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This paper proposes FREEtree, a tree-based method for high dimensional longitudinal data with correlated features. Popular machine learning approaches, like Random Forests, commonly used for variable selection do not perform well when there…
We study the structure of fermionic mass eigenstates in a pure four-dimensional deconstruction approach. Unlike the case with the usual higher dimensional deconstruction (or latticized extra dimension), here the doubling of fermionic…
Graphs are a powerful tool for analyzing large data sets, but many real-world phenomena involve interactions that go beyond the simple pairwise relationships captured by a graph. In this paper we introduce and study a simple combinatorial…
We develop the BRST approach to Lagrangian formulation for all massless half-integer higher spin fields on an arbitrary dimensional flat space. General procedure of Lagrangian construction describing the dynamics of fermionic field with any…
We describe a rich family of binary variables statistical mechanics models on a given planar graph which are equivalent to Gaussian Grassmann Graphical models (free fermions) defined on the same graph. Calculation of the partition function…
The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
A new synthesis scheme is proposed to effectively generate a random vector with prescribed joint density that induces a (latent) Gaussian tree structure. The quality of synthesis is measured by total variation distance between the…
We develop an estimation methodology for a factor model for high-dimensional matrix-valued time series, where common stochastic trends and common stationary factors can be present. We study, in particular, the estimation of (row and column)…
Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…
We study probability distributions over free algebras of trees. Probability distributions can be seen as particular (formal power) tree series [Berstel et al 82, Esik et al 03], i.e. mappings from trees to a semiring K . A widely studied…
We review various combinatorial applications of field theoretical and matrix model approaches to equilibrium statistical physics involving the enumeration of fixed and random lattice model configurations. We show how the structures of the…
We study the theoretical capacity to statistically learn local landscape information by Evolution Strategies (ESs). Specifically, we investigate the covariance matrix when constructed by ESs operating with the selection operator alone. We…
Two-part models and Tweedie generalized linear models (GLMs) have been used to model loss costs for short-term insurance contract. For most portfolios of insurance claims, there is typically a large proportion of zero claims that leads to…
Recent work in learning ontologies (hierarchical and partially-ordered structures) has leveraged the intrinsic geometry of spaces of learned representations to make predictions that automatically obey complex structural constraints. We…
Homogeneous matroids are characterized by the property that strength equals fractional arboricity, and arise in the study of base modulus [22]. For graphic matroids, Cunningham [9] provided efficient algorithms for calculating graph…
Free Space Optics (FSO) communication provides attractive bandwidth enhancement with unlicensed bands worldwide spectrum. However, the link capacity and availability are the major concern in the different atmospheric conditions. The…
Spectral projectors of second order differential operators play an important role in quantum physics and other scientific and engineering applications. In order to resolve local features and to obtain converged results, typically the number…
Gradient descent during the learning process of a neural network can be subject to many instabilities. The spectral density of the Jacobian is a key component for analyzing stability. Following the works of Pennington et al., such Jacobians…
We consider logarithmic vector fields parametrized by finite collections of weighted hyperplanes. For a finite collection of weighted hyperplanes in a two-dimensional vector space, it is known that the set of such vector fields is a free…
The frog model starts with one active particle at the root of a graph and some number of dormant particles at all nonroot vertices. Active particles follow independent random paths, waking all inactive particles they encounter. We prove…