagram. We show there exists a complex generated by these spanning trees whose homology is the reduced Khovanov homology. The spanning trees provide a filtration on the reduced Khovanov complex and a …
A new classification method based on Minimum Spanning Trees
Alexander polynomial equals spanning tree count at t=1.
New spanning tree model connects knot homology, s-invariant, and exotic discs.
For a spanning tree T of a connected graph G and for a labelling φ: E(T) \rightarrow {+, -}, φis called an alternating sign on a spanning tree T of a graph G if for any cotree edge e \in E(G)-E(T), the unique path in T joining both end vertices of e has alternating signs. In the present note, we prove that any graph ha…
We investigate the time series of the degree of minimum spanning trees obtained by using a correlation based clustering procedure which is starting from (i) asset return and (ii) volatility time series. The minimum spanning tree is obtained at different times by computing correlation among time series over a time windo…
We use a spanning tree model to prove a result of E. S. Lee on the support of Khovanov homology of alternating knots.
Study examines insurance sector linkages and systemic risk using dynamic spanning trees.
Study asymptotic expansion of graph Laplacian on discretized surfaces, relating spanning trees and cycle-rooted forests.
In this paper, we investigate the statistical features of the weighted international-trade network. By finding the maximum weight spanning trees for this network we make the extraction of the truly relevant connections forming the network's backbone. We discuss the role of large-sized countries (strongest economies) in…
Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chord diagram. We show that for any link diagram , there is an associated ribbon graph whose quasi-trees correspond bijectively to …
New algorithm for private minimum spanning tree release with improved accuracy.
Mutual info trees show higher risk in Brazilian equity network during transition.
Optimal coupling among random vectors with known statistics and correlation structure found using minimum spanning tree over measure-valued vertices.
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…
We iterate Manolescu's unoriented skein exact triangle in knot Floer homology with coefficients in the field of rational functions over . The result is a spectral sequence which converges to a stabilized version of delta-graded knot Floer homology. The page of this spectral sequence …
Estimates tree-based density from random vectors.
Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.
A new method for one-class classifiers using spanning trees and sub-spaces.
Proves bounds on spanning two-forests and random cut sizes.
Oriented ribbon graphs (dessins d'enfant) are graphs embedded in oriented surfaces. The Bollobás-Riordan-Tutte polynomial is a three-variable polynomial that extends the Tutte polynomial to oriented ribbon graphs. A quasi-tree of a ribbon graph is a spanning subgraph with one face, which is described by an ordered chor…
A new hierarchical clustering method selects representative points from sub-minimum-spanning-trees.
The classical Matrix-Tree Theorem allows one to list the spanning trees of a graph by monomials in the expansion of the determinant of a certain matrix. We prove that in the case of three-graphs (that is, hypergraphs whose edges have exactly three vertices) the spanning trees are generated by the Pfaffian of a suitably…
We use the spanning tree model for Khovanov homology to study Legendrian links. This leads to an alternative proof for Ng's Khovanov bound for the Thurston-Bennequin number and to both a necessary and a sufficient condition for this bound to be sharp.
We consider the detection of activations over graphs under Gaussian noise, where signals are piece-wise constant over the graph. Despite the wide applicability of such a detection algorithm, there has been little success in the development of computationally feasible methods with proveable theoretical guarantees for ge…
We investigate the problem of sequentially predicting the binary labels on the nodes of an arbitrary weighted graph. We show that, under a suitable parametrization of the problem, the optimal number of prediction mistakes can be characterized (up to logarithmic factors) by the cutsize of a random spanning tree of the g…
We study relations between the Alexander-Conway polynomial and Milnor higher linking numbers of links from the point of view of finite-type (Vassiliev) invariants. We give a formula for the first non-vanishing coefficient of of an m-component link L all of whose Milnor numbers van…
Lumbermark clusters data robustly, slicing limbs of mutual reachability trees.
Correlation matrices of foreign exchange rate time series are investigated for 60 world currencies. Minimal Spanning Tree (MST) graphs for the gold, silver and platinum are presented. Inverse power like scaling is discussed for these graphs as well as for four distinct currency groups (major, liquid, less liquid and no…
New method estimates root-directed tree from extreme data.
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear combination of spanning trees with negative weights. This technique is a lower-bound count…
We studied the topology of correlation networks among 34 major currencies using the concept of a minimal spanning tree and hierarchical tree for the full years of 2007-2008 when major economic turbulence occurred. We used the USD (US Dollar) and the TL (Turkish Lira) as numeraires in which the USD was the major currenc…
Determinants of theta curves and symmetric graphs are studied.
This paper proposes a new method to adapt ROMs for new parameter settings.
We investigate hierarchical structure in various complex systems according to Minimum Spanning Tree methods. Firstly, we investigate stock markets where the graphis obtained from the matrix of correlations coefficient computed between all pairs of assets by considering the synchronous time evolution of the difference o…
Three methods combine one-class classifiers with MST-CD and N-ary Trees for binary classification.
Proof of tangle theorem using graph forests.
It is conjectured that the Khovanov homology of a knot is invariant under mutation. In this paper, we review the spanning tree complex for Khovanov homology, and reformulate this conjecture using a matroid obtained from the Tait graph (checkerboard graph) G of a knot diagram K. The spanning trees of G provide a filtrat…
Graphs with specific spanning trees yield RAAGs, with applications to BBGs.
The investigations of financial markets from a complex network perspective have unveiled many phenomenological properties, in which the majority of these studies map the financial markets into one complex network. In this work, we investigate 30 world stock market indices through their visibility graphs by adopting the…
Paper introduces clock moves for plane graphs and proves Alexander polynomial properties.
The paper confirms a conjecture linking link bipyramid volume and Mahler measure.
The paper develops efficient algorithms for sampling from random spanning trees and determinantal point processes.
OCmst detects anomalies using CNN features and MSTs.
A behavior of extreme networks under deformations of their boundary sets is investigated. It is shown that analyticity of a deformation of boundary set guarantees preservation of the networks types for minimal spanning trees, minimal fillings and so-called stable shortest trees in the Euclidean space.
MSTs provide a fast and meaningful clustering method in low-dimensional data.