arXiv research

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…

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.

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…

Estimates tree-based density from random vectors.

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 …

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…

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…

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…

We empirically investigated the effects of market factors on the information flow created from N(N-1)/2 linkage relationships among stocks. We also examined the possibility of employing the minimal spanning tree (MST) method, which is capable of reducing the number of links to N-1. We determined that market factors car…

Let X and Y be infinite graphs, such that the automorphism group of X is nonamenable, and the automorphism group of Y has an infinite orbit. We prove that there is no automorphism-invariant measure on the set of spanning trees in the direct product X times Y. This implies that the minimal spanning forest corresponding …

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.

Geometric estimator calculates dependency between multivariate samples.

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 $L$, there is an associated ribbon graph whose quasi-trees correspond bijectively to …

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 $\mathbb{Z}/2\mathbb{Z}$. The result is a spectral sequence which converges to a stabilized version of delta-graded knot Floer homology. The $(E_2,d_2)$ page of this spectral sequence …

In this paper we analyzed dependencies in commodity markets investigating correlations of future contracts for commodities over the period 1998.09.01 - 2007.12.14. We constructed a minimal spanning tree based on the correlation matrix. The tree provides evidence for sector clusterization of investigated contracts. We a…

Paper proposes an algorithm to reconstruct optimal model structure from graph adjacency matrix.

Proves bounds on spanning two-forests and random cut sizes.

A new method for one-class classifiers using spanning trees and sub-spaces.

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.

We decompose the exchange rates returns of 41 currencies (incl. gold) into their sign and amplitude components. Then we group together all exchange rates with a common base currency, construct Minimal Spanning Trees for each group independently, and analyze properties of these trees. We show that both the sign and the …

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…

This paper is a contribution to interweaving two lines of research that have progressed in separate ways: network analyses of international trade and the literature on African trade and development. Gathering empirical data on African countries has important limitations and so does the space occupied by African countri…

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 calculated the cross correlations between the half-hourly times series of the ten Dow Jones US economic sectors over the period February 2000 to August 2008, the two-year intervals 2002--2003, 2004--2005, 2008--2009, and also over 11 segments within the present financial crisis, to construct minimal spanning trees (…

Nowadays, data are generated massively and rapidly from scientific fields as bioinformatics, neuroscience and astronomy to business and engineering fields. Cluster analysis, as one of the major data analysis tools, is therefore more significant than ever. We propose in this work an effective Semi-supervised Divisive Cl…

By analyzing the foreign exchange market data of various currencies, we derive a hierarchical taxonomy of currencies constructing minimal-spanning trees. Clustered structure of the currencies and the key currency in each cluster are found. The clusters match nicely with the geographical regions of corresponding countri…

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…

Mutual information minimum spanning trees are used to explore nonlinear dependencies on Brazilian equity network in the periods from June/01/2015 to January/26/2016, in which Brazil was under the government of President Dilma Rousseff, and from January/27/2016 to September/08/2016 which includes the government transiti…

We study relations between the Alexander-Conway polynomial $\nabla_L$ 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 $\nabla_L$ of an m-component link L all of whose Milnor numbers $μ_{i_1... i_p}$ van…

Lumbermark clusters data robustly, slicing limbs of mutual reachability trees.

We investigate the problem of nodes clustering under privacy constraints when representing a dataset as a graph. Our contribution is threefold. First we formally define the concept of differential privacy for structured databases such as graphs, and give an alternative definition based on a new neighborhood notion betw…

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…

Determinants of theta curves and symmetric graphs are studied.

This paper uses two hierarchical techniques, a minimal spanning tree and an ultrametric hierarchical tree, to extract a topological influence map for major currencies from the ultrametric distance matrix for 1996-2001. We find that these two techniques generate a defined and robust scale free network with meaningful ta…

We study the crash dynamics of the Warsaw Stock Exchange (WSE) by using the Minimal Spanning Tree (MST) networks. We find the transition of the complex network during its evolution from a (hierarchical) power law MST network, representing the stable state of WSE before the recent worldwide financial crash, to a superst…